© Emna Ghazali, 2017

Mechanical performance of adhesively bonded repairs in honeycomb composite sandwich structures

Thèse

Emna Ghazali

Doctorat en génie mécanique

Philosophiæ doctor (Ph. D.)

Québec, Canada

Mechanical Performance of Adhesively Bonded Repairs in Honeycomb Composite Sandwich Structures

Thèse

Emna Ghazali

Sous la direction de :

Marie-Laure Dano, directrice de recherche

Augustin Gakwaya, codirecteur de recherche

iii

Résumé

En service, les pièces aéronautiques en matériaux composites et structures sandwiches

subissent des dommages qui nécessitent des réparations. Les réparations par patch interne en

biseau, en escalier ou par combinaison des deux offrent une excellente restauration de la

résistance mécanique pour ces structures composites. Cependant, l’environnement de

réparation peut se révéler être un défi de taille quant à leur mise en œuvre, au choix des

paramètres géométriques (angle de biseau, nombre de plis extra), à leur comportement

mécanique sous différents chargements ainsi qu’à leur processus d’endommagement.

Cette thèse présente une étude expérimentale et numérique (éléments finis) du comportement

mécanique de réparations par patch interne effectuées sur des structures avec des peaux en

composites à renforts tissés fabriquées hors autoclave et âme en Nomex en nid d’abeille. Afin

de déterminer l’effet de différents paramètres géométriques sur la résistance de la réparation et

de comprendre son comportement mécanique et son processus d’endommagement, une série

de tests de caractérisation sous différents chargements (traction, compression, flexion) a été

effectuée sur des structures sandwiches faite avec deux matériaux composites tissés pour la

peau : soit du composite tissé taffetas (PW) ou satin de 8 (8HS)

Des simulations numériques ont été effectuées afin de prédire le comportement mécanique de

la réparation. Cette étude numérique a été effectuée en plusieurs étapes. Un premier modèle

iv

2D qui suppose que la colle ait un comportement linéaire élastique a été développé et permet

d’étudier la distribution des contraintes dans le joint de colle pour différentes configurations de

réparation rectangulaire. Ensuite, le modèle 2D est modifié pour tenir compte du comportement

élastoplastique de la colle et ceci permet de prédire le comportement mécanique d’une

réparation rectangulaire jusqu’à la rupture. Par la suite, un modèle 3D est développé pour

prédire le comportement de réparations circulaires sous des chargements de compression. Ce

modèle tient compte de l’endommagement progressif des peaux en composite. Les résultats de

ces simulations numériques sont comparés par la suite aux mesures expérimentales. Les

modèles par éléments finis, avec une loi de comportement élastoplastique pour le joint de colle,

permettent une estimation adéquate de la résistance ainsi que de l’endommagement des

structures sandwiches réparées. Une étude paramétrique a eu lieu afin d’étudier l’effet de

différents paramètres géométriques sur la résistance de la réparation.

La mise en œuvre et la détermination de la performance mécanique des réparations par patch

interne des structures sandwiches est une tâche complexe avec de multiples paramètres de

matériaux et de procédés. D’une manière générale, cette thèse contribue à une meilleure

compréhension du comportement mécanique des structures sandwiches réparées et de leur

processus d’endommagement. Les modèles par éléments finis développés dans ces travaux ont

été validés expérimentalement et des simulations paramétriques ont contribué à une meilleure

compréhension de l’influence des différents paramètres géométriques sur la résistance de la

réparation par patch interne.

v

Mots-clés : Structures sandwiches, Réparation collée, Simulation numérique, hors-autoclave,

Réparation en biseau, essais expérimentaux.

vi

Abstract

In service, aeronautical components made of composite materials and sandwich structures are

subject to type of damages that require repairs. Adhesively bonded repairs (scarf-scarf, step-

step or scarf-step) offer an excellent mechanical strength recovery for these composite

structures. However, the repair environment can be a significant challenge in terms of the

choice of geometrical parameters (scarf angle, addition of an overply), damage process

parameters and mechanical behavior under different loads.

This thesis presents both experimental and numerical investigations of the mechanical behavior

of internal patch repairs carried-out on Nomex honeycomb composite sandwich structures. The

skins use an out-of- autoclave woven fabric made of carbon-epoxy composite materials. In

order to determine the effect of different geometric parameters on the resistance of the internal

patch repair and to better understand its mechanical behavior and damage processes, a series

of mechanical tests under different loads (tensile, compression, bending) is conducted on the

repaired sandwich panels made with either plain weave or 8 harness satin textile composites.

Numerical simulations were carried out, in several stages, in order to determine the mechanical

behavior of the repair. First, a 2D model that assumes a linear elastic behavior of the adhesive

film was developed. This simple model allows to study the distribution of the stresses in the

adhesive joint for different configurations of rectangular patch repair. Then, the 2D model is

modified in order to account for the elastoplastic behavior of the adhesive film. The latter

allows to predict the mechanical behavior of a rectangular internal patch repair until rupture.

vii

Subsequently, a 3D model is developed to predict the mechanical behavior of circular internal

patch repairs under compressive loadings. This model takes into account the progressive

damage and failure of the woven fabric skins. The results of these numerical simulations are

validated by comparing them to experimental measurements. The finite element models that

account for the elastoplastic behavior law for the adhesive joint allow predictions of the

strength as well as the damage morphology of the repaired sandwich structures. A parametric

study has also been conducted in order to determine the influence of the geometrical design

parameters in the repair strength.

Processing and assessment of the mechanical performance of internal patch repairs on

sandwich structures is a complex task with multiple material and process parameters. In

general, this thesis contributes to a better understanding of the mechanical behavior of

adhesively bonded repaired sandwich structures and their damage process. The finite element

models developed in this work and validated experimentally have contributed through

parametric numerical simulations to an economical better understanding of the influence of

different geometric parameters on the strength and failure of internal patch repaired sandwich

panels.

Keywords: Honeycomb composite sandwich structures, Bonded repair, Progressive damage,

Step-scarf repair, Out-of-autoclave materials, Finite element analysis, and Experimental tests.

viii

Table of content

Résumé ................................................................................................................ iii

Abstract ................................................................................................................ vi

Table of content ................................................................................................ viii

List of Tables .................................................................................................... xiii

List of Figures .................................................................................................... xvi

Nomenclature ................................................................................................... xxii

Acknowledgements .......................................................................................... xxvi

Avant-Propos ................................................................................................. xxvii

Introduction ........................................................................................................... 1

Chapter 1. Literature Review ............................................................................. 8

1.1 A Review of Monolithic Composite Bonded Repair Design ..................................... 8

1.1.1 Composite Bonded Joint Repairs ........................................................................... 9

1.1.2 Analytical Methods .............................................................................................. 10

1.1.3 Finite Element Analysis Techniques ................................................................... 12

1.1.4 Failure Mechanisms of Composite Bonded Joint Repairs: Observations and

Modeling Process ............................................................................................................. 21

1.1.5 Review Summary ................................................................................................. 29

1.2 A Review of Honeycomb Sandwich Panel Bonded Repairs ................................... 29

1.2.1 Introduction .......................................................................................................... 30

1.2.2 State-of-The-Art Review of Sandwich Panel Repairs ......................................... 35

1.2.3 Concluding Remarks ............................................................................................ 44

ix

Chapter 2. Overview of the Problem and Research Focus .............................. 47

2.1 Rationale of the Thesis............................................................................................. 47

2.1.1 Assessment of the Mechanical Behavior of Honeycomb Sandwich Panels with

Bonded Repairs by Experimental Testing ....................................................................... 49

2.1.2 Development of Finite Element Models for Better Understanding and Accurate

Prediction of the Mechanical Behavior and Failure Modes of the Repaired Sandwich

Panels under Different Loadings ..................................................................................... 50

2.1.3 Validation of the Finite Element Models and Conduction of a Parametric Study

50

2.2 Methodology and Thesis Structure .......................................................................... 51

2.2.1 Methodology ........................................................................................................ 51

2.2.2 Chapters Presentation........................................................................................... 54

Chapter 3. Mechanical Characterization and Finite Element Study of

Monolithic Facesheets and Honeycomb Core .................................................... 56

3.1 Experimental Characterization of the Facesheet Materials ..................................... 57

3.1.1 Materials Description and Specimens Manufacturing ......................................... 57

3.1.2 Mechanical Testing of the Laminate Used for the Skins ..................................... 58

3.2 Mechanical Characterization of the Honeycomb Nomex Core ............................... 65

3.2.1 Out-of-Plane Compressive Tests ......................................................................... 66

3.2.2 In-Plane Tensile Tests .......................................................................................... 68

3.2.3 Nomex Tests Recapitulation ................................................................................ 69

3.3 Analytical and Finite Element Studies of the Facesheets Mechanical Behavior ..... 70

3.3.1 Classical Lamination Theory: Analytical Approach ............................................ 71

3.3.2 Finite element Analyses ....................................................................................... 73

3.4 Conclusion ............................................................................................................... 82

Chapter 4. Article 1: Mechanical Performance of Repaired Sandwich Panels:

Experimental Characterization and Finite Element Modelling .......................... 83

4.1 Introduction .............................................................................................................. 84

x

4.2 Experimental Work .................................................................................................. 88

4.2.1 Repaired Sandwich Specimen Preparation .......................................................... 88

4.2.2 Tensile tests procedure ......................................................................................... 91

4.2.3 Experimental Results ........................................................................................... 92

4.2.4 Damage Mode and Fractography Studies ............................................................ 94

4.3 Numerical Simulation .............................................................................................. 98

4.3.1 Model Description ............................................................................................... 98

4.3.2 Linear Elastic Numerical Model ........................................................................ 100

4.3.3 Non-linear Elastic Plastic Model ....................................................................... 102

4.3.4 Numerical Results and Discussion..................................................................... 106

4.4 Conclusions ............................................................................................................ 108

Chapter 5. Article 2: Parametric Study of Stepped-Scarf Bonded Joints in

Repaired Honeycomb Sandwich Composite Panels ......................................... 109

5.1 Introduction ............................................................................................................ 110

5.2 Finite Element Model Description ......................................................................... 114

5.2.1 Model Geometry and Material System Description .......................................... 114

5.2.2 Boundary Conditions and Finite Element Mesh Details.................................... 116

5.2.3 Materials Models ............................................................................................... 117

5.3 Parametric Study .................................................................................................... 118

5.4 Results .................................................................................................................... 120

5.5 Discussion .............................................................................................................. 131

5.6 Conclusions ............................................................................................................ 135

Chapter 6. Article 3: Evaluation of the mechanical performance of repaired

composite sandwich structure using different mechanical tests ....................... 138

6.1 Introduction ............................................................................................................ 139

6.2 Experimental Work ................................................................................................ 143

6.2.1 Materials ............................................................................................................ 143

6.2.2 Repair Procedure ................................................................................................ 143

xi

6.2.3 Specimen Preparation and Test Procedure ........................................................ 144

6.2.4 Results and Discussion ...................................................................................... 151

6.3 Finite Element Analysis ......................................................................................... 161

6.3.1 Model Description ............................................................................................. 161

6.3.2 Model Results .................................................................................................... 164

6.4 Conclusion ............................................................................................................. 166

Chapter 7. Article 4: Experimental and Numerical Studies of Stepped-Scarf

Circular Repair in Composite Sandwich Panels ............................................... 169

7.1 Introduction ............................................................................................................ 171

7.2 Experimental Work ................................................................................................ 175

7.2.1 Objective and Methodology ............................................................................... 175

7.2.2 Specimen Preparation ........................................................................................ 176

7.2.3 Edgewise Compressive Tests ............................................................................. 179

7.2.4 Four-Point Bend tests ......................................................................................... 181

7.3 Numerical Simulation ............................................................................................ 185

7.3.1 Finite Element Model Description ..................................................................... 185

7.3.2 Failure Criteria and Damage Evolution ............................................................. 188

7.3.3 Results and Discussions: Edgewise Compressive Tests .................................... 191

7.4 Conclusion ............................................................................................................. 195

Chapter 8. Conclusions and Perspectives ...................................................... 197

8.1 Thesis Conclusions ................................................................................................ 197

8.2 Thesis Original Contributions ................................................................................ 201

8.3 Recommendations for Future Work....................................................................... 204

References ......................................................................................................... 206

Appendix A. Mechanical performance of the 8HS honeycomb sandwich panels

........................................................................................................................... 212

A.1 Tensile Tests on Pristine and Repaired 8HS Honeycomb Sandwich Panels ......... 212

xii

Specimens Dimensions and Test Set-up ............................................................ 213

Test Results for the Pristine 8HS Honeycomb Sandwich Panels ...................... 214

Test Results for the 2D Repaired 8HS Honeycomb Sandwich Panels .............. 214

Strength Recovery of the 3°-Repaired Sandwich Panels ................................... 217

A.2 Compressive Tests on 8HS Honeycomb Sandwich Panels ................................... 218

Compressive Tests on Pristine and 2D Repaired Honeycomb Panels ............... 219

A.2.1.1 Compressive Tests on the Pristine 8HS Honeycomb Sandwich Panels ............ 219

A.2.1.2 Compressive Tests on the 2D Repaired 8HS Honeycomb Sandwich Panels .... 221

A.2.1.3 Recapitulation and Strength Recovery of the 8HS Repaired Sandwich Panels. 222

Compressive Tests on 3D Repaired and Open-Hole 8HS Honeycomb Panels . 224

A.3 Flexure Tests on Pristine and 2D Repaired 8HS Honeycomb Sandwich Panels ... 227

Long-Beam Flexure Tests .................................................................................. 227

Tests Results and Interpretation ......................................................................... 229

A.4 Results Validation .................................................................................................. 232

xiii

List of Tables

Table 1-1 Parameters effects on the peel and shear stresses [21] ........................................ 17

Table 1-2 Issues and aspects studied in the literature for composite bonded repairs ........... 29

Table 1-3 Structural efficiency of sandwich panels in terms of weight [41] ....................... 31

Table 1-4 Sandwich panels component materials used in the literature .............................. 45

Table 1-5 Repair configuration, process and cure methods for sandwich panel repairs used

in the literature ......................................................................................................................... 46

Table 1-6 Mechanical characterization and non-destructive inspection of sandwich panel

repairs used in the literature ..................................................................................................... 46

Table 1-7 Finite element model types used in the literature for sandwich honeycomb panels

.............................................................................................................................. 46

Table 3-1 Materials properties from Cytec [59] ................................................................... 57

Table 3-2 Statical analysis - tensile tests .............................................................................. 64

Table 3-3 Statical analysis - compressive tests .................................................................... 65

Table 3-4 Mechanical properties for the ECA-R Nomex core (from [63]).......................... 66

Table 3-5 Compressive mechanical properties for the over-expanded Nomex core ........... 67

Table 3-6 Tensile elastic modulus in the L-and W-directions for the over-expanded Nomex

core .............................................................................................................................. 69

Table 3-7 Mechanical properties of the over-expanded Nomex honeycomb core (ECA-R 4.8

64) .............................................................................................................................. 70

Table 3-8 Composite materials elastic properties ................................................................ 72

Table 3-9 Comparison between analytical and experimental results ................................... 73

Table 3-10 Predicted and measured elastic modulus of the quasi-isotropic laminate ........ 77

Table 3-11 Mechanical properties used for the PW composite material ........................... 80

Table 3-12 Comparison between the experimental data and the finite element prediction 80

Table 4-1 Test matrix. .......................................................................................................... 92

xiv

Table 4-2 Comparison of the ultimate stress between the sandwich skin and a [(+45/-45)/

(0/90)/ (-45/+45)/ (90/0)]2s quasi-isotropic laminate made from the same PW prepreg [74] .. 95

Table 4-3 Mechanical properties of the plain weave material. ............................................ 99

Table 4-4 Mechanical properties of the FM300-2M adhesivea. ........................................... 99

Table 4-5 Mechanical properties of the Nomex honeycomb core ..................................... 100

Table 4-6 Stiffness prediction of pristine panels. ............................................................... 101

Table 4-7 Hardening data input. ......................................................................................... 106

Table 5-1 Mechanical properties of the plain weave composite material .......................... 117

Table 5-2 Mechanical properties of the FM300-2M adhesive ........................................... 118

Table 5-3 Mechanical properties of the Nomex honeycomb core ..................................... 118

Table 5-4 Parametric model details .................................................................................... 119

Table 5-5 Baseline model values........................................................................................ 120

Table 6-1 Test matrix for different experimental tests ....................................................... 144

Table 6-2 Summary of the compressive test results ........................................................... 154

Table 6-3 Summary of the tensile test results .................................................................... 156

Table 6-4 Summary of the flexure test results ................................................................... 157

Table 6-5 Elastic material properties of the plain weave carbon-epoxy ply ...................... 163

Table 6-6 Mechanical properties of the over-expanded Nomex honeycomb core (ECA-R 4.8

64) ............................................................................................................................ 163

Table 6-7 Mechanical properties of the hexagonal Nomex honeycomb core (ECA 3.2 96) ...

............................................................................................................................ 164

Table 6-8 Mechanical properties of the FM300-2M adhesive film ................................... 164

Table 7-1 Mechanical properties of the plain weave composite material (CYCOM 5320

T650 PW). ............................................................................................................................ 178

Table 7-2 Mechanical properties of the over-expanded Nomex honeycomb core (ECA-R 4.8

64). ............................................................................................................................ 178

Table 7-3 Mechanical properties of the hexagonal Nomex honeycomb core (ECA 3.2 96) ...

............................................................................................................................ 179

Table 7-4 Mechanical properties of the FM300-2M adhesive [76]. .................................. 179

xv

Table 7-5 Test matrix. ........................................................................................................ 181

Table 7-6 Test results for different sandwich panels configuration. .................................. 183

xvi

List of Figures

Figure 1-1 Common configurations of bonded repair joints, 2D geometries .................... 10

Figure 1-2 Failure mechanisms of a bonded joint ............................................................. 22

Figure 1-3 A tension-loaded 2D scarf joint used in the literature [31] .............................. 22

Figure 1-4 Failure morphology of a low scarf repair joint angle under tensile load [31] . 24

Figure 1-5 Failure paths observed in the static tensile 2°-scarf repaired joints under

different environmental conditions [16] .................................................................................. 24

Figure 1-6 Failure morphology of a circular patch repair: (a) top surface (b) bottom surface

(adapted from [30]) .................................................................................................................. 25

Figure 1-7 Cohesive zone models’ presentation: (a) triangular law, (b) trapezoidal law [20].

.......................................................................................................................... 27

Figure 1-8 Nomenclature used to describe the sandwich panel geometric characteristics 31

Figure 1-9 Different failure modes of a sandwich panel [43]. .......................................... 35

Figure 1-10 Typical scarf-type repair procedure of a honeycomb composite sandwich panel

.......................................................................................................................... 36

Figure 1-11 Scarf-type repair patches on honeycomb sandwich panel ............................... 38

Figure 2-1 Repair configurations in sandwich honeycomb panels .................................... 49

Figure 2-2 Flowchart of the research methodology ........................................................... 51

Figure 2-3 Longitudinal-cross section modeled with 2D model ....................................... 53

Figure 2-4 Circular 3D model geometry ........................................................................... 53

Figure 3-1 Fiber architecture pattern for a) an 8HS fabric and b) a PW fabric (adapted

from[60]) .......................................................................................................................... 57

Figure 3-2 Vacuum bag arrangement and cure cycle used for the quasi-isotropic laminates

.......................................................................................................................... 59

Figure 3-3 Micrographs of PW and 8HS laminate cross-sections after cure .................... 60

Figure 3-4 CLC set-up and specimen configuration.......................................................... 61

xvii

Figure 3-5 Typical stress-strain curve for a [(+45/-45)/(0/90)/(-45/+45)/(90/0)]2s PW

specimen tested in tension ....................................................................................................... 62

Figure 3-6 Typical stress-strain curve for a [(+45/-45)/(0/90)/(-45/+45)/(90/0)]s 8HS

specimen tested in tension ....................................................................................................... 62

Figure 3-7 Typical failure for specimens tested in tension in the x- and y-directions ...... 63

Figure 3-8 Typical stress-strain curve for a [(+45/-45)/(0/90)/(-45/+45)/(90/0)]2s PW

specimen tested in compression in the x-direction .................................................................. 63

Figure 3-9 Typical stress-strain curve for a [(+45/-45)/(0/90)/(-45/+45)/(90/0)]s 8HS

specimens tested in compression in the x-direction ................................................................. 63

Figure 3-10 Typical failure mode for specimens tested in compression in the x-direction 64

Figure 3-11 Nomenclature and dimensions of a ECA-R unit cell (4.8 mm) ....................... 66

Figure 3-12 Compressive test set-up ................................................................................... 67

Figure 3-13 Typical compressive stress-strain curve .......................................................... 67

Figure 3-14 Specimen configuration and tensile test set-up ................................................ 68

Figure 3-15 Typical tensile stress-strain curves in the ribbon (L) and transverse (W)

directions .......................................................................................................................... 70

Figure 3-16 Geometry of studied and simplified specimen (not to scale) ........................... 74

Figure 3-17 Changes in Stiffness matrix to respect modelling convention ......................... 75

Figure 3-18 Boundary conditions for the 2D laminate tensile test (not to scale) ................ 75

Figure 3-19 Comparison of stress-strain curves between the experiment and the finite

element model for a [(+45/-45)/(0/90)/(-45/+45)/(90/0)]2s PW tested in tension in the x-

direction .......................................................................................................................... 81

Figure 3-20 Comparison of stress-strain curves between the experiment and the finite

element model for a [(+45/-45)/(0/90)/(-45/+45)/(90/0)]2s PW tested in compression in the x-

direction .......................................................................................................................... 81

Figure 4-1 Parent panel dimension (not to scale). ............................................................. 89

Figure 4-2 1D scarf/step repair configuration (not to scale). ............................................. 91

Figure 4-3 Tensile test set-up. ........................................................................................... 93

xviii

Figure 4-4 Axial load-strain curves obtained for the pristine and 3-repaired sandwich

specimens (strains measured by DIC on the tool facesheet). ................................................... 93

Figure 4-5 Comparison of the axial load-strain curves obtained on both facesheets of the

sandwich specimens. ................................................................................................................ 94

Figure 4-6 Tensile failure load of the pristine and repaired sandwich specimens............. 94

Figure 4-7 Failure mode of pristine panels. ....................................................................... 96

Figure 4-8 Failure mode for the 3°-repaired sandwich panels. ......................................... 96

Figure 4-9 Micrograph of the cross-section of the (a) pristine specimen, (b) repaired

sandwich specimen before testing. .......................................................................................... 97

Figure 4-10 Micrograph of the 3°-repaired sandwich specimen cross-section after failure....

.......................................................................................................................... 97

Figure 4-11 Description of the boundary conditions. .......................................................... 99

Figure 4-12 Line and local coordinate system used to extract peel and shear stresses ..... 101

Figure 4-13 Shear stress distribution along the bondline. ................................................. 102

Figure 4-14 Peel stress distribution along the bondline..................................................... 102

Figure 4-15 Finite element prediction versus experiment results for the 3°-repaired sandwich

panels. ........................................................................................................................ 107

Figure 4-16 Failure load and efficiency (η= 𝑃𝑟𝑒𝑝𝑎𝑖𝑟𝑓𝑃𝑢𝑛𝑑𝑎𝑚𝑎𝑔𝑒𝑑𝑓𝑥100) for different

scarf-step angles. .................................................................................................................... 107

Figure 5-1 Configuration of the double scarf-stepped repair joint (not to scale). ........... 115

Figure 5-2 Symmetric cross-section of the double scarf-stepped repaired sandwich panel

(not to scale). ........................................................................................................................ 116

Figure 5-3 Line and local coordinate system to extract peel and shear stresses in the

adhesive joint. ........................................................................................................................ 119

Figure 5-4 Shear and peel stress distributions along the adhesive bondline for different

scarf angles. ........................................................................................................................ 121

Figure 5-5 Repair failure stress for different scarf angles. .............................................. 122

Figure 5-6 Shear and peel stress distributions along the adhesive bondline as a function

overlap length Lo (3°-4-ply skin model). ............................................................................... 126

xix

Figure 5-7 Determination of the minimal overply overlap length ................................... 127

Figure 5-8 Repair strength prediction as function of the overlap length, Lo (3°-4-ply skin

model). ........................................................................................................................ 127

Figure 5-9 Failure morphology of a specimen with an overlap length, Lo=10. .............. 127

Figure 5-10 Shear and peel stress distributions along the adhesive bondline as a function of

number of skin plies, N (α=3o)............................................................................................... 130

Figure 5-11 Repair strength prediction as function of the number of skin plies, N (α=3°). ....

........................................................................................................................ 131

Figure 5-12 Map of the failure stress as a function of the scarf angle and number of plies, N.

........................................................................................................................ 134

Figure 5-13 Variation of the failure stress as a function of the overply and number of skin

plies, N (α=3°). ...................................................................................................................... 134

Figure 6-1 Parent panel dimension (not to scale) ............................................................ 145

Figure 6-2 2D stepped-scarf repair configuration ........................................................... 145

Figure 6-3 Specimen geometry (not to scale) .................................................................. 147

Figure 6-4 CAI fixture system used for the edgewise compressive tests ........................ 147

Figure 6-5 Location of strain gages (not to scale) ........................................................... 148

Figure 6-6 Micrograph of the repair cross-section before testing ................................... 148

Figure 6-7 Tensile test set-up. .............................................................................................. 149

Figure 6-8 Four-point bend test fixture and specimen configurations (not to scale) ....... 150

Figure 6-9 Typical force versus strain curves for pristine and 3°-repaired sandwich

specimens tested in compression ........................................................................................... 152

Figure 6-10 Force-strain curves obtained using different strain measuring instruments for

pristine and 3°-repaired sandwich specimens tested in compression .................................... 153

Figure 6-11 DIC measurement: out-of-plane displacement of 3°-repaired sandwich

specimen tested in compression at failure ............................................................................. 153

Figure 6-12 Micrograph of the repair cross-section after failure of 3°-repaired sandwich

specimen tested in compression ............................................................................................. 154

xx

Figure 6-13 Typical axial load-strain curves for the pristine and 3°-repaired sandwich

specimens tested under tension .............................................................................................. 156

Figure 6-14 Typical stress versus strain curves for pristine and 3°-repaired sandwich beams

tested under four-point bending ............................................................................................. 157

Figure 6-15 . Failure mode of a 3°-repaired sandwich beam tested under four-point bending

(repair in tension) ................................................................................................................... 157

Figure 6-16 Comparison of the failure stress of the pristine panels obtained from different

loading types. ........................................................................................................................ 160

Figure 6-17 Comparison of the failure stress of the 3°-repaired panels obtained from

different loading types. .......................................................................................................... 160

Figure 6-18 Studied longitudinal cross-section of the repaired specimens ....................... 162

Figure 6-19 Model geometry and boundary conditions for the four-point bend test ........ 163

Figure 6-20 Mesh details of the adhesive bondline ........................................................... 163

Figure 6-21 Numerical predictions versus experimental results for 3°-repaired sandwich

specimens under different load cases. .................................................................................... 165

Figure 6-22 Deformation and failure mode for a 3°-repaired beam tested under four-point

bending (repair in compression) ............................................................................................ 166

Figure 7-1 Stepped-scarf repair zone cross-section (not to scale). .................................. 178

Figure 7-2 Compressive test fixture and strain gages location. ....................................... 181

Figure 7-3 Specimens configuration and four-point bending test fixture. ....................... 183

Figure 7-4 Stress-strain curves for the pristine sandwich beams. ................................... 184

Figure 7-5 Stress-strain curves for the 3° repaired sandwich beams. .............................. 184

Figure 7-6 Failure morphology of the pristine and the 3°-repaired sandwich beams under

four-point bending. ................................................................................................................ 185

Figure 7-7 Failure stress of the pristine and 3° repaired panels under four-point bending. ..

........................................................................................................................ 185

Figure 7-8 Mesh details of the honeycomb sandwich panels. ......................................... 187

Figure 7-9 Mesh refinement details of the 3°-repaired panel .......................................... 188

Figure 7-10 Boundary conditions applied in the finite element model. ............................ 188

xxi

Figure 7-11 Finite element prediction versus experiment results for composite sandwich

panels ........................................................................................................................ 193

Figure 7-12 Failure mode for the tested composite sandwich panels. ............................... 194

Figure 7-13 Predicted failure morphology for the three panel configurations. ................. 194

xxii

Nomenclature

List of Latin symbols

Loverlap: Overlap Length

L: Total Length of the Specimen

F: Applied Force

A: Section Area

E: Elastic Modulus

G: Shear Modulus

S: Standard Deviation

N: Number of Plies

t: Total Thickness of the Specimen

w: Total Width of the Specimen

tf: Thickness of the Facesheet

ta: Thickness of the Adhesive Film

tp: Thickness of the Ply

tc: Core Thickness

xxiii

List of Greek symbols

σi: Stress (i=x, y)

ν: Poisson’s ratio

α: Scarf Angle

ρ: Density

List of acronyms

RTM: Resin Transfer Molding

C.V: Coefficient of Variation

CLT: Classical Lamination Theory

CFRP: Carbon Fiber Reinforced Plastic

U.D: Unidirectional

RT: Room Temperature

FE: Finite element

OOA: Out-of-Autoclave

PW: Plain Weave

8HS: Eight Harness Satin

DIC: Digital Image Correlation

CZM: Cohesive Zone Model

xxiv

TAST: Thick Adherend Shear Test

CAI: Compression after Impact

S8R: Eight-Node Reduced Integration Shell Elements

AGARD: Advisory Group for Aerospace Research & Development

BVID: Barely Visible Impact Damage

xxv

To my parents, sisters and brothers

xxvi

Acknowledgements

First and foremost, I would like to express my deepest gratitude to Professors Marie-Laure

Dano and Augustin Gakwaya, my research supervisors, for providing me with continuous

opportunities to grow as a young researcher. Their constant support and constructive advices

made these years at Laval University rich in terms of technical learning and personal

development. Thank you for all your support Marie-Laure and Augustin.

Many thanks to Charles-Olivier Amyot for his time and help to ensure the manufacturing and

testing of the sandwich panels. Many thanks also to Mathieu Pouliot and Jonathan Guy-Larose.

I am very thankful to the industrial partners for sharing their expertise in composite repairs,

especially David Wilson, Hasan Salek, Isabelle Paris from Bombardier Aerospace and Étienne

Bélanger from L3-Mas. Thank you for reviewing my papers.

This project was made possible by the financial support, materials provision, and access to

equipment from the Consortium for Research and Innovation in Aerospace in Quebec

(CRIAQ); the Natural Science and Engineering Research Council (NSERC), the National

Research Council Canada (NRC/CNRC), Université Laval, École Polytechnique de Montréal

McGill University, Bombardier Aerospace and L-3 MAS.

xxvii

Avant-Propos

Ce travail présente une thèse par articles comprenant quatre articles qui sont soit publié, accepté

pour publication ou soumis. Ces articles sont :

Article 1 intitulé “Mechanical performance of repaired sandwich panels: Experimental

Characterisation and finite element modeling’’ a été soumis en décembre 2016 au

journal Sandwich Structures and Materials et publié en mai 2017. L’auteur principal

pour cet article est Emna Ghazali et les co-auteurs sont : Marie-Laure Dano, Augustin

Gakwaya et Charles-Olivier Amyot.

Article 2 intitulé “Parametric study of stepped-scarf bonded joints in repaired

honeycomb sandwich composite panels’’ a été soumis au Journal of Adhesion en

novembre 2017. L’auteur principal pour cet article est Emna Ghazali et les co-auteurs

sont: Marie-Laure Dano et Augustin Gakwaya.

Article 3 intitulé “Evaluation of the mechanical performance of repaired composite

sandwich structure using different mechanical tests’’ a été soumis au Journal of

Adhesion & Adhesives en décembre 2017. L’auteur principal pour cet article est Emna

Ghazali et les co-auteurs sont: Marie-Laure Dano, Augustin Gakwaya et Charles-

Olivier Amyot.

Article 4 intitulé “Experimental and numerical studies of stepped-scarf circular repairs

in composite sandwich panels’’ a été soumis en juillet 2017 au Journal of Adhesion &

xxviii

Adhesives et accepté pour publication avec corrections mineures en octobre 2017.

L’auteur principal pour cet article est Emna Ghazali les co-auteurs sont: Marie-Laure

Dano, Augustin Gakwaya et Charles-Olivier Amyot.

Les versions intégrées dans cette thèse sont les versions publiées ou soumises des articles.

La candidate a effectué les travaux expérimentaux et numériques présentés dans ces articles à

quelques exceptions près indiqués ci-dessous :

Article 1: Mathieu Pouliot, étudiant stagiaire, a aidé à la préparation des éprouvettes.

Charles-Olivier Amyot, professionnel de recherche a aidé dans les différents tests

mécaniques.

Article 3 : Jonathan Guy La rose et Éloïse Dol, étudiants stagiaires ont aidé à la

fabrication et aux tests mécaniques de la flexion 4-points avec une étroite participation

de Charles-Olivier Amyot pour la conception du montage de flexion.

Article 4 : Charles-Olivier Amyot a aidé dans les tests de compression.

1

Introduction

Although advanced composite materials and especially honeycomb sandwich structures have

been traditionally used in aerospace applications, they have gained more popularity in high-

performance structural design in the last years. The diversity of the types of reinforcements

(carbon, glass, graphite, etc.), resins and associated manufacturing processes (autoclave, RTM,

out-of-autoclave, etc.) shows that the use of these materials (monolithic or sandwich structures)

is expanding. Their success is due to the various advantages they can offer compared to metals:

good fatigue performance, good resistance to corrosion, high-strength-to-weight ratio (light-

weight-to-stiffness ratio) etc. However, independent of the airframes materials, structural

damage inevitably occurs while in service as a consequence of accidental contact with ground

service vehicle, in-flight hailstones, bird strikes or lightning strikes that may cause critical

damages. Hence following reference [1], “the maintenance and repair of these components are

vital to ensure that the performance of these composite components remain the same as they

were initially designed”( p.919). The damage extent determines whether the component needs

to be repaired or replaced. Moreover, because of time constraint issues, repairs must be

performed as quickly as possible so that the aircraft can be returned into service as soon as

possible. After inspection, maintenance procedure will depend on damage extent. If damage is

minor (i.e., it does not affect the structural integrity of the part), then it is classified as an

allowable damage and only requires a cosmetic repair. However, when damage exceeds the

2

allowable damage size, a structural repair is needed in order to restore the initial carrying

capacities of the structure. Finally, for damage larger than the repairable damage limit size, if

an appropriate repair cannot be substantiated, the component has to be replaced. So, one of the

main challenges facing the aerospace industry with composite materials (monolithic and

sandwich) is structural repair. With the increase of the number of aircraft primary structure

components made of composite materials (either monolithic or honeycomb sandwich), it has

become necessary to develop repair methods that will restore the component’s original design

strength without compromising its structural integrity [2]. It is therefore essential to have

robust, reliable and reproducible procedures related to structural repair to restore the strength

and integrity of damaged composite and sandwich structures. However, with existing repair

technologies, structural repairs present several scientific challenges, especially with primary

structures. To repair damaged structural components, two main methods are typically

considered: bolted repairs and bonded repairs, and bonded repairs are divided into external

bonded repair patches and scarf-type bonded repair patches. Bolted repairs increase

significantly the weight of the component. Also, fasteners offer non-negligible stress

concentrations around the bolt holes. According to [1], depending on the type of damage

sustained, “different repair techniques have been developed to address each specific case’’

(p.900-904). To repair a wide range of cracks or damage to aircraft components and structures,

externally bonded composite repair patches have been shown to be effective [3]. They were

originally used for the repair of military aircraft, but have since been used on civil aircraft.

Traditionally, repairs on metallic aircraft structures were performed using bolted joints,

3

however bonded repairs are the most common repair technique used with composite materials

[4]. The advantages of utilizing bonded composite repairs [5] include:

High resistance to damage by cyclic loads, immunity to corrosion, and high formability that

allows easy forming into complex shapes.

Compared to bolted repairs, bonded repairs offer an alternative repair method that can

effectively reduce the introduction of unwanted stress risers caused by the fasteners used

in a bolted repair, which can severely hinder the performances of the repair [6].

Another disadvantage of using a bolted repair is the likelihood of damaging the surrounding

material while drilling fastener holes.

Composite materials can delaminate from improper hole drilling procedures and

from excessive heat generated from the hole drilling.

Hence to reduce the possibility of thermal delamination, diamond tipped cutting

wheels are utilized in the surface grinding equipment, together with coolant that

is used during the partitioning process.

Due to the advantages from utilizing bonded repairs, the Composite Aircraft Field Repair

Method (CAFRM) is being developed as a bonded field repair. There are two types of bonded

repairs commonly used to repair structural damage.

The first type of bonded repair is an external repair patch that can recover most of the

component’s strength. It has the advantage of being easy to perform and does not require a

4

large amount of time to complete [6]. This makes it a good candidate for a field repair

method.

The effectiveness of bonded external patch repairs depends on several design

parameters that play a vital role. These include in particular, the patch size, patch

shape, materials used, patch taper, patch fiber orientation, and curing

temperatures of the patch [6]. In order to ensure that the stresses induced into

the adhesives are within the design limits of both the material and the operating

envelope of the aircraft structure, care must be taken during the design phase of

these patches.

Most of these parameters are defined by the manufacturer’s Structural Repair

Manual (SRM) for the specific aircraft structure being repaired.

The second type of bonded repair is a scarf-type patch. Compared to external patches,

because of the matching of the repair plies to the plies in the original structures, scarf-type

patches provide higher stiffness. Moreover, the amount of stress risers in a scarf-type patch

repairs are also lower than in external patch repairs.

By matching the neutral axis of the repair patch to the original structure, scarf-

type patch repairs are more efficient in load transfer due to the reduced load

eccentricity [7].

However, aside from the advantages a scarf-type patch repair has over an external patch repair,

scarf-type patch repairs have also some disadvantages:

5

They require a large amount of original material to be removed in order to

maintain a small taper angle.

The placement of the repair plies must be accurately laid up in the repair joint

to the same orientation and order as the original structure. “The accurate

placement of repair plies can be very challenging and the risks of errors are

very high” [1].

The performance of the scarf-type patch can greatly depend on the curing

method utilized to cure the repair. “Repairs cured using different methods

compared to the original structure can greatly affect the strength of the repairs

and cause a mismatch between the original structure and the repair patch’’.

Finally, the adhesives flow under the scarf-type repair patch during curing can

be hard to control, causing the adhesives to accumulate in the bottom of the

patch thus creating a non-uniform bondline.

Due to all these characteristics, a scarf-type repair patch can be:

“Very time consuming and highly dependent on the skill level of the maintenance technician

due to the requirement of accurately removing original materials from the structure and of

precisely replacing the removed materials with new composite materials. Scarf-type repair

patch can thus hardly be considered as candidate for bonded field repair’’.

6

With the above challenges in mind, the authors in [7] then recommend that: “if a scarf type

repair is to be performed on a part that is not considered to be a lightly loaded component, the

scarf-type patch repair should be performed at a repair facility where equipment such as an

autoclave is available in order to produce repaired aircraft parts that have the same part

strength as the original structure”.

In this project, we are concerned with out-of-autoclave composites, and we will try to develop

bonded repair techniques appropriate for out-of-autoclave (OOA) woven composites with the

ultimate goal of setting up a field repair technology for this kind of composites.

This thesis research work is part of the CRIAQ COMP-507 project, which brings together

several partners from industry (BA, L-3Mas), from academics (Laval, McGill, Polytechnique)

and from government Laboratory (NRC-CNRC) for the development of reliable repair methods

and analytical and numerical tools for the repair of composite structures and primary sandwich

panels for aeronautical applications. Its objective is to propose a numerical and experimental

techniques to study the behavior of bonded repair methodology, specifically adapted to primary

sandwich composite structures.

Thesis Organization

The research work achieved in this thesis is organized through five body chapters as follows:

In chapters 1 and 2 a state of the art literature review related to bonded repair joints on

composite laminate structures is first presented. This is followed by a review of experimental

work and finite element techniques employed for modeling different repair joints for

monolithic composites. The chapter ends with review of existing techniques for bonded repairs

7

of composite sandwich structures and associated mechanical testing and finite element

modeling techniques. Finally, the justification of the work to be done and detailed objectives

and methodology of the present work are presented, and the thesis work contributions are then

highlighted.

In chapter 3, the characterization of the sandwich panel’s constituents is presented. Here, in-

plane tension and compression tests as well as out-of-plane tests for woven facesheets and

Nomex core are considered followed by the development of finite element simulation

methodology validated by the simulation of experimental tests.

In chapter 4, the experimental and numerical studies of rectangular (2D) scarf patch repairs of

sandwich panels are presented.

In chapter 5, focus is centered on the parametric study of the effect of different geometric

parameters on the strength recovery of the repaired sandwich panels under tensile loads.

In chapter 6, experimental and numerical investigations on 2D repaired sandwich panels tested

under edgewise compression and four-point bending loads are presented.

In chapter 7, experimental and numerical studies of circular scarf patch repairs are considered.

First compressive and four-point bend tests are performed to determine the behavior of the

repaired sandwich panel and beams. This is followed by the development of 3D finite-element

models with a progressive damage and failure in order to predict the stiffness and failure mode

of the repaired panels.

The thesis work then ends with a conclusion in Chapter 8 that summarizes the contributions

from this research, and gives some recommendations and perspectives for future work.

8

Chapter 1.

Literature Review

The objective of this chapter is to present a state of the art review of current practices in

composite bonded repairs technology in order to identify key issues that require further

investigations and that may form part of the core of the research work to be carried out in this

project. This chapter begins by reviewing the current design guidelines for composite bonded

repairs and then emphasizes on the main challenges associated with scarf bonded repairs,

including the geometric parameters effects on the strength recovery, the optimum taper angle

and the numerical simulation of the repair joint mechanical behavior. The second part of the

chapter then focuses on the principal theme of the thesis related to the major difficulties

encountered with bonded repairs of honeycomb sandwich panels. Finally, the chapter ends by

identifying areas where further investigations are needed.

1.1 A Review of Monolithic Composite Bonded Repair Design

This section reviews methods for designing adhesively bonded repair patches for monolithic

composites. Firstly, an overview of composite internal bonded repair techniques is presented.

Here, experimental works and observations of the failure modes of scarf joints and scarf repairs,

design improvements such as scarf angle optimization, addition of an overply and stacking

sequence are discussed. Secondly, analytical methods to study the stress distribution and the

resistance of the repair are presented. This is followed by a discussion of finite element analyses

9

methods developed for predicting the behavior of composite adhesively bonded repair joints.

Here, both 2D and 3D developed finite element models are discussed. Finally, the failure

mechanics of bonded joints are reviewed.

1.1.1 Composite Bonded Joint Repairs

Bonded joint repairs have significant advantages over fastened or bolted repair joints,

especially for aircraft composite structures. These are expressed in term of high strength-to-

weight ratio, better resistance to corrosion and absence of high stress concentrations at

fastener's holes [8]. The common configurations of bonded joints [9], applied to patch repairs

in aerospace structures, are illustrated in Figure 1-1: single and double lap joints, scarf-scarf

joints and step-step joints. Scarf and stepped bonded joints are typically preferred over double

lap (external patches) due to their higher strength recovery [10].

Scarf Joints

Scarf joints are also called smooth tapered joints or tapered-tapered joints. This type of joint

has many advantages over single and double lap joints such as the reduction in shear and peel

stresses. The stress distribution of scarf joints between identical adherends is almost uniform

and these joints have a higher strength recovery in comparison with other adhesive joints. So,

for these reasons, such joints are used for highly loaded structures. However, the repair patch

in scarf joints cannot be co-cured and need to be pre-cured before being bonded to the parent

structure.

10

Figure 1-1 Common configurations of bonded repair joints, 2D geometries

Stepped Joints

Stepped joints are used as alternative to scarf joints because they are easier to manufacture and

can be co-cured with the adhesive bondline. In theory, with an infinite number of steps, a

stepped joint becomes a scarf joint. While the strength of a scarf joint increases as the angle

decreases, however for a stepped joint with a fixed number of steps, the strength will not

continue to increase indefinitely as the angle decreases. Moreover, material removal for stepped

repairs is a more complex operation than scarfing and proper stepping requires expensive

grinding equipment [11].

1.1.2 Analytical Methods

Different approaches have been used to design bonded joint repairs. Analytical methods were

used by different authors [12,13] in the early 1970’s to study the behavior of scarf joints. Over

the years, as the capability of finite element packages increased, different finite element models

were developed to study the complex behavior of composite bonded joints and to improve the

analytical solutions. The most important points that were improved are:

• The prediction of the peel and shear stresses in the bonded joint,

11

• The modelling of extra plies used to reinforce the bonded structure,

• The modelling of a three-dimensional patch, etc.

The first research published on the use of analytical methods to study the behavior of scarf

joints were studies done by Hart-Smith [12] and Erdogan and Ratwani. [13]. In both studies, a

complete analytical method for the behavior of scarf joints used to repair composite aircraft

structures is developed. Here, the adhesive was modeled as a series of tension and shear springs

and both identical and dissimilar adherends were used.

Hart-Smith [12] showed that the ratio of the peak shear stress concentration at the stiffer

adherend tip relative to the average shear stress across the joint was observed to approach the

ratio of the adherend Young’s modulus. He observed that dissimilarities between adherend

materials contribute to the non-uniformity in the bondline shear and peel stresses. His model

also proposes a simple method for accounting of the non-linearity in the adhesive at high loads.

He was also able to suggest that the integrity of the scarf joint tips was important in maintaining

the overall integrity of the joint.

Erdogan and Ratwani [13] developed a model that was slightly more complete than Hart-Smith

[12]. In this model, they considered both the mechanical behavior of the adhesive in both shear

and normal directions to the bondline. Whereas Hart-Smith [12] assumed that the normal stress

was negligible, Erdogan and Ratwani [13] were also able to deduce from their studies that the

stress distribution in the bondline was not uniform between composite adherend. A stress

concentration in the adhesive was observed near the stiffer plies that correspond to 0°-ply

12

orientations. This was explained by the fact that load transfer through the joint occurs in these

particular locations.

Harman and Wang [14] developed an analytical technique based on the original equations

developed by Erdogan and Ratwani [13] to optimize the shape of scarf joints and to reduce the

shear and peel stress concentration in the adhesive bondline. Analytical equations were used to

conduct a sensitivity analysis to determine the optimal scarf angle for similar and dissimilar

composites adherends. The developed technique is based on a linear variation of the scarf angle

that generates a scarf profile for a given adherend modulus ratio. Harman and Wang showed

the dependency of the adhesive bondline stress distribution to the ply orientation and they

validated their analytical technique through finite element analyses.

1.1.3 Finite Element Analysis Techniques

Due to the limitation of the analytical methods to produce the singularities that a bonded

repaired joint can have, finite element analysis techniques were developed. The finite element

based numerical studies of adhesively-bonded joint repairs (internal or external patch)

considered analyses of either two-dimensional (using plane strain or plane stress assumptions)

or three-dimensional configurations. Many studies have been conducted on bonded joint

repairs of monolithic laminates.

Two-Dimensional (2 D) Analyses

Charalambides et al. [15] performed a two-dimensional numerical analysis to determine the

failure and strength of adhesively-bonded repairs on composites structures. The numerical

predictions were compared to experimental results [16] performed in unageing and ageing

13

conditions (hot/wet conditions). The adhesive bondline was modelled using a linear elastic and

a linear elastic-plastic material models. The composite plies were modelled using two different

approaches. First, the composite structure was assumed to be a homogeneous orthotropic

material. Then, each ply of the structure was modelled as an anisotropic material. Three

different failure modes in 2°-scarf repairs were observed: failure in the adhesive layer, failure

induced from delamination initiating at the corner of the overlap ply and tensile failure of the

composite adherend. Failure loads were compared with previously published experimental

work [16] and the results were found to be in good agreement for green (unaged) repaired

specimens. However, the predicted failure load, associated with delamination, did not occur

for the conditioned repair joints and no conclusion was established by the authors.

In a second approach, Campilho et al. [17–20] have conducted a lot of work to study the

mechanical behavior of external and internal bonded patch repairs. They use a two-dimensional

(2D) finite element model including a cohesive zone element and progressive damage to assess

the strength of external and adhesive repaired patch of Carbon Fiber Reinforced Plastic (CFRP)

under tensile and compressive loads. A mixed-mode cohesive damage model, for ductile

adhesives, was used in the analyses to simulate the adhesive layer behavior.

In [17], Campilho et al. published a study related to the mechanical behavior of single and

double-lap repair joints under tensile loading. A 2D finite element model was developed using

a cohesive mixed mode damage for the adhesive layer. The main objective of this work was to

determine the stress distribution along the bondline as a function of different parameters (patch

thickness, stacking sequence, overlap length…). One of the main findings of this study was the

influence of the overlap length on the failure stress of the repaired joint. For both single and

14

double lap joints, there is a critical value of the overlap length above which there is no strength

improvement.

Another study by the same authors [18] was interested in the mechanical behavior of single

and double-lap repair joints techniques. A parametric study was conducted on different

geometrical details (chamfering the patch outer face, thickening the adhesive near the overlap

outer edge, using fillets of different shapes and dimensions at the patch ends, chamfering the

outer and inner plate edges…). The effect of the shape geometry (single or double strap repair)

on the strength of the repaired structure and the stress distribution along the adhesive bondline

have been particularly considered. It was shown that with an optimal joint configuration, the

residual strength has been increased by 27% in the case of single-lap joints and by 12% for the

double-lap joints.

Later in [20, 21], Campilho et al. developed a two-dimensional (2D) finite element model for

internal scarf bonded repair joints. The aim of their work [19] was to propose a suitable finite

element model to simulate the tensile behavior of composites scarf repair structures. The main

conclusion was that the repair strength increases exponentially with the decrease of scarf angle.

Two different failure modes were observed for the repair. The first mode was observed for high

scarf angles (15°, 25° and 45°) and consists of an entire cohesive failure of the adhesive

bondline. The second failure mode was a mixed cohesive and interlaminar/intralaminar mode

failure which occurs for lower angles (3°). The difference in the failure mode was explained

by the authors as being related to the stress distribution variation along the bondline. In fact,

for higher angles, the bondline length is small and hence induces a higher stress distribution.

The model predictions in terms of failure load, relative displacement and initial stiffness were

15

also compared with experiments. A good agreement with experimental results was found on

these parameters.

Campilho et al. [20] continued the investigation of the mechanical behavior of flush scarf

repaired joints under tensile loading. As in [19], a two-dimensional (2D) finite element analysis

was performed using the cohesive mixed-mode damage model for the adhesive bondline.

Several scarf angles were studied. First, the shear and peel stress distribution along the adhesive

bondline was investigated. Then, a failure analysis was conducted to determine the strength

recovery of the repaired joint by varying the scarf angle and the laminate stacking sequence.

Peel stresses were less significant than shear stresses, for low scarf angles. Shear stresses had

peaks at the free edges of the bondline length, although these were less important than the ones

observed for lap joints [17-18]. This fact leads to an improvement of the strength of this type

of joints. The strength recovery of 2°- and 3°-scarf repaired specimens was about 100% for the

studied stacking sequences, except for the unidirectional lay-up ([032]), in which only a 47%

efficiency was obtained. However, for a 6°- scarf repaired specimen, the strength recovery was

seen to be dependent on the stacking sequence and a higher restitution was found for

[02/752/−752/902]2S stacking sequence reaching about 90% in comparison with 20% for a

unidirectional stacking sequence of [032]. With higher scarf angles (angles above 15°), a

reduction in the strength of the repaired joint was observed and the obtained efficiency was

below 40%.

Gunnion and Herszberg [21] carried out a parametric 2D finite element study of CFRP scarf

joints under tension loads. A linear elastic material stress analysis was performed. A local

coordinate system was defined to extract shear and peel stresses in the middle of the adhesive

16

bondline. Peel and shear peak stresses were evaluated for different combinations of

material/geometric parameters: scarf angle, adhesive thickness, ply thickness, laminate

thickness, over-laminate thickness and lay-up sequence. In particular, [90/0]2S, [0/90]2S, [45/0/-

45/90]S and [0]8 lay-ups were studied. The influence of laminate mismatch on peel and shear

stresses in the adhesive layer was also investigated. It was observed that the lay-up has a high

influence on the stress distributions, since stresses are higher near the 0º-plies. Using

unidirectional laminates, shear stresses are almost constant and peel peak stresses are observed

near the overlap edges. The influence of all parameters on peel and shear average and peak

stresses is summarized in Table 1-1.

Harman and Wang [14] performed a 2D elastic finite element (FE) analysis to validate the

developed analytical technique to optimize the shape of scarf joint between dissimilar

composites adherends. The developed FE model was used to evaluate the use of low stiffness

patch to repair CFRP composites structures. In this work, the authors investigated the influence

of the patch lay-up on the adhesive stress distribution. The optimized scarf repaired joint is

expected to enhance joint strength and to reduce the material to be removed. One of the main

conclusions of this work was that the variation of the scarf angle cannot minimize the shear

stress concentration in the adhesive bondline if the patch and parent laminates lay-up are not

identical.

A recent work from Bendemra et al. [22] has been conducted to study the tensile behavior of

both scarf and stepped flush bonded repair techniques in carbon-epoxy composite structures.

An elastic two-dimensional finite element model was developed. A parametric study was

performed in terms of parameters such as ply thickness, scarf angle, over-ply lap length and

17

lay-up, stacking sequence and adhesive thickness. Peel and shear stress peaks have shown a

strong sensitivity to the ply thickness, scarf angle and stacking sequence for both tapered scarf

and stepped repair joints. However, results showed that tapered scarf joints have a higher

sensitivity to adhesive thickness than stepped repair joints. For their material systems, a [-

45/90/+45/0]S laminate stacking sequence (i.e., parent structure and repair patch lay-up), an

adhesive thickness of 0.26 mm (increased from nominal thickness 0.13 mm), and over-plies

with a 5-mm lap length and [±45] stacking sequence were seen to be the optimal parameters

for a stepped joint repair. However, it should be noted that this set of parameters depends on

the ply thickness, the composite material, the adhesive film and the repair technique used.

Table 1-1 Parameters effects on the peel and shear stresses [21]

Parameter Average peel Peak peel Average

shear Peak shear

Lay-up No effect Increases if 0° plies

are in the outer

surfaces

No effect Decreases with more 0°

plies

Increases with increasing

distance between 0° plies

across the scarf

Laminate thickness No effect Decreases with

increasing laminate

thickness

No effect Decreases with increasing

laminate thickness

Mismatched

adherend

No effect Slight increase or

decrease depending

on lay-up

No effect Slight increase or decrease

depending on lay-up

Adhesive thickness No effect Increases with

increasing adhesive

thickness

No effect Increases with increasing

adhesive thickness

Scarf angle Increases with

increasing scarf

angle

Significant decrease

with scarf angle

increase

Decreases

with

increasing

scarf angle

Slightly decreases with

increasing scarf angles

Over-laminate Decreases with

increasing over-

laminate stiffness

Significant decrease

with increasing

over-laminate

stiffness

Decreases

with

increasing

over-laminate

stiffness

Significant decrease with

increasing over-laminate

stiffness

18

Three-Dimensional (3D) Analyses

Soutis and Hu [23–25] were among the first authors to study the behavior of composite scarf

repaired structures using a 3D finite element model. The studied structures were loaded in both

tensile and compressive loadings. With the developed model, the authors were able to

determine the stresses distribution in the adhesive bondline. Also, failure of the structure was

predicted and compared to experimental results. A main finding of this research was that the

optimal scarf angle was found to be 7° from the 3D model in comparison with an optimal angle

of 4° with the 2D model. This shows that a 2D finite element model gives conservative results

in comparison with a 3D model.

Pinto et al. [26] have developed a 3D finite element model to study the tensile behavior of scarf

repairs in carbon-epoxy structures using a ductile adhesive. The Cohesive Zone Model for the

simulation of damage initiation and growth in the adhesive layer was used. A parametric study

was performed on both the scarf angle and the laminate width to be repaired. It was found that

the strength increases exponentially with the reduction of the scarf angle. The addition of an

over-ply at the outer and bottom faces of the repair improves the strength recovery

approximately by 30 % and 60 %, depending on the scarf angle used.

Breitzman et al. [27] have studied the tensile behavior of scarf composite repaired joints using

a three-dimensional non-linear FE model. Only, the cohesive failure of the adhesive layer was

considered and the composite adherend failure was predicted using a static criterion applied to

the tensile fiber failure mode. The effect of the addition of an over-ply and its orientation was

examined and the scarf ratio was fixed to 1:20. It was observed that the addition of an over-ply

19

reduces the stress peaks at the junction of the 0°-plies. Another finding of this work was that

increasing the over-ply thickness has no major effect on the reduction of stress peak. A strength

recovery of 85% was obtained with one over-ply and an optimal quasi-isotropic stacking

sequence for the patch laminate.

Wang et al. [28] studied the mechanical behavior of stepped bonded joints under compressive

loading until failure. The authors developed a 3D FE model to determine the stress distribution

along the bondline and to predict the failure load and failure mechanisms of 3°-stepped joint

specimens. Geometrically linear and non-linear elastic analyses with failure criteria were

conducted. Hashin failure criteria and progressive damage laws were applied to the composite

laminates. Continuum shell elements were used for the FE mesh and cohesive elements were

placed between plies and on the interface between the adhesive layer and the composite

structure. Three configurations were studied: stepped joints with four and eight steps and a

scarf joint. The composites laminates had a [+45/02/-45/90]s stacking sequence. For the four-

step joints, each step contained two composite plies and for the eight-step joints, one step is

involved by ply. Experimental tests were also conducted for pristine composite plates, 3°-

stepped composite joints and impacted 3°-stepped composite joints. It was found that the

model predictions are in good agreement with the experimental results. However, for the

stepped joints, the finite element model considerably underestimates the compression-after-

impact strengths. The authors explained that this was due to the disbonding of the steps during

impact and concluded that further research was needed to resolve this under-prediction issue.

Also, they suggested that it is important to improve the design of stepped repairs to avoid

premature disbonding when the repaired structure is subjected to external impact.

20

Li et al. [29] developed a 3D finite element model to investigate the tensile performance of

CFRP scarf-lap joints. The model was based on cohesive zone elements for the adhesive

bondline and each ply of laminate was modeled by eight-node linear brick elements with

reduced integration (C3D8R). A thin layer of cohesive elements (0.01mm) was placed between

each 90°-ply and its adjacent layers. Three different stacking-sequences were used for the

composite adherends ([45/0/-45/90]s, [45/0/-45/90]2s and [45/0/-45/90]4s) and four scarf angles

were chosen (3.81°, 5.71°, 8.13° and 11.31°). The influence of these two design parameters on

the ultimate failure load, failure mode and lap shear strength were compared. The main

conclusions from this study are that the lap shear strength increases with the increase of the

scarf angle and that the failure load increases with the adherend thickness increase. It was found

also that the scarf joints have a stepped failure morphology in the adhesive bondline and the

major failure mode is a combination between cohesive failure and a delamination between the

90°-plies and its adjacent plies. Experimental tests were conducted and good correlations

between the test results and the numerical predictions were found in terms of failure load and

morphology.

Authors like Gunnion and Herszberg. [21], Bendemra et al. [22] have extended the 2D linear

elastic finite element models for rectangular patches to a complete 3D models for circular

patches. An identical shape for the peel and shear stresses was found using both techniques of

modelling in the applied stress direction. This result validates the use of 2D model for

parametric study.

21

1.1.4 Failure Mechanisms of Composite Bonded Joint Repairs:

Observations and Modeling Process

Experimental Failure Modes

The failure of composite bonded repair joint can be classified into different types of modes as

follow: adhesive, adherend, cohesive, or a combination of them. Figure 1-2 illustrates an

example of the adhesive, the cohesive and the mixed mode of failure of a bonded joint. To

study the failure morphology (or mode) and the load carrying capacity of repaired composite

structures, two types of repaired joints are usually manufactured: rectangular (2D) joints and

circular (3D) joints. For the first type, called 2D or rectangular joint, the repair is across the

whole width of the specimen and it is relatively simple to manufacture. This joint is widely

used in the literature and provides useful information about the failure mechanics of the

repaired joint. It can be easily modeled by a 2D finite element model assuming a plane strain

problem. Generally, specimens with 2D joints were loaded under tension [16, 20, 30–32], as

can be seen in Figure 1-3. The second type, called circular or 3D joints (because a two-

dimensional cross-section assumption can no longer be made), is more complex to

manufacture. This type of repair is representative of a true repair that could be applied in a

damaged structure. These repaired joints are tested under tension, compression or bending

loads in the literature.

22

Figure 1-2 Failure mechanisms of a bonded joint

Figure 1-3 A tension-loaded 2D scarf joint used in the literature [31]

One of the reports published by the US Air Force [32] was interested in the failure mechanics

of a 2D scarf composite joint under tensile loading, at room temperature conditions. The

authors have used an electron microscope to analyze the failure surface of the tested specimens.

The specimens were carbon-epoxy composite plates with a quasi-isotropic stacking sequence

[02/±45/90/±45/02]s. The main observations made in this report were that:

For low scarf angles (1.1°, 1.9° and 3°), the failure mode was complex. As shown in Figure

1-4, failure begins at one of the free scarf joint ends and continues through the adhesive. At

23

point B, many 90° and 45° plies fibers were pulled out. Then, failure was forced in the

adhesive surface with the presence of the 0° plies. Then failure extended to point C and a

considerable amount of delamination was observed (point C to point D).

For high scarf angles (6.2°, 9.2°), the failure occured mainly in the adhesive bondline.

Specimens contained also some regions where failure occured in the composite adherend.

Charalambides et al. [16] reported the efficiency of 2°-scarf joint specimens with overlapping

plies under static tensile loading for dry, four-months and 16-months conditioned specimens.

Temperature and moisture were found to affect the scarf joint failure mechanisms considerably.

It was shown that for the dry specimens, failure occurred in the parent side of the joint and

seemed to originate from the end of the longest overlap plies (‘Type A’), as illustrated in Figure

1-5. All the four-month conditioned joints showed a failure of ‘Type B’ and the 16-month

conditioned specimens showed ‘Type A’, ‘Type B’ and ‘Type D’ failure modes originating

from the end of the shortest overlap plies. The authors [16] explained that the failure of ‘Type

A’ is caused by the presence of high through-thickness stresses at the end of the overlap plies

which led to the formation of delamination and then caused a final catastrophic failure when a

critical value of the applied load was reached. Failure of ‘Type B’ seemed to be caused by high

longitudinal stresses. For the four-month specimens, no cracks or delamination under the long

overply plies were observed. The change in the failure path and the small increase in the static

failure load, implies that conditioning for four months might have caused an increase in the

through-thickness strength of the composite.

A circular patch repair was tested under tensile loads by Xiaoquan et al. [30]. It was observed

that the specimens failed through the middle of the scarf repaired region and the patch remained

24

attached to one-half of the plate, as seen in Figure 1-6. They observed also that fracture in the

top surface was neat and smooth in comparison with the bottom one. Electron microscopy was

used to have more details about the fracture of the specimens. It was observed that microcracks

are initiated through the weakest part of the interface. These microcracks lead to the formation

of a main crack, which spreads rapidly through the adhesive bondline when a critical value of

the load is reached.

Figure 1-4 Failure morphology of a low scarf repair joint angle under tensile load [31]

Figure 1-5 Failure paths observed in the static tensile 2°-scarf repaired joints under

different environmental conditions [16]

25

Figure 1-6 Failure morphology of a circular patch repair: (a) top surface (b) bottom

surface (adapted from [30])

Numerical Modelling of the Adhesive Joints

i. Cohesive Zone Element Technique

Several research work has been conducted to predict damage in adhesively-bonded composite

structures. Most of them [17, 20, 26, 29-30] use cohesive element models (CZM), with

triangular law, to simulate the adhesive layer damage. The CZM, with triangular law, simulates

damage by the application in most cases of a bi-linear traction-separation law between initially

coincident nodes (see Figure 1-7. a), which assumes first a linear elastic behavior of the

adhesive followed by a linear evolution of damage in the softening phase.

Researchers [34, 35] used also trapezoidal laws to simulate the behavior of adhesively-bonded

joints. For trapezoidal laws, the adhesive stiffness in opening or shear modes is the initial

stiffness of the adhesive for each pure mode. Then a plateau region is introduced to represent

the ductile behavior of the adhesive (see Figure 1-7. b) that is followed by a linear softening

with increasing damage until failure.

26

The cohesive zone element model (CZM) has the advantage of being able to model the behavior

of joint surface from its linear behavior, to the initiation and propagation of damage up to the

final failure in a single analysis.

Another advantage of CZM is the ability to predict the occurrence and propagation of an

interfacial crack without prior knowledge of the location of the initiating microcracks. These

models introduce cohesive elements of zero thickness at the joint plane between two substrates

of any material (which is a limitation of CZM models since one must know a priori where to

place CZM elements in the FE mesh).

For a traction-separation law, the stiffness matrix relating the traction stresses and

corresponding separations in tension and shear across the interface is defined by:

0 0

0 0

0 0

n nn n

s ss s

t tt t

K

K

K

(1)

where: n s t are the relative displacements in normal and transverse shear directions and

[K] is the stiffness matrix whose components can be defined as EKnn ta

and ss tt

a

GK K

t

where E is the adhesive elastic modulus, G is the shear modulus and ta is the thickness of the

adhesive.

27

ii. Elastic-Plastic Models for the Adhesive

As adhesives can reveal a non-linear behavior, plasticity models can be used to predict their

mechanical behavior and their failure mechanisms adequately. In the literature, different

plasticity models have been used [35, 37]. The Drucker-Prager plasticity model [36, 38] is well

suited for describing a pressure dependent hardening material such as epoxy adhesives and

gives results that reproduce accurately the experimental strain hardening data [36, 38].

However, this model requires much more material parameters [37] for plasticity than a classical

metal plasticity model based on the von Mises criterion that is often used because of its

simplicity.

Figure 1-7 Cohesive zone models’ presentation: (a) triangular law, (b) trapezoidal law

[20].

a. Von Mises Yield Criteria

Many authors [37, 38, 40] used the von Mises criteria to represent the mechanical behavior of

the adhesive. This criterion is a simple yield criterion that expresses yielding as a purely shear

deformation process which occurs when the effective shear stress reaches a critical value

[37, 38]. The plastic properties of the adhesive can be determined from a ASTM D5656 Thick

a) b)

28

Adherend Shear Test (TAST) [39]. During the test, the adhesive is supposed to be subjected to

pure shear stress.

b. Drucker-Prager Yield Criteria

Most adhesives under shear and compression stresses show a sensitivity to the hydrostatic

pressure especially for polymeric/toughened adhesives [37]. As the von Mises criterion cannot

take into account these hydrostatic stresses, a more complete criterion based on a simple

modification of the von Mises criteria, named the Drucker-Prager (DP) model [36, 38], includes

this sensitivity, and the simplest one is a linear DP yield criterion, given by

0e m (2)

where 0 is a material parameter related to the shear yield stress τs by:

0 3 s (3)

and m is the hydrostatic stress given in terms of principal stresses (σ1, σ2, σ3) by:

1 2 3

1( )

3m (4)

So from equations (2) to (4), it can be observed that the parameter μ is dependent on the

adhesive material and characterizes the sensitivity of yielding to the hydrostatic stress [35].

This parameter can be determined from shear and tensile tests using:

3 [ 3 1]s

T

(5)

where T is the stress from the tensile test.

29

In this work, the discussed failure mechanism is limited to answering the following question:

which part or section of the structure reach failure first and the failed part is expressed by a

failure model (dynamic failure supported by ABAQUS. Hence further aspects such as initial

and final crack length, crack growth /propagation or energy release rate are not of interest here.)

1.1.5 Review Summary

The above review covered various aspects of design, finite element simulations and failure

mechanisms of bonded joint repairs of monolithic composite structures. Table 1-2 summarizes

the different issues and aspects studied in the literature and reviewed in this chapter.

Table 1-2 Issues and aspects studied in the literature for composite bonded repairs

Joint geometry

Composite

Material

Finite element

models

Simulation of the

adhesive layer

Cure of the

repair patch Cure method

Single/double lap

Scarf-scarf

Step-step

Unidirectional

(UD)

2D

3D

CZM

Elastic-plastic

Pre-cure

Co-cure

Autoclave

Oven

1.2 A Review of Honeycomb Sandwich Panel Bonded Repairs

After reviewing the monolithic composites bonded repair technology in section 1.1, a literature

review of honeycomb sandwich panel bonded repairs techniques is presented in this section.

Sandwich panels are being used in many industries such as aerospace, and automotive for

different applications. One of the main interests of sandwich structures is their high specific

flexural rigidity. They also offer many advantages: lightness, mechanical strength, reduced

maintenance, complex shapes. Sandwich structures have gained popularity in the aeronautical

30

field. On the Airbus A380 aircraft, for example, sandwich structures are used in nacelles,

ailerons, floor, fuselage, cabin, etc. However, despite their good properties, honeycomb

sandwich structures are sensitive to impact damage, which can cause disbonding, delamination

and internal crushing. Considering their extended service life and operating conditions, the

extent of damage determines whether the sandwich components need to be repaired or replaced.

Hence, to take full advantage of their many benefits, the improvement of their performance

requires one to ensure first that these structures are durable, repairable, and maintainable. Since

fiber-reinforced composite sandwich structures are increasingly being used in primary aircraft

components, it has become necessary to develop effective repair methods that will restore the

component’s original design strength without compromising its structural integrity.

This section begins with an introduction on sandwich panels presenting their components,

benefits and drawbacks. Different failure modes for sandwich panels will be discussed as well.

Then, a detailed review of the literature on honeycomb sandwich panel repairs will be

presented. Here, the focus is on both the experimental studies and the numerical methods

developed to study the mechanical behavior of repaired sandwich panels under different loads.

Finally, a conclusion and the main settled or still open issues of the literature will be presented.

1.2.1 Introduction

Typically, sandwich panels are composed of two thin skins (or facesheets) made either from

metallic materials or from fiber-reinforced composite materials, and a thicker core material,

generally an aluminum or a Nomex honeycomb material in between as shown in Figure 1-8.

The figure indicates the nomenclature used to define the different geometric characteristics of

31

the sandwich panel. Core materials, generally low-density material, are usually in forms of

honeycomb or foam structures. Metallic (aluminum) or polymeric materials are the most

common materials used for the core. The concept behind sandwich structure is that the skins

carry the in-plane compressive and tensile stresses resulting from the applied bending moment,

while the main function of the light-weight core is to keep the two skins apart and to resist and

transfer the shear forces to the skins. By increasing the thickness of the core, the flexural

rigidity of the panel increases for a small weight penalty [40].

Table 1-3 shows the flexural stiffness and strength advantages of sandwich panels in

comparison with solid panels.

Figure 1-8 Nomenclature used to describe the sandwich panel geometric characteristics

Table 1-3 Structural efficiency of sandwich panels in terms of weight [41]

32

Relative bending

stiffness 1 7 37

Relative bending

strength 1 3.5 9.2

Relative weight 1 1.03 1.06

During service, sandwich panels are subjected to various stresses which can cause damage, the

accumulation of which can lead to their rupture. Sandwich structures remain also vulnerable to

impact damage including damage resulting from maintenance activities such as dropped tools.

Therefore, it is important to understand the main modes of deformation and damage, which can

result from the various loads to which they may be subjected in service conditions.

Honeycomb sandwich structures can fail in several ways. Depending on the geometry of the

sandwich panel and the loading type, different failure modes can be induced and set limits on

the mechanical performance of the sandwich structures. Failure of the sandwich structures may

be driven by the strength of the facesheet, core, or adhesive, by a local instability mode such

as facesheet wrinkling or facesheet dimpling, or by general instability such as global buckling

[42]. The failure load and the corresponding failure mode depend strongly on the properties of

facesheet, core and adhesive materials. The typical observed failure modes are presented in

Figure 1-9 and briefly described as follow.

Facesheet Failure

Different failure modes can occur in the skin of the sandwich panel: face wrinkling, skin

yielding and intra-cell dimpling.

i. Facesheet Yielding

33

In this case, failure occurs when one or both facesheets fails by yielding or fracture, as

presented in Figure 1-9.a. The criterion for failure is that the stress in the facesheet material,

𝜎𝑓𝑐𝑟 , exceeds its allowable stress, Y .

𝜎𝑓𝑐𝑟 ≥ 𝜎𝑌 (6)

ii. Facesheet Wrinkling

This is a type of local instability characterized by buckling of the facesheet. The buckling may

occur either inwards or outwards the core, depending on the stiffness of the core in compression

and on the adhesive strength, as presented in Figure 1-9.b. This failure is most prevalent with

thin facesheets and low-density core. The critical compressive stress that results in wrinkling

is given by Allen [42], as

𝜎𝑓𝑐𝑟 = (3/(12(3 − 𝜈𝑐𝑥𝑧)2(1 + 𝜈𝑐𝑥𝑧)2)−1/3) 𝐸𝑓𝑥

1/3𝐸𝑐3

2/3 (7)

where νcxz is the out-of-plane Poisson ratio of the core and Ec3 is the out-of-plane elastic

modulus of the core.

iii. Facesheet Dimpling

Facesheet dimpling is also known as intra-cell buckling. It is a type of local instability

characterized by local buckling of a facesheet induced from the non-continuous facesheet

support by the core. This failure mode occurs when the facesheets are thin and the cell size is

large, as seen in Figure 1-9.c.

34

Core Failure

i. Core Shear Failure

The core shear failure occurs when the applied shear stress exceeds the transverse shear

strength of the honeycomb core. This usually results in cracks inclined at 45° to the midplane.

The core material is mainly subjected to shear since it carries almost the entire transverse load,

and very little in-plane load. Low density honeycomb cores are very sensitive to this failure

mode. The transverse shear strength is given by [43]:

𝜏𝑐𝑟𝑠ℎ𝑒𝑎𝑟 = 𝜏𝑐𝑥𝑧 =

𝑡𝑐𝐺𝑐𝑥𝑧

2𝑡𝑓 (8)

where Gcxz is the core transverse shear modulus, tc and tf are the thickness of the core and

facesheets respectively, as illustrated in Figure 1-9.d.

ii. Core Crushing

This failure mode occurs when the facesheets move towards each other under the influence of

bending or through-thickness loads. This mode occurs when the core material has insufficient

compressive strength, as presented in Figure 1-9.e.

Global Buckling

The global or general buckling of a sandwich panel is a general instability of the structure, and

is similar to the classical buckling of plates or columns. Both facesheets and core remain intact

in this type of failure, as seen in Figure 1-9.f.

35

Figure 1-9 Different failure modes of a sandwich panel [43].

1.2.2 State-of-The-Art Review of Sandwich Panel Repairs

Typical Repair Procedure for Sandwich Panels

As for the monolithic composite laminates, different repair configurations exist for sandwich

honeycomb panels. Two types of bonded repairs can be used to repair a honeycomb sandwich

panel: an external type of patch repair and a scarf-type of patch repair.

The typical scarf-type repair procedure of honeycomb sandwich panels involves the removal

of the damaged area of the skins with or without core removal. The edges of the parent plies

are scarfed or stepped. The surface is cleaned and prepared to receive the adhesive and repair

plies. The damaged region is then repaired by inserting a core plug if it is necessary and

stacking skin plies with a similar or non-similar lay-up as the parent ones. These new parts are

36

bonded to the parent structure using an adhesive film. The scarf-type repair procedure is

illustrated in Figure 1-10.

Figure 1-10 Typical scarf-type repair procedure of a honeycomb composite sandwich panel

Experimental Characterization of the Honeycomb Sandwich Repair

Unlike monolithic composite structures, works on repair of sandwich panels are quite few and

limited. Different studies [44–47] have been carried out on repair techniques and

characterization of repairs on sandwich structures. Different repair techniques and processes

have been discussed in some works. The use of high and low temperatures cure cycles has been

discussed several times as in [44, 48]. It has been demonstrated that repairs cured at high

temperature show a better restoration of the strength.

The AGARD (Advisory Group for Aerospace Research & Development) [44] published a

report on repairs of sandwich structures used in military structures. Here, three different

techniques are used to repair the sandwich structure with an external patch. The patches were

37

either co-cured or pre-cured and the core either replaced or filled with a filler paste cured at

high and low temperatures cycles. Static and fatigue compression tests were carried out to

characterize the quality of the repairs. Results showed that the pre-cured patch method is the

most suitable for field-level application.

Baker et al. [45] have studied experimentally a scarf repair on a horizontal stabilizer of a F/A-

18 spacecraft composed by an Aluminum honeycomb core and CFRP skins. The repaired

structure was tested under a four-point bending load. The specimens were tested at -40ºC, room

temperature and 104ºC, in dry and wet conditions. The failure of the adhesive film was cohesive

for all test conditions. At 104ºC, the failure strains were reduced by 50%, compared to the

specimens tested at room temperature.

Rider [46] conducted a study on in-situ repairs of sandwich structures of an F-111 aircraft.

Several problems were noted during this study concerning the repair technique used. Among

the critical points studied are the humidity in the core and the importance of having an adequate

drying step for the core to avoid problems of detachment of the patch. An alternative was

proposed: after a drying step of two hours at 100 °C, surface preparation is performed followed

by a storage of the structure at 50°C which is advised before proceeding with the repair.

In the literature, rectangular and circular repair patches on sandwich structures (see Figure

1-11) were subjected to different loadings (four-point bending, tension, shear, and

compression) to determine their mechanical strength. Rectangular or 2D repair configurations

were studied under different loading in [2, 47]. Circular repairs were tested, at ambient

temperature, under edgewise compressive loading in [49, 50].

38

Figure 1-11 Scarf-type repair patches on honeycomb sandwich panel

Mahdi et al. [47] tested rectangular sandwich panel repairs (2D configuration) under four-point

bending load. Here, the scarf repair has a plain weave overply ply with a (+45/-45) lay-up and

results are obtained for a non-symmetric sandwich structure (the repaired skin lay-up is [(+45/-

45)/ (0/90)] and the undamaged skin lay-up is [(0/90)/ (0/90)]). The repaired facesheets were

loaded in both compression and tension. Two repair configurations were studied: overlap and

scarf repair. The repair was cured at low and high temperature systems. The main findings of

this work are that when loaded in compression, the scarf repairs were weaker than overlap

repairs. However, scarf repairs were stronger in tension achieving 100% of the pristine strength.

Finally, the cure temperature had no major effect on the strength recovery of the repaired

sandwich structures.

A series of experimental tests (tensile, shear and four-point bend tests) were conducted by

Tomblin et al.[2, 51] to study the effects of different process parameters on the quality of 2D

sandwich panel repairs. The repair carried out included a core removal and replacement. Two

39

different cell sizes for the core plug were considered in this work [2]: 3.175 mm and 9.525 mm.

Most of the repaired specimens tested under different loads showed a high recovery of the

residual strength (about 92%). It has also been proven that the size of the core cell plays an

important role on the performance of the repaired sandwich structure. The core with a 3.175

mm cell showed better strength recovery than one with a 9.525 mm cell size. A damage

tolerance analysis on sandwich structures was included as well [51]. As a conclusion of their

work, a methodology for the repair process along with design tools for damage tolerance on

sandwich structures were developed.

Like for composite bonded joint repairs, the scarf angle is an important parameter to consider

in the design of repairs in sandwich structures [45, 47, 52]. Several scarf angles (3°, 6°, and 9°)

[52, 53] or ratios (1/10, 1/20, 1/30 ...) [45, 54] have been studied. The results of these studies

show that with a smaller angle, a better restoration of the strength is found.

Fatigue resistance of repaired sandwich structures has also been studied in [44, 55]. But the

work in this area is very scarce. The AGARD group [44] published fatigue results on sandwich

structures loaded in compression. It showed that the repair with high temperature cure cycle

has a higher recovery than the one with low cure temperature.

Mahdi et al. [48] performed cyclic four-point bending fatigue tests on pristine (undamaged)

and 2D repaired sandwich beams. Three configurations, as for the static work [47], were

studied: an overlap and two scarf repairs. All configurations were tested in tension and in

compression. Also, two cure cycle systems were used like in [47]. From this study, the authors

showed that the overlap repair performed better in compression than the scarf repair

40

configuration. The degradation of stiffness with cycling was also investigated and was related

to the microscopic evolution of damage.

Finite Element Analyses of Honeycomb Sandwich Panel Repairs

Numerical models, with different levels of complexity, have been developed to predict the

mechanical behavior of repairs in sandwich structures. 2D elastic models, based on the

assumption of plane strain formulation, with a linear elastic behavior of the adhesive joint have

been developed in the majority of studies ([52, 53]). The purpose of these models is to

determine the distribution of shear and peel stresses along the adhesive bondline. The

distribution of stresses in scarf and overlap types of repairs was compared [52]. It has been

demonstrated that scarf repair has a homogeneous stress distribution in comparison to the

overlap repair. The peak stresses are greater at the overlap level than everywhere else. Later,

3D finite element analysis with a progressive damage model for the composite skins were

performed to study the mechanical behavior of the repaired sandwich structures under

compressive loads [49, 50].

i. 2D Finite Element Analysis

Oztelcan et al. [53] presented a finite element study on repaired sandwich helicopter blades

with GFRP facesheets and honeycomb core under a compressive loading. In this work, two

repair configurations were evaluated: an overlap repair and a scarf repair. The numerical

models used eight-node reduced integration shell elements (S8R) for the composite skins,

available in Abaqus [56]. First, a global model was used to identify the most stressed regions

of the structure, and then a smaller local model was built for the critical region and only for the

41

composite facesheets. This local model was subjected to the displacements obtained from the

global model. A subroutine was developed for the adhesive layer elements, including a

progressive damage model based on the Maximum Stress Criterion to obtain the shear stress

distributions in the adhesive. For the overlap configuration, shear stress distributions presented

a parabolic shape, symmetric relatively to the overlap central region, and peaking at the overlap

edges. The scarf repair used an angle of 3º and the parent and patch had the same lay-up. A

uniform shear stress distribution was obtained in comparison with the overlap configuration.

Moreover, increasing the compressive load, the adhesive layer was kept uniformly loaded along

all its length, resulting in a more efficient distribution of stresses, compared to the overlap

repairs.

Mahdi et al. [54] used 2D finite element models to predict the performance of both pristine and

scarf repaired sandwich panels subjected to static and fatigue four-point bend loading.

Numerical analysis results showed a good correlation in terms of stiffness prediction of both

undamaged and repaired coupons. An attempt to calculate the failure strength of the studied

sandwich beams has also been made. The Tsai–Hill criterion was chosen to predict the first-

ply failure load. However, the failure load prediction was problematic and did not show a good

correlation with experiments.

Another 2D model using cohesive elements was also developed by Chen [57]. The model was

used to study the behavior of adhesively bonded 3°-scarf-repaired sandwich structure under

four-point bending load. Good correlation between the experimental results and the numerical

predictions was found in terms of the failure load, the residual stiffness and the crack path.

42

Ramantani et al. [52] investigated the mechanical performance of repaired honeycomb panels

by numerical models using interface elements, in order to obtain the distribution of stresses at

the critical points in the adhesive joint. A 2D symmetric finite element model with a mixed

cohesive approach was developed to simulate the behavior of the repaired structure under a

four-point bending load. Scarf and overlap repair configurations were studied. The influence

of the scarf angle variation (3°, 6°, 9° and 15°) for the scarf repair and of the thickness of the

repair (thin/thick) for overlap repairs were investigated in terms of the restoration of residual

strength and stress analysis. The scarf repair with an angle of 3° showed a better distribution

of shear stresses. This was due to the fact that the adhesive joint is longer with a 3°-scarf angle.

The failure mode was also dependent on the scarf angle variation. For overlap repairs, it was

also proven that the ultimate failure load is strongly influenced by the overlap length and that

from a critical length of the overlap, there will be no influence on the ultimate load.

ii. 3D Finite Element Analysis

Baker [45] has developed a 3D finite element model to study the stresses distribution along the

adhesive bondline of a typical repair of a graphite/epoxy honeycomb sandwich structure. A

scarf angle of 3° was chosen for the repair configuration. Predictions of the shear stress

distribution along the adhesive joint have been compared with experimental results. The main

finding of this work is that the shear stress along the bondline is not uniform as is the case of

isotropic adherend.

Mahdi et al. [54] used a quasi-3D finite element model to predict the performance of both

pristine and scarf repaired sandwich panels subjected to static four-point bend loading.

43

Numerical analysis results showed a good correlation with the developed 2D model and the

experiment in terms of stiffness prediction of both undamaged and repaired coupons. However,

the ultimate load was problematic and did not show a good correlation with experiments.

The compressive behavior of circular repaired sandwich panels was investigated by Liu et al.

[49]. Both experiments and finite element analyses were conducted to study the influence of

repair variables such as scarf angle and cure cycle on the quality of the repair. A progressive

damage model, based on the Hashin’s criterion for unidirectional composite materials, was

developed and used to predict failure of the repaired sandwich panel. The adhesive film was

modeled using cohesive elements. Good correlation between experimental and numerical

results was obtained. However, since the inner diameter of the repair was small (25mm)

compared to the sandwich panel width (100 mm), the load is by-passed, and failure occurs in

the parent and not in the adhesive bondline

A recent study from Zhang et al. [50] was conducted to investigate the mechanical performance

of pristine, open-hole damage and circular scarf repair honeycomb sandwich panels under

compressive loads. A 3D finite element model was also developed. A failure criterion based

on the Hashin’s criterion with a progressive damage evolution was included for the quasi-

isotropic composite skins. The adhesive layer was modelled using cohesive elements. The

honeycomb core cells were modelled using shell elements. The honeycomb material was

considered as an elastic-plastic material. A good agreement was found in terms of ultimate

failure load and damage shape between the experimental and numerical results. Failure of the

repaired sandwich panel was due to adhesive delamination and local buckling of the patch.

Although the developed model is accurate, the computing time was quite long. Another finding

44

of this work was that the structure strength increases with the decrease of scarf angle and that

the optimum number of 0°-overplies was one to reach the highest strength.

1.2.3 Concluding Remarks

This review highlights the state-of-the -art on different topics that will be developed further in

this thesis. It allows a clear assessment of the contribution of this research. According to the

preceding literature review carried out on the repairs of sandwich structures, important issues

that retained our attention can be summarized as follows:

i. From the Experimental Point of View:

Most repairs were performed on unidirectional composites. Repairs on woven

composites have been very scarcely studied in the literature [2, 47].

The scarf-scarf type of joint was chosen as the repair configuration in most

cases. This implies that the repair patch needs to be pre-cured.

The curing of the parent structure as well as of the repair patch was done under

autoclave in most cases.

The characterization of the repair was often carried out at ambient temperature

conditions and the influence of other temperature conditions was barely studied.

Table 1-4 to Table 1-6 regroup the different experimental aspects studied in the literature on

sandwich honeycomb repairs.

45

ii. From a Numerical Point of View:

Linear elastic 2D finite element models have been developed to study the distribution of

stresses in the adhesive joint.

Cohesive elements were chosen to predict the rupture of the adhesive joint. This type

of element cannot, however, be used for the modeling of stepped-scarf repair joints.

A single study [52] was carried out on the effect of different parameters (angle.) on the

behavior of sandwich panel repairs. This study was carried out using a 2D finite element

model using cohesive elements for scarf-scarf repairs.

3D models were developed to predict the mechanical behavior of sandwich panel with

circular repairs until rupture. Failure criteria for unidirectional composite material were

used.

Table 1-7 summarizes the different aspects of the finite element models studied in the literature

for the sandwich honeycomb panel repairs.

Table 1-4 Sandwich panels component materials used in the literature

Skin Materials Honeycomb core Adhesive film

Baker [45] AS4/3501-6 U.D prepreg Aluminum alloy core FM300K

Tomblin [2] Prepreg and wet lay-up material Nomex honeycomb core FM377S

Mahdi [47] F914C woven fabric Nomex honeycomb core Redux 319A

Ramantani [52] CFRP U.D prepreg PVC foam core Epoxy resin

Liu [49] MTM44-1/HTS(12K) U.D

prepreg Nomex honeycomb core FM490A

Zhang [50] CFRP U.D prepreg Nomex honeycomb core

46

Table 1-5 Repair configuration, process and cure methods for sandwich panel repairs

used in the literature

Repair configuration Cure temperature Cure method

Tomblin [2] Scarf-step Low & high

temperature -

Mahdi [47] Scarf-step Low & high

temperature Oven/ hot bonder

Liu [49] Scraf-scraf Low & high

temperature Autoclave

Zhang [50] Scarf-scarf - Autoclave

Table 1-6 Mechanical characterization and non-destructive inspection of sandwich panel

repairs used in the literature

Test loading Environmental

conditions

Non-destructive

inspection

Tomblin [2] Four-point bending, tension, shear Room temperature C-scan, Tap Test

Mahdi [48] Four-point bending Room temperature -

Liu [49] Compression Room temperature -

Zhang [50] Compression Room temperature C-scan

Table 1-7 Finite element model types used in the literature for sandwich honeycomb

panels

Finite element

analysis Behavior of the adhesive Behavior of the composite skins

Ramantani [52] 2D Cohesive elements -

Mahdi [54] 2D, quasi-3D - Failure of first ply-Tsai-Hill criterion

Liu [49] 3D Cohesive elements Progressive failure damage- Hashin criterion

Zhang [50] 3D Cohesive elements Progressive failure damage- Hashin criterion

47

Chapter 2.

Overview of the Problem and Research Focus

2.1 Rationale of the Thesis

The main goal of this study consists in designing a reliable bonded repairs methodology for

primary sandwich honeycomb structures for aerospace applications, and particularly in

developing simulation tools and protocols for the design of sandwich composite bonded

repairs. For that purpose, a series of experimental investigations and numerical simulations of

repaired bonded honeycomb sandwich panels will be conducted.

In that regard, a state of the art literature review was performed and revealed the following

issues:

The composite materials used for the repair of sandwich panels are in most cases

standard unidirectional carbon-epoxy prepreg cured in an autoclave and the stacking

sequence for the parent and the repair patch uses only 0o or 90o plies.

Parent structures and repairs made with woven fabric composite have been very

scarcely studied in the literature. However, these materials are now widely used to

manufacture primary aerospace structures.

In most cases, repairs are cured in autoclave. However, in practice, repairs are processed

either using a hot-bonder or a heat blanket.

48

Image correlation systems to evaluate the strains on the repair patch have been scarcely

used. The use of such technique is however very helpful to observe the strain

distribution on the repair patch and understand how failure occurs.

Finite element models developed to study the mechanical behavior of repaired

sandwich panels use cohesive elements to discretize the adhesive joint. However,

cohesive elements cannot describe adequately the elastic plastic behavior of the

adhesive and relies on parameters which are difficult to evaluate.

The use of progressive damage models for unidirectional composite materials to predict

failure of the composite patch is very limited in the literature. The application of

progressive damage model to predict failure of patches made with woven-fabric

material has, to our best knowledge, never been discussed in the literature.

Finite element analyses have been so far conducted either on scarf-scarf or stepped-

stepped repair joints. In practice, stepped-scarf repair joints are widely used. This type

of repair has been simplified to a scarf-scarf configuration in finite element analyses

presented in the literature. This simplification may lead to inaccurate stress predictions

in the adhesive joint.

In most cases, the developed finite element models are not validated with experimental

results.

Based on the project main objectives and the summary of the literature review, sub-objectives

have been defined and will form the core of this thesis. They are described in the next sub-

sections.

49

2.1.1 Assessment of the Mechanical Behavior of Honeycomb Sandwich

Panels with Bonded Repairs by Experimental Testing

The first objective of this thesis focuses on the determination of the mechanical performance

of repaired honeycomb sandwich panels under different static loadings: tension, compression

and four-point bending. Two repair configurations will be used for this experimental program

(Figure 2-1):

2D repair where the repair patch has a rectangular shape and is across the whole specimen

width.

3D repair where the repair patch has a circular shape (which is widely used in practice).

Figure 2-1 Repair configurations in sandwich honeycomb panels

50

2.1.2 Development of Finite Element Models for Better Understanding and

Accurate Prediction of the Mechanical Behavior and Failure Modes of

the Repaired Sandwich Panels under Different Loadings

The second objective consists in the development of finite element models to be used as an

alternative design tools for sandwich panel repairs. Different models will be developed to

predict the mechanical behavior of the repaired sandwich panels until failure for different

loadings. These models will take into account an elastic-plastic behavior of the adhesive based

on physical parameters in comparison with the cohesive element models proposed in the

literature.

2.1.3 Validation of the Finite Element Models and Conduction of a

Parametric Study

The proposed models will be validated with experimental results. Once validated, these models

will be used to perform a parametric study to investigate the effect of different design

parameters on the strength recovery of the 2D repaired sandwich panels under tensile loads.

The results of this parametric study will be used as a guideline to select appropriate design

parameters for a given repair configuration of a honeycomb sandwich structure. The design

parameters are:

The scarf angle

The thickness of the sandwich skin

The use of an overply and its overlap length

51

2.2 Methodology and Thesis Structure

2.2.1 Methodology

Figure 2-2 outlines the methodology followed to reach the research objectives.

Figure 2-2 Flowchart of the research methodology

Experimental tests

The experimental work is divided into two main parts:

Part I: Mechanical Characterization of the Sandwich Honeycomb Constituents

Here, the mechanical properties of the constituent materials of the sandwich panels, namely the

CFRP facesheets and the honeycomb core, will be evaluated. This task will be achieved by

conducting static tensile and compressive tests, according to ASTM standards. The determined

mechanical properties of these components will be implemented later in the developed finite

element models. This is discussed in chapter 3.

Characterization tests:

- Composite skins

- Nomex core

- Adhesive film

FE models of the repaired

sandwich composite panels

Compressive, tensile and four-

point bend tests on repaired

sandwich panels Model validation

Experimental tests Numerical simulation

52

Part II: Mechanical Performance of the Repaired Sandwich Panels

Experiments will be conducted on pristine and repaired sandwich panels (2D and 3D repair

configurations) to investigate their mechanical behavior under different loading (tension,

compression and flexure). Tensile, compressive and flexure strength of the repaired specimens

will be compared with the pristine values. This is discussed in chapters 4, 5 and 6.

Finite element modelling

Two-Dimensional Finite Element Model (2D FE Model)

First a two-dimensional (2D) finite element model will be performed using the software

package Abaqus [58]. The main objectives of this FE model are to study the stresses

distribution along the adhesive bondline and to predict the mechanical behavior of the 2D repair

until failure. The corresponding model geometry is easy to create. Since the repair will be

across the width, it can be represented by a longitudinal-longitudinal-cross section (see Figure

2-3) so that plane strain assumptions can be adopted for the analysis.

As a start-up, a 2D linear elastic analysis will be conducted to determine the peel and shear

stresses distribution along the adhesive bondline. Next, a second analysis will be undertaken

and will take into account the nonlinear behavior of the adhesive film, to predict the mechanical

behavior up to failure of the 2D repair under tension and four-point bending loads. This will be

discussed in chapters 3, 4 and 5.

Three-Dimensional Finite Element Models (3D FE Model)

The second finite element model to be developed is a three-dimensional (3D) model which

takes into account the progressive damage of the woven-fabric facesheets and the elastic-plastic

53

behavior of the adhesive film. Because of the symmetry of the problem, a quarter of the model

geometry will be modeled, as presented in Figure 2-4. This model will allow predicting the

compressive mechanical behavior of pristine, open-hole damage, and circular repaired panels.

The finite element model predictions will be experimentally validated. This is discussed in

chapters 6 and 7.

Figure 2-3 Longitudinal-cross section modeled with 2D model

Figure 2-4 Circular 3D model geometry

Adhesive

Bag face

Nomex core Patch

Parent

54

The experimental and numerical investigations performed in the thesis used mainly the

following material system and processes:

Two out-of-autoclave woven-fabric prepreg materials: the plain weave (PW) and the

eight-harness satin (8HS),

A four-ply sandwich panel skin with a quasi-isotropic sequence,

A realistic repair geometry, which is a flush stepped-scarf repair geometry (for both 2D

and 3D repair configurations),

Out-of-autoclave and co-bonded repair patch.

2.2.2 Chapters Presentation

The thesis is then organized as follow.

Chapter 3 presents the experimental work done to determine the mechanical properties of the

sandwich panel constituents, namely the facesheets and the core. First, a series of tensile and

compressive tests is performed to determine the in-plane and out-of-plane mechanical

properties of the constituents. After that, the developed 2D and 3D finite element models are

verified, and numerical predictions of the laminate behavior are compared with results from

the experiments and from the classical lamination theory.

Chapter 4 details the experimental and numerical investigations conducted on the 2D repaired

sandwich panels. Specimens were tested under uniaxial tension loads and different scarf angles

were studied. The 2D model was used to predict the mechanical behavior of the repaired

structure until failure. This chapter is presented as the first research paper.

55

Chapter 5 discusses the parametric study conducted on the 2D repaired panels. Focus was on

the effect of different geometry parameters on the strength recovery of the repaired panels

under tensile loads. This chapter is presented as the second research paper.

Chapter 6 continues the experimental and numerical investigations on 2D repaired panels

tested under edgewise compression and four-point bending loads. This chapter is presented as

the third research paper.

Chapter 7 presents the experimental and numerical works conducted on the circular repaired

panels. Compressive and four-point bend tests were performed to determine the behavior of

the repaired specimen. Then, a 3D finite element with a progressive damage and failure for the

composite was developed to predict the stiffness and failure mode of the repaired panels. This

chapter is presented as the fourth and last research paper.

Finally, a conclusion (Chapter 8) summarizes the contributions from this research and gives

some recommendations and perspectives for future work.

56

Chapter 3.

Mechanical Characterization and Finite Element

Study of Monolithic Facesheets and Honeycomb

Core

This chapter presents the experimental results from tensile and compressive tests conducted on

plain weave (PW) and 8-harness satin (8HS) carbon/epoxy composite materials with a quasi-

isotropic lay-up. Both in-plane tensile and compressive properties were determined

experimentally. The honeycomb Nomex core was tested experimentally to determine the in-

plane and out-of-plane mechanical properties. Moreover, a 2D linear elastic ply-by-ply

through-the-thickness model of a quasi-isotropic laminate was developed using the software

Abaqus/Standard to predict the laminate elastic behavior. Results were then compared with the

classical lamination theory prediction and the experimental data to validate the finite element

model.

57

3.1 Experimental Characterization of the Facesheet Materials

3.1.1 Materials Description and Specimens Manufacturing

Materials Description

The honeycomb sandwich panels facesheets were fabricated from out-of-autoclave prepreg

made with Cycom T650-35 3k carbon fibers and 5320 epoxy resins. Two different woven

fabric architectures were used: plain weave (PW) and eight harness satin (8HS). Figure 3-1

shows the architecture pattern for the 8HS and for the PW woven fabric materials. The

composite material properties given by the manufacturer [59] are listed in Table 3-1.

Figure 3-1 Fiber architecture pattern for a) an 8HS fabric and b) a PW fabric (adapted from[60])

Table 3-1 Materials properties from Cytec [59]

Material Resin content (%) Weight (g/m2) Ply thickness (mm)

5320-PW 36 196 0.19

5320-8HS 36 370 0.38

a) b)

58

Specimens Manufacturing

A total of six plates were manufactured from PW and 8HS prepregs: four 304 x 457 mm2 plates

for tensile tests and two 153 x 203 mm2 plates of for compressive tests. The plates were

composed of 16 prepreg plies stacked as [(+45/-45)/(0/90)/(-45/+45)/(90/0)]2s for the PW

material, while for the 8HS material, eight prepreg plies with a stacking sequence of [(+45/-

45)/(0/90)/(-45/+45)/(90/0)]s was used. The panels were debulked for four hours prior to curing

using a vacuum bag (with 29 in Hg applied vacuum). Then, they were cured in an oven under

vacuum, using the cure cycle shown in Figure 3-2. After cure, specimens were cut from the

plates to desired test dimensions by water jet-milling machine. The quality of the specimens

was assessed using microscopic observation before testing as shown in Figure 3-3. No

microcracks were detected in the composite layers and porosities were quasi absent.

3.1.2 Mechanical Testing of the Laminate Used for the Skins

Tensile Tests

The PW and 8HS quasi-isotropic specimens were tested in tension, at room temperature

conditions, using an electromechanical MTS testing machine with a 100 kN load cell. A

constant crosshead displacement rate of 2 mm/min was used, in accordance with ASTM

standard D3039 [61]. Two series of specimens were prepared to determine the tensile properties

of the composite skins. Namely, five specimens were cut along the longitudinal direction of

the skin (0° direction or x-direction) and five more were cut along the transverse direction (90°

direction or y-direction) for both PW and 8HS laminates. The final specimen dimensions were

250 mm long, 25 mm wide and about 3 mm thick. To prevent failure from occurring in the

59

grips, aluminum tabs were bonded at the specimen ends. To measure the longitudinal and

transverse strains, a video-extensometer system was used. The applied stress was determined

using:

F

A (9)

where F is the recorded force during the test and A is the cross-section area of the specimen.

a. Vacuum bag arrangement for laminate curing

b. Cure cycle applied to the laminate

Figure 3-2 Vacuum bag arrangement and cure cycle used for the quasi-isotropic laminates

60

Figure 3-3 Micrographs of PW and 8HS laminate cross-sections after cure

Combined Loading Compression Tests

Combined loading compression (CLC) tests were performed according to ASTM standard

D6641 [62] at room temperature conditions. The speed of the test was set, as suggested in the

standards, to 0.5 mm/min. Rectangular test specimens were cut from the PW and 8HS laminates

along the 0°-orientation (x-direction) with a water jet-milling machine at a nominal size of 140

mm by 13 mm. The test set-up and the specimen configuration are presented in Figure 3-4. The

longitudinal strain was measured using two strain gages (CEA-06-125UW-350) bonded on

each side of the specimen. Aluminum tabs were bonded to avoid end crushing or bending

during the test. The applied compressive stress was determined using:

x

F

w t

(10)

where F is the applied load, w is the specimen width and t is the specimen thickness.

(a) 16-ply PW laminate: [(+45/-45)/(0/90)/(-45/+45)/(90/0)]2s

(b) 8-ply 8HS laminate: [(+45/-45)/(0/90)/(-45/+45)/(90/0)]s

61

Figure 3-4 CLC set-up and specimen configuration

Test Results and Interpretation

Figure 3-5 and Figure 3-6 show the tensile stress-strain responses in both the x-and y-directions

for the PW and 8HS specimens, respectively. It can be seen from these figures that the tensile

response is linear until an abrupt failure. No significant differences were observed between the

PW and the 8HS stress-strain curves for the different specimens. Moreover, all the observed

failure modes of the tensile specimens were fiber fracture, away from the grip area, as shown

in Figure 3-7.

The compressive stress-strain responses in the x-direction are shown in Figure 3-8 and Figure

3-9 for both the PW and 8HS composite specimens respectively. The compressive response

was slightly nonlinear in comparison with the tensile test results. Figure 3-10 shows the failure

mode of the specimens tested in compression. It should be noted that all the tested specimens

failed in the middle of the gage and limited bending was observed during the test. The bending

rate A (%) calculated following the ASTM standard [62] using

Strain gage 2

Strain gage 1

Tabs

3 mm

Y

X

62

11 22

11 22

A(%) 100

(11)

where ε11 is the deformation measured by strain gage 1 and ε22 is the deformation measured by

strain gage 2 didn’t exceeded 10%.

a. in the x-direction b. in the y-direction

Figure 3-5 Typical stress-strain curve for a [(+45/-45)/(0/90)/(-45/+45)/(90/0)]2s PW

specimen tested in tension

a. in the x-direction b. in the y-direction

Figure 3-6 Typical stress-strain curve for a [(+45/-45)/(0/90)/(-45/+45)/(90/0)]s 8HS

specimen tested in tension

63

Figure 3-7 Typical failure for specimens tested in tension in the x- and y-directions

Figure 3-8 Typical stress-strain curve for a [(+45/-45)/(0/90)/(-45/+45)/(90/0)]2s PW

specimen tested in compression in the x-direction

Figure 3-9 Typical stress-strain curve for a [(+45/-45)/(0/90)/(-45/+45)/(90/0)]s 8HS

specimens tested in compression in the x-direction

64

Figure 3-10 Typical failure mode for specimens tested in compression in the x-direction

The test results for the PW and 8HS specimens are summarized in Table 3-2 and Table 3-3 for

the tensile and compressive tests, respectively. Despite the quasi-isotropic stacking sequence

for both PW and 8HS laminates, slight differences were observed in terms of tensile strength

and elastic modulus for the longitudinal and transverse directions. It can be observed that for

both PW and 8HS, the tensile strength in the y-direction is higher than the strength in the x-

direction. Also, the material properties varied depending on the woven architecture. The PW

laminate has a higher tensile strength in both directions, however in terms of stiffness, the 8HS

laminate was slightly stiffer. The compressive strength of the PW and 8HS specimens were

lower than the tensile strength. Also, the corresponding compressive modulus for both

materials were lower than the tensile elastic modulus.

Table 3-2 Statical analysis - tensile tests

Test

direction Material

Elastic

modulus

(GPa)

S C.V

(%)

Strength

(MPa) S

C.V

(%)

Longitudinal

x-direction

PW 45.78 2.12 4.64 649.35 37.13 5.71

8HS 45.87 1.10 2.39 611.75 27.07 4.43

Transverse

y-direction

PW 43.68 0.40 0.93 652.86 34.60 5.26

8HS 46.03 1.37 2.99 628 51.50 8.41

where: S is the standard deviation and C.V(%) is the coefficient of variation.

65

Table 3-3 Statical analysis - compressive tests

Test

direction Material

Elastic

modulus

(GPa)

S C.V

(%)

Strength

(MPa) S

C.V

(%)

Longitudinal

x-direction

PW 36.65 1.30 3.54 567.88 23.99 4.22

8HS 35.46 0.077 4.26 534.54 12.67 2.37

3.2 Mechanical Characterization of the Honeycomb Nomex Core

The core used in this study to manufacture the sandwich panels is a Nomex honeycomb core

from Euro-composites [63] with a 64 kg/m3 density. The honeycomb core has a rectangular

over-expanded cell ECA-R, as depicted in Figure 3-11. The three principal directions of a

Nomex honeycomb are:

L: the longitudinal direction, also known as the ribbon direction (single wall cell

thickness);

W: the transverse direction, which is perpendicular to the ribbon one, also known as the

double wall cell direction;

T: the through-thickness direction.

An accurate knowledge of the orthotropic honeycomb core material properties is needed when

modelling sandwich structures. The required core material properties are the in-plane Young’s

moduli EL and EW, the out-of-plane Young’s modulus ET, the in-plane shear modulus GLW, the

out-of-plane shear moduli GLT and GWT, and the three Poisson ratios νLT, νWT and νLW.

Table 3-4 summarizes the material mechanical properties given by the manufacturer [63]. The

missing elastic properties will be either determined experimentally (EL, EW and ET) and the

other part of the properties will be taken from the literature (GLW, νLT, νWT and νLW )[64]. So, to

66

determine the elastic in-plane and out-of-plane moduli, tensile and compressive tests were

performed at room temperature conditions.

Table 3-4 Mechanical properties for the ECA-R Nomex core (from [63])

Density

(Kg/m3)

Bare compression Shear

σT (MPa) GTW

(MPa)

τTW

(MPa)

GTL

(MPa) τTL (MPa)

64 4.4 55.50 1.49 21.10 0.96

Figure 3-11 Nomenclature and dimensions of a ECA-R unit cell (4.8 mm)

3.2.1 Out-of-Plane Compressive Tests

The manufactured cell-structured honeycomb was subjected to a through-thickness

compressive load at a quasi-static rate of 0.5 mm/min in accordance to ASTM standard C365

[65]. The mechanical tests were carried out at room temperature conditions using an

electromechanical MTS frame with a 10 kN load cell, as shown in Figure 3-12. A video

extensometer system was used to record the deformation of the specimen and a set of five

50x50 mm2 samples were tested. The linear zone of the compressive stress-strain response is

All dimensions are in mm

67

shown in Figure 3-13. The compressive response was slightly nonlinear, at the beginning of

the test. The calculated out-of-plane elastic compressive modulus is presented in Table 3-5.

Figure 3-12 Compressive test set-up

Table 3-5 Compressive mechanical properties for the over-expanded Nomex core

Mean S Cv (%)

ET(MPa) 185 1.34 0.72

Figure 3-13 Typical compressive stress-strain curve

68

3.2.2 In-Plane Tensile Tests

Honeycomb specimens were respectively tested in the L- and W-directions to determine the

in-plane elastic moduli EL and EW. A fixture system similar to the one recommended by the

ASTM standard C363 [66] was machined to fix the specimens and to introduce the tensile

loading at room temperature conditions. The same electromechanical MTS machine with a 10

kN load cell was used to apply a displacement at a rate of 2.5 mm/min in the W-direction and

a displacement rate of 5 mm/min in the L-direction. A set of five samples were tested in each

case. Both L and W-directions samples were 254 mm long by 128 mm wide by 19 mm thick.

The strains were recorded by using a video-extensometer. For that, targets were bonded at a

distance of 70 mm on the specimen surface. Figure 3-14 shows the specimen configuration and

the experimental set-up.

a. Specimen configuration b. Test set-up

Figure 3-14 Specimen configuration and tensile test set-up

69

Figure 3-15 presents typical tensile stress-strain curves obtained in the ribbon (Figure 3-15.a)

and in the transverse (Figure 3-15.b) directions of the honeycomb core. As the curve is non-

linear at the beginning, the stiffness in both ribbon and transverse directions were taken in the

linear part of the stress-strain curves. The calculated in-plane elastic tensile moduli are

presented in the Table 3-6. The elastic modulus in the ribbon direction is much lower than that

in the transverse one. Therefore, for the over-expanded cell honeycomb structure, the

transverse direction is stiffer than the ribbon direction and when manufacturing sandwich

panels with such a honeycomb, the W-direction should be chosen along the main loading

direction. This difference in the in-plane elastic moduli is related to the particular form of the

honeycomb cell and for a hexagonal cell, the difference between the in-plane elastic moduli is

not significant.

3.2.3 Nomex Tests Recapitulation

From the conducted in-plane and out-of-plane tests, the elastic moduli of the Nomex

honeycomb core were determined. The shear moduli and the Poisson’s ratios were taken from

the manufacturer data and the literature, respectively. Table 3-7 summarizes the mechanical

properties for the Nomex honeycomb core that will be used later in the finite element models

for the repaired sandwich panels.

Table 3-6 Tensile elastic modulus in the L-and W-directions for the over-expanded

Nomex core

EL (ribbon-direction) (MPa) EW (transverse-direction) (MPa)

Mean 0.089 30.30

S 0.0007 4.66

Cv (%) 0.79 15.40

70

Table 3-7 Mechanical properties of the over-expanded Nomex honeycomb core (ECA-R

4.8 64)

EW (MPa)

EL (MPa)

ET (MPa)

30.3a

0.089a

185a

GWL (MPa)

GWT (MPa)

GLT (MPa)

1.9b

55.5c

21.1c

νWL

νWT

νLT

0.26b

0.22b

0.022b

a experimentally measured

b estimated from [64]

c from manufacturer

a. L-direction b. W-direction

Figure 3-15 Typical tensile stress-strain curves in the ribbon (L) and transverse (W)

directions

3.3 Analytical and Finite Element Studies of the Facesheets

Mechanical Behavior

The objective of this section is to validate the predicted elastic behavior of the quasi-isotropic

laminate predicted by finite elements when modeled in the (x, z) plane finite element. The FE

model predictions will be compared with the experimental results of section 3.2 and with

predictions obtained using classical lamination theory (CLT). If the finite element modelling

71

approach is shown to be valid, the repaired sandwich coupons will later be modeled using the

same approach.

3.3.1 Classical Lamination Theory: Analytical Approach

To assess the validation of the finite element approach chosen in this work later, classic

lamination theory (CLT) was used to estimate the stiffness coefficients of the quasi-isotropic

laminate for both the PW and the 8HS materials. The material properties used for the analytical

model are summarized in Table 3-8. The in-plane tensile properties (E1, E2, G12 and ν12) were

taken from tests done by Khechen [67]. The out-of-plane properties were taken from the

literature for a similar material [68].

The relation between stresses (σi, τij) and strains (εi, γij) can be written, in the local coordinate

system (1 2 3) using:

1 11 12 16 1

2 21 22 26 2

12 61 62 66 12

Q Q Q

Q Q Q

Q Q Q

(12)

where [Q] is the stiffness matrix. The relation between the stresses and strains in the global

coordinate system (x, y, z), where x is the axis oriented at an angle θ from the fiber direction,

can then be written as:

Q

(13)

where [Q̅] is the stiffness matrix written in the (x, y, z) global coordinate system by transforming

the local stiffness matrix to the global fixed frame using:

72

1 TQ T Q T

(14)

where [T] is the transformation matrix.

Next, to calculate the equivalent stiffness of the quasi-isotropic laminate, the stiffness matrix

[A] needs to be computed via a through thickness integration that results in:

1

1

(z z )

kN

ij k k

k ij

A Q

(15)

where N is the total number of plies and zk and zk-1 are the z-coordinate of the upper and lower

surfaces of layer k. Therefore, zk-zk-1 is equal to the thickness of a single ply. The equivalent

elastic moduli, which are valid for symmetric and balanced laminates are then calculated using:

2

11 22 12

22

x

A A AE

A t

(16)

2

11 22 12

11

y

A A AE

A t

(17)

where t is the total laminate thickness.

Table 3-8 Composite materials elastic properties

E1

(GPa)

E2

(GPa)

E3

(GPa)

G12

(GPa)

G13

(GPa)

G23

(GPa) ν12 ν13 ν23

PW

material 62.66 66.93 10 4.93 4.93 4.93 0.047 0.3 0.3

8HS

material 66.27 63.34 10 5.21 5.21 5.21 0.047 0.3 0.3

73

Table 3-9 Comparison between analytical and experimental results

Material 𝐄𝐱𝐄𝐱𝐩

(GPa) 𝐄𝐱𝐂𝐋𝐓(GPa) Error (%) 𝐄𝐲

𝐄𝐱𝐩(GPa) 𝐄𝐲

𝐂𝐋𝐓(GPa) Error (%)

PW 45.78 48.49 5.58 43.68 48.49 9.92

8HS 45.87 47.39 3.20 46.03 47.39 2.87

, ,

,

(%) 100

Exp CLT

x y x y

CLT

x y

E Eerror

E

The tensile elastic moduli obtained for both PW and 8HS quasi-isotropic laminates with the

analytical approach are summarized and compared with experimental results in Table 3-9.

Differences between analytical and experimental results can be explained by the experimental

errors and manufacturing imperfections.

3.3.2 Finite element Analyses

Scarf repaired joints (circular and rectangular repair shapes) are modeled in the literature using

2D solid element models (plane strain or generalized plane strain) or full 3D finite element

models [15, 21, 68]. Rectangular repair shape corresponds generally to a 3D problem, which

can be simplified to a 2D plane strain problem for which it is easier to perform a two-

dimensional analysis of the stress distribution in the adhesive and to determine the mechanical

properties of the repaired structure. Three-dimensional (3D) models are however used to obtain

a complete understanding of the behavior of circular repairs. In this section, two main models

were developed: first, a 2D FE model was considered and then a 3D finite element model was

developed. The validity of these models was verified by comparing their predictions with CLT

and experimental results.

74

Linear Elastic Numerical Model

As explained in the preceding section, 3D rectangular repair shape can be simplified to a 2D

plane strain problem. Hence a two-dimensional (2D) linear elastic model is developed here to

predict the tensile behavior of quasi-isotropic laminates. Figure 3-16 shows the 2D plane strain

finite element model as created in the longitudinal x-z plane. As the specimen is modeled along

the longitudinal cross-section, the strain components in the y-direction are negligible:

0y xy yz (18)

i. Materials Behavior and Convention

There are different material options to model a linear elastic material in Abaqus/Standard [56]

: isotropic, orthotropic or fully anisotropic. For the studied composite facesheet, the orthotropic

option was considered. At first time, the lines and columns of the stiffness matrix, for each ply

orientation, was properly swapped to be consistent with the Abaqus convention, and then a

second time, since the thickness was modeled along the y-axis instead of the z-axis (through-

thickness convention), as explained in Figure 3-17.

Figure 3-16 Geometry of studied and simplified specimen (not to scale)

z

z

y

75

ii. Boundary Conditions and Mesh Details

The applied boundary conditions are as follow: the left edge (x=0) is fully constrained and a

displacement of 1 mm is applied at the right edge (x=L), as shown in Figure 3-18. For the finite

element mesh, two types of 2D solid elements from the Abaqus library [58] were used:

- Plane strain element with reduced integration, CPE4R,

- Generalized plane strain with incompatible mode, CPEG4I.

Each single woven ply was discretized through the thickness (z-direction) using one element

and 127 elements along the x-direction.

11 12 13 11 12 13

12 22 23

13 23 33

44

55

66

Stiffness matrix(Voigt notation) Abaqus convention Through thickness convention

0 0 0 0 0

0 0 0

0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

C C C C C C

C C C

C C C

C

C

C

13 12

13 33 23

1

11

12 22 23

13 23 33

5

2 23 22

4466

664

55

4

5

0 0 00

0 0 00 0 0

0 0 00 0 0

0 0 0 0 00 0 0 0 0

0 0 0 0 00 0 0 0 0

0 0 0 0 00 0 0 0 0

C C C

C C CC C C

C C CC C C

CC

CC

CC

Figure 3-17 Changes in Stiffness matrix to respect modelling convention

Figure 3-18 Boundary conditions for the 2D laminate tensile test (not to scale)

76

iii. Results and Discussions

From the imposed displacement and applied force calculated by Abaqus [58], the elastic

modulus of the material can be determined. The applied stress is calculated using:

x

F

A (19)

where F is the summation of the calculated force at nodes located at x=L and A is the cross-

section area of the laminate. The strain is computed using:

0x L xx

u u

L

(20)

where ux is the displacement in the x-direction and L is the length of the laminate in the x-

direction.

The elastic modulus in the x-direction is then calculated using:

x

x

x

E

(21)

The results for the calculated elastic modulus xE using different finite elements are summarized

in Table 3-10. They are compared with the experimental and analytical results. It can be

observed that the finite element model with generalized plane strain element predicts the elastic

modulus very well. Plane strain elements overestimate the modulus by 4.76%. Therefore,

generalized plane strain elements will be used to model the elastic behavior of adherend of the

scarf-step repair in the next chapters. Since generalized plane strain elements are not available

in the ABAQUS/Explicit library [56], plane strain elements with reduced integration (CPE4R)

77

will be used for the failure analysis of scarf-step repaired panels using a 2D model. However,

those elements overestimate the stiffness of the laminate as it has been

Table 3-10 Predicted and measured elastic modulus of the quasi-isotropic laminate

PW material

Plane strain

elements

CPE4R

Generalized

plane strain

elements

CPEG4I

Experiment

CLT

xE (GPa) 50.8 46.9 45.78 48.49

observed. Hence, a correction coefficient is introduced to correlate the calculated stiffness with

the analytical one (calculated from CLT) as:

4

CLT

xcorrection CPE R

x

EC

E (22)

where is CLT

xE the elastic modulus calculated from CLT and4CPE R

xE is the elastic modulus

obtained using CPE4R finite elements.

3D Model with Progressive Damage Analysis

i. Progressive Damage Model

As the 2D finite element model will not be suitable for analyzing the mechanical behavior of

circular scarf repaired sandwich panels later, a 3D finite element model with progressive

damage for woven fabric composites was developed in Abaqus/Explicit [58]. Eight-node

continuum shell elements with reduced integration (SC8R) are used to model the quasi-

isotropic laminate. Each single ply is discretized using one element through the thickness. The

78

model relies on the built-in user’s subroutine ABQ_PLY_FABRIC for modelling the laminated

woven fabric skins (see Johnson [69] for more details on the material model).

The built-in woven fabric model is a two-dimensional mesomechanical model that

accommodate for elastic behavior coupled with damage in the warp and weft directions and

inelastic behavior for the in-plane shear. Progressive damage and failure analysis then relies on

two main failure mechanisms and one inelastic deformation mode [69]: fiber dominated failure

in tension or compression in the warp and weft directions and matrix failure in in-plane shear.

The stress-strain relation can be written in a 2D local coordinate system (1, 2) as follow:

12

1 1 111 11

2122 22

2 2 2

12 12

12 12

10

(1 d )

10

(1 d )

10 0

(1 d )

E E

E E

G

(23)

where E1, E2 are the initial undamaged elastic moduli in the wrap and weft directions, ν12 is the

principal Poisson’s ratio and G12 is the undamaged in-plane shear modulus. Variables d1, d2, d12

are the damage parameter associated with the warp-direction (1-direction), the damage

parameter associated with the weft-direction (2-direction) and the damage parameter related to

in-plane shear failure, respectively.

In order to distinguish between tension and compression behavior at a material point, the elastic

stiffness moduli E1 and E2 take their compressive or tensile values according to the sign of the

volumetric strain tr(ε)=ε11+ε22.

79

To reduce the simulation time, the mass scaling technique was used. To make sure that this

technique does not overly influence the underlying physics, the added kinetic energy for the

whole model had to be adjusted in such a way that it is less than 5% of the internal energy of

the whole system. In such cases, the mass scaling effects on the computed results was

negligible. The mechanical properties of the composite materials used for the built-in user

subroutine are summarized in Table 3-11. In case element deletion options are to be activated,

the built-in material subroutine offers different options to the user:

- The element is deleted when d1=dmax or d2=dmax under compressive or tensile load, or

when the plastic strain due to shear deformation reaches the maximum value,

- The element is deleted when d1=d2=dmax along both fiber directions, or when the plastic

strain due to shear deformation reaches the maximum value,

In this study, the first option to delete elements was used.

ii. Results and Discussions

Figure 3-19 and Figure 3-20 show the comparison between the stress-strain behavior obtained

from experimental measurements and from numerical simulations for the PW quasi-isotropic

laminate under tensile and compressive loadings. These figures indicate that the finite element

model generates results that are in a good agreement with test data in term of material stiffness.

However, one can notice that the finite element predictions underestimate the strength and

allowable maximum strain for both tensile and compressive loadings as summarized in Table

3-12.

80

It should be noted also that the failure modes are in accordance with the experimental results

reported in previous section. The major failure mode is the fiber fracture that first appears in

(0/90) and (90/0) plies and then, failure is propagated to (+45/-45) and (-45/+45) plies.

Table 3-11 Mechanical properties used for the PW composite material

E1t (GPa) E2t (GPa) G12 (GPa) ν12 3)

62.7 66.9 4.87 0.047 1500

E1c (GPa) E2c (GPa) X1t (MPa) X1

c (MPa) X2t (MPa)

49.3 48.7 999.7 772.2 875.6

X2c (MPa) S (MPa) G1t (N.mm-1) G1c (N.mm-1) G2t=G2c (N.mm-1)

789.7 38 22.5a 22.5a 22.5a

a taken from [70]

Table 3-12 Comparison between the experimental data and the finite element prediction

Tensile tests Compressive tests

Experimental FE Error (%) Experimental FE Error (%)

𝝈𝒙𝒇 (MPa) 649.35 627 3.44 567.88 530 6.67

S (MPa) 37.13 - - 23.99 - -

�̅�𝒙 (GPa) 45.78 47.24 36.65 35.74

S (GPa) 2.12 - - 1.30 - -

(%) 100FE Exp

x x

Exp

x

Error

81

Figure 3-19 Comparison of stress-strain curves between the experiment and the finite

element model for a [(+45/-45)/(0/90)/(-45/+45)/(90/0)]2s PW tested in tension in the x-

direction

Figure 3-20 Comparison of stress-strain curves between the experiment and the finite

element model for a [(+45/-45)/(0/90)/(-45/+45)/(90/0)]2s PW tested in compression in the x-

direction

82

3.4 Conclusion

In this chapter, results from in-plane tensile and compressive tests performed at room

temperature conditions for quasi-isotropic laminates for both PW and 8HS materials were

presented. For both materials, a slight variation was observed for the laminate tensile elastic

modulus in x- and y-directions. Moreover, the quasi-isotropic laminates exhibited a stiffer

modulus in tension than in compression. The elastic behavior of quasi-isotropic laminates was

also studied using the finite element analysis software Abaqus/Standard [58]. Here, different

elements were used to model the elastic behavior of the laminate. Results obtained with

different approaches were compared with the experimental values to validate the 2D developed

models. It was observed that the tensile modulus in the x-direction obtained with generalized

plane strain elements was closer to the experimental and CLT results. However, plane strain

elements over-estimated the modulus. Therefore, the generalized plane strain elements were

retained and will be used to predict the elastic behavior of scarf-step repaired sandwich

honeycomb panels in the next chapter. To model the failure behavior of repaired panels,

Abaqus/Explicit solver [58] will be used. Since generalized plane strain are not available in its

library, plane strain elements with reduced integration will be used along with a correction

coefficient to correlate the calculated stiffness with the experimental values. The progressive

damage model predicts well the behavior of the composite material until failure and the failure

modes agreed with the experimental test results.

83

Chapter 4.

Mechanical Characterization and Finite Element

Study of Monolithic Facesheets and Honeycomb

CoreArticle 1: Mechanical Performance of

Repaired Sandwich Panels: Experimental

Characterization and Finite Element Modelling

Emna Ghazali, Marie-Laure Dano, Augustin Gakwaya and Charles-Olivier Amyot

Résumé

Cet article présente les performances mécaniques des réparations par patch interne sur des

panneaux sandwich fabriqués avec des peaux en carbone-époxyde et une âme en nid d’abeille

Nomex. Tout d'abord, le comportement mécanique des panneaux intacts et réparés sous

chargement de tension est étudié. Les différents essais ont été effectués à température ambiante.

Ensuite, des analyses par éléments finis ont été effectuées pour prédire le comportement des

panneaux réparés. Deux modèles de matériau ont été développés pour le film adhésif: l'un est

élastique linéaire et le second est élastoplastique avec un critère de rupture en cisaillement.

Pour les peaux en composites tissés, un modèle élastique linéaire orthotropique a été utilisé.

Les prédictions du modèle numérique sont en accord avec les résultats expérimentaux. La

84

restitution de la contrainte à la rupture de la structure réparée augmente avec la diminution de

l'angle de biseau.

Abstract

This paper describes the static performance of adhesively bonded repairs on sandwich panels

made with carbon-epoxy composite skins and a Nomex core. First, the mechanical behavior of

pristine and repaired panels under tensile loading was studied. All tests were conducted under

room temperature conditions. Then finite element analyses were performed to predict the

repaired panel’s behavior. Two material models were developed for the adhesive film: one is

linear elastic and the second is elastic-plastic with a shear failure criterion. For the composite

skins, an orthotropic linear elastic model was used. Numerical model predictions are in good

agreement with the experimental results. It was found also that the strength recovery of the

repaired structure increases with the decrease of the scarf angle.

Keywords: Sandwich structures, bonded repair, finite element analysis, failure criteria.

4.1 Introduction

Since fiber-reinforced composite structures offer superior strength, higher stiffness, lighter

weight and greater durability [43], they are increasingly being used for primary aircraft

components traditionally made of metallic materials. However, despite their good properties,

composite airframe structures are more sensitive to impact damage, which can cause

disbonding, delamination and internal crushing. Considering their extended service life and

85

operating conditions, the extent of damage determines whether the composite components need

to be repaired or replaced. Hence, to take full advantage of their many benefits, the

improvement of their performances requires one to ensure first that these structures are durable,

repairable, and maintainable. Since fiber-reinforced composite sandwich structures are

increasingly being used in aircraft components, it has become necessary to develop effective

repair methods that will restore the component’s original design strength without

compromising its structural integrity.

Many studies have been conducted on bonded scarf and step joint repairs of monolithic

laminates. Campilho et al. [17, 19-20, 34, 71-72] have conducted a lot of work to study the

effects of different repair parameters (scarf angle, lay-up, adherend thickness) on the

performance of repaired laminated structures. They used a three-dimensional (3D) finite

element models with cohesive damage to assess the strength of external adhesive repaired patch

of Carbon Fiber Reinforced Plastic (CFRP) under tensile and compressive loads

[17, 34, 71-72].The effect of the shape geometry (single or double strap repair) on the strength

of the structure and the stress distribution have been particularly studied. They also developed

a two-dimensional (2D) finite element model for bonded repair joints [19, 20]. The main

conclusion was that the repair strength increases exponentially with the decrease of scarf angle.

Gunnion and Herszberg [21] developed 2D and 3D linear elastic parametric finite element

models to analyze stress distributions in the middle of the adhesive joint of CFRP scarf repaired

joints under tensile loading. This model allowed obtaining both shear and peel stress

distributions along the adhesive bondline. A parametric study was performed. The parameters

investigated included the adhesive and adherend thickness, the scarf angle and the stacking

86

sequence. The main conclusions are the low sensitivity of the adhesive stresses on mismatched

adherends lay-ups and the major reduction in peak stresses using an over-laminate ply covering

the full length of the specimen. Harman and Wang [14] developed an analytical technique to

optimize the shape of scarf joint between dissimilar adherends. Their technique uses a linear

variation of the scarf angle that generates a characteristic scarf profile for a given adherends

modulus ratio. Both analytical and the 2D and 3D elastic finite element modelling results

showed a dependence on the local ply orientation for peel and shear stress distributions in the

adhesive, for different ratios of adherends modulus. Charalambides et al. [16] tested

experimentally repaired CFRP joints using a 2°-scarf configuration. Distinct failure modes

were observed, as function of the environmental conditions (temperature and moisture) and the

type of load. They also performed a two-dimensional numerical analysis [15] in order to

simulate three different failure modes in scarf repairs: failure in the adhesive layer, failure

induced from delamination initiating at the corner of the overlap ply and tensile failure of the

composite adherends. Failure loads were compared with previously published experimental

work and the results were found to be in good agreement.

Several experimental studies and finite element analyses were also carried out to study the

behavior of repaired sandwich panels under different static loads. The compressive behavior

of repaired sandwich panels was investigated by Liu et al. [49]. Both experiments and finite

element analyses were conducted to study the influence of repair variables on the quality of the

repair. A progressive damage model was developed and good correlations between

experimental and numerical results were obtained. Ramantani et al. [52] developed a 2D

cohesive damage model to study the performance of repaired sandwich panels under four-point

87

bending loading. For overlap joints, they concluded that the repair strength increases as a

function of the overlap length and that the strength increases with lower scarf angles in the case

of scarf joints. Mahdi et al. [47, 48, 54] used 2D and quasi-3D finite element models to predict

the performance of both pristine and scarf repaired sandwich panels subjected to static and

fatigue four-point bend loading. Numerical analyses results showed a good correlation in terms

of stiffness prediction of both undamaged and repaired coupons. However, the ultimate load

prediction was problematic and did not show a good correlation with experiments. A series of

experimental tests were also conducted by Tomblin et al. [2, 51] to study the effects of different

process parameters on the repair quality of sandwich panels. A damage tolerance analysis on

sandwich structures was included as well. As a conclusion of their work, a methodology for

the repair process along with design tools for damage tolerance on sandwich structures were

developed. A recent study from Zhang et al. [50] was conducted to investigate the mechanical

performance of open-hole damage and circular scarf repairs in honeycomb sandwich panels

under compressive loads. A 3D finite- element model was also developed. A failure criterion

based on Hashin’s criterion with a progressive damage evolution was included for the

unidirectional composite skins. The adhesive layer was modeled using cohesive elements. The

honeycomb core was considered as an elastic-plastic material. A good agreement was found in

terms of ultimate failure load and damage shape between the experimental and numerical

results. Another finding of this work is that the structure strength increases with the decrease

of scarf angle and that the optimum number of overplies is one to reach the highest strength. In

the above-mentioned research works, focus was on scarf-scarf repair modelling using cohesive

zone elements for the adhesive bondline. However, this modelling technique is not suitable to

88

model a scarf-stepped repair configuration which is widely used in practice. Simplifying a

scarf-stepped configuration by a scarf-scarf configuration may lead to predict an inaccurate

stress distribution. Also, most of mentioned research works conduct parametric studies using

finite element analyses without correlating numerical predictions with experimental results.

Thus, the main objectives of this study is to (i) accurately model the scarf-stepped repair

configuration and to study its effects on the adhesive peel and shear stresses distribution and to

(ii) assess the numerical predictions with experimental data.

The paper presents a study conducted to investigate the behavior of co-cured bonded scarf

repair for primary structure sandwich panels under uniaxial static tensile load. Both finite

element analyses and experimental tests were performed. First, the repair procedure and the

experimental set-up are detailed. Force versus strain curves are presented and a series of

fractography images are shown to determine the failure mode and pattern in the sandwich

panels. Then, the finite element models developed using the commercial software ABAQUS

[56] are presented. Both elastic and elastic-plastic approaches were carried out to predict the

stress distribution along the adhesive bondline as the repaired sandwich panel was subjected to

tensile loading. Finally, the numerical predictions were compared with experimental results in

order to validate the finite element model.

4.2 Experimental Work

4.2.1 Repaired Sandwich Specimen Preparation

This section describes the repair procedure that was performed on the sandwich panel. The

sandwich panels used in this work are composed of an over-expanded Nomex honeycomb core

89

with a 19 mm thickness on which two four-ply carbon-epoxy skins were bonded. The skins are

made with an out-of-autoclave plain weave prepreg (CYCOM 5320 T650 PW from Cytec

Engineering Materials). The ply stacking sequence of the sandwich panels is [(+45/-

45)/(0/90)/(-45/+45)/(90/0)/core/(90/0)/(-45/+45)/(0/90)/(+45/-45)] where the 0o-direction is

the fabric warp direction and the 90o is the weft direction. The designations (+45/-45) and

(0/90) representing a single layer of woven fabric with the warp and weft fibres oriented at the

specified angles.

Therefore, the sandwich structure is symmetric. The mechanical performance of the

honeycomb sandwich panels repaired using a scarf/step adhesively bonded joint configuration

was studied. The panels were initially 711.2 mm-long and 406.4 mm-wide. The repair was

carried out on the tool facesheet. To simulate the material removal in the parent facesheet, each

prepreg ply had rectangular cut-out as shown in Figure 4-1.

The cut-outs were 712 mm-long and had a specific width such that, when stacked together, the

plies formed a drop-off. An adhesive film (Cytec FM 300-2M) was used to bond the two

facesheets to the core. Next, both skins and core were bonded and co-cured under vacuum bag

in an oven. The repair patch was manufactured as follows.

90

Figure 4-1 Parent panel dimension (not to scale).

After cure, the step shaped parent area was sanded with a 120-abrasive paper to reach the

desired scarf angle. This was followed by a surface cleaning with acetone and immediate

drying. The repair patch was prepared using the same parent prepreg material and the original

stacking sequence. The plies were cut to a specific width and stacked together to form an

overlap as shown in Figure 4-2. The overlap length Loverlap was determined from the scarf angle

α and the ply thickness tp using:

p

overlap

tL

tan (24)

Next, the adhesive film and prepreg plies were applied directly over the prepared cut-out

surface. The whole assembly was then cured under a vacuum bag in an oven according to the

manufacturer recommendations. Since the patch is across the whole panel length, the repair is

considered as 1D-scarf/step repair. In the context of the present study, only the inner facesheet

was repaired and the core was not replaced. A parametric study was conducted for the scarf

angle. Three different scarf angles were chosen (3°, 5° and 7°) to study the effect of this repair

91

variable on the repair strength. Rectangular test specimens were cut with a water jet-milling

machine at a nominal size of 335 mm by 102 mm. To prevent inadmissible ends failure and

premature failure, the specimen ends were reinforced with aluminum inserts and aluminum

tabs.

Figure 4-2 1D scarf/step repair configuration (not to scale).

4.2.2 Tensile tests procedure

As a next step, the repaired panels were tested in uniaxial tension using an electromechanical

‘MTS’ testing machine at a constant crosshead rate of 1 mm/min. A homemade tensile test

fixture, inspired from the one used by Tomblin et al. [2], as shown in Figure 4-3, was used for

these tests. The top and bottom grips were connected to the load cell via a universal joint. These

tests were performed in order to compare the mechanical performance of repaired panels with

pristine panels. Table 4-1 summarizes the test matrix followed for each configuration.

Core

Bag face

Parent

Adhesive

Loverlap

Tool face

tp

α (°)

Z

X

Parent Patch

92

The surface of the tool facesheet was prepared for measurement with a 3D digital image

correlation (DIC) system (Aramis by Gom [73]). The DIC software allows determining the full

in-plane and out-of-plane displacements and the strain field on the specimen surface during

testing. A video extensometer was used in order to measure the strain on the bag facesheet. The

strain measured by the DIC system was averaged on an area taken in the middle of the specimen

to obtain a single value that can be compared to the strain measured by the video extensometer.

For the repaired specimens, the strain was averaged in the middle of the patch.

4.2.3 Experimental Results

The results of the static tensile tests performed at ambient temperature on the pristine and

repaired sandwich specimens are presented in Figure 4-4 and Figure 4-5. Figure 4-4 (a) and

Figure 4-4 (b) present the load versus strain measured on the tool facesheet with the DIC system

for the pristine and the 3o-repaired specimens, respectively. As can be observed, the load-strain

behavior is mostly linear until failure for both the pristine and the 3°-repaired specimens. For

the 5°- and 7°-repaired specimens, a similar trend for the load-strain curves was also observed.

Figure 4-5 (a) and Figure 4-5 (b) present the load versus strains measured on both tool and bag

facesheets for one pristine and one 3o-repaired specimen, respectively. The uniform load

distribution in both facesheets can be assessed by the similarity in strains measured by the DIC

system and the video extensometer. For the 5°- and 7°-repaired panels, a similar behavior was

observed. Figure 4-6 compares the experimental failure load for the three investigated scarf

angles. As can be observed, the variation of scarf angle has no major effect on the ultimate

load. When the angle is equal to 3°, the ultimate failure load is about 55% of the pristine value.

93

The strength recovery for this sandwich repair configuration is quite low. Using an overply

could be beneficial to improve the strength of the repaired sandwich panel.

Table 4-1 Test matrix.

Skin material Pristine Specimens Repaired Specimens

3° 5° 7°

Plain weave 3 3 3 3

Figure 4-3 Tensile test set-up.

a. Pristine panels b. 3°-repaired panels

94

Figure 4-4 Axial load-strain curves obtained for the pristine and 3-repaired sandwich

specimens (strains measured by DIC on the tool facesheet).

a. Pristine panel b. 3°-repaired panel

Figure 4-5 Comparison of the axial load-strain curves obtained on both facesheets of the

sandwich specimens.

Figure 4-6 Tensile failure load of the pristine and repaired sandwich specimens.

Strain measurement comparison

42.50 kN 42.09 kN 41.85 kN

82.86 kN

95

4.2.4 Damage Mode and Fractography Studies

The fractured surfaces of pristine and repaired panels are shown in Figure 4-7 and Figure 4-8.

Figure 4-7 shows the ruptured facesheets of a pristine specimen. Damage occurred in both

facesheets far from the loaded ends. The failure mechanism was similar for all pristine panels.

Failure seems to be due to rupture of the skin in tension. To confirm this hypothesis, the

ultimate stress in the skin was evaluated using:

2

ultult tensiletensile

f

P

t b (25)

where tf is the facesheet thickness, b is the specimen width and ult

tensileP is the ultimate tensile

load and compared with the strength of a quasi-isotropic [(+45/-45)/ (0/90)/ (-45/+45)/ (90/0)]2s

laminate made with the same prepreg (Table 4-2). The ultimate stress in the sandwich skin is

about 87% of the quasi-isotropic laminate strength, which corroborates that the sandwich

failure mode is dominated by skin failure.

Figure 4-8shows the ruptured facesheet for the 3°-repaired panels for which failure occurred

mainly in one of the two scarf zones.

Table 4-2 Comparison of the ultimate stress between the sandwich skin and a [(+45/-45)/

(0/90)/ (-45/+45)/ (90/0)]2s quasi-isotropic laminate made from the same PW prepreg [74]

Pristine

sandwich

Quasi-isotropic

laminate

σult [MPa] Mean 536 618

S 27 19

96

Figure 4-7 Failure mode of pristine panels.

Figure 4-8 Failure mode for the 3°-repaired sandwich panels.

The quality of the pristine and of the repaired sandwich specimens was assessed using

microscopic observation before testing. As shown in Figure 4-9 (a), the pristine specimen

contains a few macro pores in the composite layers. The repaired sandwich specimen (Figure

4-9 (b)) has also some macro porosities in the composite layers. However, the repair bondline

has a very low porosity level. Cross-sections of tested repaired specimens were also examined

using optical microscopy to determine the failure modes and patterns. Figure 4-10 shows the

Failure

zone Tool faceshee

t

Bag

facesheet

Parent

Patch

Failure zone/ scarf zone

102 mm

102 mm

97

fractography images for a 3°-repaired sandwich specimen. Failure seems to be due to adhesive

and cohesive failure of the adhesive film. The adhesive is fractured along the patch side, near

the stepped plies and not on the parent side. This can be explained by the high stress

concentration in this zone. Also, macrocracks were observed in the composite plies along the

patch side.

Figure 4-9 Micrograph of the cross-section of the (a) pristine specimen, (b) repaired

sandwich specimen before testing.

Figure 4-10 Micrograph of the 3°-repaired sandwich specimen cross-section after failure.

(b)

5000 μm

Patch Parent

Adhesive bondline Macro porosity

(a)

Cohesive failure

Crack/porosity Patch laminate

6000μm

800μm

Adhesive failure

3000 μm

98

4.3 Numerical Simulation

4.3.1 Model Description

The finite element software packages ABAQUS/Standard and ABAQUS/Explicit were used to

study the response of the sandwich panels under tensile loading. Two different configurations

were studied: one corresponds to the pristine specimen and the other to the repaired specimen.

The repair joint was considered as a symmetric and plane strain problem. As such, only half

the longitudinal cross-section was modeled. The panel were 165 mm-long, 102 mm-wide and

20.5 mm-thick. The boundary conditions are defined as follow. On the left edge, the total

displacement, as measured from the experiment, was applied and, on the right edge, symmetric

boundary conditions were imposed as depicted in Figure 4-11.

Each woven ply and the adhesive film were discretized through the thickness using one and

four elements, respectively. The adhesive film along the joint as well as between the two skins

and the core was modelled. The Nomex honeycomb core was also discretized through the

thickness using 20 elements.

Two types of analyses were conducted. First, an elastic analysis with an isotropic elastic

behavior of the adhesive was performed in order to determine the stress distribution along the

bondline. ABAQUS/Standard was used to conduct this analysis. The objective of the second

analysis was to predict the mechanical behavior until failure of the repaired specimens. This

analysis took into account plastic deformation and shear failure for the adhesive and was

conducted using ABAQUS/Explicit. Two types of continuum elements were used for the

elastic finite element analysis: generalized plane strain element with incompatible modes

99

(CPEG4I) and plane strain element with reduced integration (CPE4R), both from the

ABAQUS/Standard Library. The mechanical properties of the composite materials used for the

sandwich panels are summarized in Table 4-3. The mechanical properties of the adhesive film

are indicated in Table 4-4 and the elastic properties of the Nomex honeycomb core are listed

in Table 4-5. A shear failure criterion was used to predict the failure in the adhesive film.

Figure 4-11 Description of the boundary conditions.

Table 4-3 Mechanical properties of the plain weave material.

E1 [GPa] E2 [GPa] E3 [GPa] G12[GPa] ν12 tp [mm]

64.6a 64.6a 10b 4.9a 0.047a 0.19 a experimentally measured

bassumed

Table 4-4 Mechanical properties of the FM300-2M adhesivea.

E[GPa] G [GPa] ν τy [MPa]

2.024 0.770 0.3 30

a determined from experimental data [75]

ux= 1mm u

x= 0

uRy

=uRz

=0

z x

100

Table 4-5 Mechanical properties of the Nomex honeycomb core

EW (MPa)

EL (MPa)

ET (MPa)

30.3a

0.089a

185a

GWL (MPa)

GWT (MPa)

GLT (MPa)

1.9b

55.5c

21.1c

νWL

νWT

νLT

0.26b

0.22b

0.022b

a experimentally measured

b taken from published literature [64]

c provided in material sheets

4.3.2 Linear Elastic Numerical Model

First, the effect of the element choice (CPEG4I versus CPE4R) on the stiffness prediction will

be investigated. Next, the influence of various scarf angles, namely 3°, 5° and 7°, for a scarf-

step bonded repair will be studied. The results of a 2D linear elastic, ply-by-ply and through-

the-thickness model will be presented for these three different geometric angle configurations.

The effect of this parameter on the shear and peel stress distributions along the bondline in the

middle of the adhesive will also be investigated.

Table 4-6 presents the stiffness of the pristine panels predicted using generalized plane strain

elements (CPEG4I) and plane strain elements (CPE4R). For comparison purposes, the stiffness

predicted using classical lamination theory (CLT) and the stiffness measured experimentally

are also indicated. As shown in Table 4-6, the stiffness of pristine panels predicted using plane

strain elements are overestimated by 10 % whereas the stiffness predicted using generalized

plane strain elements is very close to the experimental and CLT results. Therefore, generalized

plane strain elements will be used to model the adherends of the scarf-step repair.

In order to better understand the behavior of the repair joints, it is crucial to investigate the

stresses distribution in the weak point of the joint, which is the adhesive. Stresses in the

adhesive were extracted at nodes along a line taken in the middle of the adhesive layer as shown

101

in Figure 4-12. Figure 4-13 and Figure 4-14 compare the shear and peel stresses distributions

along the normalized bondline for the three scarf angles. As expected, stress peaks are

observed. Unlike homogeneous adherends, the stress distribution in laminated joints varies

from one ply to another and peaks occur in the vicinity of the (0/90) and (90/0) plies. Shear

stresses are much higher in magnitude than peel stresses except at the first (0/90) ply. The

maximum shear stress even exceeds the adhesive shear yield stress (given in Table 4-4).

Therefore, the adhesive begins to plastically deform. The repair joint with a 3°-scarf angle

shows the lowest shear stress values compared to 5°- and 7°-scarf repairs. The highest stress

peaks are observed for the 7°-scarf repair. Therefore, failure would be more likely to occur at

a lower load for a 5°- or 7°-scarf joint than for a 3°-scarf repair.

Table 4-6 Stiffness prediction of pristine panels.

Plane stain element

(CPE4R)

Generalized plane strain

element (CPEG4I) Experiment

CLT

𝐸𝑥̅̅ ̅ [GPa] 52.64 47.37 47.87 47.19

Figure 4-12 Line and local coordinate system used to extract peel and shear stresses

Middle of the

bondline 2

1

102

Figure 4-13 Shear stress distribution along the bondline.

Figure 4-14 Peel stress distribution along the bondline.

4.3.3 Non-linear Elastic Plastic Model

As the adhesive begins to plastically deform, it is important to implement the elastic-plastic

behavior of the adhesive film and a shear failure criterion. In the literature, different plasticity

models have been used [35–37]. The Drucker-Prager plasticity model [35, 37] is well suited

for describing pressure dependent plasticity materials such as epoxy adhesives and gives results

103

that reproduce accurately experimental strain hardening data [35]. However, this model

requires much more material parameters for plasticity than a classical metal plasticity model

based on von Mises criterion. Moreover, as observed by Shih-Pin [37], Abaqus computation

based on Drucker-Prager plasticity model presents convergence difficulty, requires a finer

mesh and therefore longer computation time than for a von Mises plasticity model. Shih-Pin

[37] observed also that as far as ultimate shear failure is concerned, classical metal plasticity

model leads to almost the same results with less numerical issue as a Drucker-Prager plasticity

model. For these reasons, it was decided in this study to use a von Mises plasticity model

combined with a shear failure criterion to assess the strength of the adhesive joint in the scarf-

stepped repair.

The plasticity model uses the von Mises yield surface with an associated plastic flow. The von

Mises criterion interprets yielding as a purely shear deformation process which occurs when

the effective shear stress e reaches a critical value o [38]. This effective stress is defined in

terms of stresses by:

2 2 2

1/22 2 21

62

xy yze x y zy z xz x

(26)

Similarly, the effective plastic strain is defined in terms of plastic strains by:

 2 2 2 2 2

1/

2

22

23

x y y z z x xy yz xz

p

e

(27)

104

The plastic properties of the adhesive were determined from a ASTM D5656 Thick Adherend

Shear Test (TAST) [75]. During the test, the adhesive is supposed to be subjected to pure shear

stress. Therefore, the effective stress e is related to the shear stress by

eσ = 3 xy (28)

In case of a 2D plane strain analysis, the effective plastic strain equation under pure shear

becomes:

3

p

xyp

e

(29)

Once the initial yield shear stress (y) is reached, the equivalent plastic strain and effective

stress were calculated from the test data using eqs. (28) and (29). The hardening input data

required to model the plasticity of the adhesive film in ABAQUS are given in Table 4-7. The

data are based on experimental results from a ASTM D5656 Thick Adherend Shear Test

(TAST) [75]. From the ASTM D5656 test results, the shear yield stress and the elastic shear

modulus were determined. A shear failure criterion was also associated with the von Mises

yield criterion to predict the failure of the adhesive. This criterion is based on the value of the

equivalent plastic strain at element integration points. Failure is assumed to occur when the

damage parameter w exceeds one [36] . This damage parameter is defined as follows:

pl

pl

f

w

(30)

105

where 𝜀̅𝑝𝑙 is the equivalent plastic strain and designated as PEEQ in ABAQUS/Explicit, ∆𝜀̅𝑝𝑙 is

the increment of PEEQ and 𝜀�̅�𝑝𝑙

is the plastic strain at failure. When the shear failure criterion

is reached at an element integration point, the material is assumed to fail at this point and the

stress components are set to zero. The element is deleted from the mesh when the material

failure is detected at all integration points.

Since the generalized plane strain elements are not available in the ABAQUS/Explicit library,

plane strain elements with reduced integration (CPE4R) were used for the analysis. However,

those elements overestimate the stiffness of the sandwich panel as it has been demonstrated in

the previous section. Hence, a correction coefficient was used to adjust the calculated stiffness.

This correlation coefficient is defined as:

4

CLTcorrection

CPE R

EC

E (31)

where ECPEG4I is the elastic modulus predicted using CPEG4I elements and ECPE4R is the elastic

modulus numerically obtained using CPE4R elements.

The shear strain, 𝛾, was converted into the plastic shear strain, 𝛾𝑝, using:

p

G

(32)

where G is the shear modulus of the adhesive.

106

4.3.4 Numerical Results and Discussion

Numerical simulations have been performed to predict the mechanical behavior of the repaired

sandwich panels and compared to experimental results. Figure 4-15 shows a comparison

between the experimental results and the numerical results obtained with Abaqus/Explicit for

the 3°-repaired configuration. As can be seen from the curves, experimental and numerical

results are fairly similar. This indicates that the finite element model can simulate the behavior

of the repaired sandwich panels accurately. To further study the influence of repair parameters

(i.e. overlap length on tensile strength), finite element analyses were conducted using models

with different scarf angles. Figure 4-16 shows the evolution of the failure load (Pf) and

efficiency (η) with the increase of the scarf angle. Experimental results presented in Figure 4-6

are also added for comparison. For scarf angles between 3° and 7°, Pf and η decrease only very

slightly. These predictions corroborate very well the failure loads obtained experimentally. For

scarf angles below 3°, these two parameters increase exponentially with angle reduction. For a

1.5°-scarf angle, the efficiency reaches 64 %. However, for scarf angles over 7°, these

parameters decrease drastically. This phenomenon is related to the decrease of the overlap

length with the increase of angle, which induces the peel and shear stresses peaks to increase

at the bondline ends and at the neighborhood of the stepped plies.

Table 4-7 Hardening data input.

Yield stress, σe [MPa] Plastic strain, εpe [-]

55 0

60 0.0017

70 0.0084

75 0.015

80 0.032

107

82 0.057

84 0.12

Figure 4-15 Finite element prediction versus experiment results for the 3°-repaired

sandwich panels.

Figure 4-16 Failure load and efficiency (η=𝑃𝑟𝑒𝑝𝑎𝑖𝑟

𝑓

𝑃𝑢𝑛𝑑𝑎𝑚𝑎𝑔𝑒𝑑𝑓 𝑥100) for different scarf-step

angles.

η (%

)

108

4.4 Conclusions

This study investigated bonded repairs in sandwich panels made with honeycomb core and out-

of-autoclave prepreg carbon-epoxy skins. Experimental tests were carried out to investigate the

tensile behavior of both pristine and repaired panels. Experimental results indicate that the

repair configuration studied in the paper recovers only 55% of the static mechanical strength

of the pristine panels for a 3°-scarf-step repair at room temperature conditions. The common

failure mode for all tested repaired specimens was the failure of the adhesive joint. Both

adhesive and cohesive failure were observed experimentally.

A 2D finite element model for the sandwich panel is proposed in the paper. Good agreement

between stiffness and strength predictions and experimental results confirmed that the

numerical model provides an effective analysis tool for the mechanical behavior prediction of

repaired sandwich panels. Also, the finite element models show that the tensile strength

increases as the scarf angle decreases due to the decrease of both peel and shear stresses peaks

in the adhesive bondline.

ACKNOWLEDGEMENTS

The author would like to thank the Natural Sciences and Engineering Research Council of

Canada (NSERC), the Consortium for Research and Innovation in Aerospace in Quebec

(CRIAQ), the National Research Council Canada (NRC), Bombardier Aerospace and L3-MAS

for funding, technical support and materials.

109

Chapter 5.

Article 2: Parametric Study of Stepped-Scarf

Bonded Joints in Repaired Honeycomb Sandwich

Composite Panels

Emna Ghazali, Marie-Laure Dano and Augustin Gakwaya

Résumé

Les réparations avec patch interne de type escalier-biseau de structures sandwich peuvent offrir

une bonne alternative plus facile à réaliser que les réparations avec patch interne de type biseau.

Cet article étudie l'effet de différents paramètres géométriques sur la distribution des

contraintes dans le joint de colle ainsi que la contrainte à la rupture de la structure réparée. Des

modèles par éléments finis élastiques linéaires et élastoplastiques non linéaires ont été

développés pour mener une étude paramétrique pourtant sur l'angle du biseau, le nombre de

plis et l'addition d'un extra-pli. Les résultats montrent que les réparations de type escalier-

biseau ont une sensibilité importante à l'épaisseur des peaux. L'utilisation d'un extra-pli fournit

une protection aux extrémités libres de l'adhésif et augmente la résistance de la structure

sandwiche réparée.

110

Abstract

Stepped-scarf patch repairs of honeycomb sandwich structures can offer a good alternative easier

to perform than tapered scarf repairs. This study investigates the effect of different stepped-scarf

joint geometrical parameters on stress distribution in the adhesive bondline and on the failure load

of repaired composite sandwich panels. Both linear elastic and non-linear elastoplastic with failure

criterion analyses were conducted to perform a parametric study focusing on scarf angle, number

of plies and the addition of an overply. Results show that stepped-scarf joints exhibit an important

sensitivity to the thickness of repaired skins. The use of an overply provides protection to the free

ends of the adhesive joint and increases the strength recovery of the repaired sandwich structure.

Keywords: Sandwich structures, bonded repair, finite element analysis, parametric study.

5.1 Introduction

Adhesively bonded joints are increasingly being used nowadays in different industry fields and

especially in the aerospace industry for its advantages in maintaining aerodynamic performance

and in ensuring uniform stress distribution. However, to insure the highest strength recovery of

the structure, different parameters such as the scarf angle, the lay-up or the adherend thickness

should be taken into account in order to design an optimal repair.

Many studies have been conducted on bonded scarf and stepped joint repairs of monolithic

laminates. Campilho et al. [17, 20, 34, 71-72] have conducted a lot of work to study the effects of

different repair parameters (scarf angle, lay-up, adherend thickness) on the performance of tapered

scarf repaired laminated structures. They used a three-dimensional (3D) finite element models

with cohesive damage to assess the strength of external adhesive repaired patch of Carbon Fiber

111

Reinforced Plastic (CFRP) under tensile and compressive loads [17, 20, 34]. The effect of the

shape geometry (single or double strap repair) on the strength of the structure and the stress

distribution have been particularly studied. They also developed a two-dimensional (2D) finite-

element model for bonded scarf repair joints[19-20]. The main conclusion was that the repair

strength increases exponentially with the decrease of scarf angle. Gunnion and Herszberg [21]

developed2D and 3D linear elastic parametric finite element models to analyse stress distributions

in the middle of the adhesive joint of CFRP scarf repaired joints under tensile loading. Their model

allowed obtaining both shear and peel stress distributions along the adhesive bondline. A

parametric study was performed. The parameters investigated included the adhesive and

adherends thickness, the scarf angle and the stacking sequence. Their main conclusions are the

low sensitivity of the adhesive stresses to mismatched adherends lay-ups and the major decrease

in peak stresses using an over-laminate ply covering the full length of the specimen.

Whereas bonded repairs of solid composite laminates have been extensively studied through

analytical, numerical or experimental works, investigations on bonded repairs of composite

sandwich structures are very limited in the literature. However, conclusions drawn for solid

composite laminates repairs are not necessarily applicable to composite sandwich repairs and it is

therefore important to pursue research efforts in this area. So far, a few experimental studies and

finite-element analyses were carried out to study the behaviour of repaired sandwich panels under

different static loads.

Mahdi et al. [47, 54] used 2D and quasi-3D finite-element models to predict the performance of

both pristine and tapered scarf repaired sandwich beams subjected to static four-point bending

loading. Numerical analyses results showed a good correlation in terms of stiffness prediction of

112

both undamaged and repaired specimens. However, the failure load prediction was problematic

and did not show a good correlation with experiments. The failure load of the beam was predicted

using Tsai-Hill failure criterion and was based on the composite first ply failure. The model was

not able to capture the complex failure modes of the repaired beams. In particular, adhesive failure

was not taken into account.

Ramantani et al. [52] developed a 2D cohesive damage model to study the performance of overlap

and tapered scarf repaired sandwich beams under four-point bending loading. The sandwich skins

and patches were constituted of 0o unidirectional laminates. The effects of different parameters

(overlap length and patch thickness for the overlap repair and scarf angle for the tapered scarf

repair) were discussed. For overlap repairs, they concluded that the repair strength increases as a

function of the overlap length and that the strength increases with lower scarf angles in the case

of scarf repairs.

A series of experimental tests were also conducted by Tomblin et al. [2, 51] to study the effects of

different process parameters (scarf angle, core cell size and repair material) on the repair quality

of sandwich panels. Two repair methods were tested: a wet-lay-up repair procedure and a prepreg

repair procedure using plain weave carbon-epoxy prepreg. A damage tolerance analysis on

sandwich structures was included as well. As a conclusion of their work, a methodology for the

repair process along with designing tools for damage tolerance on sandwich structures were

developed.

The compressive behaviour of sandwich panels with circular tapered scarf repair was investigated

by Liu et al. [49]. Both experiments and finite element analyses were conducted to study the

influence of repair variables (scarf angle and cure temperature) on the repair quality. A progressive

113

damage model was developed for the composite plies and a cohesive element model was used for

the adhesive film. Good correlation between experimental and numerical results were obtained

for different scarf angles. A recent study by Zhang et al. [50] investigated the mechanical

performance of open-hole damage and circular scarf repaired honeycomb sandwich panels under

compressive loads. A 3D finite-element model was also developed. A failure criterion based on

Hashin’s criterion with a progressive damage evolution was included for the unidirectional fiber-

reinforced composite plies used for the skins. The adhesive layer was modelled using cohesive

elements. The honeycomb core was considered as an elastic-plastic material. A good agreement

was found in terms of failure load and damage shape between the experimental and numerical

results. The influence of the scarf angle and the number of 0o-overplies was studied. Conclusions

of the study were that the structure strength increases with the decrease of scarf angle and that the

optimum number of overplies is one to reach the highest strength.

In the above-mentioned research works on bonded repairs of composite sandwich structures, focus

was on scarf-scarf repair modelling using cohesive zone elements for the adhesive bondline.

However, this modelling technique is not suitable to model a stepped-scarf repair configuration,

which is commonly used in practice. Simplifying a stepped-scarf configuration by a scarf-scarf

configuration may lead to predict inaccurate stress distributions. Also, the parametric studies that

were so far conducted on scarf repaired sandwich structures were limited to investigate the effect

of scarf angle [50, 52] and the number of overplies [50] and were not validated with experimental

results.

The aim of the research work presented in this paper is to provide an in-depth understanding

of the tensile behavior of bonded stepped-scarf repaired composite sandwich structures through

114

finite-element analyses and experiments. As in previous studies encountered in literature for

repairs in solid composite laminates, a parametric study is conducted to determine the influence

of the scarf angle, the number of plies, and the use of an overply (overlap length) on the strength

recovery of repaired composite sandwich panels. First, a 2D elastic linear model is used to

determine the peel and shear stress distributions along the bondline. Then, the 2D model is

modified and an elastic-plastic model for the adhesive is taken into account to determine the

failure stress of different repair configurations. A comparison of the baseline model predictions

with experimental results is also presented.

5.2 Finite Element Model Description

The finite-element model used for the parametric study is based on a model developed by the

authors and that is described in details in [76]. The developed model has the particularity to model

the adhesive film using solid elements and to take into account its elastic-plastic behavior that has

been experimentally determined. The model has already been presented and validated using

experimental results in [76]. Here, the goal is to use the developed model to further study repairs

of composite sandwich structures by investigating the effects of different repair configuration

parameters. The following subsections describe the model geometry, the boundary conditions, the

finite-element mesh and the materials models used in the finite element analysis of stepped-scarf

repaired honeycomb sandwich panels under tensile loading.

5.2.1 Model Geometry and Material System Description

The repaired sandwich panels considered in this study have a double stepped-scarf joint, as

shown in Figure 5-1. The repair is located on the tool facesheet. The panels are 335 mm long,

115

102 mm wide and 20.52 mm thick. They are composed of an over-expanded Nomex

honeycomb core with a 19 mm thickness on which two four-ply carbon-epoxy skins were

bonded. The skin is made with an out-of-autoclave plain weave prepreg (CYCOM 5320 T650

PW from Cytec Engineering Materials) with a 0.19 mm thickness. The ply stacking sequence

for the inner facesheet, also called the tool facesheet, is a [(+45/-45)/ (0/90)/ (-45/+45)/ (90/0)].

The outer facesheet, also called the bag facesheet, has the same lay-up as the inner one. The

patch repair has also the same lay-up as the parent structure. The skin 0°-direction is aligned

with the x-direction. The ribbon direction (L-direction) of the Nomex core is along the y-

direction. The repair patch is bonded to the parent structure by an adhesive film (FM 300-2M

from Cytec) with a 0.25 mm thickness, placed along the scarf and under the patch. Only half

of the longitudinal cross-section was modeled (Figure 5-2) using a two-dimensional model with

plane strain conditions.

Figure 5-1 Configuration of the double scarf-stepped repair joint (not to scale).

102 mm

116

Figure 5-2 Symmetric cross-section of the double scarf-stepped repaired sandwich panel

(not to scale).

5.2.2 Boundary Conditions and Finite Element Mesh Details

Looking at Figure 5-2, the boundary conditions are defined as follow. On the left edge (x=L),

a total displacement, as measured from the experiment [76], was applied and, on the right edge

(x=0), symmetric boundary conditions were imposed. Each single woven ply and the adhesive

film were discretized through the thickness using one and four elements, respectively.

The adhesive film along the joint as well as between the two skins and the core was modelled

too. The Nomex honeycomb core was discretized through thickness using five elements. Two

types of continuum elements were used for the finite element analyses. Generalized plane strain

elements with incompatible modes (CPEG4I) were used for analyses carried out with

ABAQUS/Standard. This element type was selected because it was the most appropriate to

accurately predict the adherend stiffness [76]. However, since this element type is not available

X = L X = 0

117

in the ABAQUS/Explicit library, plane strain elements with reduced integration (CPE4R) were

used for analyses carried out with ABAQUS/Explicit [56].

5.2.3 Materials Models

The finite element software packages ABAQUS/Standard and ABAQUS/Explicit [56] were used

to study the mechanical response of the repaired sandwich panels under tensile loading. Two types

of analysis were conducted. First, an elastic analysis with isotropic elastic behavior of the adhesive

and orthotropic elastic material for the composite layers was performed in order to determine the

shear and peel stress distributions along the bondline of the stepped-scarf joint. The second

analysis took into account von Mises plasticity with a shear failure criterion for the adhesive film

to predict the mechanical behavior until failure of the repaired sandwich panel. The non-linear

plastic model is described in details in [76]. A failure criterion based on maximum fiber strain was

used to predict failure of the composite skins. For both analyses, the honeycomb core was

considered as an equivalent orthotropic elastic material. The mechanical properties of the

composite material used for the sandwich panel skins are summarized in Table 5-1. The

mechanical properties of the adhesive film are indicated in Table 5-2 and the elastic properties of

the Nomex honeycomb core are listed in Table 5-3.

Table 5-1 Mechanical properties of the plain weave composite material

E1 (GPa)

E2 (GPa)

E3 (GPa)

64.6a

64.6a

10b

G12 (GPa)

G13 (GPa)

G23 (GPa)

4.9a

4.9b

4.9b

ν12

ν13

ν23

0.047a

0.3b

0.3b

a experimentally measured

b assumed

118

Table 5-2 Mechanical properties of the FM300-2M adhesive

E

(GPa)

G

(GPa) ν

τy

(MPa)

2.024 0.770 0.3 30

Table 5-3 Mechanical properties of the Nomex honeycomb core

EW (MPa)

EL (MPa)

ET (MPa)

30.3a

0.089a

185a

GWL (MPa)

GWT (MPa)

GLT (MPa)

1.9b

55.5c

21.1c

WL

WT

LT

0.26b

0.22b

0.022b

a experimentally measured

b taken from published literature [64]

c provided in material sheets [63]

5.3 Parametric Study

The finite element model was used to conduct a parametric study to provide an in-depth

understanding of the tensile behavior of bonded stepped-scarf repaired composite sandwich

structure. This loading configuration was selected because some experimental results were

available to validate the model predictions. The geometrical design parameters investigated are

the scarf angle (α), the number of plies (N) and the overlap length of the overply (Lo). These

parameters are listed in Table 5-4 and the baseline values are shown in

Table 5-5. With the exception of the scarf angle [50, 52], the effect of these parameters on

composite sandwich repairs have so far not being investigated.

The main objective of this study is to investigate the influence of these parameters on the shear

and peel stress distributions along the bondline of the stepped-scarf joint. For that, shear and

119

peel stresses were extracted from the same nodes along a line in the middle of the bondline, as

depicted in Figure 5-3. The shear stress (τ12) is tangent to the bondline 1-direction 1 of the local

1-2 plane and the peel stress (σ22) is along the 2-direction. To allow comparison of the relative

magnitude, the shear and peel stresses were normalized by the stress σx applied in the global x-

direction as follow:

12 1000x

(33)

22 1000x

(34)

The second objective of this study is to determine the strength of the repaired sandwich panel and

to compare it with the one of the pristine panel. The strength was evaluated using:

2

ff

f

P

bt (35)

where Pf is the failure load, tf is the facesheet thickness and b is the panel width.

Figure 5-3 Line and local coordinate system to extract peel and shear stresses in the

adhesive joint.

Table 5-4 Parametric model details

Parameter Value

Scarf angle, α (°) 1.5-15

Number of plies, N 2, 4 and 8

Overply lay-up (+45/-45)

120

Overlap length, Lo (mm) 0-5-10-15

Table 5-5 Baseline model values

Parameter Value

Scarf angle α (°) 3°

Adhesive thickness, ta (mm) 0.25

Ply thickness, tp (mm) 0.19

Number of plies, N 4

Overply lay-up no overply

Overlap length, Lo (mm) no overply

5.4 Results

Effect of the Scarf Angle

In this section, the influence of various scarf angles was studied by varying α from 1.5° to 15o

while other parameters were kept the same as for the baseline model. First, the effect on the

shear and peel stress distributions along the adhesive bondline is discussed. Then, to further

study the influence of the scarf angle on the tensile strength, finite element analyses with failure

criteria were conducted using geometric models with different scarf angles. The failure stress

variation as a function of the scarf angle is presented.

i. Shear and Peel Stress Distributions along the Bondline

Figure 5-4 (a) and Figure 5-4 (b) compare the normalized shear and peel stresses as a function

of the normalized distance along the bondline for different scarf angles, respectively. As

expected, the stress distribution varies from one ply to another due to the mismatch in ply

properties and peak stresses occur in the vicinity of (0/90) plies. It can also be seen that the

bondline stresses are very sensitive to the scarf angle variation. As the scarf angle decreases,

121

the peel and shear stress peaks decrease. These results are in accordance with conclusions of

previous works [21] conducted on monolithic composite repairs.

a. Shear stress distribution along the middle of the bondline.

b. Peel stress distribution along the middle of the bondline.

Figure 5-4 Shear and peel stress distributions along the adhesive bondline for different

scarf angles.

(+45/-45) (0/90) (-45/+45) (90/0)

(+45/-45) (0/90) (-45/+45) (90/0)

122

ii. Failure load

Figure 5-5 presents the variation of the repair strength with the increase of scarf angle.

Experimental results [76] are also added for comparison and validation of the model

predictions. For scarf angles between 3° and 7°, the strength decreases only very slightly. These

predictions corroborate very well the strengths obtained experimentally. For scarf angles below

3°, the strength increases with angle reduction. The highest strength is obtained for the 1.5°

scarf angle and reaches 62.7 % of the pristine panel strength. For scarf angles over 7°, the

strength decreases drastically. This phenomenon is related to the decrease of the bondline

length with the increase of the angle. This induces the shear and peel peak stresses to increase

at the bondline ends and at the neighbourhood of the stepped plies. For the failure mode, the

finite-element analysis predicts that failure occurs in the adhesive film for angles from 1.5° to

15°. The same failure mode was observed experimentally for angles from 3° to 7°.

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Figure 5-5 Repair failure stress for different scarf angles.

Effect of the Overply

Here, the effect of adding a (+45/-45) overply was investigated using the 3°-scarf joint model

with the baseline parameters. The overply is made with the same plain weave composite

material as the parent and the patch plies and has therefore the same thickness, tp. The overlap

length (Lo), defined in Figure 2, varied from 0 mm to 15 mm. The same boundary conditions

and displacement were applied as for the baseline model.

i. Shear and peel stress distributions along the bondline

Figure 5-6 shows the variation of shear and peel stresses along the bondline for different

overlap lengths. It can be observed that when the overlap length is equal to zero (Lo = 0 mm),

the peel and shear peak stresses are still important and the peel peak stress is even higher than

when no overply was added. For an overlap length equal to 5 mm, a drop in both shear and

peel peak stresses can be seen. However, since for this overlap length, the free edge of the

Experimental pristine value (N=4)

124

adhesive is not completely covered, a step is added in the bondline by the overply. This step

induces an additional peak in the shear and peel stress distributions at the beginning of the

bondline. This additional peak disappears with an overlap length of 10 mm, which covers the

entire free edge of the bondline, and an important drop in the shear and peel stresses along the

bondline is clearly visible.

Increasing the overlap length from 10 mm to 15 mm has little effect on the stresses distribution

along the adhesive bondline since the adhesive free edge was already entirely covered for

Lo = 10 mm. These results corroborate previously published results on the effect of overply on

peak stresses in scarf repair of solid composite laminates [22]. However, for monolithic

composite scarf repair [22], the critical overlap length was found equal to 5 mm instead of 10

mm in this study. This value depends in fact on different parameters and especially on the

adhesive thickness, the scarf angle and the ply thickness in the case of a stepped patch. To be

efficient, the overply should be long enough to cover entirely the free edge of the adhesive.

Referring to Figure 5-7, which represents the scarf-step repair configuration which is

considered in this study and the scarf-scarf configuration which is usually modelled in the

literature, a minimal value for the overply overlap can be determined using

sin tan

pao

ttL

in case of a scarf-step repair (36)

and

sin

ao

tL

in case of a scarf-scarf repair (37)

125

The minimal overlap length in the case of a scarf-step configuration has obviously a larger

value than in the case of a scarf-scarf configuration. This means that a finite-element model

that simplifies the repair geometry using a scarf-scarf configuration will lead to an erroneous

value for the critical overlap length.

ii. Failure Load

Figure 5-8 shows the evolution of the failure stress in the facesheet as a function of the overply

overlap length. An increase in the strength is observed as the overlap length increases. It can

also be seen that a length of 10 mm can be considered as a critical value for this configuration.

From this overlap length, no major effect on the failure stress is observed. A much higher

strength recovery is obtained in comparison with the no overply configuration. This recovery

reaches about 90% of the pristine value. A change in the failure mode was observed too. While

the failure occurs in the adhesive bondline for the baseline configuration, failure occurs no

more in the adhesive but in the composite plies when an overply is added.

iii. Finite Element Model Validation

In order to validate the numerical predictions for the overply effect, tensile tests have been

conducted using the same methodology as presented in [76]. Three specimens with one (+45/-

45) overply and an overlap length of 10 mm were tested. The measured strength is indicated in

Figure 5-8. As can be seen, the strength has increased by 39 % compared to the one obtained

when no overply was used. However, the strength measured experimentally is slightly lower

than predicted. The results confirm nevertheless the important effect of the addition of an

overply on the strength recovery. Figure 5-9 shows the failure morphology of the tested

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specimens. It can be seen that failure occurs in the patch side and not in the scarf joint as it was

observed for the specimens with no overply [76].

a. Shear Stress distribution along the middle of the bondline.

b. Peel Stress distribution along the middle of the bondline.

Figure 5-6 Shear and peel stress distributions along the adhesive bondline as a function

overlap length Lo (3°-4-ply skin model).

127

Figure 5-7 Determination of the minimal overply overlap length

Figure 5-8 Repair strength prediction as function of the overlap length, Lo (3°-4-ply skin

model).

Figure 5-9 Failure morphology of a specimen with an overlap length, Lo=10.

tp

ta

tp

ta

(b) Scarf-scarf repair configuration

(a) Scarf-step repair configuration

Experimental pristine value (N=4)

10 m

m

Patch

Parent

128

Effect of Number of Skin Plies

The number of composite plies used for sandwich skins is usually much lower than for solid

composite laminates. It is therefore essential to investigate and understand how the skin

thickness may affect the residual strength of repaired sandwich structures. To study this effect,

repaired sandwich panels with 2-ply skins, 4-ply skins and 8-ply skins were modelled. The skin

lay-up sequence for each model is as follow:

- 2-ply skin: [(+45/-45)/ (0/90)]

- 4-ply skin: [(+45/-45)/ (0/90)/ (-45/+45)/ (90/0)]

- 8-ply skin: [(+45/-45)/ (0/90)/ (-45/+45)/ (90/0)/ (+45/-45)/ (0/90)/ (-45/+45)/ (90/0)]

To maintain a ply-by-ply match, change in number of plies was applied equally to the parent

part and the patch. Boundary conditions similar to the baseline configuration were applied.

i. Shear and peel stress distributions along the bondline

The shear and peel stresses along the adhesive bondline are plotted in Figure 5-10 for different

numbers of skin plies. The results are presented for the baseline scarf angle value of 3°. It can

be observed that as the number of plies increases, the peak stresses decrease near the bondline

ends. An important factor can explain these results: as the number of plies increases, the

number of (0/90) plies in the facesheet is increasing, so the proportion of the stress carried in

the outer-most (0/90) plies decreases. This results in lower peak stresses in the adhesive

bondline.

129

ii. Failure load

Figure 5-11 compares the failure stress obtained for the repaired sandwich panel with skins of

different thicknesses. It can be observed that the strength increases with the increase of the skin

thickness. One of the reasons is that when increasing the number of plies, the number of (0/90)

plies in the facesheet increases which reduces the peak stresses in the bondline. A higher

strength recovery is therefore obtained for the thicker facesheet. For the 2-ply and 4-ply skin

models, failure occurs in the adhesive bondline. However, for the thicker skin (8-ply skin),

failure occurs no more in the adhesive bondline but in the composite plies.

130

a. Shear stress distribution along the middle of the bondline.

b. Peel stress distribution along the middle of the bondline.

Figure 5-10 Shear and peel stress distributions along the adhesive bondline as a function of

number of skin plies, N (α=3o).

131

Figure 5-11 Repair strength prediction as function of the number of skin plies, N (α=3°).

5.5 Discussion

Results of the parametric study show that peak stresses in the adhesive bondline are greatly

influenced by the scarf angle, the skin thickness and the overply overlap length. Therefore, the

strength of repaired sandwich panels will be very sensitive to theses parameters as well.

From the elastic-plastic analysis results, a map of the failure stress as a function of different

design parameters of the stepped-scarf joints was created. First, the number of skin plies (N)

was varied from two to eight, with scarf angles varying from 1.5° to 15°. Figure 5-12 shows

the evolution of the failure stress as a function of scarf angle for these numbers of plies. It can

be seen that, for a given scarf angle, the strength increases with the skin thickness. Therefore,

the higher failure stress is obtained here for an 8-ply skin sandwich. The failure mode has also

changed from failure in the adhesive bondline for N=2 and N=4 to composite failure for N=8

for scarf angles from 1.5° to 7°. For angles from 10° to 15°, the repair strength for N=8 is

Experimental pristine value

132

higher than for N=2 and N=4 but failure still occurs in the adhesive film. In the literature, a

scarf angle of 3o is often recommended for the design of scarf joints in composite structures. It

is true that for monolithic composite structures using this value allows designing high

efficiency repairs. For example, in the case of a repaired monolithic composite laminate with

a quasi-isotropic sequence ([02/452/-452/902]2s), Campilho et al. [20] obtained a full strength

recovery with a 3°-scarf angle. This angle is appropriate for monolithic composite laminates

because their lay-up counts usually at least eight plies. However, in the case of composite

sandwich structures, the skin is usually very thin and counts only a few plies. As observed in

Figure 5-12, using a 3o-scarf angle to repair a skin with four plies leads to strength recovery of

only 54%. Similarly, Ramantani et al. [52] used a 3o-scarf angle to repair a 4-ply sandwich

panel and obtained a 60% strength recovery. Therefore, due to their small skin thickness,

sandwich structures are more challenging to repair and require a lower scarf angle than

monolithic composite laminates.

The effect of adding an overply was also investigated for different skin thicknesses. Figure

5-13 presents the evolution of the failure stress as a function of the skin thickness for a repair

with no overply and a repair with a 10 mm-overlap length overply. The scarf angle was fixed

to 3°. The figure highlights the important effect of the addition of an overply for 2-ply and 4-

ply skin sandwiches. The strength becomes twice as important and failure occurs in the

composite plies. For the 8-ply skin sandwich, the increase in failure stress due to the overply is

less important since the strength was already high without an overply. The failure mode

remains the same (composite failure) as with no overply. Therefore, when repairing a thick

skin sandwich panel with a small scarf angle using an overply is not essential to obtain a good

133

strength recovery. However, an overply is still useful to improve repair durability and protects

the tip of the scarf from being damaged.

It is confirmed from previous studies and this study that the failure stress of the repaired

composite sandwich panel increases as the scarf angle decreases. So, it is recommended to use

small scarf angle to insure a high strength recovery of the repaired sandwich structure. Large

scarf angles lead to smaller bond length, higher peak stresses in the adhesive and therefore

lower repair strength. On the other hand, smaller scarf angles requires removing a higher

quantity of composite material from the parent skin, which induces a larger repair area in the

structure. From this study, we highlight the importance of the addition of an overply to restitute

the strength of the repaired structure. Therefore, an alternative to using a very small scarf angle

to restore the structure strength is to add an overply with an overlap length that covers entirely

the free edge of the adhesive. This will allow designing an efficient repair using a more

reasonable scarf angle that does not require removing a great quantity of undamaged material.

For very thin facesheet, however, it is recommended to use a very small scarf angle and an

overply to obtain a high strength restitution.

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Figure 5-12 Map of the failure stress as a function of the scarf angle and number of plies,

N.

Figure 5-13 Variation of the failure stress as a function of the overply and number of skin

plies, N (α=3°).

Failure in the adhesive film

Failure in the composite plies

Experimental pristine value (N=4)

Experimental pristine value

135

5.6 Conclusions

The effect of geometrical design parameters (scarf angle, overply overlap length, number of

skin plies) on the shear and peel stress distributions in the adhesive bondline and on the failure

stress of a stepped-scarf repair of composite sandwich structures have been thoroughly

investigated. Two material models were used for the adhesive film: a linear elastic and a non-

linear elastoplastic model with shear failure criterion. A failure criterion based on maximum

fiber strain was used to predict failure of the composite skins. It has been shown, by both

numerical analyses and experiments, that the geometrical design parameters can influence

greatly stresses distributions along the bondline and the repair strength.

Stresses distribution along the adhesive bondline

Results showed that the shear and peel peak stresses are very sensitive to scarf angle, the

addition of an overply and the number of skin plies. It was shown that the adhesive peel and

shear stresses vary greatly along the adhesive bondline as a function of the ply orientation with

the (0/90) plies inducing the most critical stress peaks. As the number of plies in the skin

increases, the load is transferred through more (0/90) plies and the stress peaks decrease. With

the addition of an overply with an overlap length that covers entirely the free edges of the

adhesive, a considerable decrease of the peak stresses is observed. Hence, it can be concluded

that the addition of an overply can provide a good protection to the adhesive joint and reduce

the peak stresses that may cause premature failure of the repaired structure.

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Failure stress prediction

Two possible types of failure were taken into account in order to predict the residual strength

of the repaired sandwich panels with the different design parameters: failure in the adhesive

bondline and failure in the composite plies.

It was observed that failure occurs in the adhesive film for angles from 1.5° to 15°. The highest

strength is obtained for the 1.5° scarf angle and reaches 62.7 % of the pristine panel strength.

With the addition of an overply the strength recovery increases to about 90% for a 3°-scarf

angle. Failure occurs mainly in the composite skins and no more in the adhesive film where the

stress peaks are reduced because of the overply.

With the increase of the number of skin plies, failure stress of the repaired composite sandwich

panel increases. For the 2-ply and 4-ply skin models, failure occurs in the adhesive bondline.

However, for the thicker 8-ply skin, failure occurs no more in the adhesive bondline but in the

composite plies.

Correlation between experimental and finite-element results

Experimental results were used to validate the numerical predictions in terms of failure stress

and failure path. Comparison with the experimental results confirmed that the developed model

provides a good prediction of the repaired joint strength and failure mode and it may be used

as an alternative design tool to study the mechanical behavior of repaired composite sandwich

panel.

137

From this study, we highlight the considerable effect of the skin thickness and the addition of

an overply on the residual strength of repaired sandwich structures. Due to their small

thickness, sandwich skins are much more critical to repair than solid composite laminates. It is

crucial in the design of efficient repair for sandwich structures to use smaller scarf angles than

for solid composite laminates and to use an overply.

Acknowledgements

We would like to thank the Natural Sciences and Engineering Research Council of Canada

(NSERC), the Consortium for Research and Innovation in Aerospace in Quebec (CRIAQ), the

National Research Council Canada (NRC), Bombardier Aerospace and L3-MAS for funding,

technical support and materials.

138

Chapter 6.

Article 3: Evaluation of the mechanical

performance of repaired composite sandwich

structure using different mechanical tests

Emna Ghazali, Marie-Laure Dano, Augustin Gakwaya and Charles-Olivier Amyot

Résumé

Cet article décrit les performances mécaniques de réparations collées sur des panneaux

sandwich fabriqués avec des peaux en de carbone-époxy et une âme Nomex. Tout d'abord, le

comportement mécanique des panneaux sandwich intacts et réparés sous chargement de

compression et de flexion en quatre points a été étudié. Ensuite, des analyses bidimensionnelles

(2D) par éléments finis sont effectuées pour prédire la résistance à la rupture des réparations

sous chargement de flexion quatre points. Un comportement élastoplastique avec un critère de

rupture en cisaillement a été considéré pour le film adhésif. L’âme en nid d'abeilles est

modélisée par un matériau élastique orthotrope linéaire équivalent et les peaux composites sont

considérées comme un matériau linéaire orthotrope avec un critère de contraintes maximales

pour déterminer la rupture du premier pli. Les résultats expérimentaux obtenus à partir des

essais de flexion quatre points et de compression sont similaires à la fois pour les panneaux

sandwich intacts et réparés.

139

Abstract

This paper studies the static mechanical performance of adhesively bonded repairs on sandwich

panels made with carbon-epoxy composite skins and a Nomex core. First, the mechanical

behavior of pristine and repaired sandwich panels under edgewise compressive, tensile and

four-point bending loadings is studied experimentally. Then two-dimensional (2D) finite

element analyses are performed to predict the repair strength under the different load cases.

The adhesive film behavior is described using an elastic-plastic model with a shear failure

criterion while the honeycomb core is assumed to respond like an equivalent orthotropic linear

elastic material and the composite skins are considered as an orthotropic linear material with a

maximum strain criterion used to determine the fiber failure load. Results from the tensile and

four-point bend tests are comparable for both pristine and repaired sandwich specimens.

However, edgewise compression and four-point bend tests have not provided equivalent

results. The study concludes that flexure tests are preferred over tensile and edgewise

compressive tests. It provides a reliable and simple test method to determine the mechanical

behavior of repaired sandwich panels.

Keywords: sandwich, repair, compression, tension, flexure tests, 2D finite element analysis

6.1 Introduction

Composite sandwich structures are increasingly being used for primary aircraft components

because of their superior structural performance such as high strength, high stiffness, long

fatigue life, and light weightiness [43]. Although composite structures offer many other

advantages over traditional metallic structures such as better fatigue resistance and being less

140

prone to deterioration caused by corrosion and cracking, they are more sensitive to other type

of damage such as impact damage that may cause delamination, disbonding and internal

material crushing. As these damages can cause severe reduction in strength and stiffness and

may lead to the structure failure, it is crucial to have effective repair methods capable of

restoring the structural performance of damaged composite structures. In the literature, two

major repair configurations have been investigated: bolted and bonded repair patches [77, 78].

Bonded patch joining (scarf, step, overlap) are often used when high strength recovery and

aerodynamic requirements need to be satisfied [79]. The mechanical performance of repaired

composite structures is usually assessed by experimental testing. For that, robust and reliable

methods need to be provided.

To study the mechanical performance of repaired honeycomb sandwich structures, several

experimental studies have been carried out under different static loads. The studied repairs were

either across the width of the specimen [47] or circular [49]. Edgewise compressive tests are

the most common test methods that have been used in the literature. To perform such test

methods, a CAI fixture system is widely used. The included anti-buckling guides may help to

prevent buckling failure from occurring during the test. However, ends-failure crushing cannot

easily be prevented from occurring, especially for pristine sandwich panels.

The AGARD (Advisory Group for Aerospace Research & Development) [44] published a

report on repairs of sandwich structures used in military structures. The sandwich structure was

repaired using external patches. The patches were either co-cured or pre-cured and the core

either replaced or filled with a filler paste cured at high and low temperatures cycles. Static and

fatigue edgewise compressive tests were carried out to characterize the behavior of the repairs.

141

Results showed that the pre-cured patch method is the most suitable for field-level application.

Liu et al. [49] investigated the mechanical performance of circular repaired sandwich panels

using the edgewise compressive tests, at room temperature conditions. Recently, Zhang et al.

[50] published a study on the mechanical performance of honeycomb sandwich panels with

open-hole damage and circular scarf repair under compressive loads. A good agreement was

found in terms of ultimate failure load and damage shape between the experimental and

numerical results. Failure of the repaired sandwich panel was due to adhesive delamination and

patch local buckling.

Strength of repaired honeycomb sandwich panels has also been assessed in the literature using

four-point bending. Baker et al. [45] have studied experimentally a scarf repair on a horizontal

stabilizer of an F/A-18 spacecraft composed by an aluminum honeycomb core and CFRP skins.

The repaired structure was tested under a four-point bending load. The specimens were tested

at -40ºC, room temperature and 104ºC, in dry and wet conditions. The failure of the adhesive

film was cohesive for all test conditions. At 104ºC, the failure strains were reduced by 50%,

compared to the ones of the specimens tested at room temperature. Mahdi et al. [47] have

studied the performance of both pristine and scarf repaired sandwich panels subjected to static

four-point bending loads. The repaired facesheets were loaded in both compression and tension.

Two repair configurations were studied: overlap and scarf repair. The repair was cured at low

and high temperature systems. The main findings of this work are that when loaded in

compression, the scarf repairs were weaker than overlap repairs. However, scarf repairs were

stronger in tension achieving 100% of the pristine strength. To perform such tests, long beams

were manufactured by the authors and a large fixture system was used.

142

A series of experimental tests (tensile, shear and four-point bend tests) were conducted by

Tomblin et al. [2] to study the effects of different process parameters on the quality of 2D

sandwich panel scarf repairs. Most of the repaired specimens tested under different loads

showed a high strength recovery (about 92%). As a conclusion of their work, a methodology

for the repair process along with design tools for damage tolerance on sandwich structures were

developed.

Currently, no comparison study of the effect of each test method to assess the mechanical

performance of repaired honeycomb sandwich panels has been conducted in the literature. This

paper investigates the assessment of the mechanical performance of both pristine and repaired

panels using three different mechanical tests: tensile, edgewise compressive and four-point

bend tests. It focuses on one aspect of a larger research program on the repair of sandwich

structures [80]. Its objective is to compare the performance of different test methods used to

assess the mechanical behavior of repaired honeycomb sandwich panels. Both experiments and

finite element analyses are performed. Firstly, the repair procedure and the experimental set-

up are detailed. Force or stress versus strain curves are presented for the different experimental

tests and a series of fractography images are shown to determine the failure mode and pattern

of the repaired sandwich panels. Secondly, the finite element models developed using the

commercial software ABAQUS [56] are discussed. The obtained numerical results are

compared with experimental results to validate the finite element model predictions of the

failure load of the repaired sandwich panel under different loadings.

143

6.2 Experimental Work

6.2.1 Materials

The composite honeycomb sandwich panels were composed of four-ply woven Carbon Fiber

Reinforced Polymers (CFRP) skins bonded to an over-expanded or a hexagonal Nomex

honeycomb cores with a 19 mm and 25.4 mm thickness, respectively. The skin material was a

plain weave out-of-autoclave (OOA) semi-impregnated prepreg (CYCOM 5320 T650 PW

from Cytec Engineering Materials). The laminate used for the two skins had a [(+45/-45)/

(0/90)/ (-45/+45)/ (90/0)] quasi-isotropic stacking sequence. The Cytec FM® 300-2M adhesive

film used to bond the skins to core is a toughened epoxy B-staged adhesive film. This adhesive

film is common for repair and had a nominal thickness of 0.25 mm. The presence of polyester

fibers non-woven carrier, which accounts for 5–10 wt. %, ensures constant bondline thickness.

The over-expanded Nomex core is a phenolic resin impregnated aramid honeycomb core (Euro

Composites ECA-R 4.8 64), with a cell size of 4.8 mm and a density of 64 kg/m3. The

hexagonal Nomex core was a phenolic resin impregnated aramid honeycomb (Euro

Composites ECA 3.2 96), with a cell size of 3.2 mm and a density of 96 kg/m3.

6.2.2 Repair Procedure

The mechanical behavior of sandwich panels repaired using a stepped-scarf bonded joint

configuration was studied. The actual repair was carried out on the tool facesheet (TF). To

create the scarf in the parent facesheet, each prepreg ply had an initial rectangular cut-out as

shown in Figure 6-1. The cut-outs had a specific width such that when stacked together the

144

plies formed a drop-off. The FM300-2M adhesive film was used to bond the two facesheets to

the core. Then, both skins and core were co-cured under vacuum bag in an oven.

The repair patch was manufactured as follows. After cure of the parent part, the step shaped

parent area was sanded by a 120-abrasive paper to reach the desired scarf angle. This was

followed by a surface clean up with acetone and completed immediately by drying. The repair

patch was prepared using the same parent prepreg material and the original stacking sequence.

The plies were cut to a specific width and stacked together to form an overlap as shown in

Figure 6-2. The overlap distance Loverlap was determined from the scarf angle α and the ply

thickness tp using:

tan

p

overlap

tL

(38)

6.2.3 Specimen Preparation and Test Procedure

As a next step, static mechanical tests were performed to compare the performance of the

repaired panels with that of the pristine. The sandwich specimens were tested under

compressive, tensile and four-point bending loadings. Table 6-1 summarizes the test matrix

followed for each load configuration. As seen, repairs with three different scarf angles were

tested in tension and compression whereas only 3o-scarf angle repairs were tested in flexure.

Table 6-1 Test matrix for different experimental tests

Configuration Angle (°) Tension Compression Flexion

Pristine - 3 4 3

Repair

3 3 3 2 (TF in tension)

3 (TF in compression)

5 3 3 -

7 3 3 -

145

Figure 6-1 Parent panel dimension (not to scale)

Figure 6-2 2D stepped-scarf repair configuration

Edgewise Compressive Tests

The pristine and repaired sandwich panels were cut into rectangular test specimens using water

jet at a nominal size of 305 mm by 102 mm. To prevent end-failure, special considerations in

the panel preparation were made. A section of the core material was removed at the top and at

the bottom of the specimen and replaced with a high stiffness potting material to reinforce the

edges. This section was 13 mm high and 102 mm wide. Aluminum tabs were then bonded at

both ends to ensure a smooth load transfer in the potting-Nomex core junction, as seen in Figure

6-3.

α

α

146

A fixture system similar to the one recommended by the ASTM standard D7137 [81] for

compression after impact (CAI) test was used to hold the specimens and to introduce

compressive loading, as shown in Figure 6-4. Specimens were tested at a crosshead

displacement rate of 0.5 mm/min, according to ASTM standard C364 [82], in an

electromechanical MTS machine with a 100 kN load cell. Three strain gages were bonded on

the specimens to make sure that there is no bending due to specimen misalignment and to study

the strain distribution on the skins. Gage 1 was bonded in the middle of the tool face (Figure

6-5.a) and the two others, gages 2 and 3, on the bag face, as depicted in Figure 6-5.b. The tool

face surface of the specimen was also prepared for measurement with a 3D digital image

correlation (DIC) system (Aramis by Gom [73]). The DIC software was then used to determine

the full in-plane and out-of-plane displacements and strain field on the specimen tool face

surface during testing. The applied load and the strain response were recorded during the test.

The quality of the repair was assessed by microscopic observation before testing (see

micrograph of Figure 6-6). No micro-cracks or damaged cells were observed in the repair area.

Moreover, no porosity was visible along the repair bondline. However, macro porosity was

observed in the adhesive between the core and the skins.

147

Figure 6-3 Specimen geometry (not to scale)

Figure 6-4 CAI fixture system used for the edgewise compressive tests

a. Pristine sandwich panel b. Repaired sandwich panel

Aluminum tabs

148

Figure 6-5 Location of strain gages (not to scale)

Figure 6-6 Micrograph of the repair cross-section before testing

Uniaxial Tensile Tests

Rectangular pristine and repaired test specimens were cut with a water jet-milling machine at

a nominal size of 335 mm by 102 mm to be tested under uniaxial tensile loading. To prevent

ends failure, the specimen ends were reinforced with aluminum inserts and aluminum tabs.

Specimens were tested with the same 100 kN electromechanical testing machine, at a constant

crosshead rate of 1 mm/min. A homemade tensile test fixture, inspired from the one used by

Tomblin et al. [2], as shown in Figure 6-7, was used for these tests. The surface of the tool

facesheet was prepared for measurement with a 3D digital image correlation (DIC) system

(Aramis by Gom [73]). A video extensometer was used to measure the strain on the bag

a. Tool face (TF) b. Bag face (BF)

Patch

Porosity

Parent

149

facesheet. The strain field measured by the DIC system was averaged on an area taken in the

middle of the specimen to obtain a single value that can be compared to the strain measured by

the video extensometer. For the repaired specimens, the strain was averaged in the middle of

the patch.

Figure 6-7 Tensile test set-up.

Four-Point Bend Tests

Long sandwich beams were used for the pristine configuration (686 x 76.2 mm2) in comparison

to the 3°-repaired beams (610 x 76.2 mm2). The length had to be increased to prevent core

shear and core crushing failure modes from occurring. Specimens were tested using the same

100kN electromechanical testing machine at a crosshead rate of 8 mm/min. A fixture system

similar to the one used in the ASTM standard D7249 [83] was machined, as illustrated in Figure

6-8. Four 3 mm-thick rubber pads were used under the loading points to prevent core crushing.

The loading points were placed at different distances for the pristine and repaired sandwich

150

beams respectively, as seen in Figure 6-8.b and Figure 6-8.c. Strains gages and a DIC system

were used to measure the strains on the specimens. First, the repaired beams were placed in the

fixture with the repair on the top so that compressive load was applied on the repaired skin.

Then, they were placed in the fixture with the repair on the bottom so that tensile load was

applied to the repaired skin.

Figure 6-8 Four-point bend test fixture and specimen configurations (not to scale)

L

S

a. Four-point bending fixture

c. Repaired sandwich beam

b. Pristine sandwich beam

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6.2.4 Results and Discussion

Edgewise Compressive Tests

The compressive test results are presented in Figure 6-12 to Figure 12. The load versus strain

curves obtained for the pristine and for the 3°-repaired specimens are shown in Figure 6-9. It

can be observed that the behavior of the tested specimens remains linear until failure occurs

suddenly. Similar results were observed for the specimens repaired using 5°- and 7°- scarf

angles. Several curves representing the force versus strain measured using different instruments

are shown in Figure 6-10. It can be observed that the strains measured on the bag facesheet

(gages 2 and 3) are slightly different from the strains measured on the tool facesheet (gage 1

and DIC). This difference was noticed for all tested specimens (pristine and repaired). This

may be due to the presence of a slight bending in the tested specimens.

Different failure modes were observed for the pristine and for the repaired sandwich panels.

For the pristine panels, failure occurred near the loaded edges which may be caused by a lack

of uniformity of the load distribution in the specimen. The repaired specimens failed away from

the loaded ends by local buckling in the scarf area, as clearly shown with the DIC measurement

presented in Figure 6-11. An out-of-plane displacement was observed and measured by the

DIC system. To determine the appropriate failure modes and pattern induced in the tested

repaired specimens, fractography was performed using optical microscopy. Figure 6-12 shows

the resulting micrographic images. From that figure, cracks can easily be observed in the parent

laminate, a few core cells are fractured, and no damage was noticed in the patch or in the

adhesive. Failure seems to be due to skin wrinkling as shown in Figure 6-11. Severe

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discontinuity in the structure stiffness may be responsible for the observed failure mode.

Results obtained for the tested specimens are summarized in Table 6-2. The strength was

evaluated from the applied load by:

2

f

f

P

t w (39)

where tf is the facesheet thickness, w is the specimen width and P is the failure compressive

load.

A reduction in residual compressive strength for the repaired panels was observed. Only 53 %

of the strength was recovered for the 3°-repaired panels. It can be noticed also that the strength

increases slightly with the increase of the scarf angle and it reaches about 67.5% for the 7°-

repaired panels. These results may be explained by the type of failure mode encountered (local

buckling of the repaired facesheet). As the scarf angle increases, the scarf length decreases, and

the discontinuity area is reduced.

Figure 6-9 Typical force versus strain curves for pristine and 3°-repaired sandwich

specimens tested in compression

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Figure 6-10 Force-strain curves obtained using different strain measuring instruments for

pristine and 3°-repaired sandwich specimens tested in compression

Figure 6-11 DIC measurement: out-of-plane displacement of 3°-repaired sandwich

specimen tested in compression at failure

[mm]

Patch

repair

Parent

Parent

a. Pristine sandwich specimens

b. 3°-repaired sandwich

specimens

154

Figure 6-12 Micrograph of the repair cross-section after failure of 3°-repaired sandwich

specimen tested in compression

Table 6-2 Summary of the compressive test results

Configuration Angle

(°)

Failure strength

(MPa)

Strength recovery

(%)

Pristine - 74.40 -

Repair

3 198.02 52.89

5 228.06 60.91

7 252.53 67.45

Uniaxial Tensile Tests

The results of the static tensile tests performed on the pristine and the 3°-repaired sandwich

specimens are presented in Figure 6-13. The graphics represent the load versus strain measured

on the tool facesheet with the DIC system. As can be observed, the load-strain behavior is

mostly linear until failure for both the pristine and the 3°-repaired specimens. For the 5°- and

7°-repaired specimens, a similar trend for the load-strain curves was also observed. A summary

of the tensile test results for the different configurations is shown in Table 6-3. The failure

stress is calculated using equation (2) as for the compressive tests. For the pristine panels,

Crack/porosity

Parent laminate

Damaged cell

Crack

Parent laminate

155

damage occurred in both facesheets far from the loaded ends. For the repaired panels, failure

occurred mainly in one of the two scarf zones for the different studied scarf angles.

Four-Point Bend Tests

The stress in the sandwich beam skins tested under four-point bending is calculated using:

( )

2( )

f

f

P S L

d c bt

(40)

where P is the applied force, S is the support span, L is the load span, c is the core thickness, d

is the measured total thickness of the sandwich panel, b is the width of the specimen and tf is

the facesheet thickness.

Figure 6-14 shows the flexure stress-strain responses for the pristine and for the 3°-repaired

sandwich beams with the repaired facesheet loaded in compression or in tension. The stress-

strain curve for the pristine beam is very smooth because the strains were measured using strain

gages. The observed non-smoothness in the stress-strains curves of the 3°-repaired beams is

due to noise induced in the strain measurement with the DIC system. The obtained

experimental curves indicate that the flexure response is linear until failure suddenly occurs.

For the pristine beams, failure occurs in the facesheet loaded in compression. However, for the

3°-repaired sandwich beams loaded in tension, failure occurs along one of the double scarf, as

illustrated in Figure 6-15. The same failure mode is observed when the 3°-repaired sandwich

beam is loaded in compression, i.e. the failure occurred in one of the double scarf. A summary

of the flexure test results for the different studied configurations is shown in Table 6-4.

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It can be noted that when the repair is loaded under four-point bending with the repaired face

in compression, a strength recovery of 55.16 % is obtained. However, a higher recovery of

63.68% is obtained when the repaired face is loaded in tension. These results show that the

repaired beams are more efficient when loaded in tension than in compression.

Figure 6-13 Typical axial load-strain curves for the pristine and 3°-repaired sandwich

specimens tested under tension

Table 6-3 Summary of the tensile test results

Configuration Angle

(°)

Failure strength

(MPa)

Strength recovery

(%)

Pristine - 537 -

Repair

3 276 51.39

5 272.54 50.75

7 271 50.46

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Figure 6-14 Typical stress versus strain curves for pristine and 3°-repaired sandwich beams

tested under four-point bending

Figure 6-15 . Failure mode of a 3°-repaired sandwich beam tested under four-point bending

(repair in tension)

Table 6-4 Summary of the flexure test results

Configuration Angle

(°)

Failure strength

(MPa)

Strength recovery

(%)

Pristine - 420.60 -

Repair in compression 3 232.02 55.16

Repair in tension 3 267.85 63.68

Parent Patch

158

Comparison and Discussion

The main objective of the flexure tests conducted on the composite sandwich beams was to

validate the results obtained for the pristine and for the repaired panels tested under edgewise

compressive and uniaxial tensile loads.

Figure 16 shows the failure stress obtained for static edgewise compressive, uniaxial tension

and four-point bend tests for the pristine specimens. As seen in Figure 6-16, pristine sandwich

specimens exhibit a higher strength in tension than in compression. This explains why, when

tested in flexure, failure occurs on the compressive side of the pristine sandwich beam. A higher

strength was obtained from the four-point bend tests in comparison with the edgewise

compressive tests. These results are explained by the difference in the failure mode. Pristine

specimens failed at the CAI fixture loading points in the free-length between the contact surface

and the anti-buckling support, when loaded under edgewise compressive load. This makes it

difficult to obtain a valid pristine compressive strength. However, pristine beams tested under

four-point bending failed on the compressive side within the load span away from the loading

points.

Figure 6-17 presents the failure stress for the pristine and the 3°-repaired specimens tested

under flexure loading with the repair face loaded in compression and in tension with those

obtained under uniaxial compression and tension loads. Here, the failure stress obtained in the

case of uniaxial tension and four-point bending (with the repair in tension) is quite similar.

Both test methods revealed the same failure mode for the 3°-repaired specimens, i.e. an

adhesive failure in one of the double scarf.

159

The 3°-repaired specimens tested under four-point bending (with the repair in compression)

reached a higher failure stress in comparison with the 3°-repaired specimens tested under

edgewise compressive load. A local facesheet buckling mode, a facesheet wrinkling (as

depicted in Figure 6-11) was detected for the repaired specimen under edgewise compression

and may explain this difference in the stress value.

From the different tests results, the four-point bend test was found to be less sensible to loading

issues caused by the fixture system in comparison with the edgewise compression tests.

Compressive tests were found to be susceptible to the test fixture and ends-crushing failure,

especially for the pristine panels. Tensile tests provided reliable results. However, they were

very expensive in terms of time and resources to be performed (cost of test fixtures and

specimen preparation). The Digital Image Correlation system, however, could easily be used

with the uniaxial loading tests since the specimen surface was clearly visible. Difficulties using

DIC were encountered with the flexure tests since the fixture does not allow a direct access to

the specimen surface. Mirrors can be used but may cause strain measurement variation.

Another drawback of the flexure tests is the need for large beams to avoid premature failure

modes such as core crushing or core shear and therefore large test fixtures are required.

Despite the mentioned disadvantages, four-point bend tests can assess correctly the mechanical

behavior of pristine and repaired sandwich panels and offer the facility of specimen

preparation. As such, four-point bend test is suitable and simple as test method for evaluation

of the mechanical performance of repaired sandwich panels.

160

Figure 6-16 Comparison of the failure stress of the pristine panels obtained from different

loading types.

Figure 6-17 Comparison of the failure stress of the 3°-repaired panels obtained from

different loading types.

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6.3 Finite Element Analysis

In this section, numerical simulation of the carried-out experiments was performed in order to

evaluate the ability of a previously developed finite element model to capture the

experimentally observed behavior of the repaired sandwich specimens. The finite element

model has been developed and validated using tensile tests in previous work [76].

6.3.1 Model Description

The analysis takes into account von Mises plasticity with a shear failure criterion for the

adhesive film [76] to predict the mechanical behavior of the bonded joints until failure. Because

a rectangular repair patch across the panel width was studied, a plane strain assumption was

adopted in the finite element modeling process to study the mechanical behavior of the adhesive

joint as a two-dimensional (2D) problem. Hence, a longitudinal cross-section corresponding to

the middle of the panel away from the edge in the width direction was modeled. Since the

repaired beam was symmetric with respect to its midsection, one can exploit this symmetry

condition and model only half of the repaired panel, as illustrated in Figure 6-18. The

mechanical properties of the CFRP woven composites, the two honeycomb cores and the

adhesive film are listed in Table 6-5, Table 6-6, Table 6-7and Table 6-8, respectively.

The finite element (FE) models were developed using the commercial software ABAQUS [56].

Two-dimensional quadrilateral plane strain solid elements with reduced integration CPE4R,

from Abaqus element library [56], were used to model the two skins, the honeycomb core and

the adhesive film. For the edgewise compressive and uniaxial tensile tests, a displacement as

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measured from the experiment was applied at the left edge (x=L) and symmetric conditions

were imposed on the right edge (x=0).

For the four-point bend model, the section between the two loading points was subjected to a

constant moment. This moment was applied at a reference point. The element nodes were

linked to the reference point using TIE constraints. The boundary conditions are defined as

follow. The left edge (x=L) was subjected to a moment, determined from the ultimate force

applied experimentally, by a kinematic coupling constraint point (reference point), as described

in Figure 6-19. On the right edge (x=0), symmetric boundary conditions were imposed.

Each single woven ply and the adhesive film were discretized through the thickness using two

and four elements respectively, as illustrated in Figure 6-20. The adhesive film along the joint

as well as between the two skins and the core was modelled too. The Nomex honeycomb core

was discretized through the thickness using five elements.

Figure 6-18 Studied longitudinal cross-section of the repaired specimens

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Figure 6-19 Model geometry and boundary conditions for the four-point bend test

Figure 6-20 Mesh details of the adhesive bondline

Table 6-5 Elastic material properties of the plain weave carbon-epoxy ply

E1 (GPa)

E2 (GPa)

E3 (GPa)

64.6a

64.6a

10b

G12 (GPa)

G13 (GPa)

G23 (GPa)

4.9a

4.9b

4.9b

ν12

ν13

ν23

0.047a

0.3b

0.3b

a experimentally measured

b assumed

Table 6-6 Mechanical properties of the over-expanded Nomex honeycomb core (ECA-R

4.8 64)

EW (MPa)

EL (MPa)

ET (MPa)

30.3a

0.089a

185a

GWL (MPa)

GWT (MPa)

GLT (MPa)

1.9b

55.5c

21.1c

νWL

νWT

νLT

0.26b

0.22b

0.022b

a experimentally measured

b estimated from [64]

c from manufacturer

RP

Symmetric

conditions M

X=0 X=L

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Table 6-7 Mechanical properties of the hexagonal Nomex honeycomb core (ECA 3.2 96)

EW (MPa)

EL (MPa)

ET (MPa)

19.2

25.6

379.2

GWL (MPa)

GWT (MPa)

GLT (MPa)

5.13

68a

96a

νWL

νWT

νLT

0.85

0.020

0.027

a from manufacturer. The other values are estimated based on [64]

Table 6-8 Mechanical properties of the FM300-2M adhesive film

E (GPa) ν12 τy (MPa)

2.024 0.3 30

6.3.2 Model Results

The model was used to predict the mechanical behavior of the 3°-repaired sandwich panels

until failure for the tensile, compression and flexure tests. Figure 6-21 compares the predicted

and experimental measured strength values. The failure stress was well predicted for the 3°-

repaired sandwich panels under tensile and four-point bending loads. For the 3°-repaired

sandwich panels under edgewise compressive loads, the FE model overestimates the strength.

This is because the experimentally obtained failure is due to face wrinkling and this failure

mode is not considered in the developed FE model. An error inferior to 15% was found for the

different load cases. This error value was calculated using:

(%) 100FE Exp

x x

Exp

x

Error

(41)

The deformed shape of the repaired sandwich beam predicted by the FE model is presented in

Figure 6-22 when loaded under four-point bending with the repair on the compressive side. As

can be seen, failure occurs mainly in the adhesive bondline and propagates in the adhesive

between the core and the facesheet. When loaded under four-point bending with the repair in

tension, a similar failure morphology was obtained. This failure mode is in accordance with

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the failure observed experimentally. These results, in term of strength and failure mode

predictions, validate the use of the developed finite element model for predicting the

mechanical behavior of the repaired sandwich panels under four-point bending and uniaxial

tensile loads. However, for the compressive tests, as the face wrinkling failure mode is not

taken into account in the model, the strength is not well predicted. An improvement of the FE

model is needed to well predict the behavior of repaired panels under edgewise compressive

loads.

Figure 6-21 Numerical predictions versus experimental results for 3°-repaired sandwich

specimens under different load cases.

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Figure 6-22 Deformation and failure mode for a 3°-repaired beam tested under four-point

bending (repair in compression)

6.4 Conclusion

Bonded repair has been conducted on composite sandwich panels and several mechanical tests

were carried out to evaluate their strength. Pristine and repaired specimens were tested under

four-point bending with the repair loaded in compression and in tension, under uniaxial tension

and edgewise compression. The influence of the experimental test used to determine the

performance of pristine and stepped-scarf repaired composite sandwich structures has been

thoroughly investigated. The main results are:

Strength recovery and failure mode

A low strength recovery was observed for the repaired sandwich panels. This may be explained

by the fact that failure mainly occurs in the adhesive. The use of an overply would have

probably decreased the stress in the adhesive joint and increased the repair strength.

Experimental mechanical tests

Parent Patch

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Different experimental tests were used to determine the mechanical performance of pristine

and repaired composite sandwich panels. Results showed that failure stress and failure mode

are similar for repairs loaded in tension through uniaxial tensile tests or four-point bend tests.

However, edgewise compression and four-point bend tests do not provide equivalent results.

The strength obtained through four-point bending is higher for both the pristine and the repaired

panels.

Each experimental method has its advantages and drawbacks. Both tensile and compressive

tests were expensive in terms of fixture systems and specimen preparation, but they offer the

possibility of using DIC that facilitates the detection of failure modes. Flexure tests provide

similar results as the tensile tests but have the advantage of being faster and easier to perform

since no specimen preparation is required. However, long sandwich beams and a large fixture

system need to be manufactured in order to prevent the occurrence of premature failure such

as core shear or crushing, depending on the core and skin material properties.

Correlation between experimental and numerical finite element results:

Experimental results were used to validate the numerical predictions in terms of failure stress

and failure mode. Comparison of numerical results with the experimental results confirmed

that the developed model provides a good prediction of the repaired joint strength and failure

mode and hence may be used as an alternative design tool to study the mechanical behavior of

repaired composite sandwich panel.

The objective of this study was to evaluate the use of experimental test methods to determine

the mechanical performance of repaired honeycomb sandwich panels. From the results, it can

168

be concluded that flexure tests are preferred over tensile and edgewise compressive tests. It

provides a reliable and simple test method to determine the mechanical behavior of repaired

sandwich panels.

ACKNOWLEDGEMENT

We would like to thank the Natural Sciences and Engineering Research Council of Canada

(NSERC), the Consortium for Research and Innovation in Aerospace in Quebec (CRIAQ), the

National Research Council Canada (NRC), Bombardier Aerospace and L3-MAS for funding,

technical support and materials

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Chapter 7.

Article 4: Experimental and Numerical Studies of

Stepped-Scarf Circular Repair in Composite

Sandwich Panels

Emna Ghazali, Marie-Laure Dano, Augustin Gakwaya and Charles-Olivier Amyot

Résumé

Cet article étudie la performance mécanique des réparations circulaires collées sur des

panneaux sandwich fabriqués avec des peaux composées de carbone-époxy et une âme en

Nomex. Tout d'abord, le comportement mécanique des panneaux sandwich intacts,

endommagés et réparés sous chargement de compression est étudié. Ensuite, des poutres

sandwich intactes et réparées sont testées sous un chargement de flexion quatre points où la

réparation circulaire est chargée en tension. Enfin, des analyses par éléments finis sont

effectuées pour prédire la résistance à la rupture des structures sandwich réparées. Le film

adhésif a été considéré comme un matériau élastoplastique avec un critère de rupture en

cisaillement. L’âme en nid d'abeille se comporte comme un matériau élastique linéaire tandis

que pour les peaux composites, un modèle d’endommagement progressif pour les composites

tissés est utilisé pour prédire le comportement de la peau jusqu'à la rupture. La corrélation entre

la rigidité et la résistance obtenues à la fois par les mesures expérimentales et les prédictions

170

par éléments finis, pour les structures étudiées, indique que le modèle par éléments finis

développé est un outil d'analyse efficace pour la prédiction du comportement mécanique des

panneaux réparés.

Abstract

This paper investigates the static mechanical performance of bonded circular repairs on

sandwich panels made with carbon-epoxy composite skins and a Nomex core. First, the

mechanical behavior of pristine, open-hole and repaired sandwich panels under edgewise

compressive loading is studied. Next, pristine and repaired sandwich beams are tested under

four-point bending with the circular repair loaded in tension. Then, finite element analyses are

performed to predict the strength of the repaired sandwich panel. The adhesive film was

considered as an elastic-plastic material with a shear failure criterion. The honeycomb core is

assumed to behave as a linear elastic material while for the composite skins, a progressive

damage model for woven fabric composites is used to predict the skin behavior until rupture.

The good agreement between stiffness and strength levels obtained from both experimental

measurements and finite element predictions, for pristine, open-hole and repaired sandwich

panels, indicates that an effective analysis tool for the mechanical behavior of the repaired

panels has been set-up.

Keywords: composite sandwich structures, adhesively bonded repair, finite element analysis,

progressive damage

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7.1 Introduction

Since fiber-reinforced composite structures offer superior strength, higher stiffness, lighter

weight and greater durability [43], they are increasingly being used for primary aircraft

components traditionally made of metallic materials. However, despite their good properties,

composite airframe structures are more sensitive to impact damage which can cause

disbonding, delamination and internal crushing. Considering their extended service life and

operating conditions, the extent of damage determines whether the composite components need

to be repaired or replaced. Hence, to take full advantage of their many benefits, it is necessary

to ensure that these structures are durable, repairable, and maintainable. Since fiber-reinforced

composite sandwich structures are increasingly being used in aircraft components, it has

become necessary to develop effective repair methods that will restore the component’s

original design strength.

Several studies have been conducted on bonded scarf and stepped joint repairs of monolithic

composites laminates. Campilho et al. [17, 20, 34, 71-72] have conducted a lot of work to study

the effects of different repair parameters (scarf angle, lay-up, and adherend thickness) on the

performance of repaired laminated structures. They used three-dimensional (3D) finite element

(FE) models with cohesive damage to assess the strength of external adhesive repaired carbon-

fiber reinforced polymers (CFRP) under tensile and compressive loads [17, 20, 34]. The effect

of the shape geometry (single or double strap repair) on the strength of the structure and on the

stresses distribution in the repair joint has been particularly studied. They also developed two-

dimensional (2D) FE models for bonded repair joints [19, 20].The main conclusion was that

the repair strength increases exponentially with the decrease of scarf angle. Gunnion and

172

Herszberg [21] developed 2D and 3D linear elastic parametric finite element models to analyze

stresses distribution in the middle of the adhesive joint of CFRP scarf repaired joints under

tensile loading. This model allowed obtaining both shear and peeling stresses distribution along

the adhesive bondline. A linear geometrical analysis was performed. The investigated

parameters included the adhesive and adherend thickness, the scarf angle and the stacking

sequence. The main conclusions of their study were the low sensitivity of the adhesive stresses

on mismatched adherends lay-ups and the major reduction in peak stresses observed when an

over-laminate ply was used to cover the full length of the specimen. Harman and Wang [14]

developed an analytical technique to optimize the shape of the scarf joints between dissimilar

adherends. Their technique used a linear variation of the scarf angle that generates a

characteristic scarf profile for a given adherends modulus ratio. Both analytical and 2D and 3D

elastic FE modelling results showed a dependence on the local ply orientation for peel and

shear stresses distribution in the adhesive, for different ratios of adherends moduli.

Charalambides et al. [16] tested experimentally repaired CFRP joints using a 2°-scarf

configuration. Distinct failure modes were observed as functions of the environmental

conditions (temperature and moisture) and of the load type. They also performed a two-

dimensional numerical analysis [15] in order to simulate three different failure modes in scarf

repairs: failure in the adhesive layer, failure induced from delamination initiating at the corner

of the overlap ply and tensile failure of the composite adherends. Failure loads were compared

with previously published experimental work, and the results were found to be in good

agreement.

173

The above-mentioned studies investigated repairs of composite laminates. Several

experimental studies and finite element analyses were also carried out to study the behavior of

repaired sandwich panels under four-point bending and compressive loads. The repair was

either extended across the width of the specimens (2D repair) [2, 47] or circular (3D repair)

[49, 50]. A series of experimental tests were conducted by Tomblin et al. [2, 51] to study the

effects of different process parameters on the quality of 2D repairs in sandwich panels. A

damage tolerance analysis of the sandwich structures was also included in their studies. As an

outcome of their work, a methodology for the repair process and the set-up of design tools for

damage tolerance analysis of sandwich structures were developed. On the other hand, Mahdi

et al. [47, 54] used 2D and quasi-3D finite element models to predict the performance of both

pristine and sandwich panels with 2D scarf repairs subjected to static and fatigue four-point

bending. Failure prediction was based on first ply failure using the Tsai-Hill criterion for the

composite skin, but failure of the adhesive was not considered. Numerical analysis results

showed a good correlation in terms of stiffness prediction of both undamaged and repaired

specimens. However, the predicted ultimate load was problematic and did not show a good

correlation with experiment. Ramantani et al. [52] studied also the performance of repaired

sandwich panels under four-point bending. They developed a 2D cohesive mixed-mode

damage model via interface elements placed along the adhesive bondline. Composite failure

was not considered. For overlap joints, they concluded that the repair strength increases as a

function of the overlap length and that the strength increases with lower scarf angles in the case

of scarf joints. The compressive behavior of sandwich panels with circular bonded repairs was

investigated by Liu et al. [49]. Both experiments and finite element analyses were conducted

174

to study the influence of repair variables such as scarf angle and cure cycle on the quality of

the repair. A progressive damage model, based on Hashin’s criterion for the composite

material, was developed and used to predict failure of the repaired sandwich panel. The

adhesive film was modeled using cohesive elements. Good correlation between experimental

and numerical results was obtained. However, it should be pointed out that since the inner

diameter of the repair was small (25 mm) compared to the sandwich panel width (100 mm),

the load was by-passed, and failure occurred in the parent and not in the adhesive bondline. A

very recent study from Zhang et al. [50] was conducted to investigate the mechanical

performance of honeycomb sandwich panels with open-hole damage and circular scarf repair

under compressive loads. A three-dimensional FE model was developed. Failure criteria based

on Hashin’s criterion with a progressive damage evolution were included for the composite

facesheets. The adhesive layer was modeled using cohesive elements and the honeycomb core

was considered as an elastic-plastic material. Good agreement was found in terms of ultimate

failure load and damage shape between the experimental and numerical results. Failure of the

repaired sandwich panel was due to adhesive delamination and patch local buckling. Another

finding of this work is that the structure strength increases with the decrease of the scarf angle

and that the optimum number of overply layers is one in order to reach the highest strength.

In the above-mentioned research works on sandwich repairs, focus was mainly on scarf-scarf

repair and failure of the adhesive film was taken into account using cohesive zone elements.

However, in practice stepped-scarf repair configurations are often used for which this

modelling technique cannot be applied. Hence, one of the aims of the present study is to account

175

for the effect of the stepped patch on the adhesive peel and shear stresses distribution and

strength prediction.

This paper presents one aspect of a larger research program on the repair of sandwich structures

[80]. Here, the behavior of co-bonded circular scarf repair of sandwich composite panels under

edgewise static compressive and four-point bending loads is studied. Both experimental tests

and finite element analyses are performed. First, the repair procedure and the experimental set-

up are detailed. Force versus strain curves are presented and a series of failure morphology are

shown to determine the failure mode and pattern. Then, the FE models developed using the

commercial software Abaqus [56] are presented. Elastic-plastic analysis model with shear

failure for the adhesive coupled with the application of a failure criterion for the composite

skins is used to predict the ultimate load of the repaired sandwich structure subjected to

compressive loading. Finally, the numerical results are compared with experimental results to

validate the developed finite element models.

7.2 Experimental Work

7.2.1 Objective and Methodology

An experimental program has been set up to study the mechanical behavior of sandwich panels

with a circular flush repair on one of the two facesheets. A flush repair patch was selected over

an external repair patch because it offers structural strength as well as an aerodynamically

smooth surface. In practice, facesheets in sandwich structures work either in tension, in

compression or in shear. In this study, only the tensile and compressive behaviors of the

repaired facesheet were considered.

176

To introduce a compressive load in the repaired facesheet, it was chosen to perform a

compressive test on the repaired sandwich panel. The test configuration allows having a clear

view of the circular repair as it is loaded in compression and digital image correlation systems

can therefore be used to measure the strains on the repaired facesheet. To load the repaired

facesheet in tension, a four-point bending test was preferred over a tensile test because it is

easier to conduct on large specimens and the specimens do not require any special preparation.

7.2.2 Specimen Preparation

The sandwich composite panels used in this work are composed of a Nomex honeycomb core

on which two out-of-autoclave four-ply plain weave (PW) carbon-epoxy skins are bonded

using a FM300-2M adhesive film. The cured composite ply thickness was approximately 0.19

mm and the film adhesive thickness was 0.25 mm. An over-expanded honeycomb core with a

19-mm thickness was used for the sandwich panels tested in compression. For the sandwich

beams tested under four-point bending load, a higher density hexagonal cell core with a 25.4

mm thickness was used to prevent core crushing from occurring. The elastic properties of the

composite material, the two Nomex honeycomb cores and the adhesive film are given in Tables

7-1, 7-2, 7-3 and 7-4, respectively. The inner facesheet, also called the tool facesheet, is a

[(+45/-45)/ (0/90)/ (-45/+45)/ (90/0)] quasi-isotropic laminate. The outer facesheet, also called

the bag facesheet, has the same lay-up as the inner one. Specimens were tested under edgewise

compressive and four-point bending loads. Pristine, open-hole damaged and repaired sandwich

panels were tested under compressive loads. The hole was created to simulate damage that

177

could have been induced, for example, by impact. For the flexure tests, two configurations were

tested: pristine and repaired panels with the circular repair loaded in tension.

The pristine panel was manufactured as follows: both skins were bonded to the Nomex core

using the FM300-2M adhesive film and co-bonded under vacuum bag in an oven. For the

repaired and open-hole panels, the repair or the hole was carried out on the tool facesheet and

no core replacement was made. The hole and inner repair diameter was 50 mm. To simulate

material removal in the repaired skin, cut-outs were done in the prepreg plies with specific

diameters, so that, when stacked together, the prepreg plies formed a circular drop-off. The two

facesheets were bonded to the core using the same adhesive film as for the pristine panel. Next,

both skins and core were co-bonded under vacuum bag in an oven. The cure cycle consisted of

a four-hour room temperature vacuum hold followed by a two-hour 121°C dwell and a two-

hour post-cure at 180 °C. Vacuum-bag only pressure was applied during the whole cure cycle.

Then, the repair patch was manufactured as follows. After cure, the step-shaped parent area

was sanded with a 120-abrasive paper to reach the desired scarf angle (3o in this study). This

was followed by a surface cleaning with acetone and immediate drying. The repair patch was

prepared using the same prepreg material and stacking sequence as the parent skin. The plies

were cut to a specific diameter and stacked together to form an overlap as shown in Figure 7-1.

Next, the adhesive film and prepreg plies were applied directly over the prepared cut-out

surface. The patch and the parent were then co-bonded under a vacuum bag in an oven

according to the manufacturer recommendations.

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Figure 7-1 Stepped-scarf repair zone cross-section (not to scale).

Table 7-1 Mechanical properties of the plain weave composite material (CYCOM 5320

T650 PW).

E1t (GPa) E2t (GPa) G12 (GPa) ν12 ρ(kg/m3)

62.7 66.9 4.87 0.047 1500

E1c (GPa) E2c (GPa) X1t (MPa) X1

c (MPa) X2t (MPa)

49.3 48.7 999.7 772.2 875.6

X2c (MPa) S (MPa) G1t (N.mm-1) G1c (N.mm-1) G2t=G2c (N.mm-1)

789.7 38 22.5a 22.5a 22.5a

a Taken from [70]

Table 7-2 Mechanical properties of the over-expanded Nomex honeycomb core (ECA-R

4.8 64).

EW (MPa)

EL (MPa)

ET (MPa)

30.3a

0.089a

185a

GWL (MPa)

GWT (MPa)

GLT (MPa)

1.9b

55.5c

21.1c

WL

WT

LT

0.26b

0.22b

0.022b

a experimentally measured

b estimated from [64]

c from manufacturer

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Table 7-3 Mechanical properties of the hexagonal Nomex honeycomb core (ECA 3.2 96)

EW (MPa)

EL(MPa)

ET (MPa)

19.2

25.6

379.2

GWL (MPa)

GWT (MPa)

GLT (MPa)

5.13

68

96

νWL

νLT

νWT

0.85

0.020

0.224

a from manufacturer. The other values are estimated based on [64]

Table 7-4 Mechanical properties of the FM300-2M adhesive [76].

E (GPa) ν τy (MPa)

2.024 0.4 30

7.2.3 Edgewise Compressive Tests

Test Procedure

For the compressive tests, square test specimens were cut with a water jet-milling machine at

a nominal size of 203 mm by 203 mm. To prevent inadmissible ends failure and premature

failure, special considerations and panel preparations were made. A section of the core material

was removed at the top and bottom of the specimen and filled with a high stiffness potting

material to reinforce the edges. This section was 13 mm high and 203 mm wide. Aluminum

tabs were bonded at both ends to ensure a smooth load transfer in the potting-Nomex core

junction. Three strain gages were bonded on the specimens to detect possible bending due to

specimen misalignment and to study the strain distribution on the skins. Gage #1 was bonded

in the middle of the bag facesheet and the other gages (#2 and #3) were bonded on the tool

facesheet, as depicted in Figure 7-2.a. The surface of the specimen was also prepared for

measurement by a 3D digital image correlation (DIC) system (Aramis by GOM [73]). The DIC

post-processing software is used for the determination of the full in-plane and out-of-plane

displacements and strain field on the specimen surface during testing. The focus was directed

toward the front of the tool facesheet for the pristine, repaired and open-hole specimens.

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As a next step, the pristine, open-hole and repaired panels were subjected to edgewise

compression loading using an electromechanical MTS testing machine with a 250 kN load cell

at a constant crosshead rate of 0.5 mm/min. Specimens were placed in a compressive test

fixture, similar to the fixture recommended by the ASTM D7137 [81] for compression after

impact, as shown in Figure 7-2.b. These tests were performed in order to compare the

mechanical performance of repaired panels versus pristine and open-hole damaged panels.

Table 7-5 summarizes the test matrix conducted for each configuration. The stress in the skin

was evaluated according to

2 f

Ft W

(42)

where F is the force recorded during the test, tf is the skin thickness and W is the width of the

specimen.

Test Results

The stiffness and strength obtained for the static compressive tests performed at ambient

temperature on the pristine, open-hole and repaired coupons are listed in Table 7-6. As can be

seen from the table, sandwich panels with open-hole have the lowest compressive strength due

to the high stress concentration around the edges of the hole and the strength recovery was only

about 45%. However, higher strength recovery was obtained after repair. Compared to the

pristine sandwich panels, the strength recovery of repaired panels reaches about 85 %. This

high strength recovery indicates that the repair process conducted on the sandwich panel can

restore efficiently its mechanical performance.

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Table 7-5 Test matrix.

Skin material Pristine

Specimens

Open-hole Specimens Repaired

Specimens

Plain Weave (PW) 4 2 3

Figure 7-2 Compressive test fixture and strain gages location.

7.2.4 Four-Point Bend tests

Test Procedure

Long-beam flexure tests were performed on the pristine and 3°-repaired sandwich beams in

accordance with the ASTM standard D7249 [83] standard. The test fixture and the specimen

dimensions were carefully selected to ensure that failure occurs in the composite facesheets

and to prevent core shear failure. As shown in Figure 7-3, the load span (L) and the support

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span (S) were taken equal to 153 mm and 660.4 mm respectively. The pristine sandwich beams

were 76.2 by 686 mm2 and the repaired sandwich beams were 203 mm wide and 686 mm long.

Specimens were tested, at room temperature conditions, using an electromechanical MTS test

frame with a 100 kN load cell. A crosshead rate of 8 mm/min was used for these tests. Strains

gages and a digital image correlation (DIC) system [73] were used to measure the strains on

the specimens. Here, the repaired facesheet was loaded under tension.

The stress developed in the facesheets was calculated according to ASTM standard D7249

standard using:

( - )

2( )c f

P S Ld t Wt

(43)

where F is the force applied during the test, tc is the core thickness, d is the measured total

thickness of the sandwich panel, W is the width of the specimen and tf is the facesheet thickness.

Test Results

Figure 7-4 and Figure 7-5 show the flexure stress-strain responses for the pristine and repaired

sandwich beams with the repair loaded in tension. It can be observed from the figures that the

flexure response is linear until failure occurs suddenly. Moreover, all the observed failure

modes for the pristine and repaired beams were fiber fracture, away from the load points, on

the side loaded in compression, as shown in Figure 7-6. Therefore, failure occurred in the

middle of the pristine bag facesheet, loaded in compression, and not in the repaired facesheet.

This failure mode shows the efficiency and the high strength recovery of sandwich panels with

circular repair loaded in tension.

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Figure 7-7 recapitulates the flexure failure stress for the pristine and repaired panels. It can be

observed that when the repair is loaded in tension, a higher strength recovery was obtained,

around 95% of the pristine value.

Table 7-6 Test results for different sandwich panels configuration.

Specimen

configuration

Specimen

number

Scarf

angle (°)

Stiffness

(GPa)

Failure stress

(MPa)

Strength

recoverya (%)

Pristine 4 - 40.03 374.40 100

Open-hole 2 - 36.88 169.66 45.31

Repaired 3 3° 41.91 318.47 85.06

a Strength recovery (%)= 𝜎𝑓

𝜎𝑝𝑟𝑖𝑠𝑡𝑖𝑛𝑒𝑓 × 100

Figure 7-3 Specimens configuration and four-point bending test fixture.

184

Figure 7-4 Stress-strain curves for the pristine sandwich beams.

Figure 7-5 Stress-strain curves for the 3° repaired sandwich beams.

185

Figure 7-6 Failure morphology of the pristine and the 3°-repaired sandwich beams under

four-point bending.

Figure 7-7 Failure stress of the pristine and 3° repaired panels under four-point bending.

7.3 Numerical Simulation

7.3.1 Finite Element Model Description

The finite element software Abaqus/Explicit was used to predict the response of the repaired

sandwich panels under edgewise compressive loading. The behavior of the repaired sandwich

beam under four-point bending was not modelled since the repair did not fail for this test. Three

different configurations were studied just like the experimental tests, i.e., pristine, open-hole

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and repaired panels. Each FE model involves three components: the tool facesheet, the Nomex

core and the bag facesheet. As, the specimen for all tested configurations is symmetric, only a

quarter of the panel was modeled. So, the panel quarter dimensions were 102 mm long, 102

mm wide and 20.52 mm thick. For both repair and open-hole specimens, the repair and open-

hole zones have finer meshes. The adhesive film along the bondline was discretized through

the thickness using four continuum solid elements (C3D8R and C3D6R). Each single woven

ply was discretized through the thickness using one thick continuum shell element (SC8R).

The Nomex honeycomb core was also discretized through the thickness using at most five

continuum solid elements (C3D8R) as shown in Figure 7-8.

For the repaired panel, a refined mesh was used for the patch and adhesive edges where strain

gradients occur (Figure 7-9). To ensure mesh matching, the parent, the patch, the adhesive and

the core were discretized with the same in-plane mesh density. A mesh convergence study was

conducted to verify the accuracy of the finite element models. Here, the total elastic strain

energy was used as indicator (ALLSE in Abaqus [56]). Considering the complexity of the FE

model, the zones that have the highest percentage of strain energy were identified and then

were progressively refined.

Bonding between the composite facesheets and the Nomex core was assumed perfect and a tie

constraint was applied at the core/facesheet interface. Also, the contact between the adhesive

film and the core was considered perfect and a tie constraint was applied. The facesheets had

the same lay-up as in the experiments [(+45/-45)/ (0/90)/ (-45/+45)/ (90/0)] and each single ply

had a thickness of 0.19 mm. The Nomex honeycomb core had a thickness of 19 mm. The

mechanical properties of the composite materials used for the sandwich panels are summarized

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in Table 7-1. The mechanical properties of the adhesive film are indicated in Erreur ! Source

du renvoi introuvable. and the elastic properties of the Nomex honeycomb core are listed in

Table 7-2.

For the current finite element analysis, the honeycomb core is assumed to behave as an

orthotropic linear elastic material. The adhesive film behavior is described using an isotropic

elastic plastic model and a shear failure criterion is used to predict the adhesive failure. The

composite material is modeled as an orthotropic elastic material with progressive stiffness

degradation and plastic deformation under shear loading. Delamination was not taken into

account.

The boundary conditions are defined as indicated in Figure 7-10. On the bottom edge,

symmetry conditions along the y-axis were imposed, on the free top edge, a compressive

displacement, as measured from the experiment, was applied. The out-of-plane displacements

were constrained on the right edge side blocked by the fixture along the in-plane direction of

the model and symmetric conditions along the x-axis were applied.

Figure 7-8 Mesh details of the honeycomb sandwich panels.

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Figure 7-9 Mesh refinement details of the 3°-repaired panel

Figure 7-10 Boundary conditions applied in the finite element model.

7.3.2 Failure Criteria and Damage Evolution

Composite Material

Progressive damage of the woven fabric composite skins of the sandwich panels was modelled

in the Abaqus/Explicit environment [56]. The continuum damage mechanics model is based

on the built-in user’s material subroutine called ABQ-PLY_FABRIC, proposed by Johnson et

al [69], for 2D woven fabric composites. The quasi-isotropic laminate is modeled by stacking

Parent

Adhesive

Patch

Patch mesh details

through thickness

Ply 4

Ply 3

Ply 2

Ply 1

Ply 1

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layers of continuum shell elements with reduced integration (SC8R) through the thickness. The

laminate is composed of four plies each displaying an orthotropic behavior with progressive

damage. The behavior of a damaged ply is described by the following stress-strain relation in

the local material coordinate system (1, 2):

12

1 1 111 11

2122 22

2 2 2

12 12

12 12

1 0(1 d )

1 0(1 d )

10 0(1 d )

E E

E E

G

(44)

where E1, E2 are the initial undamaged elastic moduli respectively in the warp and weft

directions of the woven fabric, ν12 is the in-plane Poisson’s ratio and G12 is the undamaged in-

plane shear modulus. The damage variables d1, d2 and d12 are associated with the warp- and

weft-directions and the in-plane shear failure, respectively.

For woven fabric composite materials, it is assumed that there are two main failure mechanisms

[69]:

- Fiber-dominated failure in tension or compression in the two fiber directions,

- Matrix failure in in-plane shear.

In order to take into account both tension and compression stiffness in the model, the elastic

values E1, E2 are assumed to take their compressive or tensile values depending on the sign of

tr(ε)=ε11+ε22. The built-in subroutine offers two different options to delete elements from the

model:

190

- The element is deleted when d1=dmax or d2=dmax under compressive or tensile load, or

when the plastic strain due to shear deformation reaches the maximum value, 𝜀𝑝𝑙 =

𝜀𝑚𝑎𝑥𝑝𝑙

- The element is deleted when d1=d2=dmax along both fiber directions, or when the plastic

strain due to shear deformation reaches the maximum value, 𝜀𝑝𝑙 = 𝜀𝑚𝑎𝑥𝑝𝑙

In this study, the first option to delete elements was used. To reduce the time required to

complete the simulation of the quasi-static compressive test using Abaqus/Explicit, the mass

scaling technique was used, following guidelines described in Abaqus user’s manual [56]. To

ensure that there is no influence of the artificial mass added to the system on its global physical

response, the injected kinetic energy of the whole model was verified, and it was less than 5%

of the internal energy of the whole system. So, mass scaling has no major effect in the obtained

results.

Adhesive Film Material

The adhesive film was not modeled using cohesive elements as it was the case in previous

studies from the literature [49, 50, 52]. Cohesive zone model are based on several parameters

that are difficult to measure and that are often estimated by trial and error. Instead, 3D solid

elements were used to discretize the adhesive. These elements used in conjunction with an

elastic-plastic material model and the von Mises yield criterion allow to predict the elastic-

plastic behavior of the adhesive [76]. The material mechanical properties required for the model

were determined experimentally. A shear failure criterion was also associated with the von

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Mises yield criterion to predict the adhesive failure. This criterion is based on the value of the

equivalent plastic strain at element integration points. Failure is assumed to occur when the

damage parameter w exceeds one. This damage parameter is defined as:

pl

pl

f

w

(45)

where 𝜀 ̅𝑝𝑙 is the equivalent plastic strain and designated as PEEQ in ABAQUS/Explicit, ∆𝜀 ̅𝑝𝑙

is the increment of PEEQ and 𝜀�̅�𝑝𝑙

is the plastic strain at failure. When the shear failure criterion

is reached at an element integration point, the material is assumed to fail at this point and the

stress components are set to zero. The element is deleted from the mesh when the material

failure is detected at all integration points.

7.3.3 Results and Discussions: Edgewise Compressive Tests

Stiffness and Strength

Figure 7-11.a to Figure 7-11.c show the compressive stress-strain curves for the pristine, the

open-hole and the 3°-repaired sandwich panels. As can be observed from these curves,

experimental and numerical results are fairly similar. This indicates that the finite element

model can accurately predict the compressive behavior of the pristine, open-hole and repaired

sandwich panels. We can also observe that for all tested specimens, the stress-strain curves are

linear until failure which occurs suddenly (when the maximum value is reached). It is worth

noting that the ultimate strain reached for the repaired panels far exceeds the design ultimate

strain requirements of the order of 5000 µε usually used in the aeronautical industry [84].

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Failure Mode and Damage Shape

The experimental fractured surfaces of pristine, open-hole and repaired sandwich panels are

shown in Figure 7-12.a to Figure 7-12.c. Figure 7-12.a shows the damage shape of the pristine

panels after compressive loading. It can be observed that damage occurs mainly at the top and

bottom ends near the support and loading zones. This may be explained by the non-uniform

loading experienced in these zones. Figure 7-12b shows the ruptured facesheet of an open-hole

specimen. Damage expands from the equators of the open-hole to the unloaded ends of the

panel. The failure mechanism was similar for all open-hole panels. This can be explained by

the high stress concentration that occurs at the equators of the open-hole. Figure 7-12.c shows

the ruptured facesheet for the 3°-repaired panels for which failure occurred mainly along the

top edge of the patch and that expanded to the unloaded parent ends. Figure 7-13.a to Figure

7-13.c show the failure morphology of the three configurations obtained from the numerical

predictions. It can be observed that the predicted damage shape is in accordance with the

experimentally observed failure morphology for each configuration. From the numerical

simulation, failure occurs according to the following scenario. For the pristine panel, rupture

occurs mainly near the loading edges, where stress concentration is present. It was found that

failure occurs in the 0°-plies in compression. Then, matrix failure occurs immediately followed

by total failure of the specimen. For the open-hole specimen, failure occurs also in the 0°-plies

and propagated to the other plies. For the 3°-repaired specimens, failure occurs first in the

adhesive bondline located under the patch, then failure propagates through the adhesive and

finally the 0°-plies located in the parent side fail in compression. Finally, failure occurs

simultaneously in the other plies which leads to the global failure of the specimen.

193

a. Pristine panels.

b. Open-hole panels.

c. 3°-repaired panels.

Figure 7-11 Finite element prediction versus experiment results for composite sandwich

panels

194

Figure 7-12 Failure mode for the tested composite sandwich panels.

Figure 7-13 Predicted failure morphology for the three panel configurations.

195

7.4 Conclusion

This study investigated bonded repairs in composite sandwich panels made with honeycomb

core and out-of-autoclave woven prepreg carbon-epoxy skins. Experimental tests were carried

out to investigate the compressive behavior of pristine, damaged and repaired sandwich panels.

Flexure tests were also conducted to study the behavior of the repaired skin loaded in tension.

Experimental results indicate that the repair configuration can recover up to 85% of the static

mechanical strength of the pristine panels for a 3°-stepped-scarf patch under compressive loads

and can recover up to 95% of the pristine value under flexure loads with the repair loaded in

tension. These results show the high ability of the circular repair to restitute the pristine strength

value. Also, it has been observed that the circular repair loaded in tension is stronger than when

it is loaded in compression.

3D finite element analysis models were proposed in the paper to predict the behavior of pristine,

damaged and repaired sandwich panels under compressive loads. Good agreement between

stiffness and strength predictions and experimental results confirmed that the developed

numerical model provides an effective analysis tool for the mechanical behavior prediction of

repaired composite sandwich panels.

This study investigated the mechanical behavior of bonded repairs in composite sandwich

panels under room temperature conditions. However, bonded repairs are exposed to different

environmental conditions (cold, hot/wet conditions) during their service life which will affect

their long-term performance. The effects of environmental conditions on the mechanical

196

behavior of bonded repairs must be accounted for in the design and will be investigated in a

follow-up study.

Acknowledgements

We would like to thank the Natural Sciences and Engineering Research Council of Canada

(NSERC), the Consortium for Research and Innovation in Aerospace in Quebec (CRIAQ), the

National Research Council Canada (NRC), Bombardier Aerospace and L3-MAS for funding,

technical support and materials.

197

Chapter 8.

Conclusions and Perspectives

8.1 Thesis Conclusions

The general objective of this study was to propose a reliable bonded repair methodology for

primary sandwich honeycomb structures for aerospace applications, and particularly through

the development of numerical tools and protocols for the design of sandwich composite bonded

repairs. For that purpose, a series of experimental investigations and numerical simulations of

repaired bonded honeycomb sandwich panels were conducted. The following approaches were

taken to address the problem:

Assessment of the mechanical behavior of honeycomb sandwich panels with

bonded repairs by experimental testing.

Development of finite element models for better understanding and accurately

predicting the mechanical behavior and the failure modes of the repaired

sandwich panels under different loadings.

Validation of the finite element models and conduction of a parametric study.

This report has presented an experimental and numerical investigations of the mechanical

performance of stepped-scarf repairs in composite honeycomb sandwich panels under different

loading: tension, compression and four-point bending. The finite element models have been

conducted for predicting the strength and failure mode of repaired composite sandwich panels

198

with two repair configurations: 2D repair and 3D repair. These models have been

complemented by experimental studies which provided data for model validation. The

experimental study revealed that the repaired sandwich panel with the repair facesheet loaded

in tension is stiffer than the repaired sandwich panels with the repair loaded in compression.

The finite element model generally agreed well with the failure stress and mode observed in

the experiments for these different configurations.

In chapter 1, a state of the art literature review allowed to point out the need and the importance

of developing a novel methodology for bonded repair of woven composite sandwich primary

aircraft structures. In particular, the following issues were highlighted:

The use of out-of-autoclave woven fabric materials are scarcely discussed in the

literature.

The modelling of a real repair geometry; stepped-scarf configuration by the finite

element method and the study of the effect for different geometric design parameters in

the repair strength were seen to require further studies in order to develop a reliable

analytical tool for current and future bonded repairs of advanced composite aircraft

structures.

Chapter 2 presented the thesis objectives and the methodology used to achieve them.

Chapter 3 presented the experimental work performed to determine the mechanical properties

of the sandwich materials constituents, namely the composite facesheets and the core. First, the

tensile and compressive tests allowed to determine the in-plane properties of the composite

materials. It was observed that the two PW and 8HS composite materials had similar

199

mechanical behavior under tension and compression. Also, the elastic in-plane tensile and

through-thickness compressive moduli of the Nomex core were determined. From the test

results, it was observed that the over-expanded core was stiffer in the W-direction. The

mechanical behavior of the core under failure needs however further investigation. Then, 2D

and 3D finite element models were developed and validated by comparing the predicted

mechanical behavior of a quasi-isotropic laminate with results from experiments and classical

lamination theory. The finite element predictions showed a good agreement with both CLT and

experiments in terms of stiffness when the CPEGI elements from Abaqus library were used.

The 3D model takes into account the progressive damage failure of woven fabric facesheets

and showed a good correlation in terms of the failure stress. Further improvement could be

achieved by developing more elaborated models taking into account the experimental

variability.

In Chapter 4, results on the experimental and numerical investigations conducted on the 2D

repaired sandwich panels under tensile loading were presented. The effect of varying the scarf

angles (3°, 5°, 7°) was studied and it was shown that for a rectangular repair patch across the

plate specimen, a 2D plane strain FE model can predict reasonably well the mechanical

behavior of the repaired structure until failure. The main achievement of this work was that

with the use of an elastic-plastic behavior of the adhesive film with a shear failure criterion, we

could accurately predict the failure stress and mode of the tested specimens. Also, from both

numerical simulations and experiments, it was observed that there is no major effect of the

scarf angle on the strength recovery, for angles from 3° to 7°. Further investigations should be

considered to determine the effect of the scarf angle under various environmental conditions.

200

In Chapter 5, a parametric study on the strength recovery of 2D repaired panels was conducted.

The effect of different geometric parameters (scarf angle, number of plies and skin thickness)

on the strength recovery of the repaired panels was studied under tensile loads and it was found

that the addition of one (+45/-45) overply improved the strength of the repair by 40% in

comparison with the case when no overply was used. Another finding from this work was the

important effect of the skin thickness on the strength recovery. Thick skin sandwich panels

(eight-ply skin panel) showed a much higher strength recovery in comparison with thin one

(two-ply skin panel). The failure was no more in the adhesive but in the composite part of the

structure.

In Chapter 6, the experimental and numerical investigations performed on 2D repaired panels

were extended to study their behavior under edgewise compression and their behavior using a

four-point bending load configuration. Here, a comparison between four-point bend, and

edgewise compressive tests was presented. Four-point bend tests require longer specimen but

are easier to perform than compressive tests to determine the mechanical behavior of the

sandwich panel for a repair loaded in compression.

In Chapter 7, circular repaired sandwich panels were studied experimentally and numerically.

First, the behavior of repaired specimens under compressive load was determined

experimentally. The behavior of the circular repair under tension was then determined by

conducting a four-point bending test with the repair on the bottom beam surface. Results show

that 85% of the strength was recovered when the repair is loaded in compression and about

90% was recovered when the repair is loaded in tension. These results show the ability of the

developed repair technique to restore a high level of the pristine strength. Then, the

201

development and implementation of a 3D finite element model with a progressive damage and

failure model for the woven fabric composite was carried out to predict the stiffness and failure

mode of the repaired sandwich panels under compression. The finite element predictions were

in good agreement with the experimental results, which confirms that the developed finite

element model may be used as an alternative tool to study the mechanical behavior of repaired

sandwich structures.

8.2 Thesis Original Contributions

This project achieved its primary objectives of:

Assessing the mechanical behavior of repaired composite sandwich panels under

different loads: tension, compression and four-point bending.

Proposing a finite element model for repaired composite sandwich panels that can

reliably produce good estimates of the failure strength and mode for different repair

configurations (rectangular and circular repairs) and under different loads (tension,

compression and four-point bending) while considering all the major design parameters

of repaired composite sandwich panels.

This study presents a comprehensive investigation on methods of characterization of out-of-

autoclave stepped-scarf repaired composite sandwich panels. The development of finite

element modelling technics and experimental methods for characterization and validation of

the mechanical performance of repaired panels were presented through extensive review of

reported studies on both repaired monolithic and sandwich composites structures. The review

covered different static characterization methodologies, analytical formulations and finite

202

element modelling technics. Also, the effect of various geometrical design parameters on the

strength recovery of the repaired structure addressed in earlier studies were thoroughly

discussed. The major contributions of the research work are summarized as follows:

A FE model describing and predicting the mechanical behavior of the stepped-scarf

repair on sandwich honeycomb panels with different configurations under different load

cases (compression, tension, four-point bending) was developed.

The finite element models provide a simple tool and a good alternative to predict the

mechanical behavior of the stepped-scarf repaired sandwich panels under different load cases.

Overall, the FE calculations successfully predicted the failure strength and mode of the repaired

sandwich panels. The stepped-scarf repair patch, like the one performed experimentally, was

studied and a better understanding of the adhesive joint’s behavior is provided. The determination

of the stress distribution along the adhesive bondline helped to understand the failure mode that

occurs. Good agreement between stiffness and strength predictions and experimental results

confirmed that the developed numerical model provides an effective analysis tool for the

mechanical behavior prediction of repaired composite sandwich panels. These models have been

developed based on the physical parameters of the adhesive film.

A better understanding of the geometrical design parameters effects on the mechanical

performance of the sandwich repaired panels

A guideline for the design of stepped-scarf repair was conducted with a parametric

study using the developed FE model and allows to study the effect of different geometric

parameters on the strength recovery of the repaired sandwich structure. This guideline may

give instructions and better understanding for the choice of the scarf angle, the number of

overply depending on the sandwich structure to be repaired. An interesting finding here is the

203

influence of the skin thickness on the repair strength recovery. Thin skin sandwich panels are

very sensitive to the repair and small scarf angle should be used. The addition of an overply is

primordial for thin skins. From the parametric study, the use of an overply shows a higher

strength recovery and a change in the failure mode of the repaired panels. This result was

validated by experiments.

A determination of a database of mechanical properties for out-of-autoclave (OOA)

composites materials for repairing primary aerospace honeycomb sandwich structures

A comprehensive review of reported studies on experimental methods for the

characterization and determination of the mechanical performance of repaired sandwich panels

were conducted. An experimental characterization program was developed to identify the

performance of the repaired panels under different load cases (compression, tension, four-point

bend). Furthermore, the complexities associated with the experimental characterization and

disagreements between experimental results from the different tests were addressed. To

demonstrate the validity of the different results, a comparison was made in terms of the

stiffness, failure stress and mode. Considering this, a first database of the mechanical

performance of repaired sandwich panels was developed on the basis of the different

mechanical tests results and compared to the predicted calculation from the finite element

models. At our best knowledge, this is a first database about these new out-of-autoclave

composite materials (PW and 8HS), as a candidate for repairing honeycomb sandwich primary

structures, to be completed at room temperature conditions. These materials are expected to be

increasingly used in the aerospace applications and had not been used yet for repairs of

composite primary structures.

204

8.3 Recommendations for Future Work

From the above indicated conclusions and contributions, one then deduces that the following

issues need further investigations. In short terms, in order to complete the work presented here,

the following works should be accomplished:

The parent structures and repairs were cured out-of-autoclave in an oven. More

investigations of the mechanical behavior of co-bonded repaired composite sandwich

panels using a hot-bonder or heat blanket need to be assessed and compared with the

mechanical performance for a co-bond cured in oven.

The mechanical performance was conducted under static loads. So, it is important to

understand the behavior of the repaired composite sandwich panels under dynamic

loads.

Aerospace structures are very sensitive to impact damage. Hence, a sensitivity study

of the repaired patch to impact damage should be undertaken in the short and long-term

range.

The compression-after-impact (CAI) should be used to assess the performance of

impacted repaired composite sandwich panels using both numerical and experimental

methods.

As a long-term work, it would be interesting to eventually assess eventually the developed

methodology as a potential candidate for field repair technology of advanced woven composite,

by further investigating the following issues:

205

The rectangular and circular repaired sandwich panels have been tested at room

temperature conditions. Environmental conditions have not been included in this work.

As the mechanical properties of the adhesive film are very affected by temperature and

humidity, tests under different environmental conditions (cold, hot and humid) should

be conducted to determine the performance of the repaired panels under in service

conditions.

Fatigue and ageing of bonded repair structures are still an open issue and should be

considered for further investigations.

As the repaired panels are co-bonded using a heat blanket or hot bonder in practice,

measurement and identification of thermal residual stresses may be an important point

to be considered.

A modification of the developed finite element model to consider the thermal residual

stresses may be necessary to estimate the residual stress effect in the repair mechanical

performance.

206

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Appendix A.

Mechanical performance of the 8HS honeycomb

sandwich panels

With the increasing use of composite materials in aerospace primary structures, the need for

reliable repair methods is growing in the aeronautical industry. In this research work, an

investigation of OOA prepregs as potential candidates to produce stepped-scarf bonded repairs

on sandwich honeycomb panels, with only vacuum bag pressure, was conducted. The main

objective was to better understand the mechanical performance of the repaired sandwich panels

in function of skin material morphology (architecture), geometric design parameters and

applied load cases. This appendix is dedicated to the presentation of performed experimental

tests in order to determine the mechanical performance of repaired sandwich panels with

different prepreg composite skin material for the case of eight harness satin material (8HS).

A.1 Tensile Tests on Pristine and Repaired 8HS Honeycomb

Sandwich Panels

The 8HS honeycomb sandwich specimens were tested in tension, at room temperature

conditions, as for the PW panels. Two main groups of specimens were prepared to determine

the tensile properties of the panels. Namely, three 2D repaired coupons with 3° scarf angle and

three pristine panels for the strength recovery comparison.

213

Specimens Dimensions and Test Set-up

The pristine and the repaired 8HS sandwich panels considered in the experimental studies were

335 mm long, 102 mm wide and 22.04 mm thick. Tensile tests were performed using the same

set-up and the same displacement rate of 2 mm/min as for the PW panels. Here, both the DIC

system and the video extensometer were also used to measure the deformation of the panels,

as shown in Figure A-1.

The repaired panels had also a double step-scarf joint. The repair was carried out on the tool

facesheet. The sandwich panels were composed of an over-expanded Nomex honeycomb core

with a 19-mm thickness on which two four-ply carbons-epoxy skins were bonded. The skin

was made with an out-of-autoclave plain weave prepreg (CYCOM 5320 T650 8HS from Cytec

Engineering Materials) with a 0.38 mm thickness. The ply stacking sequence for the tool

facesheet is a [(+45/-45)/ (0/90)/ (-45/+45)/ (90/0)]. The bag facesheet has the same lay-up as

the inner one. The patch repair has also the same lay-up as the parent structure. The skin 0°-

direction is aligned with the x-direction. The ribbon direction of the Nomex core is

perpendicular to the x-direction. The repair patch is bonded to the parent structure by the same

adhesive film (FM 300-2M from Cytec) with a 0.25 mm thickness, placed along the scarf and

under the patch.

214

Figure A-1. Tensile test set-up for 8HS sandwich panels

Test Results for the Pristine 8HS Honeycomb Sandwich Panels

The results of the static tensile tests performed at ambient temperature on the pristine sandwich

panels, are presented in Figures A-2 and A-3. Figure 2 presents the load versus strain measured

on the tool facesheet using the DIC system for the pristine panels. It can be observed from these

figures that the load-strain behavior is mostly linear until failure for both pristine panels. Figure

A-3 presents the load-strain curves measured on both the tool and the bag facesheets for one

pristine specimen. The uniform load distribution in both facesheets can be assessed by the

similarity in strains measured by both the DIC system and the video extensometer.

Test Results for the 2D Repaired 8HS Honeycomb Sandwich Panels

Here, only 3°-repaired 8HS panels were tested under tensile loads, at room temperature

conditions. Figure A-4 presents the load-strain curves measured on the tool face sheet with the

215

DIC system for the 3°-repaired specimens. It can be observed, as for the pristine panels, that

the behavior of the tested repaired panels is linear until the occurrence of the brittle failure.

Figure A-2. Load-strain curves of the tensile tests of the pristine 8HS sandwich specimen

Figure A-3. Comparison of the axial load-strain curves obtained on both facesheets of the

8HS pristine sandwich specimen.

216

Figure A-5 presents the load-strain curves measured on both the tool (repaired) and the bag

facesheets for one 3°-repaired specimen. The uniform load distribution in both facesheets can

be assessed by the similarity in strains measured by both the DIC system and the video

extensometer. For the 3°-repaired panels, failure occurred mainly in one of the two scarf zones.

This failure is similar to the 3°-repaired PW panels failure.

Figure A-4. Axial load-strain curves obtained for the 3°-repaired 8HS sandwich specimens

(strains measured by DIC on the tool facesheet (repaired facesheet)).

217

Figure A-5. Comparison of the axial load-strain curves obtained on both facesheets of the 3°

repaired 8HS sandwich specimen.

Strength Recovery of the 3°-Repaired Sandwich Panels

The test results for the pristine and for the 3°-repaired 8HS specimens are summarized in Table

A-1. Figure A-6 compares the experimental failure strength (σf) obtained for the 3°-repaired

panels with that measured for the pristine panel. As it can be observed from this figure, the

failure strength is about 60.20 % of the pristine value. The strength recovery for this sandwich

repair configuration is quite low. However, it is quite higher than the value obtained for the

PW repaired panels (55 %). Using an over-ply could be beneficial to improve the strength of

the repaired 8HS sandwich panel as for the PW repaired sandwich panel.

Table A-1. Tensile results for 8HS sandwich panels

Configuration Angle

(°)

Elastic modulus

(GPa)

Failure strength

(MPa)

Strength recovery

(%)

8HS-Pristine - 45.90 488 -

8HS-Repair 3 46.48 293.42 60.12

218

Figure A-6. Tensile failure stress of the pristine and 3°-repaired sandwich specimens.

A.2 Compressive Tests on 8HS Honeycomb Sandwich Panels

As a next step, static edgewise compressive tests were performed in order to compare the

compressive performance of the repaired panels with that of the pristine panels. As for PW

materials, two sets of sandwich panels were considered: one with three 8HS pristine specimens

and the other with three 8HS repaired specimens. Special considerations and panel preparation

were made as for the PW panels. Strain gauges and DIC system were also used to measure the

strain of both the tool and the bag facesheets of the specimens, as illustrated in Figure A-7. As

for PW material, two repair configurations were tested: the 2D rectangular shape repair and the

3D circular patch repair.

219

Compressive Tests on Pristine and 2D Repaired Honeycomb Panels

A.2.1.1 Compressive Tests on the Pristine 8HS Honeycomb Sandwich Panels

The 8HS pristine specimens were tested to failure under compressive loading, at room

temperature conditions. Specimens were cut, in a rectangular shape, by water jet at a nominal

size of 305 mm by 102 mm. The compressive test results are presented in Figures A-8 and A-

9. The load-strain curves for the pristine panels are shown in Figure A-8. It can be observed

from this figure that the load-strain curve is mostly linear until a sudden failure of the panel.

Different measurements of the load versus strain, obtained with various instruments, are shown

in Figure A-9. The uniform load distribution in both facesheets can be assessed by the similarity

in strains measured by different instruments (strain gages and DIC), as for the tensile

specimens. It should be noted also that all the failure zones were located away from the loaded

ends.

Figure A-7. Strain gages locations on the tested specimens

220

Figure A-8. Force versus strain curves of pristine panels

Figure A-9. Force versus strain curves measured by different instruments on both facesheets

of the pristine sandwich panel

221

A.2.1.2 Compressive Tests on the 2D Repaired 8HS Honeycomb Sandwich Panels

The compressive test results are presented in Figures A-10 and A-11. The load versus strain

curves obtained for the 3°-repaired panels are shown in Figure A-10. It can be seen from the

figure that the load-strain curve is mostly linear until the occurrence of a sudden failure, as for

the pristine panel. A good repeatability was also observed for the test. The difference in the

load carried by the pristine and the repaired facesheets can be seen by the difference in strain

measured by gage 1 and DIC versus that measured by gage 2, as illustrated in Figure A-11. The

failure mechanisms were similar for all the repaired specimens. Local buckling in the scarf area

was observed, as it was the case for the PW repaired sandwich panel.

Figure A-10. Force versus strain curves of 3°-repaired panels

222

Figure A-11. Force versus strain curves measured by different instruments on both facesheets

of the 3° repaired sandwich panel

A.2.1.3 Recapitulation and Strength Recovery of the 8HS Repaired Sandwich

Panels

Three scarf angles were tested here: 3°, 5° and 7°. Table A-2 summarizes the results of the

tested specimens and the strength recovery for each scarf angle. It can be observed that the

strength recovery increases as the scarf angle increases. From the DIC measurement, local

buckling of the repaired facesheet was observed for the 3°, 5° and 7° repaired specimens, as

can be seen in Figure A-12. This failure mode may explain the fact that the strength recovery

increases with the increase of the scarf angle. Similar results were also observed for the PW

material panels. Figure A-13 compares the experimental failure strength (σf) for different scarf

angles for both PW and 8HS materials with the pristine panels. As can be observed, the failure

stress of the 3°-repaired PW panel is lower than the 3°-repaired 8HS panel. However, the

223

strength of the 5°-and 7°-repair panels increases at a slower rate than for the PW repaired

panels.

Table A-2. Compressive results for 8HS sandwich panels

Configuration Angle

(°)

Elastic modulus

(GPa)

Failure strength

(MPa)

Strength recovery

(%)

8HS-Pristine - 40.46 376.01 -

8HS-Repair

3 36.78 232.25 61.76

5 36.18 233.41 62.07

7 37.16 245.39 65.26

Figure A-12. Typical failure mode of 3°-, 5°- and 7°-repaired 8HS sandwich panels under

edgewise compressive load

224

Figure A-13. Comparison of the compressive strength for PW and 8HS sandwich panels

under edgewise compressive load

Compressive Tests on 3D Repaired and Open-Hole 8HS Honeycomb

Panels

Two different configurations were tested under edgewise compressive loads: two open-hole

panels and two 3-repaired panels. For the open-hole panel, a hole diameter of 50 mm was used.

Specimens were cut, by water jet at a nominal size of 203 mm by 203 mm. The repair was

carried out on the tool facesheet. The patch repair is a four-ply carbon-epoxy laminated

composite. The skin is made with an out-of-autoclave plain weave prepreg (CYCOM 5320

T650 8HS from Cytec Engineering Materials) with a 0.38 mm thickness. The ply stacking

sequence for the tool facesheet is [(+45/-45)/ (0/90)/ (-45/+45)/ (90/0)]. The bag facesheet has

the same lay-up as the inner face.

225

The compressive test results for both the repaired and the open-hole specimens, are presented

in Figures A-14 and A-15, respectively. It can be observed from these figures that the load-

strain curves are mostly linear until sudden failure for both configurations. Figures A-16.a and

A-16.b show the ruptured facesheet of an open-hole and a repaired specimen, respectively. For

the open-hole panel, damage expands from the equators of the open-hole to the unloaded ends

of the panel. The failure mechanism was similar for all the two tested panels. This can be

explained by the high stress concentration that occurs at the equators of the open-hole. Figure

16.b shows the ruptured facesheet for the 3°-repaired panels for which failure occurred mainly

along the top edge of the patch and that expands to the unload parents ends.

The results of the static compressive tests performed, at ambient temperature, on the pristine,

on the open-hole and on the repaired specimens are listed in Table A-3. As can be seen, 8HS

sandwich panels with open-hole have the lowest compressive failure strength due to the high

stress concentration around the edges of the hole and the recovery was only about 43%. Higher

failure strength was obtained for the repaired specimens. Compared to the pristine sandwich

panels, the strength recovery of the repaired panels reaches about 82 %. This higher strength

recovery indicates that the repair process conducted can restore efficiently the mechanical

performance of the damaged panels. These results are in accordance with results obtained for

the PW panels. One then can conclude that the circular patch is more efficient than the

rectangular patch. The failure mode was also different, and no buckling was observed for the

circular patch as for the 2D rectangular patch.

226

Table A-3. Compressive results of the studied configurations.

Configuration Angle

(°)

Elastic modulus

(GPa)

Failure strength

(MPa)

Strength recovery

(%)

Pristine - 40.46 376.01 100

Open-hole - 38.45 161.16 42.86

Repaired 3° 39.86 306.04 81.39

Figure A-14. Force versus strain curves of 3-circular 8HS repaired panels

Figure A-15. Force versus strain curves for 8HS open-hole honeycomb panels

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Figure A-16. Failure modes for specimens tested in compression: a. Open-hole panel,

b. 3°-repaired panel

A.3 Flexure Tests on Pristine and 2D Repaired 8HS Honeycomb

Sandwich Panels

Long-Beam Flexure Tests

Long-beam flexure tests were conducted to the 8HS pristine and repaired specimens in

accordance with the ASTM standard D7249. Specimens were tested, at room temperature

conditions, using an electromechanical MTS test frame with a100 kN load cell. A crosshead

rate of 8 mm/min was used for these tests. Strain gages, bonded in the middle of the bag and

tool facesheets, were used to measure the strain on the specimens and a fixture system as the

one used in the standard was machined, as illustrated in Figure A-17. The support span (S) and

the load span (L) were taken equal to 153 mm and 1067 mm respectively, in order to ensure

that failure occurs in the composite facesheets and to prevent core shear failure. Two main

groups of specimens were prepared to determine the flexure properties of the 8HS sandwich

beams. Namely, three pristine specimens and six 2D repaired specimens made with 5320-8HS

composite facesheets bonded with the FM300-2M adhesive film to a hexagonal Nomex

a. b.

228

honeycomb core, with a density of 96 kg/m3. The patch repair was a rectangular patch and the

studied scarf angle was 3°. Table 4 summarizes the test matrix employed for each

configuration. The failure stress was calculated using:

( )

2( )

f

f

F S L

d c Wt

(1)

where: F is the maximum recorded force during the test, c is the core thickness, d is the

measured total thickness of the sandwich panel, W is the width of the specimen and tf is the

facesheet thickness.

Figure A-17. Four-point bending fixture system

Table A-4. Test matrix for pristine and repaired specimens

Pristine specimens

3°-Repaired specimens

Repaired face in tension Repaired face in

compression

Number of

specimens 3 3 3

Dimensions (mm2) 76.2 x 1117.6 76.2 x 1117.6 76.2 x 1117.6

L

S

229

Tests Results and Interpretation

Figures A-18 to A-20 show the flexure stress-strain responses for the pristine and repaired

specimens when the repair tool facesheet is loaded in compression and in tension, respectively.

It can be seen from Figures A-18 to A-20 that the flexure response is linear until the failure

suddenly occurs. Moreover, all the observed failure modes of the tensile specimens were fiber

fracture, away from the load spans, as shown in Figures A-21 and A-22. Compressive skin

failure was observed for the pristine panel. For the repaired specimen with the repair tool loaded

in compression, the failure occurs along the scarf and the patch was entirely detached from the

panel, as illustrated in Figure A-22.a. For the repaired specimen with the repair tool loaded in

tension, the failure occurs in the parent side not too far from the scarf joint and then propagated

through the core and along the bag facesheet, as seen in Figure A-22.b.

Table 5 provides a summary of the flexure test results for the different studied configurations.

It can be observed that when the repair is loaded in tension, a higher strength recovery was

obtained in comparison with the one obtained when the repair is loaded in compression. These

results show that the 2D rectangular shape of the repair is more efficient in tension than in

compression.

Table A-5. Flexure results for 8HS sandwich panels

Configuration Angle

(°)

Deflexion

(mm)

Failure strength

(MPa)

Strength recovery

(%)

Pristine - 67.47 341.08 -

Repair in tension 3 56.25 270.34 79.26

Repair in compression 3 51.45 258 75.64

230

Figure A-18. Stress-strain curves for the 8HS pristine panels

Figure A-19. Stress-strain curves for the repaired facesheet loaded in compression

231

Figure A-20. Stress-strain curves for the repaired facesheet loaded in tension

Figure A-21. Typical failure of the pristine specimen

a. Repair in compression b. Repair in tension

Figure A-22. Failure modes for the 3°-repaired panel.

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A.4 Results Validation

The main objective of the flexure tests conducted for the 8HS skin material panels is to validate

the results obtained for the pristine and for the repaired panels under uniaxial tension and

compression loads.

Figure A-23 compares the failure stress obtained from static tensile and compression tests with

the value obtain under flexure loading for the pristine panels. It can be seen that the pristine

panels are more resistant in tension than in compression. For the flexure tests, failure occurs in

the facesheet loaded in compression. It can be observed also that the stress failure value

obtained from the compression tests is in accordance with the result obtained from the flexure

tests.

Figure A-24 compares the results for the 2D repaired panels, with a 3°-scarf angle, when the

repaired sandwich panel is loaded in flexure with the repaired facesheet either in tension or in

compression, and when it is loaded in uniaxial tension and compression. As for the pristine

panels, the value obtained for the repaired specimens from the uniaxial tension and

compression and from the flexure tests when the repair is loaded in compression or in tension

are quite similar.

233

Figure A-23. Comparison of the failure stress of the pristine panels obtained from different

loading types.

Figure A-24. Comparison of the failure stress of the 3°-repaired panels (2D repair

configuration) obtained from different loading types.

234

These results confirm that uniaxial tensile or compressive tests can be used to determine the

mechanical strength of repairs in sandwich honeycomb panels) is valid. From these results, it

is clear that the repair is quite strong when it is subjected to tensile loading applied either by

uniaxial tension and flexure.

From all the conducted tests for both the rectangular and the circular repair shapes, it is now

clear that the 3D circular repair is stronger than the 2D rectangular repair in both loading cases:

tension and compression. This may be explained by the difference in the shape and the stress

concentration in the adhesive bondline. Also, for the circular shape, the repair is surrounded by

the intact parent material however for the rectangular repair shape, the repair was along the

whole width of the panel.