investigating failure in composite stiffener run …...energy release rates for debonding and...
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IMPERIAL COLLEGE LONDON
INVESTIGATING FAILURE IN COMPOSITE STIFFENER RUN-OUTS
Spyridon Psarras
Department of Aeronautics South Kensington Campus Imperial College London
London SW7 2AZ U.K.
This thesis is submitted for the degree of Doctor of Philosophy of Imperial College London
2013
'' Πάντες ἄνθρωποι τοῦ εἰδέναι ὀρέγονται φύσει.''
Αριστοτἐλης
Abstract The aim of this thesis is to improve the understanding of failure initiation and propagation, in
stractural composites featuring geometrical discontinuities. In particular, this study focuses
on stiffener run-outs as these are particularly significant in the aerospace industry. The
improved understanding achieved in this project results in a direct comparison of the
performance of different stiffener run-out configurations, and contributes towards validating
the applicability of failure models to representative structural components.
In this work, the use of a compliant web design for improved damage tolerance in stiffener
run-outs is investigated. Three different configurations were compared to establish the merits
of a compliant design: a baseline configuration, a configuration with optimised tapering and a
compliant configuration. The performance of these configurations, in terms of strength and
damage tolerance, was compared numerically using a parametric finite element analysis. The
energy release rates for debonding and delamination, for different crack lengths across the
specimen width, were used for this comparison.
The three configurations were subsequently manufactured and tested. The manufacturing
process used in this study led to sound skin-stiffener run-outs whose design was validated
against a numerical study. In order to monitor the failure process, Acoustic Emission (AE)
equipment and Digital Image Correlation (DIC) were used. AE data recorded during skin-
stiffener run-out compression tests proved useful to analyse the failure processes which take
place in these specimens.
The predicted failure loads, based on the energy release rates, showed good accuracy,
particularly when the distribution of energy release rate across the width of the specimen was
taken into account. It was shown that the compliant configuration failed by debonding and
showed improved damage tolerance compared to the baseline and tapered stiffener run-outs.
It can be concluded that the variation of the energy release rate across the width should be
considered when stiffener run-outs are designed. The results further show that, in the design
of skin-stiffener run-outs, it is important to consider the possibility of failure modes other
than debonding, and that compliant termination schemes offer the possibility of improved
damage tolerance.
Acknowledgments The author would like to acknowledge the funding of this research from the Engineering and
Physical Sciences Research Council and the Ministry of Defence under the project
EP/E023967/1 is gratefully acknowledged.
For their constant supervision, guidance and advice throughout the last four years, the author
would like to thank both his supervisors, Dr. Silvestre Pinho and Prof. Brian Falzon.
The interest, involvement and participation of Dr. Irene Guiamatsia, Dr. Jesper Arkensen, Mr.
Nikolaos Sogias, Mr. Vinoo Mohan, Mr. José M L Gutiérrez and author's research group
colleagues is acknowledged.
The author would also like to thank Mr. Gary Senior and Mr. Jon Cole for help with the
manufacturing process of specimens; and Mr. Joseph Meggyesi for help with experimental
testing.
Finally, the author would like to acknowledge his family for their constant support and
inspiration.
Declaration The work in this thesis is based on research carried out at Imperial College London and it is
all the authors own work unless referenced.
Contents
Table of contents
ABSTRACT ................................................................................................................................................... 3
1 INTRODUCTION .............................................................................................................................17
1.1 BACKGROUND AND MOTIVATION ...................................................................................................17 1.2 OBJECTIVES .....................................................................................................................................20 1.3 OUTLINE ..........................................................................................................................................21 1.4 DISSEMINATIONS AND PUBLICATIONS ...........................................................................................22
2 LITERATURE REVIEW ................................................................................................................23
2.1 COMPOSITE FRACTURE AND FAILURE MECHANISMS ....................................................................23 2.1.1 Failure in composites ...........................................................................................................23 2.1.2 Failure criteria .....................................................................................................................26
2.2 INTERACTION BETW EEN DAMAGE MECHANISMS ...........................................................................28 2.3 FAILURE MODELS ............................................................................................................................28
2.3.1 Fracture mechanics..............................................................................................................28 2.3.2 VCCT.....................................................................................................................................29 2.3.3 Damage mechanics ..............................................................................................................29 2.3.4 Cohesive models ...................................................................................................................29 2.3.5 X-FEM...................................................................................................................................32
2.4 STRESS CONCENTRATION PROBLEM ...............................................................................................33 2.4.1 Open hole problem ...............................................................................................................33 2.4.2 Adhesive Joints .....................................................................................................................34
2.5 COMPOSITE PANEL AND STIFFENER DESIGN .................................................................................36 2.6 STIFFENER BUCKLING .....................................................................................................................38 2.7 DAMAGE IN STIFFENERS .................................................................................................................41
2.7.1 Experimental state of art......................................................................................................41
Contents - Table of contents
2.7.2 Simulation state of the art ....................................................................................................45 2.8 DISCUSSION AND CONCLUSIONS .....................................................................................................47
3 MATERIAL CHARACTERIZATION .........................................................................................50
3.1 INTRODUCTION ................................................................................................................................50 3.2 STIFFNESS AND STRENGTH CHARACTERIZATION ..........................................................................50
3.2.1 Introduction ..........................................................................................................................50 3.2.2 Manufacturing ......................................................................................................................50 3.2.3 Testing ...................................................................................................................................54 3.2.4 Results ...................................................................................................................................65
3.3 FRACTURE TOUGHNESS CHARACTERIZATION ...............................................................................66 3.3.1 Introduction ..........................................................................................................................66 3.3.2 Manufacturing ......................................................................................................................66
3.4 TESTING ...........................................................................................................................................68 3.4.1 DCB .......................................................................................................................................68 3.4.2 4 ENF ....................................................................................................................................72
4 NUMERICAL DESIGN OF STIFFENER RUN-OUTS FOR DAMAGE TOLERANCE....75
4.1 INTRODUCTION ................................................................................................................................75 4.2 STRESS PROFILE AT INTERFACES WITH GEOMETRICAL AND MATERIAL DISCONTINUITIES...........76
4.2.1 Theoretical Analysis .............................................................................................................76 4.2.2 Stiffener run-out Designs .....................................................................................................82
4.3 FE MODELS .....................................................................................................................................86 4.3.1 The Model .............................................................................................................................86 4.3.2 Mesh Sensitivity Study..........................................................................................................86 4.3.3 Model analysis and results ..................................................................................................88
4.4 ENERGY RELEASE RATE FOR DEBONDING ......................................................................................94 4.4.1 The FE model........................................................................................................................95 4.4.2 The Python script................................................................................................................102
4.5 RESULTS FROM MODELLING .........................................................................................................102 4.5.1 Energy Release rate along crack.......................................................................................102 4.5.2 2nd iteration .........................................................................................................................104 4.5.3 Energy release rate along the width of the crack tip .......................................................109 4.5.4 Modelling debonding failure using VCCT........................................................................111
4.6 CONCLUSIONS ...............................................................................................................................113
5 MANUFACTURING AND TESTING PROCEDURES...........................................................114
5.1 MANUFACTURING OF STIFFENER SPECIMENS ..............................................................................114
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Contents - Table of contents
5.1.1 Skin ......................................................................................................................................114 5.1.2 Stiffener ...............................................................................................................................116 5.1.3 Filler....................................................................................................................................117 5.1.4 Bonding ...............................................................................................................................119
5.2 TESTING OF STIFFENER RUN-OUTS................................................................................................121 5.2.1 Digital Image Correlation .................................................................................................121 5.2.2 Acoustic Emission ..............................................................................................................121 5.2.3 Results .................................................................................................................................122
5.3 2ND ITERATION ...............................................................................................................................125 5.4 CONCLUSIONS ...............................................................................................................................129
6 DETAILED DAMAGE MODELLING FOR TAPERED RUN-OUT STIFFENERS..........130
6.1 INTRODUCTION ..............................................................................................................................130 6.2 BEBONDING OF THE TAPERED STIFFENER ....................................................................................131
6.2.1 Mode interaction ................................................................................................................134 6.2.2 Response of the Numerical Model.....................................................................................135
6.3 MODELING THE INTERLAMINAR FAILURE OF THE TAPERED STIFFENER......................................136 6.3.1 Cohesive zone damage modelling definitions...................................................................136 6.3.2 Response of the model ........................................................................................................136
6.4 MODELLING THE INTRALAMINAR FAILURE ..................................................................................137 6.5 MODELING THE EXPERIMENTAL RESULTS ....................................................................................142
6.5.1 Interaction properties ........................................................................................................143 6.5.2 Delamination investigation around the filler tip point ....................................................144 6.5.3 Delamination investigation across the filler ....................................................................144
6.6 MODELING USING XFEM .............................................................................................................147 6.7 MODELING USING LARC...............................................................................................................149 6.8 COMPARISON OF THE FAILURE MODELS .......................................................................................151 6.9 CONCLUSIONS ...............................................................................................................................152
7 CONCLUSIONS..............................................................................................................................153
7.1 NUMERICAL ANALYSIS..................................................................................................................154 7.2 THE MANUFACTURING AND TESTING PROCESSES ........................................................................154 7.3 DETAIL MODELING OF RUN-OUT STIFFENERS ...............................................................................155
8 FUTURE WORK ............................................................................................................................157
8.1 USING THIS STUDY IN OTHER STRUCTURES ..................................................................................157 8.2 OTHER PARAMETERS IN THE PARAMETRIC STUDY .......................................................................157 8.3 STUDY IN FATIGUE ........................................................................................................................157
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Contents - Table of contents
8.4 EXPLOITING FURTHER THE PYTHON SCRIPT, THE MANUFACTURING METHOD AND THE TEST
RESULTS .........................................................................................................................................158 8.5 OBTAIN FAILURE DATA FOR DAMAGE MODELS ............................................................................158
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Figures
Table of figures
Figure 1.1: Composites in Airbus A380 [1]...............................................................17
Figure 1.2: Premature wing-structure failure at the stiffener run-out region..
[2] ........................................................................................................18
Figure 1.3: Use of stiffeners.......................................................................................19
Figure 1.4: Stiffener run-out and its consisting parts. .................................................20
Figure 2.1: Micrograph from a kink band ..................................................................26
Figure 2.2: Intra and interlaminar failure, (0,90)s.......................................................31
Figure 2.3: DCB specimen ..........................................................................................31
Figure 2.4: Load versus displacement curve obtained from the simulation with
the analytical solution..........................................................................32
Figure 2.5: Complete failure of a composite plate with a hole [41] ...........................34
Figure 2.6: Scheme of a single lap [42] ......................................................................35
Figure 2.7: Bonded Joint Failure Scenarios ................................................................35
Figure 2.8: Stiffened plate geometry [48] ...................................................................37
Figure 2.9: I-stiffened panel. Buckling at 11 tonnes, failure at 48 tonnes [55] ..........39
Figure 2.10: Component specimen [57]......................................................................40
Figure 2.11: Summary of growth directions [60] .......................................................42
Figure 2.12: Edge view of the damaged specimens [66] ............................................44
Figure 2.13: Stringer stiffened panel subjected to shear loading [73] ........................47
Figure 3.1: Arrangement for producing laminates in Autoclave [47].........................51
Figure 3.2: Schematic of plates ...................................................................................51
Figure 3.3: The C-scans of the plates..........................................................................52
Figure 3.4: Manufacturing of compression specimen [9] ...........................................53
Figure 3.5: Specimen dimensions ...............................................................................54
Figures - Table of figures
Figure 3.6 : Compression specimens inside the rig ....................................................55
Figure 3.7: Compression specimens after testing .......................................................55
Figure 3.8: Failure strengths of longitudinal compression specimens .......................56
Figure 3.9: Bending versus strain for the longitudinal compression specimen ..........56
Figure 3.10: Stress-strain curves for the longitudinal compression specimens ..........57
Figure 3.11: Failure strengths of the transverse compression specimens ...................57
Figure 3.12: Bending versus strain for the transverse compression specimen ...........58
Figure 3.13: Stress-strain curves for the transverse compression specimens ............58
Figure 3.14: Testing of tensile specimen ....................................................................59
Figure 3.15: Tensile specimens after testing, 0o on the left and 90o on the right........60
Figure 3.16: Failure strength of the longitudinal tension specimens ..........................60
Figure 3.17: Stress-strain curves of the longitudinal tension specimens ....................61
Figure 3.18: Failure strength of the transverse tension specimens .............................61
Figure 3.19: Stress-strain curves of the transverse tension specimens .......................62
Figure 3.20: Shear specimens after testing .................................................................62
Figure 3.21: Failure strength of shear specimens ......................................................63
Figure 3.22: Stress-Strain curves of the shear specimens that were tested
without unloading ................................................................................64
Figure 3.23: Stress-Strain curves of shear specimens that were tested with
unloading .............................................................................................64
Figure 3.24: Schematic of plate for the fracture toughness specimens and the
C-scan of the plate ...............................................................................67
Figure 3.25: Precraking of a DCB specimen ..............................................................68
Figure 3.26: DCB specimen [7] ..................................................................................69
Figure 3.27: Testing a DCB specimen ........................................................................69
Figure 3.28: Load-displacement traces for DCB specimens......................................70
Figure 3.29: R-curves for DCB specimens using the Modified Beam Theory
(MBT) Method ....................................................................................70
Figure 3.30: R-curves for DCB specimens using the Compliance Calibration
(CC) Method........................................................................................72
Figure 3.31: the 4ENF test fixture ..............................................................................72
Figure 3.32: Testing a 4ENF specimen.......................................................................73
Figure 3.33: Load displacement curves for the 4ENF specimens...............................74
Figure 3.34: R-curves for 4ENF specimens ................................................................74
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Figures - Table of figures
Figure 4.1 : Close-form model ....................................................................................76
Figure 4.2: Free Body Diagram ..................................................................................78
Figure 4.3 : Plot of peeling stresses from analytical solution .....................................80
Figure 4.4: A study on how variables (a) and (b) affect the solution. ......81
Figure 4.5: Stiffener dimensions in mm [63] ..............................................................82
Figure 4.6 : The designs of the stiffeners that were studied. .....................................83
Figure 4.7: An example of naming code of meshing models, here a 1-10-80
model. ..................................................................................................87
Figure 4.8: Peeling stresses for different meshes along path 1 ..................................87
Figure 4.9: Max peeling stresses for different meshes................................................88
Figure 4.10: The paths where the stresses were calculated.........................................88
Figure 4.11: Peeling stresses along Path 1 ..................................................................89
Figure 4.12: Shear stresses along Path 1 .....................................................................89
Figure 4.13: Peeling stresses in Path 1 near the edge of the stiffener .........................90
Figure 4.14: Shear stresses in Path 1 near the edge of the stiffener...........................91
Figure 4.15: Peeling stresses in Path 2........................................................................92
Figure 4.16: Shear stresses in Path 2...........................................................................92
Figure 4.17: Peeling stresses in Path 3........................................................................93
Figure 4.18: Shear stresses in Path 3...........................................................................93
Figure 4.19: Designs and dimensions in mm of a) the baseline stiffener and b)
the parametric stiffener. .......................................................................94
Figure 4.20: The FE model of a specimen with the boundary conditions. .................96
Figure 4.21: Commonly used element families [4].....................................................96
Figure 4.22: Stacking sequence for the skin ...............................................................97
Figure 4.23: Course mesh for the modified design with 3D continuum elements......98
Figure 4.24: Surfaces constraints between the skin (master surface-red) and the
adhesive (slave surface-pink) ...............................................................99
Figure 4.25: Modified model with BC-1 on the left edge (clamped) and BC-2
on the right edge ( zU =1) ...................................................................100
Figure 4.26: Strain energy with composite lay-up (blue line) and with material
orientations (red line) ........................................................................101
Figure 4.27: Normalized energy release rates as a function of crack length (a)
comparison between Baseline stiffener design and selected
k 1 2/D D
Figures - Table of figures
Tapered stiffener with b = 3 mm, c = 10 mm and d =6.25 mm),
(b) Influence of parameter b on G, (c) Influence of parameter c
on G and (d) Influence of parameter d on G. ....................................103
Figure 4.28: (a) Front view of failed specimen; (b) Exploded view showing the
failed area; (c) Front view of Bottom part showing 00 plies ; (d)
Bottom view of the Upper part showing delaminated 450 plies ........104
Figure 4.29: Compliant Skin-Stiffener designs.........................................................105
Figure 4.30: a) Tapered stiffener after testing, b) FE model showing
delamination path, and c) FE model of a specimen with
boundary conditions. .........................................................................106
Figure 4.31: Normalized strain energy release rates as a function of crack
length showing a comparison between designs. The points were
obtained numerically and the curves are spline fits...........................107
Figure 4.32: Normalized energy release rates of the Compliant design of
different (w, h) values for (a) debonding and (b) delamination ........107
Figure 4.33: Stiffener design configurations (dimensions in mm). .........................108
Figure 4.34: Normalized strain energy release rates as a function of crack
length; comparison between Baseline stiffener design (Figure
4.33α), Tapered stiffener (Figure 4.33Figure 4.19b) and
Compliant stiffener (Figure 4.33Figure 4.19c) with dimensions
b=3 mm, c=10 mm and d=6.25 mm. .................................................109
Figure 4.35: Normalized GT/Gc across the crack tip for crack a = 1 mm for the
Baseline, Tapered and Compliant specimens....................................110
Figure 4.36: Comparing the results of the parametric study with the VCCT
method (a) along the crack and (b) along the width of the
stiffener..............................................................................................112
Figure 4.37: The refined model that was used in the VCCT method ......................113
Figure 5.1: Hand lay-up for the skin plates. ..................................................................115
Figure 5.2: Curing procedure on the Autoclave.......................................................115
Figure 5.3: The cutting schedule ..............................................................................116
Figure 5.4: Mould for the stiffener. All dimensions are in mm. ..............................117
Figure 5.5: Mould for the filler. All dimensions are in mm......................................118
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Figures - Table of figures
Figure 5.6: Micrographics of (a) the stiffener, (b) a zoomed area of the
stiffener, (c) filler made by stacked stripes and (d) filler made by
twisted tows. ......................................................................................118
Figure 5.7: Bonding stage with the skin, the stiffener and the adhesive film in
the wooden mould .............................................................................119
Figure 5.8: Specimens’ ends potted in epoxy resin .........................................................120
Figure 5.9: (a) Baseline stiffener specimen; (b) Tapered stiffener specimen
(identical flange geometry to Compliant type (b-i) profile of the
Tapered stiffener specimen; (b-ii) profile of the Compliant
stiffener specimen..............................................................................120
Figure 5.10: AE testing equpment ............................................................................122
Figure. 5.11: Failure loads for the baseline design and the modified design
specimens, as well as the predicted failure loads using Eq.
3.23. ...................................................................................................122
Figure 5.12: Load-Displacement and AE Amplitude-Displacement curves for
the baseline and the modified stiffener. The numbered pictures
present the displacements obtained with the DIC. ............................123
Figure. 5.13: A. (a) Baseline stiffener; (b)-(c) detail before and after failure
respectively; (d)-(e) clean debonded surfaces in the skin and
stiffener respectively. B. (a) Tapered stiffener; (b)-(c) detail
before and after failure respectively; (d)-(e) delaminated
surfaces in the skin and stiffener respectively. ..................................124
Figure.5.14: Peak frequencies versus displacement for (a) Baseline and (b)
Tapered stiffeners. .............................................................................124
Figure. 5.15: (a) Design of the Compliant stiffener (b) Normalized energy
release rates as a function of debonding and delamination length
for the three configurations (c) Load-displacement curves for the
three configurations (d) Failed surface of Compliant specimen ......125
Figure 5.16: (a) Baseline stiffener, (b) Tapered Stiffener and (c) Compliant
Stiffener after failure respectively. ....................................................126
Figure 5.17: Loads and Peak frequencies versus displacement for a) the
Baseline b) the Tapered and c) the Compliant stiffeners. A scale
on the right hand side indicates the mode of failure typically
associated with these peak frequencies [80]......................................127
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Figures - Table of figures
Figure 5.18: The average signal level (ASL) of the three designs.............................128
Figure 6.1: The parts of the FE model ......................................................................131
Figure 6.2: Illustration of imposed cohesive properties for debonding mode. .........132
Figure 6.3: (a) Traction-separation law for cohesive zone models (b) Modified
law to implemented in FEM ..............................................................132
Figure 6.4: Finite element model of modified specimen. ........................................133
Figure 6.5: Damage growth pattern predicted by a cohesive model for the
modified specimen compared with energy release rate
predictions using VCCT ....................................................................135
Figure 6.6: Contour plot of CSDMG at the 0o/45o interface....................................137
Figure 6.7: Delamination occurred in the Tapered stiffener....................................137
Figure 6.8: Illustration of (a) 00 plies with Hashin damage model and (b)
cohesive properties at 00/450 interface ..............................................140
Figure 6.9: Contour plot of damage variable for matrix compression ......................141
Figure 6.10: Matrix crack at right flange in the experimentally failed specimen ....141
Figure 6.11: Crack bridging in the experimentally failed specimen .........................143
Figure 6.12: Cohesive properties imposed (Pink dots) on (a) Left stringer; (b)
Right stringer .....................................................................................143
Figure 6.13 Contour plot of cohesive damage variable with crack bridging
around the filler .................................................................................144
Figure 6.14: Contour plot of cohesive damage variable with crack bridging
across the filler at lowest plane. ........................................................145
Figure 6.15: Load-displacement of crack bridging plane models.............................146
Figure 6.16: Failure sequence of the stiffener from the XFEM model. (a) the
stiffener started to debond (b) without any delamination. (c) The
debonding propagated and the first XFEM element failed.(d)
without any delamination. (e) Debonding with failed filler
XFEM elements (f) accompanied with delamination........................148
Figure 6.17: Load- displacement curve of the XFEM model ..................................149
Figure 6.18: Load-displacement of LaRC'05 model and SDV8, matrix failure
post-history. .......................................................................................150
Figure 6.19: The failure loads of different failure models ........................................151
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Tables
Table 2-1: Composite failure criteria ..................................................................................... 27
Table 3-1: Function and characteristics of the manufactured plates...................................... 52
Table 3-2: Nominal dimensions of specimens ...................................................................... 53
Table 3-3: Comparison of the material properties ................................................................. 65
Table 3-4: Function and characteristics of the manufactured plate ....................................... 66
Table 3-5: Nominal dimensions of the fracture toughness specimens................................... 67
Table 4-1 : Values [63] .......................................................................................................... 80
Table 4-2 : Lay-up details ...................................................................................................... 84
Table 4-3: Material properties of IM7/8552 ......................................................................... 85
Table 4-4: Material properties for FM300 measured in house .............................................. 95
Table 4-5: Stacking sequence for the skin and the stiffener.......................................................... 97
Table 4-6: Mesh Sensitivity Study results................................................................................. 101
Table 4-7: Predicted failure load.......................................................................................... 111
Table 5-1: Composite ply orientations ................................................................................. 116
Table 5-2: Failure loads for the different specimen types, as well as the predicted
failure loads using Eq. 3.23. .............................................................................. 126
Table 6-1: Cohesive interaction properties .......................................................................... 133
Table 6-2: Debonding loads of the Tapered stiffner ............................................................ 135
Table 6-3: Intralaminar properties of IM7/8552 .................................................................. 139
Table 6-4: Failure loads of filler crack planes compared to experimental........................... 146
Table 6-5: XFEM interaction properties ............................................................................. 147
Chapter 1
Introduction
1 Introduction
1.1 Background and motivation The increasing demand for aerostructures with high stiffness/strength to weight ratio
has resulted in the increased use of laminated composite materials for structural
components. Figure shows the many composite parts that exist on the Airbus A 380.
Figure 1.1: Composites in Airbus A380 [1]
Chapter 1 - Introduction
There is great effort in developing analytical and numerical models in order to design
composite parts for aerostructures. The relevance to the aerospace industry has to do
with the significant cost reductions that reliable virtual component testing should
allow. Also, composite components are often over-designed and thus overweight and
costly. The understanding of the damage mechanisms and failure processes drives to
further improvements and better understanding of the behaviour of aerostructures.
Research has tended to focus on specific aspects of damage modelling in order to
gain detailed insight into the various damage mechanisms; however a model that
encompasses all aspects associated with failure and that is applicable to complex
composites is still lacking.
Figure 1.2: Premature wing-structure failure at the stiffener run-out region.. [2]
Laminated carbon-fibre composite structures are susceptible to failure from any local
stress concentration which gives rise to through-thickness stresses, Figure 1.2. Stress
concentrations induced by the presence of geometrical discontinuities in components
are becoming all the more critical, since composite laminates are brittle materials and
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Chapter 1 - Introduction
are very sensitive to 3-D stress fields (intralaminar and interlaminar), so requiring an
increased level of accuracy in the analysis of their behaviour during failure.
Furthermore, the lack of reliable predictive models means that qualification and
certification of composite structures is time consuming and expensive, since extensive
coupon and element testing is required. Recently there have been significant
developments in the understanding and predictive tools for composites. By exploiting
these developments, the primary objective of the EDAVCOS programme (Efficient
Design And Verification of Composite Structures) [3] was to determine a cost
efficient route to certification for composite structures. This entailed a validated
analysis-based procedure for structural verification from initial design to final
certification. The targets were a 50% reduction of the total cost for verification and
60% time scale reduction. A key aspect of the EDAVCOS programme was the
development of predictive models for stiffened structures containing defects.
The buckling characteristics of thin plates are improved considerably by using
stiffening concepts such as skin/stiffener configurations or honeycomb sandwich
configurations rather than increasing the plate thickness, Figure 1.3, which is less
structurally efficient.
Figure 1.3: Use of stiffeners
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Chapter 1 - Introduction
1.2 Objectives Composite damage modelling is a vibrant area of contemporary research, fuelled by
the strategic decision of the global aerospace industry to increase the amount of
composite materials used in structural aircraft components.
The latest generation of large passenger aircraft also use mostly carbon-fibre
composite material in their primary structure and there is a trend towards the
utilization of bonding of subcomponents in preference of mechanical fastening.
Current design philosophy requires that certain stiffeners are terminated (Figure 1.4),
for example due to an intersecting structural feature or an inspection cut-out. In these
circumstances, the loading in the stiffener must be diffused into the skin, leading to
complex three-dimensional stress-states. The development and utilization of reliable
virtual component testing, in the design of composite aerostructures, can potentially
yield significant cost reductions. Such reliability requires a thorough understanding
of the damage mechanisms and failure processes in realistic aerostructures,
particularly in critical regions such as stiffener run-outs.
Figure 1.4: Stiffener run-out and its consisting parts.
The current state-of-the-art is to model the initiation of damage followed by
propagation, whether this be unstable to failure or arrested at a structural feature. The
modelling of realistic composite structures containing geometrical discontinuities,
Web
AdhesiveFillerSkin
Flange
Noodle region
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Chapter 1 - Introduction
such as stiffener sun-outs, faces significant difficulties and available tools are often
not capable of simulating the complex mechanisms of crack propagation.
In this thesis numerical models of the stiffened run-outs will be created and the
capability to predict the failure mechanisms observed will be assessed. The
mechanisms of damage initiation and propagation will be investigated using acoustic
and digital imaging monitoring equipment. The overall aim of this thesis is to analyse
the mechanical response of skin-stiffener run-outs. In particular, the following
objectives are addressed:
1. To propose a reliable methodology for the design of damage tolerant skin-
stiffener run-outs.
2. To develop well-defined skin-stiffener run-out configurations with improved
damage tolerance under compressive loads.
3. To develop an accurate manufacturing procedure for skin-stiffener run-outs,
with particular emphasis on the quality of the noodle region.
4. To investigate the potential and limitations of advanced failure models in the
analysis of skin-stiffener run-outs.
1.3 Outline
This thesis is organized into the following Chapters:
Chapter 2 reviews the literature in composite stiffener run-outs; the review starts with
composite failure, where failure mechanisms and interaction between them are
reviewed. It follows with stiffened panels focusing on their behaviour and the ways of
designing them, and ends with stiffener run-outs, where the modelling and testing
procedures are presented.
Chapter 3 describes the tests that were performed in order to characterize a specific
composite material, IM7/8552 carbon epoxy, and validate the FE models that was
developed.
Chapter 4 presents a numerical investigation that was developed with the commercial
software ABAQUS [4]. A number of numerical models were developed which
enabled the investigation of stiffener run-out designs. Based on the results of this
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Chapter 1 - Introduction
analysis, a new run-out design was generated and a design optimization was followed
by using the scripting computer language Python [5].
In Chapter 5 the main topics are the manufacturing of the stiffener run-out
specimens with a selection of termination schemes and the testing procedure, where
the specimens were loaded in compression until failure and monitored using Digital
Image Correlation (DIC) and Acoustic Emission (AE).
Chapter 6 outlines more detailed FE models that simulate the exact failure of the
tested stiffener run-outs. Different ways of approaching the failure are compared
giving explanations of some experimental observations and an insight into the way of
modelling the failure in composite run-out stiffeners and the problems that can arise.
Finally, the conclusions of this thesis are highlighted in Chapter 7 and possible future
work is discussed in Chapter 8.
1.4 Disseminations and Publications The work presented in this chapter resulted in the following disseminations and
publications:
1. Psarras, S., S.T. Pinho, and B.G. Falzon, Investigating the use of compliant webs in the damage-tolerant design of stiffener run-outs, accepted to Compos. B-Eng. 2012
2. Psarras, S., S.T. Pinho, and B.G. Falzon, Damage-tolerant design of stiffener run-outs A finite element approach, in Finite Element Analysis - New Trends and Developments, InTech Publishing. Publication date: August 2012, (ISBN 980-953-307-396-0)
3. Psarras, S., S.T. Pinho, and B.G. Falzon, Investigating the Damage Tolerance Design of Stiffener Run-outs, 15th European Conference on Composite Materials, Italy, Venice, 24th June 2012
4. Psarras, S., S.T. Pinho, and B.G. Falzon, Design of composite stiffener run-outs for damage tolerance. Finite Elements in Analysis and Design, 2011. 47(8): p. 949-954
5. Psarras, S., S.T. Pinho, and B.G. Falzon, Investigation of Stiffener Run-out Failure, 3rd Asian-Pacific International Symposium on Aerospace Symposium and 14th Australian Aeronautical Conference, Melbourne, Australia, 28th February 2011.
6. Psarras, S., S.T. Pinho, and B.G. Falzon, Investigation of Stiffener Run-out Failure, 14th European Conference on Composite Materials, Budapest, Hungary, 7th June 2010.
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2 Literature Review
2.1 Composite Fracture and Failure Mechanisms The two constituents of a composite ply, matrix and fibre, have complementary roles
within the structure: the fibres carry the majority of the load while the matrix ensures
the continuity, cohesion and to an extent, the structural integrity of the composite
structure. Composite failure happens by mechanisms involving the individual failure
of each constituent, as well as additional mechanisms created by their interaction.
2.1.1 Failure in composites
Damage in composite materials, by observing the fracture surface, can be separated
into the following failure modes
• Interface crack
• In-ply crack
• Delamination
• Crack jumping
• Fibre breakage and bridging
This separation happens because fibre strain to failure can be greater or less than the
matrix. In dealing with damage progression it is postulated that the composite loses its
Chapter 2 - Literature Review
stiffness gradually until complete failure, when composite can no longer transmit
load. The load in the composite is the sum of the load in the fibres and matrix:
c f mP P P= + (2.1)
where P is the load and the symbols c , f and m are for composite, fibre and matrix
respectively. For P Aσ= and assuming that /f f cV A A= then
( )1c f f m fV Vσ σ σ= + − (2.2)
The above equation gives a relation between the composite, matrix and fibre stresses.
In order to see how this equation works, assuming that the fibre and the matrix are
elastic materials. If the fibre’s strain to failure is bigger than matrix’s, the load will be
carried from the fibres. When the fibres break, the load will be transferred to the
matrix. But the strength of the matrix is too low to carry the load and it will result to
the failure of the matrix. So the failure will happen when
( )1c f f m fV Vσ σ σ> + − (2.3)
In case that the matrix strain is bigger, the matrix will continue to carry the load and
the fibres will break. The matrix will carry load until
( )1c m fVσ σ= − (2.4)
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If the fibres are made of a ductile material and the matrix is brittle, when the matrix
cracks, the load is shared between the fibre and the matrix.
( )' '' 1f f f f m fV V Vσ σ σ= + − (2.5)
where 'fσ is the stress carried by the fibre and matrix just prior to matrix cracking and
''fσ is the stress on fibre segments that bridge the crack. The progression of damage,
in typical carbon-fibre structural composites, is usually in the following sequence:
i) Matrix Cracking
The number of cracks depend on the type of the load. If the load is static, the number
of cracks will be lower than that caused by fatigue load. The ply thickness and the
direction of the fibres in neighbouring plies are also factors in nature and density of
cracks. As an example, in a uniaxial tension at a [0/90/45]s composite, the cracks will
start from the 90o ply and then will appear in the 45o ply.
ii) Delamination
Delamination is a life-limiting failure mode for laminated composites. It happens
because there are no fibres normal to the plane of lamination and the thin layers of
plies are low energy failure paths. A characteristic of delamination is that it has a
tendency to grow during cyclic loading. The interlaminar stresses can be calculated
using analytical models. In order to do this it is important to remember the type of
laminate, properties of the materials and the type of loading
iii) Fibre failure and interface debonding
When there is a strong interfacial bond between the matrix and the fibre, the crack
grows into the matrix and as a result a smooth cracked surface is created. On the other
hand, when there is a weak interfacial bond the failure surface is characterized by an
irregular surface and fibre pullout. In compression, misaligned fibres micro-buckle
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under the maximum compressive stress, usually followed by in-plane or out-of-plane
kinking and delamination from adjacent plies, as shown in Figure 2.1.
Figure 2.1: Micrograph from a kink band
2.1.2 Failure criteria
The strain energy release rates (SERR) vary tremendously from one failure
mechanism to another - Beaumont [6] derived the expressions for the SERR
associated with the micro-mechanism of composite failure - which impacts the
evolution of damage.
Several criteria, often based on the stress field within the material, are used to detect
the occurrence of each of the mechanisms previously described; these are listed in
Table 2-1.
The first criteria that were used were based on average stresses that were generated by
strength comparison and curve fitting, without taking account into the detailed
analysis of the failure processes. Most criteria reflect the interaction between failure
modes that are observed experimentally. Criteria that do not assume interaction and
predict failure are the Maximum stress and strain criteria [7, 8] . These correlate the
strength with stresses and strains respectively, having the advantage of an easy to use
model to predict failure.
It is worth noting that these are failure initiation criteria; while any structural material
is inherently flawed, it is understood that the onset of damage corresponds to the
moment when micro-defects transform into a crack, and this happens for certain
measurable stress thresholds. When all stresses are taken into account in the failure
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process, then interaction criteria are used. This type of criteria are the Tsai-Hill and
Tsai-Wu criteria and usually are in a form of a simple equation.
Moving to micro level, criteria such as Hashin [9] and Hashin-Rotem [10] take into
account the fibre and matrix failure and distinguish the failure modes. These mode-
differentiating criteria are proven to be more accurate and reliable in reproducing the
experimental observations, and are implemented in most finite element software.
Table 2-1: Composite failure criteria
Failure Criterion Interaction Prediction
Maximum stress
Maximum strain
Tsai-Hill
Tai-Wu stress
Tsai-Wu strain
Hashin
Puck
LaRC05
Additional references of interest include the results of the world wide failure exercise
[8, 10-17], an initiative of Soden and Hinton[18], Puck [19] and failure criteria
developed in conjunction with the NASA Langley Research Centre - LaRC03, Davila
et al. [20]. Recently, Pinho et al. [21-23] developed further the criterion to LaRC’05,
an advanced failure model that relies on physical criteria at the microscopic level, that
accurately predict lamina failure when comparing experimental data to various
strength based criteria.
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2.2 Interaction between damage mechanisms A combination of damage mechanisms that interact with each other can result in
damage development in composites. These damage mechanisms can occur separately,
but when they interact with each other can lead to local material weakening at higher
rates. Greenhalgh [24] had observed experimentally that stiffened panel configurations
loaded in different ways suffered from delamination that started from matrix cracks.
This is a design limiting factor in many cases because of the presence of matrix cracks . At
the intersection of delamination fronts with incipient matrix cracks, large gradients in
the strain energy were encountered in an analytical study by Noh and Whitcomb [25],
emphasising how matrix cracks can influence and accelerate delamination growth.
2.3 Failure models
2.3.1 Fracture mechanics
The energy absorbing micro mechanisms in composites depend on several factors
such as the formation of the fracture surface of the crack, micro cracking and
secondary cracks, and the plastic deformation of the matrix in the crack tip region. For
a cracked body this energy is:
H W U= − (2.6)
where W is the work supplied by the external forces and U is the elastic strain energy
stored in the body. The criterion for crack growth is
cH G Aδ δ≥ (2.7)
where CG is the work required to create a unit crack area and Aδ the interface in the
crack area. The strain energy release rate is
HGA
∂=
∂ (2.8)
However, the fracture mechanics approach cannot always be easily incorporated in a
direct way into a progressive failure methodology because its application requires an
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initial flaw. A common procedure consists in using first stress- strain criterion to
predict failure initiation and then use fracture mechanics for the crack propagation.
2.3.2 VCCT
Numerical approaches based on fracture mechanics require an initial flaw and they are
used in conjunction with techniques such as the Virtual Crack Closure (VCC) method
for the determination of the strain energy release rate. The VCC method is based on
Irwin’s assumption that when a crack extends by a small amount, the energy released
in the process is equal to work required to close the crack to its original length. The
energy release rates can then be computed from the nodal forces and displacements
obtained from the solution of a finite element model and crack propagation is
simulated by advancing the crack front when the local energy release rate rises to a
critical value. The method predicts delamination growth well; however, as
aforementioned, the structure must be pre-cracked and different meshes may be
required for each delamination front as soon as the crack advances.
2.3.3 Damage mechanics
Damage mechanics is another method for representing damage in composites.. The
first Damage Mechanics concepts were presented by Kachanov [26] and Rabotnov
[27]. Later, Ladeveze [28] proposed an in-plane model based on damage mechanics
to predict matrix micro cracking and fibre/matrix debonding in unidirectional
composites. The use of damage meso-modelling allows simulating and predicting the
damage state at any point of the structure until complete failure.
2.3.4 Cohesive models
Based on fracture mechanics concepts, the area under the curve defined by a traction
vs. displacement jump constitutive law is equal to the fracture energy or energy per
unit of area, and once this energy is consumed the crack propagates. In order to
simulate mixed mode delamination, stress based criteria are typically used for
initiation and interactive mixed-mode energy release rate criteria based on
experimental evidence is used for the propagation
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An efficient implementation of cohesive models for delamination modelling which
has been widely reported in the literature consists of interface elements (also called
cohesive or decohesion elements). Interface elements offer the possibility of coupling
stress based criteria and fracture mechanics based criteria in a unified way. Therefore,
they enable the model to predict both initiation and growth of delamination. For bi-
dimensional problems, interface elements can be defined as a one dimensional
element inserted between two adjacent layers. In a similar way, they can be extended
for three-dimensional problems, in which the one dimensional elements are replaced
by two dimensional elements connecting adjacent layers.
In elastic cases, the interface elements are very stiff in order to ensure the transference
of displacement and traction between the adjacent layers. To model delamination
growth, an interfacial material behaviour is assumed to control the relative
displacements and traction between layers and as soon as certain failure criteria are
fulfilled, the delamination is allowed to initiate and propagate.
Crisfield and Davies [29] proposed a continuous interface element for delamination
modelling in fibre composites. The interface element was embedded between two
eight-noded isoparametric plane strain elements. A bi-linear softening stress-relative
displacement relationship was assumed for the interface material model and linear and
quadratic interaction criteria were used for mixed-mode prediction. For unloading
conditions, a simple elastic damage model was adopted in which the material was
assumed to unload directly towards the origin. Daudeville and Ladeveze [30]
proposed a delamination model based on a damage mechanics approach. In their
model, connecting layers were used to represent the resin rich interface between two
adjacent layers. Excellent agreement was obtained between simulations, experimental
and closed form solutions for mode I, mode II and mixed-mode delamination,
respectively.
To the knowledge of the author, this procedure has only been applied for the study of
impact damage; however, it might be a useful tool for enabling models with both
interface and in-plane damage to simulate such situations as crack jumping from an
interface to another or to model ply-damage inducing delamination as per Figure 2.2.
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Figure 2.2: Intra and interlaminar failure, (0,90)s
As an example, a 2-dimensional Double Cantilever Beam (DCB) model was
performed with interface elements at every layer in ABAQUS CAE [4] using
COH2D4 elements and viscous regularization (μ=2.5×10-4), Figure 2.3. The
specimen was 170 mm long, 20 mm wide, 3.6 mm thick and the pre-crack length was
50 mm. The average mode I fracture toughness registered during the test is GIC = 0.28
kJ/m2 and the flexural Young’s modulus is E = 115 GPa. The specimen had three
main parts, two were the solid parts, which represented the adherents, and the third
part consisted of interface elements with thickness 0.001 mm. The appropriate
boundary conditions were set in order to represent the test conditions.
Figure 2.3: DCB specimen
The cohesive elements are extended in order to represent crack propagation and the
main material part separation from each other. The load versus displacement curve
Delamination
Intralaminar
170
3.6
crack50
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obtained from the simulation is presented together with the analytical solution for
propagation in Figure 2.4.
Figure 2.4: Load versus displacement curve obtained from the simulation with the analytical solution
2.3.5 X-FEM
The extended finite element method (XFEM) offers a solution to two aspects of the
crack propagation problem: refinement around the crack tip, and the discontinuous
displacement field across the crack. Regarding the refinement issue, a typical FEM
solution is the use of p-refinement or special elements such as the quarter point
element, Barsoum[31], Lim et al.[32]. A more efficient strategy recognizes that the
required refinement is only a consequence of the fact that isoparametric shape
functions are inadequate for the interpolation in regions of highly varying gradients or
discontinuities. The idea is hence to incorporate the known field variation in the
interpolation functions. The extended finite element method is really a solution to
avoid mesh refinement in regions and gives excellent results for crack propagation.
However, the added-value for problems involving cohesive crack growth in
composite materials is not obvious.
0
10
20
30
40
50
60
0 5 10 15 20
Load
(KN
)
Displacement (mm)
DCB-2
corrected beam theory
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2.4 Stress concentration problem
2.4.1 Open hole problem
One of the simplest example of stress concentration is a hole on a composite plate.
Open hole tests are currently a part of qualification process for composite parts. The
examination of the mechanical response of a composite plate with a hole is important
for aerospace applications where bolts and rivets are used for joining purposes.
Plates with open holes have been tested in tension and compression. A finite-element
approach has been developed by Wisnom and Chang [33] for modelling the detailed
damage development in notched composites. It was designed in a way that the model
could allow the delamination between the plies. Cross ply laminates were tested in
tension and a model that predicts the development of a delamination zone was
presented.
Pierron et al [34, 35] tested open hole composite specimens in tension using full-field
strain measurements. The strains were derived from displacements using local
differentiations and polynomial fitting. Another way of monitoring the damage
process were used by Yashiro et al. [36]. Fiber Bragg Grating (FBG) sensors
confirmed myltiple types of damage (e.g., splits, transverse cracks and delamination)
near the holes of CFRP laminates.
The interlaminar stress distributions around a circular hole in symmetric composite
laminates under in-plane tensile loading investigated by Hu et al [37]. 3D finite
elements were used. The delamination location and initiation were predicted by using
the finite elements and Ko-Lin stress results [38] together with a quadratic failure
criterion.
Independent polynomial spline approximation of displacement and interlaminar
tractions is proposed by E.V Iarve [39] for stress analysis in laminates with open
holes. Excellent agreement has been observed for interlaminar stresses in a [45/-45]s
AS4/3501-6 laminate under uniaxial tension. The polynomial spline approximation,
ideally suited for problems concerned with the singular solution behaviour, has been
applied to three dimensional stress analysis. The effect of thickness, ply orientation
and hole size were examined too [38]. Large fibre reinforced composite structures can
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Chapter 2 - Literature Review
give much lower strengths than small test specimens, so a proper understanding of
scaling is vital for their safe and efficient use.
The most important variables of scaling effects on the strength of composites with
open holes have been identified from experimental tests as hole size, ply and laminate
thickness. These have been scaled both independently and simultaneously over a large
range of combinations by J. Lee [40]. The laminates that were tested were
unidirectional and multidirectional and it was found that the hole size effected the
strength reduction more than the thickness and the dimensions of the specimens. The
same size effects were studied by G Green [41] with the difference that ratios of hole
diameter to width and length were kept constant, Figure 2.5. There, the delamination
was controlled by the ratio of the ply thickness to hole diameter.
Figure 2.5: Complete failure of a composite plate with a hole [41]
2.4.2 Adhesive Joints The use of adhesive bonding, Figure 2.6, rather than mechanical fasteners offers the
potential for reduced weight and cost. Their benefit is that they behave in a
predictable and reliable way, but adherend and adhesive stress distributions in the
overlap length near (and especially on) the free surface are quite different from those
occurring in the interior.
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Chapter 2 - Literature Review
Figure 2.6: Scheme of a single lap [42]
The possible failure scenarios of bonded lap joints are listed below and can be seen in
Figure 2.7.
Figure 2.7: Bonded Joint Failure Scenarios
A geometrically nonlinear model for elastic adhesive joints is derived by U. Edlund
[43]. Starting from a three-dimensional problem, a linearly varying displacement
through the thickness of the adhesive is assumed and a geometrically two-dimensional
theory for the adhesive layer is obtained. P.C. Pandey and S. Narasimhan [42]
presented a 3D viscoplastic analysis of adhesively bonded single lap joint considering
material and geometric nonlinearity. The specimens were tested according the ASTM
standard. Several types of joints were examined and observations have been made in
particular on peel and shear stresses in the adhesive layer.
1
2
3
4
5
1. Damage Initiation at Adhesive/Adherend Interface2. Damage Propagation Along Weak Interface3. Secondary Damage Initiation Site4. Transverse Tension Failure in Adherend Plies5. Adherend or Adhesive Strength Failure
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E. Oterkus et al. [44] presented a semi-analytical solution method to analyse the
geometrically nonlinear response of bonded composite lap joints with tapered and/or
non tapered adherend edges under uniaxial tension. H. Osnes and A. Andersen [45]
investigated which level of loads or prescribed end displacements led to significant
nonlinear effects. The joints examined were made of cross-ply laminates having 0 or
90 surface layers. L. da Silva and R. Adams [46] proposed techniques to reduce the
transverse stresses in the composite. They examined the effect of temperature and
they also found that, in joints with metals and composites, it is more advantageous to
have the composite as the outer adherend.
2.5 Composite Panel and Stiffener Design The collapse load of metallic stiffened panels in uniaxial tension or compression can
be determined by considering the yield strength of the material. For example, Dobbs
and Nelson [47] presented an efficient optimality criteria method for the automated
minimum weight design of structural components.
Designing composite structures is more complicated than designing metal structures
due to the increased number of possible local failures, which are usually
micromechanically governed and complex. Fibre breaking, matrix cracking, fibre
matrix debonding, and separation of individual layers can result in delaminations as
well as cracks and splits within individual layers. Microbuckling and shear failures
are also common types of failures under compressive loadings. A local damage
condition may be due to accumulation of these failures, and the final failure may be
governed by several of them.
Gόrdal and Haftka [48] used a general purpose mathematical optimization algorithm
in order to create an automated procedure for designing minimum-weight composite
panels, Figure 2.8, subject to a local damage constraint under tensile loading. Panel
fracture was predicted by using a strain based criterion and results given for both
unstiffened and stiffened plates.
Failure of a composite stiffened panel subjected to compressive loading is usually
induced by the separation failure at the skin/stiffener interface. Hyer and Cohen [49]
presented a method for computing the stress state that exists between a composite
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Chapter 2 - Literature Review
skin and the flanges of a cocured composite stiffener based upon finite element
analyses and an elasticity solution. The method presented relied upon an elasticity
approach for computing the stresses in the local area of the stiffener flange edge and
the composite skin. The local analysis was based upon an eigenvalue expansion of
the stress functions that govern the stresses in the interface region. Cohen and Hyer
[50] developed this method further by including geometric nonlinearities. The
results indicated that the inclusion of geometric nonlinearities is very important for
an accurate determination of the interface stresses.
Figure 2.8: Stiffened plate geometry [48]
Kassapoglou and Dinicola [51] presented a different solution technique to a similar
problem. The solutions of the governing set of partial differential equations were
used in conjunction with an energy minimisation approach to determine unknown
constants in analytically determined stress expressions. The method presented had
the advantage of being in closed form and very efficient. This method has the
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Chapter 2 - Literature Review
advantage of being less time consuming by avoiding costly finite element analysis.
Experimentation on skin/stiffener debonding has been investigated by using the four-
point bending test. Specimen edge effects in this type of test greatly influence the
skin/stiifener separation process and therefore the test does not accurately simulate
skin/stiffener debonding in actual structures.
A new method was proposed by Todoroki and Sekishiro [52] for stacking sequence
optimization to maximize the buckling load of blade-stiffened panels. A panel with
four blade-type stiffeners was adopted as a target structure for optimization. Because
of the lack of experimental data and for most practical laminated composite
structures, fibre angles were limited to a small of 0, 45, −45 and 90.
2.6 Stiffener buckling Having a very thin panel section is undesirable for two reasons. Firstly, stiffened
plates used in aircraft structures are often subject to load reversal and must be
designed to resist some compressive loads. Some panels, such as appearing skin
panels are also predominantly loaded in compression during flight. Stiffened plates
with thin panel sections might fail prematurely due to local buckling. Secondly, plates
designed to carry the applied loads mostly by the stiffeners can fail catastrophically
due to stiffener damage. To prevent thin panel sections, stress constraints with
alternative load paths or increased safety factors should be used.
Jaunky et al [53] described an approach to incorporate the effects of local skin-
stiffener interaction and presented numerical results for panel buckling. The skin-
stiffener interaction effects were introduced by computing the stiffness of the stiffener
and the skin at the stiffener region. The results from the numerical examples
considered suggest that skin-stiffener interaction effects should be included in the
smeared stiffener theory to obtain good correlation with results from detailed finite
element analyses. Hence, the smeared stiffener theory with skin-stiffener interaction
effects included is still a useful preliminary design tool and results in buckling loads
that are more accurate than the results from the traditional smeared stiffener approach.
As mentioned previously, buckling may also be a consideration in the design of
aircraft panels. Buckling resistant panels do require stiffeners with deep blades. Such
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designs can be achieved by imposing a blade with specified width and thickness band
redesigning the plates with this new geometry. Kong et al. [54] studied the
postbuckling behaviour of graphite/epoxy panels under uniaxial compression. Their
analytical studies consisted of finite element models adopting the maximum stress
criterion. Matrix failure, shear failure and fibre failure were considered and compared
favourably with experimental result.
Stevens et al [55] investigated the post buckling behaviour of a flat stiffened, co-cured
carbon fibre composite, loaded in compression. The panel was painted white for
shadow Moiré photography. Also, a telescopic arm of an ultrasonic scanning facility
was used in order to detect the initiation of damage in the postbuckled panel and
instrumentation associated with data logging and acoustic emission sensing. The
failure mechanism was an interlaminar shear stress failure arising from the
combination of compressive loading on the postbuckled stiffener blade and the
twisting induced at the node-line of the buckled stiffener. A panel after failure can be
seen in Figure 2.9.
Figure 2.9: I-stiffened panel. Buckling at 11 tonnes, failure at 48 tonnes [55]
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Chapter 2 - Literature Review
Most stiffened panel applications require some form of cutout for such purposes as
access. Nemeth et al. [56] studied the postbuckling behaviour of several graphite/epoxy
plates and several isotropic plates with central circular cutouts under compressive
loading. The experimental results indicated that the cutout size and plate orthotropy
greatly governed the change in axial stiffness of a plate at its buckling load. The results
also revealed that some of the highly orthotropic plates with cutouts exhibited greater
postbuckling stiffness than the corresponding plate without a cutout.
The postbuckling behaviour of a panel with blade-stiffeners incorporating tapered
flanges were investigated by Falzon et al [57]. The component consisted of a stiffener
and its associated skin, as shown in Figure 2.10, loaded in uniaxial compression. The
length was chosen so that the wavelength of torsional buckling was similar to the
wavelength observed in the panel. The failure of the component was identical, i.e. a
mid-plane delamination of the stiffener web at a nodal-line.
Figure 2.10: Component specimen [57]
The failure mechanism, observed in this study, also has potential implications for the
designer. It suggests that the optimizing of stiffener flanges by tapering, to reduce the
interfacial shear and peeling stresses, may be effective enough to shift the initial
damage site to a different location— in this case on a node-line at the edge of the web.
This provides the opportunity of introducing design improvements in this region, for
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Chapter 2 - Literature Review
example stitching, to further delay the onset of damage and the quick progression to
complete failure of the structure. The failure mechanism was an interlaminar shear
stress failure arising from the combination of compressive loading on the postbuckled
stiffener blade and the twisting induced at the node-line of the buckled stiffener.
Falzon and Stevens [58] presented a combined experimental and numerical buckling
and postbuckling investigation of hat-stiffened panels undergoing mode transition.
The skin bay bounded by the stiffeners was observed to buckle at a fraction of the
ultimate load supported by the panel, which contained a cut-out in the centre of their
skins. The first two specimens tested did not contain a hole in the centre of the skin.
The first panel failed earlier than the second specimen. This was accounted for by a
defect contained in the structure before testing. A mode-jump from three to five half-
waves was observed. The difference between the two panels was attributed to the
thicker skin of the second specimen. The authors concluded that the ultimate failure of
the specimens was due to interlaminar shear failure in the stiffener. This could be
deduced by inspecting the failure site. However, no photographs, microsections or
ultra sonic scans of the damaged area were provided.
2.7 Damage in Stiffeners
2.7.1 Experimental state of art
The in-plane compressive behaviour of thin-skin stiffened composite panels with a
stress concentrator in the form of an open hole were examined by Zhuk et al [59] .
Experimental studies, using ultrasonic C-scan images and X-ray radiography,
indicated that the overall damage resembles a hole. Under uniaxial compression
loading, 0 fibre microbuckling surrounded by delamination grows laterally (like a
crack) from the impact site as the applied load is increased. These local buckled
regions continued to propagate, first in discrete increments and then rapidly at failure
load. The damage pattern was very similar to that observed in laminated plates with
open holes loaded in compression. Also, the maximum stress failure criterion was
employed to estimate the residual compressive strength of the panel. The influence of
the stiffener on the compressive strength of the thin-skin panel was examined and
included in the analysis. Good agreement between experimental measurements and
predicted values for the critical failure load was obtained.
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Chapter 2 - Literature Review
Greenhalgh et al [60] generated documented and controlled experimental data for
validating predictive models of stiffened panels containing defects and damage, based
on EDAVCOS [3]. Two types of defect were characterised; embedded defects
(representative of inclusions introduced into the component during fabrication) and
impact damage (representative of the damage which may be introduced by tool drop).
The damage was located at two sites; within the bay between stringers and partly
under the stringer foot. The panel failed in compression, from the impact site, before
skin/stringer debonding could initiate and a secondary mechanism occurred prior to
skin/stringer detachment developing. Parallel to that, the authors tested and analysed
the failure of stringer run-out elements that served as benchmarks for validating
predictive methods. The local geometry of the stringer run-out was varied to deduce
its effect upon the performance under tensile loading. The failure processes at the
stiffener run-out region were characterised to understand the failure mechanisms at
the run-out, and to give some guidance as to how to optimise future designs. A
summary of the fracture directions is shown in Figure 2.11. This demonstrates how
the crack growth extended along the stringer, by migrating through the skin plies until
it reached the −45/0 ply interface in which it remained.
Figure 2.11: Summary of growth directions [60]
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Chapter 2 - Literature Review
Based on this work, Meeks et al [61] investigated the detailed damage mechanisms
for skin/stiffener detachment in an undamaged panel were characterised and related to
the stress conditions. This work provided an insight into the processes that control
post-buckled performance of stiffened panels 2D models and concluded that element
tests do not capture the true physics of skin/stiffener detachment: a full 3D approach
is required.
Greenhalgh and Garcia [62] deduced the failure processes in the elements, and to
characterise the effect of local geometry of the stringer run-out on the failure process,
by testing specimens in tension. The analysis showed that the critical failure
mechanism in the elements was the development of +45 ply splitting at the skin
surface, initially under mode I dominated intralaminar fracture. However, as these
splits grew beneath the stringer foot, the mode II component increased. This led to
mixed-mode delamination growth, extending parallel to the +45 ply, at the
skin/adhesive interface. Subsequently, the delamination migrated through the skin via
ply splits, ultimately reaching the interface between the second and third (−45/0)
plies, in which it remained until catastrophic failure. The conclusion of this research
was that the development and migration of delaminations via ply splits plays an
important role and needs to be modelled.
Falzon and Davies [63, 64] investigated the failure of thick-sectioned stiffener run-out
specimens loaded in uniaxial compression. The research was separated in two parts,
the experiments and the FE analysis. For all tests, failure initiated at the edge of the
run-out and propagated across the skin–stiffener interface. It was found that the
failure load of each specimen was greatly influenced by intentional changes in the
geometric features of these specimens. High frictional forces at the edge of the run-
out were also deduced from a fractographic analysis, indicating Mode II initial failure
mode, failure by skin–stiffener disbonding due to high interlaminar stresses that
develop at the end of the stiffener run-out.
Faggiani and Falzon [65] tested two run-out specimens and analyzed them
numerically. The specimens were co-cured and included an effective skin section on
top of which was mounted a tapered blade-stiffener. The sizing of the specimens was
such as to ensure that interlaminar shear stress failure occurred within the skin-flange
interfaces. The first specimen failed catastrophocaly at the 90/0 interface of the
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Chapter 2 - Literature Review
closing plies, located between the bottom of the stiffener flanges and the skin top
surface. Crack initiation and propagation was almost instantaneous and highly
unstable, with the crack propagating suddenly across the whole interface. A marked
increase in activity was recorded by acoustic emission monitoring just prior to failure,
but the specimen could not be unloaded quickly enough to arrest the crack
propagation. In the second specimen, crack initiation and unstable propagation was
followed by stable crack growth allowing the test to be stopped before the crack had
propagated throughout the whole specimen. This failure behaviour was in contrast
with the sudden and completely unstable nature of the first specimen with the thinner
skin.
Hosseini-Toudeshky et al [66] investigated the damage mechanisms in a composite
bonded skin/stiffener constructions under monotonic tension loading. The approach
used experiments to identify the failure mechanisms. The tested specimens consisted
of a bonded skin and flange assembly. Typical specimens are shown in Figure 2.12.
Figure 2.12: Edge view of the damaged specimens [66]
Observations on the performed experiments show matrix crack initiation and
propagation in the skin and near the flange tip, causing the flange to almost fully
debonded from the skin in some cases, interlaminar debounding and fibre breakage up
to the failure of the components. With increasing the applied load, the matrix cracks
propagated through the thickness to reach the next layer and caused delamination
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Chapter 2 - Literature Review
between the two layers. With increasing the applied load this delamination is
propagated up to the occurrence of unstable delamination.
2.7.2 Simulation state of the art
An understanding of how damage is initiated and the physics behind its progression
take priority in damage simulation. This field of research is very wide in scope, due to
the numerous configurations under which a structure can be loaded and damaged.
Several damage characterisation investigations have been undertaken by Greenhalgh
et al. [67] with specific attention to the behaviour of damaged composite stiffened
panels subjected to compressive loading. Single plane defects were embedded in the
panels at various locations during manufacture. The moving mesh technique was used
to model delamination buckling, global panel buckling and damage growth. Finite
clement models were constructed using separate layers of shell elements for the two
skin sublaminates, linked by constraint equations outside the defect. The models were
successful in representing the local buckling, damage initiation and evolution. The
technique was shown to be efficient at simulating single plane delamination growth.
The authors recommended further research to model crack migration and damage
growth beneath substructures such as stiffeners. It was noted that the damage shape
tended to be elliptical and its orientation was a function of the loading direction.
The development of an efficient three-dimensional finite element was presented by
Falzon et al. [68] It was designed for modelling composite laminates and used in a
mixed-mode fracture mechanics example. The main advantage of this formulation
is the ability to model bending of a laminated composite structure with a single 3-D
element through the thickness, thereby improving the computational efficiency of
calculating strain energy release rates.
A sophisticated finite element model was developed by Wisnom and Chang [33] in
order to approach in detail the development of damage in notched composites. Each
of the laminate's plies was represented by an element connected by interface
elements defined within ABAQUS. The interface elements introduced nonlinear
springs between the plies so that, prior to reaching a critical stress, the stiffness
between the plies is elastic and thereafter plastic. The model successfully
represented the physical processes of splitting and delamination observed in
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Chapter 2 - Literature Review
experimentation. However, this model is limited by the computational power
needed to solve a structural problem since a composite structure encountered in a
real-life application will typically have twenty or more plies.
Falzon et al [69] presented an experimental and numerical study of the failure of
thick-sectioned stiffener run-out specimens loaded in uniaxial compression. The
experiments revealed that failure was initiated at the edge of the run-out and
propagated across the skin–stiffener interface. High frictional forces at the edge of the
run-out were also deduced from a fractographic analysis and it was proposed that
these forces may enhance the fracture toughness of the specimens.
The stiffeners tested in [63] were also numerically studied by Cosentino and Weaver
[70]. An nonlinear approach was developed and the results of the tests were used to
for validation purposes The correlation with the test results was fairly good and
further development of the approach was proposed, especially when the stiffeners are
non-symmetric.
Zhang et al [71] and Madhi et al [72, 73] used strain gages to investigate the
performance of repaired thin-skinned, blade-stiffened composite and the FE method
was used as a designing tool. It is thought that the failure may have initiated at a crack
in the skin, with the initial crack growing perpendicularly to the applied stress and
leading to stiffener debonds, and ultimately to collapse of the skin and the stiffeners.
The knowledge of the failure mechanisms could probably help to explain these types
of problems.
Structures under shear loading were analysed by Krueger [74]. A stringer reinforced
composite panel was modelled with shell elements, while the stringer foot, web and
noodle were modelled with a local 3D solid model and the mixed- mode strain energy
release rates were calculated. The stiffened panel that used is illustrated in Figure
2.13. It was concluded that the shear loading causes buckling on the panel, which
subsequently results in skin/stringer separation at the location of an embedded defect.
Alterations in local stiffness caused differences in the failure index distributions. The reason
for different local stiffnesses having occurred is that different modelling techniques were
used in the noodle and transition radius between the shell elements and the 3D solid
elements.
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Chapter 2 - Literature Review
Figure 2.13: Stringer stiffened panel subjected to shear loading [74]
2.8 Discussion and conclusions Aerospace structures demand several constraints upon their design, most notably
strength, stiffness, weight and cost. Thin plates are usually efficient at carrying in-
plane loads. The minimum plate thickness is often governed by a stiffness constraint
in the form of buckling capacity rather than strength.
Damage tolerant structures are often designed based upon empirical data derived from
experience in earlier applications. The design cycle therefore relies quite substantially
upon a testing and validation program, which is both time consuming and prohibitively
expensive. A need arises for improved design guidelines and analysis methods to
evaluate a particular design more accurately.
A summary of research efforts into damage modelling of stiffened composite panels
subjected to tensile and compressive loads has been presented and summarized in
Appendix A. The literature indicates that the majority of damage modelling techniques
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Chapter 2 - Literature Review
comprise of failure criteria, fracture mechanics and damage mechanics approaches,
although not necessarily all three. The ideal damage model for predicting the
residual strength of stiffened multidirectional composite panels, from the composite
designer's perspective should:
• Calculate the applied stress at which unstable fracture occurs
• Predict the evolution of a damaged region to assess the possibility of repair
work
• Capture the main damage modes e.g. delamination, fibre-breakage
• Be computationally inexpensive
• Be applicable to a component of any shape, stacking sequence and
subjected to any loading condition
Research has tended to focus on specific aspects of damage modelling in order to
gain detailed insight into the various damage mechanisms; however, a model that
encompasses all aspects associated with compressive failure is still lacking.
On the specific problem of skin-stiffener debonding, a large body of experimental and
analytical work carried out on the response and failure of stiffened composite
aerostructures loaded in uniaxial compression [57] has demonstrated the vulnerability
of co-cured and secondary bonded structures to interlaminar and peel stresses at the
skin-stiffener interface. The main advantage of these bonding procedures is the
significant potential weight saving over mechanically fastened structures. This
interface weakness therefore is of major concern in stiffener run-out regions where the
stiffener is terminated due to a cutout, intersecting a rib, or some other structural
feature that interrupts the load path. It is also of major concern that current design
rules are inadequate in accounting for skin-stiffener failure at these critical regions.
In a previous work [63, 64] a series of tests, with a stiffener/plate loaded in
compression, revealed high compressive through-thickness stresses which resulted in
considerable frictional shearing resistance and increased the apparent fracture
toughness needed to estimate the debonding loads. This lead to strengths that were
more than double those predicted and the need for further investigation is clear.
A set of single-stiffener panels where the stiffener is run-out, short of the loaded edge,
will be tested in compression. Testing specimens in compression can provide a
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Chapter 2 - Literature Review
challenging benchmark for the developed numerical models that can use for more
complex types of failure. The loading offset induces significant through-thickness
loads which, in compression, may enhance the apparent fracture toughness. While the
mechanics is understood reasonably well, there is still considerable debate on the
details of failure initiation and propagation at these critical location Careful
observations using DIC and AE will be undertaken to deduce the nature of
delamination/debonding which will help guide the development of the analysis tools.
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Chapter 3 - Material Characterization
Chapter 3
Material Characterization
3 Material Characterization
3.1 Introduction This section presents the characterization of strength and stiffness tests for IM7/8552
carbon epoxy. The material was supplied by Hexcel with layer thickness of 0.25 mm.
The tests were carried out in the Department of Aeronautics, Imperial College
London. The testing machines used for the tests were the Zwick testing machine and
Instron testing machine.
3.2 Stiffness and Strength Characterization
3.2.1 Introduction
The in-plane stiffness and strengths were measured, in accordance with the respective
standards. More specifically, the transverse/longitudinal tensile (ASTM D3039-76
[75]) /compressive (Imperial College method [76]) stiffnesses and strengths were
measured, as well as the non-linear in-plane shear response (ASTM D3518D-3518M
[77]).
3.2.2 Manufacturing
In order to manufacture the specimens, appropriate laminates were first needed.
Appropriate lengths were cut from the composite roll and stacked until the required
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Chapter 3 - Material Characterization
thickness was achieved. Each group of four plies was compacted to prevent air
entrapment, Figure 3.1. Three plates were manufactured, labelled No.1, No.2 and
No3, as can be seen in Figure 3.2.
Figure 3.1: Arrangement for producing laminates in Autoclave [47]
Figure 3.2: Schematic of plates
The dimensions of each plate and the type of specimens that they produced can be
seen in Table 3-1. When the laminates were ready, they were placed in the Autoclave
for curing, see Figure 3.1. After curing, and to ensure that there were no defects in the
laminate, the ultrasonic C-scan was used Figure 3.3, where on the upper right corner
the red circle is a coin that was used as point of reference).
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Chapter 3 - Material Characterization
Table 3-1: Function and characteristics of the manufactured plates
Plate Test
Dimensions
(mm)
number
of
layers layup
Thickness
(mm)
No.1 tensile 0, compression 0 300x330 8 (0o)8 2
No.2 tensile 90,compression 90 300x330 16 (0o)16 4
No.3 shear 300x300 16 (±450 )8S 4
Figure 3.3: The C-scans of the plates
End tabs were bonded on the plates using 3M Scotch-Weld. The surfaces of the
plates, where the end tabs placed, as well as the tabs, were cleaned using air pressured
sand and cleaned before the gluing of the end tabs.
The plates with the end tabs were placed on the vacuum table for curing the glue. For
the compression specimens, reverse-chamfered end tabs were used. These tabs were
bonded in two stages, first from the one side and then from the other in order to have
constant glue thickness, as seen in Figure 3.4.
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Chapter 3 - Material Characterization
Figure 3.4: Manufacturing of compression specimen [9]
Finally, the specimens were cut using a wet saw machine with diamond blade to the
appropriate dimensions (Table 3-2) from the respective plates. The 0o tension
specimens were cut from plate No.1 and named t0, t from tension and 0 from the 0o
direction of the fibres.
The same naming code was used for the rest of the specimens, c from compression,
90 from the 90o direction and s from shear. The c0 specimens were cut from No1
plate. From the No2 plate were cut the t90 and c90 specimens and plate No3 was
used only for the s specimens.
Table 3-2: Nominal dimensions of specimens
Test specimen end tab
width
(mm)
length (mm) thickness
(mm)
length (mm) thickness (mm)
Tension 0o 15 250 2 56 1.5
Tension 90o 25 175 4 25 1.5
Compression 0o 10 90 2 40 1.5
Compression 90o 10 90 4 40 1.5
Shear 25 250 4 56 1.5
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Chapter 3 - Material Characterization
Figure 3.5: Specimen dimensions
3.2.3 Testing
The testing machines used for the tests were the Zwick testing machine for the
compression tests and Instron testing machine for the tension and shear tests. The
loading rates depended on the test, 1mm/min for the compression tests and 2mm/min
for the tension and shear tests. Load and crosshead displacement were recorded
continuously by a PC data logger connected to the load cell and the testing machine.
3.2.3.1 Compression
The Imperial College method for testing composite materials in compression [76] was
used. In order to ensure that the specimens were fitted exactly in the rig, a load of
0.5 kN was applied to the specimens before the tightening of the bolts. 2 mm strain
gauges (FLA-2-11) were placed on the specimens on both sides for measuring the
strains and monitor the bending, Figure 3.6.
During the test a problem with the front gauge of the specimen c0-2 prevented the
data collection and the analysis was based only on the rear gauge data. A problem
occurred with the data collection of the specimen c90-4.
Eight specimens were tested in longitudinal compression. Figure 3.8 shows the failure
strengths of the specimens. The average strength is 1,572.9 MPa with a coefficient of
variation of 6.6%. For all tests, the bending was lower than 5%, as it can be seen in
Figure 3.9, except for specimen c0-5, where the bending is around 6%. Figure 3.10
presents the stress-strain curves of the specimens. The average longitudinal modulus
is 154.1 GPa with a coefficient of variation of 1.5%.
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Chapter 3 - Material Characterization
Figure 3.6 : Compression specimens inside the rig
Figure 3.7: Compression specimens after testing
In transverse compression the same number of specimens, as in longitudinal, was
tested. The only difference was that the specimens had double the thickness. Figure
3.11 presents the failure strengths; the average strength is 254.6 MPa with a
coefficient of variation of 4.6%. As it can be seen in Figure 3.12, the bending was
lower than 10%. The stress-strain curves are presented in Figure 3.13. The transverse
modulus is 9.8 GPa with a coefficient of variation of 4.4%.
specimen
rig
Strain gage
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Chapter 3 - Material Characterization
Figure 3.8: Failure strengths of longitudinal compression specimens
Figure 3.9: Bending versus strain for the longitudinal compression specimen
1631 1609 1639
1469
1676 1530 1484 1545
0
200
400
600
800
1000
1200
1400
1600
1800
c0-1 c0-2 c0-3 c0-4 c0-5 c0-6 c0-7 c0-8
stre
ngth
(MPa
)
specimens
0%
5%
10%
15%
20%
25%
30%
0 0.002 0.004 0.006 0.008 0.01
Bend
ing
Strain
c0-1
c0-3
c0-4
c0-5
c0-6
c0-7
c0-8
5%
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Chapter 3 - Material Characterization
Figure 3.10: Stress-strain curves for the longitudinal compression specimens
Figure 3.11: Failure strengths of the transverse compression specimens
0
200
400
600
800
1000
1200
1400
1600
1800
0 0.002 0.004 0.006 0.008 0.01 0.012
Stre
ss (M
Pa)
Strain
c0-1 c0-3 c0-4 c0-5 c0-6 c0-7 c0-8
248.2 260.3
246.6 250.6 266.3 262.2
249.3 253.3
0
50
100
150
200
250
300
c90-1 c90-2 c90-3 c90-4 c90-5 c90-6 c90-7 c90-8
Stre
ngth
(MPa
)
Specimen
Page | 57
Chapter 3 - Material Characterization
Figure 3.12: Bending versus strain for the transverse compression specimen
Figure 3.13: Stress-strain curves for the transverse compression specimens
0%
5%
10%
15%
20%
25%
30%
0 0.002 0.004 0.006 0.008 0.01
Bend
ing
Strain
c90-1
c90-2
c90-3
c90-5
c90-6
c90-7
c90-8
5%
0
20
40
60
80
100
120
140
160
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016
Stre
ss (M
Pa)
Strain
c90-1
c90-2
c90-3
c90-5
c90-6
c90-7
c90-8
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Chapter 3 - Material Characterization
3.2.3.1.1 Tensile
The tensile test method can be found as ASTM D3039-76 [75]. It is a method that
allows determination of the properties of the lamina. For longitudinal tension, three
strain gauges were placed on the first two specimens for measuring bending, as
described in ASTM D3039-76, and on the rest of them cross strain gauges FCA-3-11
were placed. On the transverse tension specimens gauges (FLA-6-11) were placed in
the loading direction Figure 3.14. Specimens t90-1 and t90-2 were destroyed
accidentally.
Figure 3.14: Testing of tensile specimen
Seven specimens were tested in longitudinal tension. Figure 3.16 shows the failure
strengths of the specimens. The average strength is 2,260 MPa with a coefficient of
variation of 7.35%. Figure 3.17 presents the stress-strain curves of the specimens. The
average longitudinal modulus is 176.6 GPa with a coefficient of variation of 6.8%.
In transverse tension, the same number of specimens, as in longitudinal, was tested.
Specimens t90-2 and t90-3 destroyed accidently from a collapse of the the testing
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Chapter 3 - Material Characterization
machine’s jaw. Figure 3.18 presents the failure strengths; the average strength is 62
MPa with a coefficient of variation of 7.6%. The stress-strain curves are presented in
Figure 3.19. The average transverse modulus is 8.6 GPa with a coefficient of variation
of 14.3%.
Figure 3.15: Tensile specimens after testing, 0o on the left and 90o on the right
Figure 3.16: Failure strength of the longitudinal tension specimens
2143.6 2163 2130.9 2324.5 2372 2426
0
500
1000
1500
2000
2500
t0-1 t0-2 t0-3 t0-4 t0-5 t0-7
Stre
nght
(MPa
)
Specimens
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Chapter 3 - Material Characterization
Figure 3.17: Stress-strain curves of the longitudinal tension specimens
Figure 3.18: Failure strength of the transverse tension specimens
0
10
20
30
40
50
60
70
80
0 1 2 3 4 5 6 7
Load
(KN
)
Displacement (mm)
t0-1 t0-2 t0-3 t0-4 t0-5 t0-7
64.1 64.7 62
57.3 58.5
0
10
20
30
40
50
60
70
t90-3 t90-4 t90-5 t90-6 t90-7
Stre
nght
(MPa
)
Specimens
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Chapter 3 - Material Characterization
Figure 3.19: Stress-strain curves of the transverse tension specimens
3.2.3.2 Shear
The shear tests used in order to find shear strengths, ultimate shear strains and shear
modulus. The method that was used for measuring the in plane properties of the
material is the [ 45]s± coupon test method that is describing from the ASTM
D3518D-3518M [77].
Figure 3.20: Shear specimens after testing
0
10
20
30
40
50
60
70
0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008
Stre
ss (M
Pa)
Strain
c90-3
c90-4
c90-5
c90-6
c90-7
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Chapter 3 - Material Characterization
The shear strain (γ) was computed using the longitudinal strain (εl) and transverse
strain (εtr), as:
l trγ ε ε= − (3.1)
The shear stress (τ) was computed from the applied load (P) and initial cross sectional
area (Ao) as suggested by the ASTM standard:
02
PA
τ = (3.2)
Figure 3.21: Failure strength of shear specimens
Seven specimens were tested, Figure 3.20. Strain gauges FCA-6-11 were used for the
data collection. Figure 3.21 shows the failure strengths of the specimens. Specimens
s-5, s-6, s-7 and s45-3c were loaded and unloaded. The average strength is 101.2 MPa
with a coefficient of variation of 4%. Figure 3.22 and Figure 3.23 present the stress
versus strain for straight loaded and loaded-unloaded specimens respectively. There
were problems with the data collection for specimens s-2 and s-3, s45-4 had a strain
105.3 98.3 101.2 101.6 99.8 101.5 101.7 100.1 101.5
0
20
40
60
80
100
120
s-1 s-4 s-5 s-6 s-7 s45-3c s45-5c s45-6c s45-7c
Stre
nght
(MPa
)
Specimens
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Chapter 3 - Material Characterization
gage misalignment. The average transverse modulus is 4.48 GPa with a coefficient of
variation of 22%.
Figure 3.22: Stress-Strain curves of the shear specimens that were tested without unloading
Figure 3.23: Stress-Strain curves of shear specimens that were tested with unloading
0
10
20
30
40
50
60
70
80
90
100
0 0.005 0.01 0.015 0.02
Stre
ss (
MPa
)
Strain
s45-1
s45-4
s45-5c
s45-7c
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Chapter 3 - Material Characterization
3.2.4 Results
All the test results collected in Table 3-3, which also includes a comparison with the
material manufacturer values.
Table 3-3: Comparison of the material properties
IM7/8552 Material
Properties
from Hexcel
Measured
Properties
Difference
Longitudinal Young’s
Modulus
Tension 165 GPa 177 GPa 7.0%
Compression 145 GPa 154 GPa 6.3%
Transverse Young’s
Modulus
Tension 9.4 GPa 8.6 GPa 8.5%
Compression 10.6 GPa 9.8 GPa 10.2%
Shear modulus 4.5 GPa 4.48 GPa 0.4%
Longitudinal Strength
Tension 2.6 GPa 2.2GMPa 13.0%
Compression 1.5 GPa 1.57 GPa 4.8%
Transverse Strength
Tension 60 MPa 62 MPa 3.3%
Compression 290 MPa 254.6 MPa 12.2%
Shear strength 90 MPa 101.2 MPa 12.4%
Poisson’s ratio 0.3 0.34 13 .3%
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Chapter 3 - Material Characterization
3.3 Fracture Toughness Characterization
3.3.1 Introduction
The energy release rate, G, is a parameter which characterizes the propensity of a
crack to grow. The critical value of this crack driving force, Gc, is called critical
energy release rate (or fracture toughness) and it is taken as a property of the material
and it is used to characterise the ability of a material to resist fracture in the presence
of cracks.
3.3.2 Manufacturing
Appropriate layers measuring 300x330 mm2 were cut from the roll and stacked over
each other. Each block of 4 plies was compacted to prevent the air entrapment. The
nominal thickness of the laminate was 3 mm, but the layup was done in two halves in
order to insert at the midplane of the laminate a non-stick, fluoroethylene polymer
film, of thickness ≈12.5 μm, and form an initiation site for the delamination, Table
3-4.
Table 3-4: Function and characteristics of the manufactured plate
Plate Test Dimensions
(mm)
number of
layers
layup Thickness
(mm)
No.4 DCB, 4ENF,
MMB
300x330 12 (0o)12 3
When the laminate was ready, it was placed in the auto-clave for curing. After curing
and to ensure that there were no defects in the laminate, the ultrasonic C-scan was
used, Figure 3.24. The dimensions of each plate and the type of specimens that were
produced can be seen in Table 3-5. The specimens were cut, using a wet saw machine
with diamond blade, to the appropriate dimensions.
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Chapter 3 - Material Characterization
Figure 3.24: Schematic of plate for the fracture toughness specimens and the C-scan of the plate
Table 3-5: Nominal dimensions of the fracture toughness specimens
Test specimen a
width
(mm)
length
(mm)
thickness (mm) ao
(mm)
insert lenght
(mm)
DCB 20 170 3 50 60
4 ENF 20 140 3 40 50
MMB 20 135 3 25 35
Double cantilever beam (DCB) specimens were manufactured for mode I according
to ASTM designation D5528 [78], 4 point end notch flexure for mode II [79] and
mixed mode bending tests for mixed modes I and II [80]. End tabs were bonded on
the DCB and MMB specimens. The surfaces of the specimens, where the end tabs
were placed, as well as the tabs, were cleaned using grit blasting and cleaned before
the gluing of the end tabs. The end tabs were glued with an epoxy adhesive and left
overnight under applied pressure to promote good bonding.
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Chapter 3 - Material Characterization
Finally, all the specimens were precracked so as to break the resin inclusion that had
been created at the end of the film and in a way that prevents the crack to propagate
extensively, as shown in Figure 3.25.
Figure 3.25: Precraking of a DCB specimen
3.4 Testing The testing machine that was used for the tests was an Instron testing machine,
equipped with a 10 KN load cell. The loading rates were 0.5 mm/min for the DCB
tests and 0.2 mm/min for the 4 ENF and MMB tests that performed for another
project [81]. Load and crosshead displacement were recorded continuously by a PC
data logger connected to the load cell and the Instron machine at a sampling rate of 2
samples per second. The crack tip was monitored using a CCD camera displaying an
enlarged image in a TV screen. An event marker was used to send a signal to the
computer as the crack tip passes through each mark on the specimen.
3.4.1 DCB
The ASTM designation D5528 [78] was used for this test method, which describes the
determination of the opening Mode I interlaminar fracture toughness, GIc, of
continuous fibre-reinforced composite materials using the double cantilever beam
(DCB) specimen with end blocks, as shown in Figure 3.26.
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Chapter 3 - Material Characterization
Figure 3.26: DCB specimen [7]
The specimens are painted white on one side and fine lines of 1mm increments for the
first 5mm of growth from the delamination front band, and then in 5mm increments
for a further 20mm were scribed with a height gauge to facilitate the observation of
the delamination. An example of a DCB test can be seen in Figure 3.27, where in the
inset the inserted film and the area that the interlaminar crack propagated can be
observed.
Figure 3.27: Testing a DCB specimen
The Modified Beam Theory Method [7] was used for the data analysis. Five
specimens were tested, the load-displacement curves are presented in Figure 3.28, and
Page | 69
Chapter 3 - Material Characterization
compared very well with the corrected beam theory as in Figure 2.4. The results of the
R-curves using the Modified Beam Theory (MBT) are shown in Figure 3.29.
Figure 3.28: Load-displacement traces for DCB specimens
Figure 3.29: R-curves for DCB specimens using the Modified Beam Theory (MBT) Method
0
5
10
15
20
25
30
35
40
0 2 4 6 8 10 12 14 16 18 20 22
Load
(kN
)
Displacement (mm)
DCB-1 DCB-2 DCB-3 DCB-4 DCB-5
0
50
100
150
200
250
300
350
400
450
0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12
GIC
(J/
m2 )
Delamination length, a [m]
DCB-1
DCB-2
DCB-3
DCB-4
DCB-5
Page | 70
Chapter 3 - Material Characterization
The mode I interlaminar fracture toughness is calculated according to the modified
beam theory,
32 ( )Ic
PGb
δα
=+ ∆
(3.3)
where GIc is the fracture toughness, P is the load, δ is the opening displacement, b is
the specimen width, a is the crack length and Δ is a correction term applied to the
crack length.
The latter is determined from the experimental data after generating a least square plot
of the cubic root of compliance, C1/3, as a function of delamination length, a. The
correction term Δ is the value that should be added to the crack length to make the
plot go through the origin. The compliance, C, is defined as δ/P. The average GIc is
302 J/m2 with coefficient of variation of 13.6%.
Using the Compliance Calibration (CC) Method, which generates a least squares plot
of log (d/P) versus log (a) and n is the slope,
2IcnPG
bδα
= (3.4)
the average GIc is 293 J/m2 with coefficient of variation of 16% and results of each
specimen can be seen in Figure 3.30.
Page | 71
Chapter 3 - Material Characterization
Figure 3.30: R-curves for DCB specimens using the Compliance Calibration (CC) Method
3.4.2 4 ENF
The four point bend end-notched flexure (4ENF) test (Figure 4.32) has been proposed
as a new test to characterise mode II delamination [79]. This test has several
advantages over other tests including reduced friction, stable delamination growth and
simple fixture design. However, because it is a relatively new test, it has not been
validated on a wide range of material types. The 4ENF was also successfully used in
fatigue to characterise delamination growth and derivation of threshold values [82].
Figure 3.31: the 4ENF test fixture
0
50
100
150
200
250
300
350
400
450
0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12
GIC
(J/
m2 )
Delamination length, a [m]
DCB-1 DCB-2 DCB-3 DCB-4 DCB-5
Page | 72
Chapter 3 - Material Characterization
The specimens had a delamination starter length of 40 mm from the edge of the
specimen. One of the edges of the specimen was polished, and painted white on which
fine lines of 1 mm increments for the first 10 mm of growth from the delamination
front and then in 5 mm increments to a crack length of at least 70 mm were scribed
with a gauge height to aid the observation of the delamination (Figure 4.33).
Figure 3.32: Testing a 4ENF specimen
Data reduction for 4ENF test are in accordance with reference [83]. The results of the
4ENF test are calculated by considering the linear relationship between compliance,
C, and delamination length, a,
0 C ma C= + (3.5)
and generating a least squares fit of the experimental data to determine m and C0.
Mode II interlaminar fracture toughness IICG was calculated as [79]
2 2IIc
P mGw
= (3.6)
where w is the specimen width and P is the applied load.
The compliance calibration was performed in the 4ENF using specimens with
different initial crack lengths: The constant m is the slope of the best fit straight line
on the graph of compliance against delamination length. The average IICG is 630.9
Page | 73
Chapter 3 - Material Characterization
N/m with coefficient of variation of 14%. The loads versus the displacement are
displayed in Figure 3.33.
Figure 3.33: Load displacement curves for the 4ENF specimens
Figure 3.34: R-curves for 4ENF specimens
0.00
0.20
0.40
0.60
0.80
1.00
1.20
0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50
Load
(kN
)
Displacement (mm)
4ENF-2 4ENF-3 4ENF-4 4ENF-5
0
100
200
300
400
500
600
700
800
0.04 0.05 0.06 0.07 0.08 0.09 0.1
GIIC
(J/
m2 )
Delamination length, a (m)
4ENF-2
4ENF-3
4ENF-4
4ENF-5
Page | 74
Chapter 4
Numerical Design of
Stiffener Run-outs for
Damage Tolerance
4 Numerical Design of Stiffener Run-outs for
Damage Tolerance
4.1 Introduction The effect of different parameters such as material and geometry can be economically
explored by using virtual tests rather than real tests. This chapter introduces a model
that predicts the peeling stresses at bonded interfaces. The model is based on a tested
baseline design and the effect of geometrical details on the stress magnitude and
distribution are discussed. This is followed by a study of different stiffener run-out
designs models where the effects of the design parameters on the stresses between the
skin and the stiffener were investigated. The results led to the development of a
parametric approach to find an optimal run-out design for increased damage tolerance.
Chapter 4 - Numerical Design of Stiffener Run-outs for Damage Tolerance
4.2 Stress profile at interfaces with geometrical and material
discontinuities The recent trend of incorporating more composite material in primary aircraft
structures has highlighted the vulnerability of stiffened aerostructures to through-
thickness stresses, which may lead to delamination and debonding at the skin–
stiffener interface, leading to collapse. Stiffener run-out regions are particularly
susceptible to this problem and cannot be avoided due to the necessity to terminate
stiffeners at rib intersections or at cutouts, interrupting the stiffener load path.
4.2.1 Theoretical Analysis
Previous investigations [60, 61, 63, 64] on the response of stiffened composite panels
loaded in uniaxial compression, have shown that the torsion rigidity of the stiffeners
prevents the rotation following the deformation of the buckled skin. This gives rise to
high peel stresses which result in either failure initiating at the edge of the stiffener
flange and propagating towards the stiffener centreline or failure may initiate at the
‘noodle’ region below the stiffener web and propagate out towards the edge of the
flange. For these reasons, a good understanding of the stress state at the geometric and
material discontinuity that constitutes a run-out is of paramount importance. A closed-
form model is developed that predicts peel stresses in adhesively bonded joints, as
shown in Figure 4.1.
Figure 4.1 : Close-form model
1tat
2t
2c
1E
2EaE
xNxN
Adherend 1Adhesive
Adherend 2
Page | 76
Chapter 4 - Numerical Design of Stiffener Run-outs for Damage Tolerance
This model predicts peel stress using a beam on elastic foundation (BOEF) approach.
By accounting for the coupling of peel stress terms within the governing equation, this
model is suitable for the stress analysis of generic asymmetric joints, that is, joints
that have adherends of mismatched elastic modulus and thickness.
In order to calculate the peel stress, the lap joint is modelled by two beams connected
by a distributed elastic spring with a thickness at given by:
a
a
Ekt
= (3.1)
where aE is the Young's modulus of the adhesive as shown in Figure 4.1. These
eccentricity bending moments are responsible for the peel stress component. A fourth-
order linear differential equation for the relative vertical displacement, w, based on
BOEF interaction between the adherends, can be derived as
(3.2)
where 1 2w w w= − is the relative vertical displacement components of the adherends
1 and 2. 1 1 11 /D E I= and 2 2 21 /D E I= , where E and I are the Young modulus and
inertia respectively of the adherends 1 and 2. Equation 3.2 is solved for the relative
vertical displacement, w ; by the general solution [84]:
( ) ( )1 2 3 4( ) cos sin cos sinx xw x e C x C x e C x C xβ ββ β β β−= + + + (3.3)
where
14
1 2
1 1 12
kD D
β
= +
(3.4)
The variables 1C , 2C , 3C and 4C can be found from the boundary conditions of the
free body diagram shown in Figure 4.2.
Page | 77
Chapter 4 - Numerical Design of Stiffener Run-outs for Damage Tolerance
Figure 4.2: Free Body Diagram
For x c= −
1( ) 0M c− = (3.5)
1( ) 0Q c− = (3.6)
1( ) 0N c− = (3.7)
2
222 2 2( ) d wM c D M
dx− = = (3.8)
3
22 2 23( ) d wQ c D Q
dx− = = (3.9)
2 ( ) xN c N− = (3.10)
For x c=
1( ) 0M c = (3.11)
1( ) 0Q c = (3.12)
1( ) 0N c = (3.13)
aE
1E
2E
c− xc
2M2M2Q 2Q
xN xN
Page | 78
Chapter 4 - Numerical Design of Stiffener Run-outs for Damage Tolerance
2
222 2 2( ) d wM c D M
dx= = − (3.14)
2
22 2 22( ) d wQ c D Q
dx= = − (3.15)
2 ( ) xN c N= − (3.16)
From equations 3.5 and 3.8 it is extracted that
2
22
2x c
d w Mdx D=− = − (3.17)
From equations 3.6 and 3.9 it is extracted that
3
23
2x c
d w Qdx D=− = − (3.18)
From equations 3.11 and 3.14 it is extracted that
2
22
2x c
d w Mdx D= = (3.19)
From equations 3.12 and 3.15 it is extracted that
3
23
2x c
d w Qdx D= = (3.20)
Solving equation 3.3 using as boundary conditions equations 3.17 to 3.20 leads to the
values of 1C , 2C , 3C and 4C .
The peeling stresses are finally:
p kwσ = (3.21)
Page | 79
Chapter 4 - Numerical Design of Stiffener Run-outs for Damage Tolerance
The plot of the peeling stresses of the half section and for values in Table 4-1, that are
similar to the stiffener that is examined later, can be seen in Figure 4.3.
Table 4-1 : Values [63]
Variables Values
xN 180 kN
1t 60 mm
2t 8 mm
at 1 mm
1E 124.4 GPa
2E 102.4 GPa
aE 1 GPa
Figure 4.3 : Plot of peeling stresses from analytical solution
A study on how the solution of equation 3.21 is affected by the variables and
is presented in Figure 4.4. From Figure 4.4a can be assumed that when k is
increased, the higher the peeling stresses are closer to the end of the specimen by
decreasing the area of action. Also, when the is decreasing, as can be seen in
Figure 4.4b, the peeling stresses are getting smaller and reducing the affected area. In
real structures, as in stiffeners, the stresses can be decreased by changing 1D and as
-12-10
-8-6-4-2024
0 100 200 300 400
Peel
ing
Stre
ss [M
Pax1
03 ]
length [mm]
k
1 2/D D
1 2/D D
Page | 80
Chapter 4 - Numerical Design of Stiffener Run-outs for Damage Tolerance
1D is geometrically dependent, the design of the stiffener run-out can play an
important role in the failure procedure. This can be used, for example, by tapering the
tip of the stiffener in order to decrease the stresses. It is clear that the modification of
the run-out design could play an important role in the stress field and this was studied
in next paragraphs by using finite element simulations.
Figure 4.4: A study on how variables (a) and (b) affect the solution.
-10-8-6-4-2024
0 100 200 300 400
Peel
ing
Stre
ss [M
Pa x
103 ]
lenght [m
D1=0.5*D2
D1=D2
D1=2*D2
(a)
(b)
-20
-15
-10
-5
0
5
0 100 200 300 400
Peel
ing
Stre
ss [M
Pa x
103 ]
lenght [m
0.5*k
k
2*k
length [mm]
length [mm]
k 1 2/D D
Page | 81
Chapter 4 - Numerical Design of Stiffener Run-outs for Damage Tolerance
4.2.2 Stiffener run-out Designs
The current capability to use finite element simulations to predict the mechanical
response of the run-out was assessed. The objective was to investigate experimentally
how the geometry of the run-out determines the failure sequences, and how the failure
could be optimized by carefully designing the run-out. Representative structural
components were selected [63] and defined, sized as in Figure 4.5, and prediction with
nominal geometry were made using ABAQUS.
Figure 4.5: Stiffener dimensions in mm [63]
The results of these models helped in undertaking the distribution of peel stresses at the
skin-stiffener interface. Different stiffener designs, as presented in Figure 4.6, were
studied:
• Stif 0. The run-out type Stif 0 had an overall length of 440 mm and a width of
120 mm. The length of the stiffener was 400 mm, leaving an unsupported skin
section of 40 mm. The skin thickness was 8 mm.
Page | 82
Chapter 4 - Numerical Design of Stiffener Run-outs for Damage Tolerance
Figure 4.6 : The designs of the stiffeners that were studied.
• Stif 1. This stiffener blade was tapered linearly over a distance of 200 mm, to a
height of 30 mm above the skin at the edge of the run-out. The specimen can
be seen in Figure 4.5. It can be observed that the taper does not go down to the
skin, which simplifies the manufacturing. This results in a step discontinuity in
400
40
60
120
400
40
60
120
200
20
400
40
60
120
200
400
40
60
120
200
300
40
40
120
200
100
300
40
80
120
200
100
Stif 0
Stif 4 Stif 5
Stif 3Stif 2
Stif 1
Page | 83
Chapter 4 - Numerical Design of Stiffener Run-outs for Damage Tolerance
the cross-sectional area, which gives rise to a stress concentration at the edge
of the stiffener.
• Stif 2. This has the taper of the blade going down to the skin. This type of
design aims to minimise the discontinuity between the stiffener and the skin at
the stiffeners tip. Two different types of tapering were used, the linear and the
curved, in order to detect the effects of different tapered types of the blade.
• Based on this design, Stif 3 was studied with different tapered blade. The
blade was tapered with a curvature in order to detect any effects of a non-
linear tapared blade. The effect of the blade design was investigated in order to
determine the local notch stress distribution.
• In order to specify the role of the flange of the stiffener and the importance
that it played to the behaviour of the structure, Stif 4 was introduced. This
design is similar to Stif 2, but the flange was narrower to the tip following the
tapering of the blade.
• In addition to the previous design, Stif 5 had a widened flange targeting on the
stress distribution of the local stresses to the skin. Here the two designs, Stif 4
and Stif 5, were the design with the tapered flange and the design with the
wide flange. Also, this design could provide information about the role of the
flange in stiffener run-outs.
The lay-up for the half stiffener is quoted from the bottom flange surface to the free
surface and is shown in Table 4-2. The material used was IM7/8552 and the
properties are shown in the Table 4-3. The lay-up used in the models was similar to
skin-stiffener run-outs tested by Falzon [63]. The skin lay-up is given from the outer
to inner surfaces of the specimen with the outer layer defined as the smooth surface
which would form part of the aerodynamic surface in a wing structure and the inner
surface defined as the surface on which the stiffener is mounted.
Table 4-2 : Lay-up details
Lay-up details for specimens Lay-up
Skin [45/−45/0/90/02/−45/45/02/90/02/45/−45/0]S
Stiffener (per half section) [0/90/02/−45/45/04/−45/45/02/90/03/90/0]
Page | 84
Chapter 4 - Numerical Design of Stiffener Run-outs for Damage Tolerance
Table 4-3: Material properties of IM7/8552
Properties IM7/8552
Longitudinal Young’s Modulus xE Tension 176.6 GPa
xE Compression 154.1 GPa
Transverse Young’s Modulus yE Tension 8.6 GPa
yE Compression 9.8 GPa
Out of plane Young’s Modulus zE Tension 10.5 GPa
zE Compression 9.4 GPa
Shear modulus xyG 4.5 GPa
Out of plane Shear modulus xzG 4.3 GPa
Out of plane Shear modulus yzG 3.2 GPa
Longitudinal Strength Tension 2.3 GPa
Compression 1.6 GPa
Transverse Strength Tension 0.06 GPa
Compression 0.25 GPa
Shear strength 0.1 GPa
Poisson’s ratio xyν 0.34
Poisson’s ratio xzν 0.31
Poisson’s ratio yzν 0.48
Mode I critical strain energy release rate IcG 0.21 kJ/m2
Mode II critical strain energy release rate IIcG
0.61 kJ/m2
Page | 85
Chapter 4 - Numerical Design of Stiffener Run-outs for Damage Tolerance
4.3 FE Models
4.3.1 The Model
The FE models were created in ABAQUS [4]. The main model had 5 different parts,
the skin, the adhesive that was between the skin and the stiffener, the 2 parts of the
stiffener and the filler that is used in order to fill the gap that was created because of
the curvature of the stiffener parts.
All the composite parts were created using the composite module and the properties
that given were the material properties of the IM7/8552. The adhesive had the matrix
properties of IM5/8552 and the filler had elastic behaviour of a 0 ply.
All the specimens were loaded on the unsupported skin with a constant load of 180
kN, while the other side was fixed. All parts were modelled with three dimensional
hexahedral solid elements, C3D8, to accurately capture stresses in the through-
thickness direction. Also, solid elements are capable of modelling several layers of
different materials for the analysis of laminated composites. The analysis made use of
ABAQUS/Standard which well suited to quasi-static and low-speed dynamic events.
4.3.2 Mesh Sensitivity Study
The mesh sensitivity was examined by applying different meshes to the configuration
Stif 2. The region that was more critical is near the tip of the stiffener and for this
reason a finer mesh was needed there. The bias module in ABAQUS was used and the
meshes were named from the element thickness.
The naming code of meshing models was ‘mesh x1-x2-x3’, where x1 was the
‘thickness’ of the finite elements, x2 was the step of bias and x3 was the number of
elements in bias (see
Figure 4.7). There element thickness x1 was the direction in which the elements had
the specified thickness and bias x2-x3 the area where the bias module was used. The
criterion that was used in order to validate the mesh sensitivity was the maximum
peeling stress in the adhesive, because this stress plays an important role in skin-
stiffener debonding. The adhesive, which is 0.1 mm thick, was modelled with two
elements through the thickness.
Page | 86
Chapter 4 - Numerical Design of Stiffener Run-outs for Damage Tolerance
Figure 4.7: An example of naming code of meshing models, here a 1-10-80 model.
The first mesh (mesh 5-10-80, shown in Figure 4.8) was the benchmark. By
decreasing the element thickness from 5 to 3 and then to 1, the results could be
observed to be quite different near the stiffener edge, which was the critical area
(Figure 4.8). As shown in Figure 4.8 and Figure 4.9 , the third mesh gave converged
results and was therefore used for the rest of the analysis.
Figure 4.8: Peeling stresses for different meshes along path 1
-30
-25
-20
-15
-10
-5
0
5
10
15
350 360 370 380 390 400
Stre
ss [
MPa
x103 ]
Lenght [mm]
Peeling stresses
1. mesh 5-10-80 2. mesh 3-10-80
3. mesh 1-10-80 4. mesh 1-10-120
Length [mm]
Page | 87
Chapter 4 - Numerical Design of Stiffener Run-outs for Damage Tolerance
Figure 4.9: Max peeling stresses for different meshes
4.3.3 Model analysis and results
The peeling stresses were studied in 3 different paths in the adhesive, as can be seen
in Figure 4.10. All the paths were in the middle of the adhesive and between the 2
through-thickness elements.
Figure 4.10: The paths where the stresses were calculated
Path 1 was along the stiffener and in the middle, just beneath the blade, in order to
capture the effect of the blade design on the stresses. In addition, this path
0
2
4
6
8
10
12
1. mesh 2. mesh 3. mesh 4. mesh
Stre
ss [M
Pa x
103 ]
max peeling stresses
Page | 88
Chapter 4 - Numerical Design of Stiffener Run-outs for Damage Tolerance
corresponds to the one used in the theoretical analysis previously shown. The peeling
stresses, copared with the analytical solution from Figure 4.3, in this path are shown
in Figure 4.11 while the shear stresses are shown in Figure 4.12.
Figure 4.11: Peeling stresses along Path 1
Figure 4.12: Shear stresses along Path 1
-60
-50
-40
-30
-20
-10
0
10
0 100 200 300 400
stres
s [M
Pa]
length [mm]
Path-1 peeling stresses
Stif 0Stif 1Stif 2Stif 3Stif 4Stif 5Analytical
0
5
10
15
20
25
0 100 200 300 400
stres
s [M
Pa]
length [mm]
Path-1 shear stresses
Stif 0Stif 1Stif 2Stif 3Stif 4Stif 5
Page | 89
Chapter 4 - Numerical Design of Stiffener Run-outs for Damage Tolerance
All the designs had the same behaviour until the middle of the stiffener, where the
taper starts. The biggest differences were at the end of the stiffener, something that is
expected from the numerical analysis. Comparing the different designs with each
other, a closer look was needed, as in Figure 4.13 and Figure 4.14, in order to
determine the differences and the effects of the designs on the peeling stresses.
Figure 4.13: Peeling stresses in Path 1 near the edge of the stiffener
It is clear that reducing the geometrical discontinuity at the tip of the stiffener, the
stresses are affected. The benchmark was the design Stif 0. Comparing the stresses
with those from Stif 1, it can be inferred that the taper did not lead to a significant
decrease of the peeling stresses. In contrast, by analysing the curves for Stif 2 to Stif
5, it can be observed that alleviating the geometrical discontinuity has a significant
effect in decreasing the peel stresses as well as the shear stresses, Figure 4.13 and
Figure 4.14. By comparing the designs Stif 2 and Stif 3, it can be concluded that the
curvature of the taper does not have a significant contribution to the peel stresses and
to the shear stresses, Figure 4.13 and Figure 4.14.
-60
-50
-40
-30
-20
-10
0
10
370 375 380 385 390 395 400
stres
s [M
Pa]
length [mm]
Zoom of Path-1 peeling stresses
Stif 0Stif 1Stif 2Stif 3Stif 4Stif 5Analytical
Page | 90
Chapter 4 - Numerical Design of Stiffener Run-outs for Damage Tolerance
Figure 4.14: Shear stresses in Path 1 near the edge of the stiffener
By comparing designs Stif 2, Stif 4 and Stif 5, the role of the shape of the flange can
be understood – reducing the width of the flange near the tip of the stiffener will
increase the peeling and shear stresses, and conversely increasing the width of the
flange leads to a reduction in stresses. It can be concluded that design Stif 5 gave the
lower peel stresses along path 1 from all designs compared.
Path 2 was selected in order to examine the stress distribution between the centre of
the stiffener and the flanges, Figure 4.10. Path 2 intersects path 1 at the region that
showed maximum peeling stress for design Stif 0, 20 mm from run-out tip. The
results can be seen in Figure 4.15 for peeling stresses and Figure 4.16 for shear
stresses.
For Stif 1, the peeling stresses are higher close to the edge of the flange. The taper
introduced in Stif 2 can be observed to not have a significant effect on the stress
profile of the peeling stresses when there is a reduction in shear stresses. Alleviating
the geometrical discontinuity (Stif 2 to 5) does have a big effect on the profile, and
increasing the width of the flange (Stif 5) is again seen to be beneficial as it leads to a
more uniform stress distribution.
0
5
10
15
20
25
370 375 380 385 390 395 400
stres
s [M
Pa]
length [mm]
Zoom of Path-1 shear stresses
Stif 0Stif 1Stif 2Stif 3Stif 4Stif 5
Page | 91
Chapter 4 - Numerical Design of Stiffener Run-outs for Damage Tolerance
Figure 4.15: Peeling stresses in Path 2
Figure 4.16: Shear stresses in Path 2
The peeling and shear stresses were analysed along another path, path 3 (see Figure
4.10). Path 3 was used to investigate in more detail the peeling stresses next to the
-2
-1
0
1
2
3
4
5
-50 -30 -10 10 30 50
stres
s [M
Pa]
length [mm]
Path-2 peeling stresses
Stif 0Stif 1Stif 2Stif 3Stif 4Stif 5
0
5
10
15
20
25
30
-50 -30 -10 10 30 50
stres
s [M
Pa]
length [mm]
Path-2 shear stresses
Stif 0Stif 1Stif 2Stif 3Stif 4Stif 5
Page | 92
Chapter 4 - Numerical Design of Stiffener Run-outs for Damage Tolerance
discontinuity between the skin and the stiffener. The results for the designs
investigated are shown in Figure 4.17 and Figure 4.18.
Figure 4.17: Peeling stresses in Path 3
Figure 4.18: Shear stresses in Path 3
-45
-40
-35
-30
-25
-20
-15
-10
-5
0-50 -40 -30 -20 -10 0 10 20 30 40 50
stres
s [M
Pa]
length [mm]
Path-3 peeling stresses
Stif 0Stif 1Stif 2Stif 3Stif 4Stif 5
0
5
10
15
20
25
30
35
40
45
-50 -40 -30 -20 -10 0 10 20 30 40 50
stres
s [M
Pa]
length [mm]
Path-3 shear stresses
Stif 0Stif 1Stif 2Stif 3Stif 4Stif 5
Page | 93
Chapter 4 - Numerical Design of Stiffener Run-outs for Damage Tolerance
The results are qualitatively similar to those from path 2, with Stif 5 giving the best
performance. In conclusion, it can be stated that both the tapering of the run-out and a
widening of the flange can have a positive effect in reducing the peel and shear
stresses and obtaining a more uniform stress distribution in the width direction.
4.4 Energy release rate for debonding While the analysis of stress distributions is helpful in understanding qualitatively how
several geometrical parameters can affect the mechanical response of a run-out, a
quantitative analysis can be achieved by calculating the energy release rate for
debonding. For an FE model with 3D solid elements and assuming constant crack
length a all across the skin-stiffener interface, the total strain energy release rate can
be calculated [85]. This means that the total strain energy release rate can be
calculated from the difference in the strain energies between two same geometry FE
models, e.g. Figure 4.19a geometry, for a given debond length a in the skin- stiffener
interface. By calculating the total strain energy release rate while the debond
propagates, 𝐺 = 𝑑𝑈 𝑑𝑎⁄ , any increase of the value will indicate unstable debonding.
Figure 4.19: Designs and dimensions in mm of a) the baseline stiffener and b) the parametric stiffener.
100
10
2.5
1.25
15
2
1530
(a)
b 20
(b)
50
30
1020
d
c
aa
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Chapter 4 - Numerical Design of Stiffener Run-outs for Damage Tolerance
With this aim, the structural performance for debond stability of a baseline skin-
stiffener configuration under longitudinal compression, with geometry and
dimensions shown in Figure 4.19a, was compared to that of a modified parametric
configuration shown in Figure 4.19b.
The modified configuration has a widening flange towards the termination end of the
stiffener but this added material is offset by the taper of the stiffener web. This results
in a stiffener design with a similar overall weight to the baseline design.
For the parametric configuration, various values of b, c and d were analysed. The
materials used in this study are IM7/8552 carbon/epoxy pre-preg, with ply thickness
0.25 mm, for the skin and the stiffener, and FM300 adhesive film (0.15 mm thick) for
the bondline, with properties shown in Table 4-3 and Table 4-4 respectively.
Table 4-4: Material properties for FM300 measured in house
Material Exx [GPa]
Eyy [GPa]
Gxy [GPa]
vxy X
[MPa] Y
[MPa] S
[MPa] GIc
[kJ/m2] GIIc
[kJ/m2] η
FM300 2.38 - 0.68 - 61 - 49.8 0.9 2.5 8.0
In test results shown in Chapter 2.7, with geometry similar to that in Figure 4.19a, the
specimens failed by unstable debonding of the stiffener from the skin. Therefore, the
different configurations in this study were assessed by comparing the energy release
rates of the run-outs for a given displacement and for several initial debond lengths.
4.4.1 The FE model
All the FE simulations of the parametric study were carried out in ABAQUS and the
parameterized models were created using Python. The main model has five different
parts: the skin, the adhesive between the skin and the stiffener, the two parts of the
stiffener and the filler. A mesh sensitivity study was carried out to ensure that all
results presented are mesh converged. The FE model with boundary conditions is
shown in Figure 4.20.
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Chapter 4 - Numerical Design of Stiffener Run-outs for Damage Tolerance
Figure 4.20: The FE model of a specimen with the boundary conditions.
4.4.1.1 Assigning Element Type
The next step involves assigning element types to the various parts. Figure 4.21
shows the element families that are used most commonly in a stress analysis.
Figure 4.21: Commonly used element families [4]
In this study the 3D continuum elements (C3D8) were used, an 8-node linear brick
element, nodes at corners, and uses linear interpolation in each direction [4]. These
elements are capable of modelling several layers of different materials for the analysis
of laminated composites, which is ideal for this numerical study.
4.4.1.2 Stacking Sequence
The skin consists of eight plies and the stiffener consists of five plies. In order to keep
the same size ratio of the larger stiffeners described before, there was a limitation on
the number of plies. In particular, the stiffener thickness was chosen in order to have a
variety of ply orientations. The stacking sequences used for the skin and the stiffener are
shown in Table 4-5.
Displacement
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Chapter 4 - Numerical Design of Stiffener Run-outs for Damage Tolerance
Table 4-5: Stacking sequence for the skin and the stiffener
Part Stacking Sequence
Skin [45/-45/0/90]s
Stiffener (per half section) [0/90/-45/45/0]
Figure 4.22 shows the composite ply orientations for the skin. The thickness of each
ply is 0.25 mm (double thickness) and the number of integration points per ply is set to 1.
The same procedure was followed for the stiffeners.
Figure 4.22: Stacking sequence for the skin
4.4.1.3 Mesh
The number and the distribution of elements is in great importance in FE analysis. In
this analysis the “sweep” technique was used and the algorithm was specified as
“Advancing Front”. The coarse mesh of the modified design is shown in Figure 4.23 .
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Chapter 4 - Numerical Design of Stiffener Run-outs for Damage Tolerance
Figure 4.23: Course mesh for the modified design with 3D continuum elements
4.4.1.4 Step
Each ABAQUS model uses two steps in the analysis procedure; The first one is the
Initial step that cannot be edited, deleted, renamed, copied or replaced and it is created
by the software at the beginning of the model’s step sequence. In addition, the initial step
allows the user to define initial boundary conditions, predefined fields and interactions [4].
The second one is the Analysis step. This step defines the type of analysis to be performed
during the step, i.e. static, dynamic or transient heat transfer analysis. There are no
restrictions to the number of steps the user can define, but there are limitations to the
step sequence.
In this study, the type of analysis was “Static, General” and the time period was set to
“1”. The “Automatic Incrementation” procedure was preferred, since a general static step
analysis was performed. The maximum number of increments was set to 1000 to
reassure that the analysis will not halt if the step exceeds the number of increments.
The default value for the maximum number of increments is 100.
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Chapter 4 - Numerical Design of Stiffener Run-outs for Damage Tolerance
4.4.1.5 Constraints
Constraints were defined in the Assembly module for the initial positions of instances.
The type of constraint created for this model was the “tie constraint”, and as the name
suggests, ties two surfaces together for the duration of the simulation. It makes the
translational and rotational degrees of freedom equal for the two surfaces. This tie
allows the user to fuse together two regions even though the meshes created on the
surfaces of the regions may be dissimilar [8]. Figure 4.24 shows how the master and the
slave surfaces are displayed in the model.
Figure 4.24: Surfaces constraints between the skin (master surface-red) and the adhesive (slave surface-pink)
4.4.1.6 Boundary Conditions In the current study, two boundary conditions (BC) were defined. The first BC, named
DC-1, was applied on the left edge of the stiffener, Figure 4.25, and constrained all
displacements and rotations . The second BC, named BC-2 was applied on the left edge of
the stiffener and all displacements and rotations were constrained apart from the zU
which was set to zU =1. zU is the displacement in the z-direction and represents the
machine’s crosshead displacement.
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Chapter 4 - Numerical Design of Stiffener Run-outs for Damage Tolerance
Figure 4.25: Modified model with BC-1 on the left edge (clamped) and BC-2 on the right edge ( zU =1)
4.4.1.7 Mesh Sensitivity Study
A finite element analysis leads to an approximate solution and it can only guarantee
that equilibrium is satisfied on an average sense over an element. As a consequence,
the accuracy of the results is expected to improve when the size of the element is
decreased.
Moreover, in regions of stress concentrations, it is necessary to increase the accuracy of the
FE solution by either using elements with higher-order shape functions (p-refinement) or by
using a finer mesh of elements (h-refinement). The goal that a designer needs to achieve is
to select the best mesh density which is not prohibitively expensive to run and at the
same it will provide accurate and acceptable results [86].
In this study, three different meshes were used; the coarse mesh, the intermediate
mesh and the fine mesh. In Table 4-6, the strain energy and the running time of each
model using a standard Pentium Core 2 Duo, 2.6 GHz with 4 GB RAM computer are
presented.
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Chapter 4 - Numerical Design of Stiffener Run-outs for Damage Tolerance
Table 4-6: Mesh Sensitivity Study results.
Mesh Strain Energy (KJ)
Number of Elements
Running Time (minutes)
Deviation (%)
Coarse 30150 13100 25 -
Intermediate 30138 18700 35 0.039
Fine 30109 51000 90 0.096
Moreover, the partitioning technique was used. It's ply was represented as separate
material with own orientation the in order to simulate the composite lay-up. As a result,
8 partitions were created for the skin and 5 for each stiffener and material orientation
was applied.
The results obtained from both approaches were similar, Figure 4.26, and the solution can
be considered converged for all meshes. Since the running time for the intermediate
mesh was 35 minutes and the results appeared accurate and acceptable, this specific density
of elements was selected for the rest of this study.
Figure 4.26: Strain energy with composite lay-up (blue line) and with material orientations (red line)
29.829.929.930.030.030.130.130.230.230.330.3
0 10000 20000 30000 40000 50000 60000
Stra
in en
ergy
(KJ)
Number of elements
Strain energy with composite lay up
Strain energy with material orientation
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Chapter 4 - Numerical Design of Stiffener Run-outs for Damage Tolerance
4.4.2 The Python script
In order to perform the parametric study, a large number of models has to be created
and a script that generates these models is needed. This script was written in Python
[5] because of the advantage of using the ABAQUS scripting interface. The script
created automatically generates all models and runs them automatically. The major
advantages of the script are the automation, and reduced user time and effort required
for model generation.
The script generates parametric stiffener run-out models, generates models with
different crack lengths, and runs all models with ABAQUS. The script uses a basic
stiffener run-out configuration and changes the design each time according to the
parameter values. When a new design is generated, the script propagates the crack and
the energy release rate is calculated for every step. This procedure is repeated for all
the parameter values.
4.5 Results from modelling
4.5.1 Energy Release rate along crack
The results of the parametric study for the design presented in Figure 4.19 are shown
in Figure 4.27, where the values of GT = GΙ + GΙΙ + GΙΙΙ, the total energy release rate,
have been normalized to the GT of the reference parametric stiffener for 0.5 mm of
crack length. The variables Gi , where i = I, II, III, refer to the strain energy release
rates associated with Mode I, ‘opening mode’, II, ‘sliding shear mode’ and III,
‘scissoring mode.’
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Chapter 4 - Numerical Design of Stiffener Run-outs for Damage Tolerance
Figure 4.27: Normalized energy release rates as a function of crack length (a) comparison between Baseline stiffener design and selected Tapered stiffener with b = 3 mm, c = 10 mm and d =6.25 mm), (b) Influence of parameter b on G,
(c) Influence of parameter c on G and (d) Influence of parameter d on G.
Figure 4.27a compares the normalised energy release rate for the Baseline and
reference parametric stiffeners. The negative slope of the GT(a) curve for the latter
indicates stability of crack growth (assuming constant fracture toughness). The
influence of parameters b, c, and d is presented in Figure 4.27b, 3c and 3d. It is
observed that since the objective of the optimisation routine was to enhance crack
growth stability, results for the reference modified stiffener are presented since this
configuration was the derived optimum. Figure 4.27a compares the normalised energy
release rate for the baseline and selected parametric stiffeners. Given the objective of
optimising for stability of crack growth, the configuration with 3b mm= , 10c mm=
and 6.25d mm= was selected to be carried out for the following stages of this study
and named Tapered design.
(a) (b)
(c) (d)
a [mm] a [mm]
0.6
0.7
0.8
0.9
1.0
1.1
0 1 2 3 4 5 6 7 8 9 10
Nor
mal
ized
GT
a [mm]
Baseline Stiffener
Selected Modified Stiffener
0.6
0.7
0.8
0.9
1.0
1.1
0 1 2 3 4 5 6 7 8 9 10
Nor
mal
ized
GT
a [mm]
Parameter b
b = 1 mm
b = 2
b = 3 mm (Selected)
0.6
0.7
0.8
0.9
1.0
1.1
0 1 2 3 4 5 6 7 8 9 10
Nor
mal
ized
GT
a [mm]
Parameter c
c = 2 mm
c = 6 mm
c = 10 mm (Selected)
0.6
0.7
0.8
0.9
1.0
1.1
0 1 2 3 4 5 6 7 8 9 10
Nor
mal
ized
GT
a [mm]
Parameter d
d = 9
d = 6.25 mm (Selected)
d = 4 mm
Page | 103
Chapter 4 - Numerical Design of Stiffener Run-outs for Damage Tolerance
As will be described in greater detail in the next chapter, while the Baseline
specimens did fail by debonding, the Tapered specimens did not: interlaminar and
intralaminar failures were the main failure modes of the modified run-out stiffener.
After examination of the specimens, it was observed that the specimens failed through
delamination between 0o and 45o (Figure 4.28). For this reason, a second iteration
of the models was carried out, including the modelling of delamination.
Figure 4.28: (a) Front view of failed specimen; (b) Exploded view showing the failed area; (c) Front view of Bottom part
showing 00 plies ; (d) Bottom view of the Upper part showing delaminated 450 plies
4.5.2 2nd iteration
A more detailed analysis of different configurations, which accounts for delamination,
was therefore undertaken. Three specimens were analysed. These include the Baseline
and the Tapered configuration with the parameters identified in the previous section.
The third configuration stemmed from the experience and sensibility gained during
the project. It appeared reasonable that adding a compliant region ahead of the run out
tip would reduce the stresses at the tip and thus contribute to a more stable crack
growth. Therefore, the merits of a compliant termination scheme were also
investigated.
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Chapter 4 - Numerical Design of Stiffener Run-outs for Damage Tolerance
4.5.2.1 Compliant skin-stiffener configurations
Four new configurations were analyzed, Figure 4.29(a)-(d). The first design, Tip-
Tapered (Figure 4.29a), was a stiffener run-out tapered down to the edge, in order to
remove the discontinuity, with a widening in the flange to avoid the delamination. By
having a widening flange, together with a tapered web, this configuration increases
the compliance of the run-out region. The second design, Notch-Tapered (Figure
4.29b), had a 45o notch (filled with an adhesive spew fillet) cut at the base of the
stiffener. The insertion of the adhesive at the base was used in order to increase the
local compliance and thus reduce the local peeling stresses. Two more designs were
developed by considering the potential benefits of local stiffness variations; one with
a step tapered blade, Step-Tapered (Figure 4.29c), and the other with a curved cut,
Curve-Tapered (Figure 4.29d).
Figure 4.29: Compliant Skin-Stiffener designs
The new FE model that was created in order to investigate these specimens is shown
in Figure 4.30b and Figure 4.30c. The different configurations in this study were
b 20
(a) Tip-Tapered stiffener configuration
50
30
1020c
a
50
30
1020
d
bc
(c) Step-Tapered stiffener configuration
20
b 20
(b) Notch-Tapered stiffener configuration
50
30
1020
d
c
a
50
30
1020
d
bc
(d) Curve-Tapered stiffener configuration
(0,0)
(15, 8)(42.5, 11.5)
(30.5, 4.2)
2nd order polynomial
a a
(w, h)
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Chapter 4 - Numerical Design of Stiffener Run-outs for Damage Tolerance
assessed by comparing the energy release rates of the run-outs for a given end
displacement and for several initial debond lengths, following the procedure described
previously.
Figure 4.30: a) Tapered stiffener after testing, b) FE model showing delamination path, and c) FE model of a specimen with boundary conditions.
The results of the normalised strain energy release rates are shown in Figure 4.31,
where the values of GT = GΙ + GΙΙ + GΙΙΙ, the total strain energy release rate, have been
normalized by the GT of the Tapered stiffener (Figure 4.19(b) for 0.5 mm crack
length. The negative slope of the G(a) curve indicates crack growth stability, while a
positive slope indicates instability (assuming constant fracture toughness). From a
comparison of the four designs, it can be assumed that the best performance is
expected by the Curve-tapered design. In order to optimize the design of the Curve-
tapered specimen, Figure 4.29(d), a parametric study for the parameters w and h was
assessed. The results of this study are presented in Figure 4.32, (a) for debonding and
(b) for delamination. In all cases, the energy release rate for delamination is lower
than for debonding. The designs expected to have stable debonding are the ones with
parameters (30, 9.2) and (30, 6.5). Because of the lower energy release rate of the
second, this Curve-tapered design was selected and taken forward in the rest of this
study as Compliant design.
Displacement
(a) (b)
(c)
Delamination area
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Chapter 4 - Numerical Design of Stiffener Run-outs for Damage Tolerance
Figure 4.31: Normalized strain energy release rates as a function of crack length showing a comparison between designs. The points were obtained numerically and the curves are spline fits.
Figure 4.32: Normalized energy release rates of the Compliant design of different (w, h) values for (a) debonding and (b) delamination
Debonding
Delamination
Tip-Tap. Notch-Tap. Step-Tap. Curve-Tap.
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 1 2 3 4 5
Nor
mal
ised
GT
a [mm]
(a) (b)
0.8
0.85
0.9
0.95
1
0 1 2 3 4 5
Nor
mali
sed
GT
a [mm]
Debonding
(30, 9.2)
(25, 6.5)
(30, 6.5)
(30,5.4)
(35, 6.5)
0
0.05
0.1
0.15
0.2
0.25
0 1 2 3 4 5
Nor
mali
sed
GT
a [mm]
Delamination
(30, 9.2)
(25, 6.5)
(30, 6.5)
(30,5.4)
(35, 6.5)
Page | 107
Chapter 4 - Numerical Design of Stiffener Run-outs for Damage Tolerance
4.5.2.2 Energy release rate along crack
The structural performance of three different skin-stiffener configurations – Baseline
(B), Tapered (T) and Compliant (C) – under longitudinal compression, with geometry
and dimensions shown in Figure 4.33, was assessed. Compared to the Baseline
stiffener (Figure 4.33a), the other two configurations have a widening flange towards
the termination end of the stiffener but this added material is offset by the taper of the
stiffener web (Tapered configuration, Figure 4.33b). The third configuration includes
taper with a curvature (Compliant, Figure 4.33c).
Figure 4.33: Stiffener design configurations (dimensions in mm).
The three different configurations were analysed for debonding and delamination
growth stability. The results of this analysis are presented in Figure 4.34, where the
100
10
2.5
1.25
15
2
20
1530
(a) Baseline stiffener configuration
50
30
1020
d
bc
a
50
30
1020
d
bc
20
(b) Tapered stiffener configuration
(c) Compliant stiffener configuration
(0,0)
(15, 8)(42.5, 11.5)
(30.5, 4.2)
2nd order polynomial
Page | 108
Chapter 4 - Numerical Design of Stiffener Run-outs for Damage Tolerance
values of GT = GΙ + GΙΙ + GΙΙΙ, the total strain energy release rate, have been
normalized to the GT of the reference parametric stiffener for 0.5 mm of crack length.
The negative slope of the G(a) curve indicates stability of crack growth, while a
positive slope indicates instability (assuming constant fracture toughness).
Recalling the failure modes obtained experimentally [87] the Baseline stiffener
failed by debonding and the Tapered stiffener initially experienced debonding until it
finally failed by delamination. This is in agreement with the predictions in Figure
4.34. Consequently, both models were able to correctly describe these experimental
results [87]. In addition, the stability analysis for the Compliant stiffener predicts that
this design will fail stably by debonding, Figure 4.34.
Figure 4.34: Normalized strain energy release rates as a function of crack length; comparison between Baseline stiffener design (Figure 4.33α), Tapered stiffener (Figure 4.33Figure 4.19b) and Compliant stiffener (Figure 4.33Figure 4.19c)
with dimensions b=3 mm, c=10 mm and d=6.25 mm.
4.5.3 Energy release rate along the width of the crack tip
The strain energy release rate along the width of the crack tip was calculated for the
Baseline, Tapered and Compliant configurations (Figure 4.33). Fracture initiation is
Debonding
Delamination
Baseline Tapered Compliant
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 1 2 3 4 5
Nor
mal
ized
GT
a [mm]
Page | 109
Chapter 4 - Numerical Design of Stiffener Run-outs for Damage Tolerance
expected when the GT exceeds the fracture toughness Gc for a given mixed-mode ratio
GII / GT at each point along the crack tip. In other words, propagation at each point
occurs when GT / Gc >1 [74, 88]. The interlaminar fracture toughness Gc can be
calculated by using the following equation [89]:
( ) IIcc Ic IIc Ic
T
GG G G GG
η
= + −
(3.22)
where GIc and GIIc are the experimental values of fracture toughness for mode I and II
and η is determined by curve fitting (see Table 4-4). The value of Gc is normalised to
the width-average value for the Tapered specimen. Figure 4.35 shows that the trend is
similar for the Baseline and Tapered specimen types but is different in the centre of
the Compliant stiffener. This is due the difference in the web of the stiffeners.
Figure 4.35: Normalized GT/Gc across the crack tip for crack a = 1 mm for the Baseline, Tapered and Compliant specimens.
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
0 2 4 6 8
Nor
mal
ised
GT / G
c
Distance across width [mm]
Baseline Tapered Compliant
Page | 110
Chapter 4 - Numerical Design of Stiffener Run-outs for Damage Tolerance
The curved taper has reduced the normalized strain energy release rate in the centre
without affecting the trend in the flange. According to equation 1 in [88] 𝐺𝐶 ∝ 𝑃2.
The maximum value of the energy release rate can be used to predict the load
corresponding to the initiation of fracture using:
c
FE T
P GP G
= (3.23)
where P is the load at initiation of fracture, PFE is the load from the FE model, Gc the
critical strain energy release rate (Equation 1.26), and GT is the strain energy release
rate predicted by the FE model as defined previously. Two different predictions for P
can be made: one using the maximum value of GT along the width, and another using
the average, Table 4-7.
Table 4-7: Predicted failure load
Predicted failure load [kN]
Based on Gavg Based on Gmax
Baseline Stiffener 19.00 16.56
Tapered Stiffener 19.17 17.45
Compliant Stiffener 19.93 18.17
4.5.4 Modeling debonding failure using VCCT
The implemented VCCT method in ABAQUS standard, developed by Boeing and
Simulia, suggested promising results, especially when the mismatched meshes had
only 3% error comparing with pairing meshes. Replacing the cohesive contact, two
surfaces (‘top’ and ‘bottom’) represented the interface plane, while the node set
‘bonded’ are those nodes on the slave surface (‘top’) behind the crack front. As can be
Page | 111
Chapter 4 - Numerical Design of Stiffener Run-outs for Damage Tolerance
seen in Figure 4.36(a) there was good correlation between the VCCT and the
parametric study.
Figure 4.36: Comparing the results of the parametric study with the VCCT method (a) along the crack and (b) along the width of the stiffener.
On the other hand, the VCCT method could not capture the detail at the flange edge
and the weakness of the method was exposed. Generally, the discontinuities in the
geometry increase the normalised GT/GC and this trend couldn't be captured. In order
to capture the detail in the edge of the flange, the mesh resolution was increased and
was biased towards the sides, Figure 4.37, and the results can be seen in Figure
4.36(b). Despite the good results, the size of the model and the time needed for
running it prevent for further developments using VCCT.
0.5
0.7
0.9
1.1
1.3
1.5
0 1 2 3 4 5 6 7
Nor
mal
ised
GT/
GC
Distance along the crack tip [mm]
Baseline Stiffener
VCCT script results
0.9
1
1.1
1.2
0 1 2 3 4 5 6 7 8 9 10
Nor
mal
ised
GT/
GC
a [mm]
VCCT script results
Reference Data
Baseline Stiffener
Baseline Stiffener
VCCT results
VCCT results
(a) (b)
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Chapter 4 - Numerical Design of Stiffener Run-outs for Damage Tolerance
Figure 4.37: The refined model that was used in the VCCT method
4.6 Conclusions A closed-form model was initially developed that predicted peel stresses in adhesively
bonded joints. The closed-form model permitted an investigation to compare the
singular stress fields at discontinuities, leading to a better understanding of the
problem.
By using FE models, similar peeling stress fields, as well as shear stress fields, were
obtained specifically for skin stiffener run-outs. The effect of the termination on the
singular stresses was examined in detail and it was hypothesised from observation of
the said fields that a tapered blade paired with a flange widening to the end of the
stiffener should reduce the peeling stresses.
Baseline, tapered and compliant stiffener run-out configurations were then analysed
using VCCT for debonding and delamination. The analyses led to predictions of the
failure modes more likely to happen for each specimen type, as well as information on
the stability of crack growth. They also led to quantitative data that can be used to
predict failure loads. This will be addressed in the following chapter, where a
comparison with experimental values will be performed.
Page | 113
Chapter 4
Manufacturing and testing
procedures
5 Manufacturing and testing procedures
5.1 Manufacturing of Stiffener Specimens All specimens were manufactured at Imperial College of London (four specimens for
each design). Each one of them consists of four main parts: the skin, the stiffener, the
adhesive and the filler. The skin and the stiffeners were manufactured using hand lay-up and
cured in the Autoclave according to Hexcel’s recommendations. The adhesive is actually a
film of 0.15mm thickness which is used in the bondline between the skin and the
stiffener and its material is FM300. Moreover, the filler was made by composite strips
of IM7/8552. The strips were gently twisted to enhance consolidation. Finally, all parts were
bonded using wooden moulds in order to ensure that the stiffeners were placed at the
exact position on the skin while pressure was applied.
5.1.1 Skin
The skin was composed of eight plies. The skin stacking sequence is shown in Table
5-1. The prepreg was removed from the freezer and was left to reach room
temperature before it was unrapped. This prevents moisture from condensing on the
Chapter 4 - Manufacturing and testing procedures
cold prepreg. Two rectangular unidirectional laminates, 300mm long and 150mm wide,
were cut and stacked. The ply by ply stacking procedure is shown in Figure 5.1.
Figure 5.1: Hand lay-up for the skin plates.
Having layed-up half of the plies (four plies), the sub-laminates were consolidated
using the vacuum table for 2 minutes. The next step for the manufacturing process was to
cure the plates in the Autoclave. According to Hexcel, the plates need to be cured at
110oC for 60 minutes and then at 180oC for 120 minutes (Figure 5.2).
Figure 5.2: Curing procedure on the Autoclave
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Chapter 4 - Manufacturing and testing procedures
The whole procedure was carried out under vacuum. The size of each skin was
110mm by 30mm. However, the plates were cut into shapes of 140mm by 30mm
since the specimens needed to be end-tabbed before they were ready to be tested. The
cutting schedule is shown in Figure 5.3.
Figure 5.3: The cutting schedule
5.1.2 Stiffener
The stiffener part is probably the most vital part of a stiffener run-out. In most studies,
failure initiates at the edge of the run-out and propagates along the skin-stiffener [60,
61] [63, 64] interface [66, 90-96]. Hence, the geometric features of these specimens
in the area of the stiffener strongly affect their failure load. As a result, a significant
effort was put on this part of the work so as to achieve the best quality of the
specimens.
Table 5-1: Composite ply orientations
Part Ply orientations
Skin [45/−45/0/90]S
Stiffener (per half section) [0/90/−45/45/0]
Page | 116
Chapter 4 - Manufacturing and testing procedures
The composite lay-ups for the skin and the stiffener are shown in Table 5-1.
Aluminium blocks were machined and used as moulds in order to give the exact
geometry and dimensions to the produced stiffeners. The shape and the dimensions of
the stiffener mould can be seen in Figure 5.4.
Figure 5.4: Mould for the stiffener. All dimensions are in mm.
The stiffeners and the composite skin were manufactured using hand lay-up and cured
in an Autoclave according to Hexcel’s recommendations (60 minutes at 110C then
120 minutes at 180C under vacuum). Figure 5.4 also shows the two parts of the mould
after the lay-up and the whole stiffener after the curing (small picture top right). The curing
cycle is the same used for the skin. In this step, the stiffener was cured along with the filler
to avoid wrinkling of the fibres.
5.1.3 Filler
The filler required a particularly careful manufacture for two main reasons. Firstly, a
homogeneous filler was needed in order to avoid a weak area with potential defects in
the stiffener. Secondly, the exact shape is very important for avoiding wrinkling of the
stiffener plies. A second mould was designed and manufactured from the machined
aluminium blocks, Figure 5.5. The quality of the stiffener is illustrated in Figure 5.6.
20
3.75
32
700
5
6 10
1.25
16.5
15R 1.25
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Chapter 4 - Manufacturing and testing procedures
Figure 5.5: Mould for the filler. All dimensions are in mm.
Figure 5.6: Micrographics of (a) the stiffener, (b) a zoomed area of the stiffener, (c) filler made by stacked stripes and (d) filler made by twisted tows.
The filler was made by composite strips of IM7/8552, with two manufacturing
procedures being compared. In the first one, the strips were simply stacked in the
mould, leading to some voids (Figure 5.6c). In the second one, the strips were gently
and slightly twisted to enhance consolidation, leading to an improved quality for the
R 2.5
700
(a)
(b)
(c)
(d)
1 mm
0.25 mm
0.2 mm
0.2 mm
Page | 118
Chapter 4 - Manufacturing and testing procedures
filler (Figure 5.6d). Following the manufacture (including cure) of the filler, the
stiffener was cured using the filler and the mould in Figure 5.4.
5.1.4 Bonding
The three types of stiffeners (Baseline, Tapered and Compliant) were machined to the
required shapes and dimensions, Figure 4.33, and bonded onto the skin with the
adhesive by the following procedure. Having all the parts prepared, they were bonded
together in order to create a single part, i.e. the stiffener run-out. This final step requires
the skin to be bonded on the stiffener using an adhesive. As reported before, the
material of the adhesive is FM300 and its properties are listed in Table 4-4. The
surfaces that were to be bonded were grit blasted and degreased. Wooden moulds
were used at the bonding stage in order to ensure that the stiffeners were bonded at the
exact positions on the skin while pressure was applied. Figure 5.7 shows the bonding
stage of the manufacturing process.
Figure 5.7: Bonding stage with the skin, the stiffener and the adhesive film in the wooden mould
In the final stage, the specimens’ ends were potted in epoxy resin, and subsequently
the ends were machined so as to ensure suitable load transfer during the experiments.
The specimens with the epoxy resin potted on the one end are shown in Figure 5.8. The
specimens types that were manufactured were the Baseline, the Tapered and the Compliant,
Page | 119
Chapter 4 - Manufacturing and testing procedures
Figure 5.9. For the use of Digital Image Correlation (DIC), the specimens’ surface
was finally coated with a random and contrasting speckle pattern.
Figure 5.8: Specimens’ ends potted in epoxy resin
Figure 5.9: (a) Baseline stiffener specimen; (b) Tapered stiffener specimen (identical flange geometry to Compliant type (b-i) profile of the Tapered stiffener specimen; (b-ii) profile of the Compliant stiffener specimen.
(a)
(b)
(i) (ii)
Page | 120
Chapter 4 - Manufacturing and testing procedures
5.2 Testing of stiffener run-outs The tests were carried out in an Instron testing machine, equipped with a 100 KN load
cell, at a loading rate of 0.2 mm/min. Load and crosshead displacement were
recorded continuously by a PC data logger connected to the load cell and the Instron
machine at a sampling rate of 2 Hz. The specimens were aligned by careful
measurement in the loading direction to avoid bending. The Imperial Data Acquisition
(IDA) program was used to record load and displacement during the tests. A high
resolution camera was used to take photos periodically in order to detect any surface
damage and debonding.
5.2.1 Digital Image Correlation
The strains and the displacements were measured with the application of DIC using
the Aramis 1.3M system developed by GOM [97]. This consisted of two pairs of
cameras that used Schneider-Kreuznach lenses (50mm) and produced images with a
resolution of 1280x1024 pixels. These were processed using the Aramis software.
5.2.2 Acoustic Emission
Acoustic Emission sensors were used to identify and investigate failures within the
specimens during testing. The AE equipment was manufactured by Physical Acoustic
Corporation (PAC) and failure was monitored by AEwin software. Broadband (WD)
sensors with an operating frequency range of 100 KHz to 1000 KHz were used and
positioned in order to obtain the best results without affecting the specimens
behaviour [81].
Figure 5.10 shows a specimen tested in compression in the Instron machine. The picture
was taken on the last seconds of the compression testing just before failure, since
bending on the skin has already occurred. Moreover, on the bottom of the picture we
can see the AE sensor.
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Chapter 4 - Manufacturing and testing procedures
Figure 5.10: AE testing equpment
5.2.3 Results
The three different stiffener run-out designs that were manufactured were tested to
failure. The Baseline stiffeners had an average failure load of 16.5 KN while the
Tapered stiffeners had an average failure load of 17.6 KN, Figure. 5.11.
Figure. 5.11: Failure loads for the baseline design and the modified design specimens, as well as the predicted failure loads using Eq. 3.23.
Baseline Stiffener Tapered Stiffener
0.00
5.00
10.00
15.00
20.00
Pred G
Pred Gmax
Spec 1 Spec 2 Spec 3 Pred G
Pred Gmax
Spec 1 Spec 2 Spec 3
Load
[KN
]
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Chapter 4 - Manufacturing and testing procedures
The same figure also shows that the predicted loads (using Eq. 3.23) match well with
the experimental values. Figure 5.12 shows the load versus displacement curves for
selected specimens of the two stiffener designs. The displacement field close to the
critical area of the expected debonding, obtained using DIC, is presented in the
same figure for different stages until final failure.
Figure 5.12: Load-Displacement and AE Amplitude-Displacement curves for the baseline and the modified stiffener. The numbered pictures present the displacements obtained with the DIC.
While the baseline stiffeners failed due to debonding of the skin-stiffener interface,
Figure. 5.13A, the modified stiffeners failed by delamination between the 0o and 45o
stiffener plies, Figure. 5.13B.
20
30
40
50
60
70
80
90
0
5
10
15
20
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Am
plitu
de [d
B]
Load
[KN
]
Displacement [mm]
Load Baseline Stiffener
Load Modified Stiffener
Amplitude Baseline Stiffener
Amplitude Modified Stiffener
1
1 2 3 4
2
3
4
Load Baseline Stiffener
Load Tapered Stiffener
Amplitude Baseline Stiffener
Amplitude Tapered Stiffener
Page | 123
Chapter 4 - Manufacturing and testing procedures
Figure. 5.13: A. (a) Baseline stiffener; (b)-(c) detail before and after failure respectively; (d)-(e) clean debonded surfaces in the skin and stiffener respectively.
B. (a) Tapered stiffener; (b)-(c) detail before and after failure respectively; (d)-(e) delaminated surfaces in the skin and stiffener respectively.
Failure was unstable for both specimen types (Figure 5.12). The acoustic emission
signals (Figure 5.12) show that there was an increase in AE activity 0.01 mm before
catastrophic failure for the baseline specimen. For the modified specimen type, the
increase in AE emission started about 0.05 mm before catastrophic failure.
Figure.5.14 shows the peak frequency during the tests for both specimen types. A
scale on the right hand side indicates the mode of failure typically associated with
these peak frequencies [81].
Figure.5.14: Peak frequencies versus displacement for (a) Baseline and (b) Tapered stiffeners.
(a)
(b) (c)
(d) (e) (a) (e)(d)
(c)(b)
A B
Matrix cracking
Delamination
Fibre / matrix debonding
Fibre failure
Fibre pull-out
10
110
210
310
410
510
610
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Peak
Fre
quen
cy [K
Hz]
Displacement [mm]
10
110
210
310
410
510
610
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Peak
Fre
quen
sy [K
Hz]
Displacement [mm]
(a) (b)
P-FRQ Baseline Stiffener P-FRQ Tapered Stiffener
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Chapter 4 - Manufacturing and testing procedures
5.3 2nd Iteration The modified design failed by delamination, which had not been considered in the
initial numerical study (see section 4.4.1). Models including delamination were then
numerically investigated in detail (see section 4.5.2). A more detailed parametric
analysis of different configurations suggested that a compliant configuration (Figure.
5.15 a) with dimensions b=3 mm, c=10 mm and d=6.25 mm would have an improved
and stable response ( Figure. 5.15b). The response of these stiffeners is compared to
the Baseline and Tapered in this section. Figure. 5.15c shows representative load
versus displacement curves for the three specimen types, while Figure. 5.15d shows
the fracture surface of the Compliant specimen, failed by debonding.
Figure. 5.15: (a) Design of the Compliant stiffener (b) Normalized energy release rates as a function of debonding and delamination length for the three configurations (c) Load-displacement curves for the three configurations (d) Failed
surface of Compliant specimen
We recall that the Baseline stiffeners had an average failure load of 16.5 kN while the
Tapered stiffeners had an average failure load of 17.7 kN. In contrast, the Compliant
50
30
1020
d
bc
0
5
10
15
20
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Load
[KN
]
Displacement [mm]
Load Baseline Stiffener
Load Modified Stiffener
Load Modified-2 Stiffener
Failure initiation points
(a) (b)
(c) (d)
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
0 1 2 3 4 5
Nor
mal
ized
GT
a [mm]
Baseline debonding
Modified Debonding
Modified-2 Debonding
Baseline Delamination
Modified Delamination
Modified-2 Delamination
Baseline Debonding
Tapered Debonding
Compliant Debonding
Baseline Delamination
Tapered Delamination
Compliant Delamination
Baseline Stiffener
Tapered Stiffener
Compliant Stiffener
Failure initiation point
Page | 125
Chapter 4 - Manufacturing and testing procedures
had an average failure load of 18 kN, Table 5-2. The fracture surfaces for selected
specimens are shown in Figure Figure 5.16, and the load versus displacement curves
for selected specimens of the three stiffener designs are superposed with the
respective AE signals in Figure 5.17. The predicted loads (using Eq. 3.23) match well
with the experimental values when the maximum G across the width is used, Table
5-2.
Figure 5.16: (a) Baseline stiffener, (b) Tapered Stiffener and (c) Compliant Stiffener after failure respectively.
Table 5-2: Failure loads for the different specimen types, as well as the predicted failure loads using Eq. 3.23.
Predicted failure load [kN]
(% difference with respect to experimental)
Experimental
failure load
[kN]
Based on Gavg Based on Gmax
Baseline Stiffener
19.00
(+15.2%)
16.56
(+0.4%)
16.49 +0.34-0.39
Tapered Stiffener
19.17
(+8.2%)
17.45
(-1.5%)
17.72 +0.16-0.22
Compliant Stiffener
19.93
(+10.6%)
18.17
(+0.8%)
18.02 +0.16-0.29
(a) (b) (c)
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Chapter 4 - Manufacturing and testing procedures
Figure 5.17: Loads and Peak frequencies versus displacement for a) the Baseline b) the Tapered and c) the Compliant stiffeners. A scale on the right hand side indicates the mode of failure typically associated with these peak frequencies
[81].
Matrix cracking
Delamination
Fibre / matrix debonding
Fibre failure
Fibre pull-out
(a)
Baseline Stiffener
(b)
Tapered Stiffener
Compliant Stiffener
(c)
Matrix cracking
Delamination
Fibre / matrix debonding
Fibre failure
Fibre pull-out
Matrix cracking
Delamination
Fibre / matrix debonding
Fibre failure
Fibre pull-out
10
110
210
310
410
510
610
0
5
10
15
20
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Peak
Fre
quec
y [k
Hz]
Load
[kN
]
Dislacement [mm]
10
110
210
310
410
510
610
0
5
10
15
20
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Peak
Freq
uenc
y [kH
z]
Load
[kN
]
Displacement [mm]
10
110
210
310
410
510
610
0
5
10
15
20
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Peak
Fre
quen
cy [K
Hz]
Load
[kN
]
Displacement [mm]
Page | 127
Chapter 4 - Manufacturing and testing procedures
The acoustic emission signals (Figure 5.17) show that there was an increase in AE
activity 0.01 mm before catastrophic failure for the Baseline specimen. This activity
corresponded mostly to delamination and matrix cracking according to the signal
classification from Gutkin [81]. For the Tapered specimen type, the increase in AE
emission started about 0.05 mm before catastrophic failure but more peak frequencies
detected in the fibre/matrix debonding range, which is in line with the experiments.
The Compliant specimen had an increase in AE activity (corresponding to matrix
cracking) 0.1 mm before final failure. Also, in addition to load-displacement
information, Figure 5.17 shows the peak frequency during the tests for all specimen
types. The Tapered specimen configuration promoted a combination of failure modes
including delamination and fibre bridging which preceded catastrophic failure. In
addition, the Compliant stiffener, according to AE data and as visually observed
(Figure 5.17, Figure. 5.13c), suffered only from debonding. Another parameter, that
was taken into account, was the average signal level (ASL) and the results are
presented in Figure 5.18.
.
Figure 5.18: The average signal level (ASL) of the three designs
20
30
40
50
60
70
80
90
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Am
plitu
de [d
b]
Displacement [mm]
ASL
Baseline
Tapered
Compliant
Page | 128
Chapter 4 - Manufacturing and testing procedures
The Baseline design showed an increase in amplitude before the sudden and unstable
failure. On the other hand, the Tapered design registered peak frequencies 0.05 mm
before failure, indicating that the initiation of the damage started at that point.
Finally, in the Compliant design, the amplitude starts increasing 0.1mm before the
failure and increasing progressively until final failure. It is worth noting that these
peak frequencies were beyond the end-displacements at which the other two designs
failed.
5.4 Conclusions The experimental failure loads show good agreement with the predicted ones (Figure.
5.11 and Table 4.7). This indicates the FE models predicted accurately the energy
release rates for the specimens tested, and that the quality of the manufacturing,
particularly at the noodle region, (Figure 5.6) was suitable for this study. The
predictions using the maximum energy release rate across the width are in slightly
better agreement with the experiments (than using the width-average), which suggests
that it is appropriate to consider the width-variation of the energy release rate in these
studies. The load-displacement and AE amplitude-displacement curves (Figure 5.17),
as well as the peak frequency-displacement plots (Figure 5.18), show that the
Compliant design is more damage tolerant than the original one. The AE monitoring
proved to be valuable in detecting and analysing the failure modes experienced by the
specimens.
Page | 129
Chapter 6
Detailed damage
modelling for Tapered
run-out stiffeners
6 Detailed damage modelling for Tapered run-out
stiffeners
6.1 Introduction During the testing procedure, the Tapered stiffeners had an unexpected delamination
in the flange that led to an intralaminar failure in the form of a matrix crack across the
0o ply near the filler's end and continued delaminating between the filler and 0o ply.
FE models were created to numerically investigate the problem, including both
interlaminar and intralaminar fracture mechanisms with different damage modelling
techniques. Surface-based cohesive behaviour was used for Cohesive Zone Modelling
(CZM) in order to capture debonding and delamination of the stiffener. The
intralaminar fracture was captured by using Hashin [9] and LaRC [21-23] damage
criteria with a smeared crack formulation as well as XFEM. The analyses were
performed in ABAQUS 6.10.
Chapter 6 - Detailed damage modelling for Tapered run-out stiffeners
6.2 Bebonding of the Tapered Stiffener As mentioned before, understanding and subsequently predicting debonding of the
stiffener was the primary objective of the research. In this section, debonding of the
Tapered specimen is modelled using a cohesive zone model. The results of this
analysis can be compared with the calculations made using the critical strain energy
release rate across the width of the specimen, as described in Section 4.5.3.
The unexpected delamination of the Tapered stiffener between 00 and 450 plies led to
the four part stiffener modelling: two part models corresponding to the 00 plies for left
and right sides respectively and two part models corresponding to the remaining five
plies of orientation (00/ 900/-450/450) respectively, Figure 6.1. The list of part models
are listed below:
1. Skin - single part of (450/-450/00/ 900)S laminate
2. Filler - made-up of 00 fibres
3. Left - 00 lamina of the stringer
4. Left - single part of (00/ 900/-450/450) laminate of the stringer
5. Right - 00 lamina of the stringer
6. Right - single part of (00/ 900/-450/450) laminate of the stringer
Figure 6.1: The parts of the FE model
0 plies
Rest of plies
Filler
Skin
Page | 131
Chapter 6 - Detailed damage modelling for Tapered run-out stiffeners
The interface between the skin and the stiffener was connected by using surface-based
cohesive layer, as seen in Figure 6.2. Cohesive zone modelling is generally used for
the numerical simulation of interlaminar failure in the form of delaminations where
the damage of the cohesive zone is developed at the crack that may occur.
Figure 6.2: Illustration of imposed cohesive properties for debonding mode.
Damage initiation is driven by traction separation law and the value of the maximum
traction to, Figure 6.3. New crack surfaces are formed when the fracture toughness Gc
is equal to the area surface under the traction-separation curve. Considering the nature
of predictions made by the parametric study, the model was analysed with cohesive
interaction properties of adhesive FM 300 and listed in Table 6-1, where damage
initiation and damage evolution are based on FM300 material properties and elastic
behaviour are tuned values for the model.
Figure 6.3: (a) Traction-separation law for cohesive zone models (b) Modified law to implemented in FEM
Cohesive interaction
Page | 132
Chapter 6 - Detailed damage modelling for Tapered run-out stiffeners
Table 6-1: Cohesive interaction properties
FM300 (adhesive)
Normal direction
First shear direction
Second shear direction
BK law η
Initial linear elastic
behaviour
Knn in Nmm-3 Kss in Nmm-3 Ktt in Nmm-3
1000000 1000000 1000000
Damage initiation
N in MPa S1 in MPa S2 in MPa 50 100 100
Damage evolution
Gn in N/mm Gs in N/mm Gt in N/mm 8
0.9 2.5 2.5 All parts were modelled using three dimensional hexahedral solid linear elements,
C3D8, to effectively capture the resulting three-dimensional stress states and provide
a better representation of the geometry. The element is fully integrated thus avoiding
potential problems associated with reduced integration. While solid elements are
capable of modelling the distinct layers of a composite with one or more elements
through the ply thickness, the formulation also allows for the representation of a
stacking sequence with a single element. This latter approach was adopted in this
present study for computational efficiency.
“Tie constraints” were used to ‘fasten’ the different parts of the finite element model
together which allows for dissimilar mesh densities between parts [4]. This facilitated the
optimisation process which required frequent changes in the geometry and dimension
design variables which could lead to a mismatch in the meshes of adjoining sections. The
FE model with boundary conditions is shown in Figure 6.4 that is similar to the
parametric study model in order comparisons to be made.
Figure 6.4: Finite element model of modified specimen.
Displacement
Page | 133
Chapter 6 - Detailed damage modelling for Tapered run-out stiffeners
6.2.1 Mode interaction A quadratic interaction criterion was used for the traction components:
2 2 2
0 0 0 1n s t
n s t
t t tt t t
+ + =
(5.1)
where, t0n , t0
s and t0t are the peak values of the contact stress when the separation is
either purely normal to the interface or purely in the first or the second shear direction
respectively.
When the initiation criterion is met, the cohesive stiffness degrades with rate that is
defined by the damage evolution model. The overall damage of the contact point is
represented by a scalar damage variable, D. After damage initiation, the damage
varies monotonically from 0 to 1 on increasing the loading.
As mentioned before, the fracture energy is equal to the area under the traction-
separation curve Figure 6.2(b) and an energy-based damage evolution approach is
used. For the mode-mix definition of fracture energies the BK law was selected,
which is based on Benzeggagh-Kenane’s criterion [88]. The BK criterion defines the
energy dissipated as
( ) c c c cSn s n
T
GG G G GG
η
+ − =
(5.2)
with, T n sG G G= + (5.3)
S t sG G G= + (5.4)
where Gn, Gs and Gt are the fracture toughness values in the normal and two shear
directions respectively which have been measured for the material IM7/8552, Table
6-1. In this study the BK mode-mix power parameter η had the value of 1.6, a value
that corresponds to material IM7/8552 and obtained experimentally by Maimi [98,
99].
Page | 134
Chapter 6 - Detailed damage modelling for Tapered run-out stiffeners
6.2.2 Response of the Numerical Model
The debonding failure load predicted by the model was compared with the debonding
loads predicted by using the energy release rate and the experimental results, Table
6-2.
Table 6-2: Debonding loads of the Tapered stiffner
Experiment Gavg Prediction
Gmax Prediction
Cohesive layer Prediction
Failure load [kN] 17.7 19.2 17.5 18.7
Difference from experiments
- 8.5% 1.1% 5.6%
Recalling the results from the energy release rate analysis, when the maximum energy
release rate across the width of the stiffener was used the predictions were closer to
the experimental results. In addition, when the average energy release rate was used,
the difference from the experimental results had an over-prediction of 8.5%. By using
the cohesive zone model, the difference with the experimental results was 5.6%.
Figure 6.5: Damage growth pattern predicted by a cohesive model for the modified specimen compared with energy release rate predictions using VCCT
Correlation of debonding damage growth across width of the stiffener
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
0 2 4 6 8
Nor
mal
ised
GT
/ Gc
Distance across width [mm]
Baseline Tapered Compliant
Page | 135
Chapter 6 - Detailed damage modelling for Tapered run-out stiffeners
Also, the debonding growth along the width of the specimen matches with the
predictions made using strain energy release rate across the width of the stiffener as
can be seen in Figure 6.5. Comparing the FE model pattern with the Tapered curve on
the right, it is clear that there is a correlation between the crack front and the energy
release rate profile.
6.3 Modeling the interlaminar failure of the Tapered
Stiffener To investigate delamination, a model was created with a cohesive zone at the interface
of the 00 and 450 plies of the stiffener.
6.3.1 Cohesive zone damage modelling definitions
A surface-based cohesive behaviour was defined at the mentioned interface with the
penalty stiffnesses from Table 5.1 and the IM7/8552 interface properties in Table 4-3.
6.3.2 Response of the model
From the response of the model it was concluded that the damage started from the
flange interface of the stiffener and expanded to the filler area. The propagation of the
delamination stopped where the web region is starting as can be seen in Figure 6.6,
where the contour plot of the cohesive damage variable (CSDMG) can be seen. The
undamaged webs were retaining the overall stiffness of the model without affecting its
linear performance up to 19.2 kN. where the first damage next to the flange edges
starts. The damage stays there up to 17.7 kN and propagates constantly towards the
centre of the stiffener and the filler area. At 19.7 kN the damage propagates at high
rate up to 19.8 kN until the final failure.
According to the observations of the failed specimen, as can be seen in Figure 6.7, the
damage predicted follows the actual failure. The only difference is that the crack in
the actual specimen seems to jump from the 0o/45o interface to the 0o/filler interface.
This intralaminar failure is numerically investigated in the following section.
Page | 136
Chapter 6 - Detailed damage modelling for Tapered run-out stiffeners
Figure 6.6: Contour plot of CSDMG at the 0o/45o interface.
Figure 6.7: Delamination occurred in the Tapered stiffener
6.4 Modeling the intralaminar failure In order to investigate the intralaminar failure of the specimen, that could not be
readily captured with the interface-based cohesive damage zone models, a new model
has been built using Hashin’s damage model. Hashin damage model predicts
intralaminar failures in fibre-reinforced composite materials and is available in
ABAQUS. This failure model is capable of predicting four major failure modes such
as:
0
5
10
15
20
25
0 0.1 0.2 0.3 0.4
Load
[kN
]
displacement [mm]
Experiments
Cohesive
Page | 137
Chapter 6 - Detailed damage modelling for Tapered run-out stiffeners
• Fibre tensile failure
• Fibre compressive failure
• Matrix tensile failure
• Matrix compressive failure
The damage initiation predictions are based on Hashin’s theory [9]. This model
considers four damage initiation criteria with respect to the four failure modes listed
above. The initiation criteria in the four damage modes are described as in the
following equations,
For fibre tension failure:
2
11 tf TF
Xσ =
(5.5)
For fibre compression failure:
2
11 cf CF
Xσ =
(5.6)
For matrix tension failure:
2 2
22 12 tm T LF
Y Sσ τ = +
(5.7)
For matrix compression failure:
22 2
22 22 12 1 2 2
Cc
m T T C LYF
S S Y Sσ σ τ = + − +
(5.8)
where σ11, σ22 and τ12 are the nominal stress components, XT is the longitudinal
tensile strength, XC is the longitudinal compressive strength, YT is the transverse
tensile strength, YC is the transverse compressive strength, SL is the longitudinal shear
strength and ST is the transverse shear strength of the composite material. According
to this criterion, when the above equations reach a value of one then damage is
assumed to initiate.
Page | 138
Chapter 6 - Detailed damage modelling for Tapered run-out stiffeners
In the damage initiation process, an energy based damage evolution model has been
used. The scalar damage variables for each failure are calculated and they
monotonically evolve from 0 to 1 on increasing the loading after the damage
initiation. A progressive degradation of material stiffness occurs and leads to material
failure for all four damage variables of the respective failure modes.
This damage evolution model is based on the four critical energy release rates for
fibre tension, fibre compression, matrix tension and matrix compression respectively
of the material IM7/8552. In Table 6-3 the intralaminar ply properties of IM7/8552
that were used in this study are presented. These values were obtained from
experimental measurements done by Camanho et al [100].
Table 6-3: Intralaminar properties of IM7/8552
Intralaminar properties of IM7/8552 Energy [N/mm]
Fibre Tensile Fracture Energy 81.5
Fibre Compressive Fracture Energy 106.3
Matrix Tensile Fracture Energy 0.277
Matrix Compressive Fracture Energy 0.788
Hashin's damage failure model is included in ABAQUS but can only be used with
plane stress formulation elements such us shell, continuum shell and membrane
elements. The ABAQUS ability to use combined types of elements in the same model
resulted in the usage of continuum shell elements only in the area were intralaminar
fracture was expected. The 0o plies of the stiffener were modelled with eight-noded
continuum shell element (SC8R), Figure 6.8a. In order to avoid any hourglass issues
an hourglass stiffness enhanced formulation was deemed necessary. Also, cohesive
interactiona was assumed in the interface of the 00 and 450 plies of the stiffener as can
be seen in Figure 6.8b.
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Chapter 6 - Detailed damage modelling for Tapered run-out stiffeners
Figure 6.8: Illustration of (a) 00 plies with Hashin damage model and (b) cohesive properties at 00/450 interface
The rest of the elements of the entire model, except the 00 plies, were formulated with
fully integrated solid elements (C3D8). In order to overcome the convergence
problems caused by stiffness degradations and softening mechanisms, a viscous
stabilization coefficient of 10-5 was introduced in the analysis.
According to the numerical model's results, the failure mode predicted by the Hashin
damage model is dominant matrix failure in compression in the filler area that
correlates with the region of expected failure of the observed failed specimen (Figure
5.10). The result of this particular numerical model that incorporates the Hashin
model had greatly contributed to understanding the sequence of damage in the
experiments. The contour plots of the damage variable for the matrix compression
failure mode is illustrated in Figure 6.9. This result clearly predicts compression
failure of the matrix near the ends of filler.
From the sequence of damage plots in Figure 6.9, stiffness degradation due to matrix
failure begins slowly at a load of 17.2 kN. The matrix failure propagates parallel to
the filler at the right flange at a load of 17.6 kN. Following the matrix damage on the
right side, the matrix failure also propagates on the left side at a load of 17.9 kN. This
prediction of location of the failure initiation correlates very well with the image in
Figure 6.10. The degradation of the matrix, firstly on the right-hand flange and then
on the left side, is captured and describes the sequence of intralaminar damage up to
the failure load of 19.8 kN.
00 plies with Hashin’sdamage model
Surface with cohesive properties interaction
(a) (b)
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Chapter 6 - Detailed damage modelling for Tapered run-out stiffeners
Figure 6.9: Contour plot of damage variable for matrix compression
The Hashin model contributed greatly to learn more about the location of initiation of
damage and the sequence of intralaminar fracture as it happened in the sample,
Figure 6.10. The sequence of failure can be described in detail by observing the
damage fields at various intervals of displacement applied during the analysis.
Figure 6.10: Matrix crack at right flange in the experimentally failed specimen
0
5
10
15
20
25
0 0.1 0.2 0.3 0.4 0.5
Load
[kN
]
displacement [mm]
Experiments
Hashin
Page | 141
Chapter 6 - Detailed damage modelling for Tapered run-out stiffeners
The Hashin model helped in predicting matrix crack initiation at the right flange. It
showed an increase in propagation of crack through the 00 right ply matrix at a load
of 17.85 kN. The matrix crack initiated in the left-hand flange at a load of 17.9 kN.
The final image at the end of the analysis, Figure 6.9, shows that both sides become
greatly degraded. Although, the Hashin model has helped in the numerical
investigation on the identification of intralaminar failure modes of initiation sites and
sequences, the option to delete the element of complete degradation of a particular
failure mode between the four modes is not currently available in ABAQUS 6.10. The
function of element deletion in the current model allows the removal of the element
only when all the damage variables in each of four modes reach a value of one. A gap
is created by the deletion of elements in the model.
6.5 Modeling the experimental results As a result of the conclusions drawn by the use of the Hashin model in the previous
section, new numerical models were constructed considering the following modes of
failure:
1. Delamination at the interface of the 00 and 450 plies of the stiffener in the right
and left flanges until the appearance of the matrix cracking positions.
2. Matrix failure through the 00 plies near the ends of the filler on the left and
right sides.
3. Continuation of delamination along the 00 plies on the left and right sides.
The failure modes described above have been incorporated into numerical models by
modeling a part of the assembly with appropriate interfaces and properties of
interaction. As can be seen in Figure 6.11, the delamination between the interface of
layers 00 and the filler does not propagate vertically in the web section. In reality, the
delamination between these interfaces on both sides is joined at a certain point around
the filler by a matrix crack.
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Chapter 6 - Detailed damage modelling for Tapered run-out stiffeners
Figure 6.11: Crack bridging in the experimentally failed specimen
6.5.1 Interaction properties
As discussed before, the ABAQUS surface-based cohesive behaviour was used to
model the interlaminar failures. The interaction properties are as explained in Section
3.1.7 and were defined using the property assign Interaction Manager module in
ABAQUS. The definition of cohesive layer delamination between 00 and 450 plies of
reinforcement is shown in Figure 6.12.
Figure 6.12: Cohesive properties imposed (Pink dots) on (a) Left stringer; (b) Right stringer
The pink spots correspond to regions in which the interactions surface-based cohesion
is applied with the respective zone template for cohesive delamination. The skin and
0o plies with the filler were defined with the tie constraints interactions in order to
idealize the co-bonding condition in the sample. The interface between the webs of
vertical left and right stringer are tied.
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Chapter 6 - Detailed damage modelling for Tapered run-out stiffeners
6.5.2 Delamination investigation around the filler tip point The numerical model predicted the delamination but showed that the delamination did
not propagate until the tip of the filler but instead stopped in between the top and
bottom of the filler. This can be seen in Figure 6.13 where interlaminar and
intralaminar fracture of the interfaces is shown through the cohesive damage variable.
From the above numerical model, it was clear that the bridging of the delaminations
(00 plies/filler) did not happen around the filler and a detailed investigation across the
filler was needed. The response of the model with a crack plane across the filler was
investigated and it is presented in the next section.
Figure 6.13 Contour plot of cohesive damage variable with crack bridging around the filler
6.5.3 Delamination investigation across the filler
A numerical model was built with the crack bridging plane across the filler. The crack
bridging is parallel to the filler and 2.25mm from filler tip. In the present numerical
model the crack bridging occurred across the filler at the lowest plane. This is shown
in Figure 6.14.
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Chapter 6 - Detailed damage modelling for Tapered run-out stiffeners
Figure 6.14: Contour plot of cohesive damage variable with crack bridging across the filler at lowest plane.
The crack bridging between the right and the left sides of the stiffener was evaluated.
In order to carry out this study, a parametric analysis of horizontal crack planes across
the filler was performed. The models that were generated from the study are:
• Model 1 – With crack bridging plane at 0.694 mm from the filler tip point.
• Model 2 – With crack bridging plane at 0.9375 mm from the filler tip point.
• Model 3 – With crack bridging plane at 1.25 mm from the filler tip point, mid
plane
• Model 4 – With crack bridging plane at 1.40625 mm from the filler tip point.
• Model 5 – With crack bridging plane at 1.5625 mm from the filler tip point.
• Model 6 – With crack bridging plane at 1.71875 mm from the filler tip point.
• Model 7 – With crack bridging plane at 1.875 mm from the filler tip point,
3/4th plane
• Model 8 – With crack bridging plane at 2.0625 mm from the filler tip point.
• Model 9 – With crack bridging plane at 2.25 mm from the filler tip point,
which is the lowest plane and it is in line with the horizontal interface of 00
and 450 plies.
In models 1, 2 and 3, there were no damage across the filler and webs and were
rejected because of an inaccurate representation of the failure process. The rest of the
Page | 145
Chapter 6 - Detailed damage modelling for Tapered run-out stiffeners
models and the results are listed in Table 6-4. The load-displacement curves are
presented in Figure 6.15.
Table 6-4: Failure loads of filler crack planes compared to experimental
Failure load [kN]
Experime
nt Model
4 Model
5 Model
6 Model
7 Model
8 Model
9
Initiation 17.61 17.18 17.18 17.19 17.19 17.28 17.07
Maximum 17.78 18.26 18.02 18.01 17.99 17.91 17.68 Initiation Error % -2.37 -2.36 -2.32 -2.32 -1.81 -3.00
Max Error % 2.73 1.37 1.34 1.22 0.70 -0.55
Figure 6.15: Load-displacement of crack bridging plane models
Models 4 and 5 had an unstable behaviour before final failure. As the crack plane was
moving to the skin direction, the crack propagation was becoming more stable
0
2
4
6
8
10
12
14
16
18
20
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
Lo
ad [k
N]
displacement [mm]
Model 4
Model 5
Model 6
Model 8
Model 8
Model 9
Experiments
Page | 146
Chapter 6 - Detailed damage modelling for Tapered run-out stiffeners
resulting in model 8 having behaviour very close to the experimental results. The only
disadvantage was that its crack plane was far from the experimental one. this resulted
in moving to the next modelling strategy that incorporates the XFEM damage model
and described in the next section.
6.6 Modeling using XFEM A new model was built by using the XFEM method described before in paragraph
2.3.5. The mesh density of the model remained the same in order to compare this
model with the previous ones and compare with each other. In the new model, the 0o
plies of the stiffener that attach to the skin were merged with the filler in order to
create a new part. In this new part, the XFEM method was applied with the properties
that are listed in Table 6-5, where damage initiation and damage evolution are based
on IM7/8552 material properties and elastic behaviour are tuned values for the
model.
Table 6-5: XFEM interaction properties
FM300 (adhesive) Normal direction First shear
direction Second shear
direction BK
law η Initial linear
elastic behaviour
Knn in Nmm-3 Kss in Nmm-3 Ktt in Nmm-3
1000000 1000000 1000000
Damage initiation
N in MPa S1 in MPa S2 in MPa
50 50 50
Damage evolution
Gn in N/mm Gs in N/mm Gt in N/mm 1.6
0.2 0.6 0.6
Also the cohesive contact for debonding remained as well as for for delamination.
Having all the failure procedures in one model, the interaction of the failures were
investigated and the results are summarized in Figure 6.16.
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Chapter 6 - Detailed damage modelling for Tapered run-out stiffeners
Figure 6.16: Failure sequence of the stiffener from the XFEM model. (a) the stiffener started to debond (b) without any
delamination. (c) The debonding propagated and the first XFEM element failed.(d) without any delamination. (e) Debonding with failed filler XFEM elements (f) accompanied with delamination.
According to the XFEM model the stiffener handled a maximum load of 21.5 kN
before the final failure,
Figure 6.17. In this model, failure starts with debond of the stiffener's tip
without any delamination or 0o/filler failure, Figure 6.16a,b. The debonds are the red
areas that consign the loss of contact and as can be seen they start from the centre and
the ends of the stiffener, as expected from the parametric study analysis . When the
applied load reaches 17.9 kN, the first failure of the XFEM element occurs but no
delamination failure occurs yet, Figure 6.16c,d, while the debond propagated further.
At a load of 21.5 kN, the crack in the filler reached the left side of the stiffener, while
the delamination in the filler area started, Figure 6.16e,f. From the behaviour of this
model, it can be inferred that failure started by debonding of the stiffener, that led to
a crack in/around the filler and finally coupled with delamination.
(a)
(c)
(b)
(d)
(e) (f)
Page | 148
Chapter 6 - Detailed damage modelling for Tapered run-out stiffeners
Figure 6.17: Load- displacement curve of the XFEM model
6.7 Modeling using LaRC LaRC'05 failure model is based on failure criteria at the microscopic level with the
physical mechanics of continuous damage. Further details on the model LaRC'05 can
be found in [22, 23]. The important features of this model are summed hereinafter.
Firstly, the non-linear behaviour of the composite in the matrix-dominated directions
is taken into account, as well as the hydrostatic pressure dependence. Secondly, a
distinction is made between all the processes of possible failure, fibre tensile failure,
matrix compressive failure, matrix tensile failure and fibre kinking failure. For each
failure process, a failure index is calculated at the ply level, depending on the ply
thickness and the stacking sequence.
Once failure has started, the failure propagation is modelled by introducing a damage
variable d (as for the indices of failure, there is a damage variable for each process of
failure). The components of the tensile fracture plane were gradually and linearly
degraded.
0
5
10
15
20
25
0 0.1 0.2 0.3 0.4 0.5
Load
[kN
]
displacement [mm]
Experiments
XFEM
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Chapter 6 - Detailed damage modelling for Tapered run-out stiffeners
In order to include these features in modelling, the XFEM method described in the
previous paragraph was replaced by the LaRC'05 failure model using a smeared
formulation. The values given to the code inputs and post-history outputs are listed in
Appendix B. The values in the table are a combination of values from the material
characterization performed and values proposed by Vyas et al [101].
According to the results of the numerical analysis, the failure of the stiffener started
by dedonding of the skin. The debonding procedure followed the trend that the energy
release rate study predicted, from the centre and the edges of the stiffener. Then, the
failure jumped to the 0o ply and the filler and continued from there, see Figure 6.18
where the matrix failure of the model is presented. The maximum load that this model
handled was 18.7kN, quite close to the experimental failure load. The only
disadvantage of this method is that it is time consuming.
Figure 6.18: Load-displacement of LaRC'05 model and SDV8, matrix failure post-history.
1
23 4
1
2
3
4
Page | 150
Chapter 6 - Detailed damage modelling for Tapered run-out stiffeners
6.8 Comparison of the failure models All the models analyzed had a common mesh density in order to evaluate the
capability of capturing the damage in the stiffener and the ability to capture the real
specimen failure. Recalling the test data for the Tapered stiffener, the damage
procedure that was expected to be modeled was a combination of debonding and
delamination. In Figure 6.19, the load-displacement curves for the failure models
generated in this study are presented.
Figure 6.19: The failure loads of different failure models
All the numerical analysis results can be compared with each other as well as with the
experimental failure load. The cohesive model can give quite good predictions for the
failure load but does not properly describe the damage in/around the filler. The
Hashin damage model can fill this gap but it has to be used with the cohesive model.
The failure load when only the Hashine damage is used is 19.8 kN but when it is
0
5
10
15
20
25
0 0.1 0.2 0.3 0.4 0.5
Load
[kN
]
displacement [mm]
Experiments
Cohesive
Hashin
Coh+Hashin
XFEM
Larc05
Page | 151
Chapter 6 - Detailed damage modelling for Tapered run-out stiffeners
combined which cohesive elements the failure load drops to 17.9 kN. The XFEM
model captures the failure load but over-predicts the failure load by reaching 21.5 kN,
the highest in the numerical analysis. Finally, the LaRC05 has predicted accurately
the failure load, by predicting it to be 18.8 kN , as well as the damage sequence.
6.9 Conclusions
The numerical study performed in this chapter gave a good insight into the presence
of crack bridging across the filler between the filler tip point and the lowest crack
plane in line with the horizontal interface of 00 and 450 plies. The numerical models
over predicted the failure loads to different extents, but they gave another view on the
processes by which failure occurred.
Page | 152
Chapter 7
Conclusions
7 Conclusions This study led to a parametric study that resulted in an improved damage tolerant
design of stiffener run-out, the Compliant run-out. In addition, the manufacturing
process that was developed led to quality stiffener run-out specimens. The key
findings of this thesis can be categorized and highlighted as:
1. Numerical analysis
• An insight was given in the stress-design relation in stiffener run-outs
that led in the analysis of different termination schemes.
• Good prediction of failure loads were made by using the parametric
analysis that based on the strain energy release rates
• The predictions of failure load were more accurate when the maximum
strain energy release rate was taken account, which suggests that it is
appropriate to consider the width-variation of the energy release rate in
these studies.
2. Manufacturing and testing
• The manufacturing process that designed was led to sound skin-
stiffener run-outs
• The AE monitoring proved to be valuable in detecting and analysing
the failure modes experienced by the specimens.
• Compliant termination schemes offer the possibility of improved
damage tolerance.
3. Detail modelling of run-out stiffeners
Chapter 7 - Conclusions
• Compared to other modelling approaches, the parametric study gave
very good predictions.
• Other modelling techniques can be considered taking account time-
accuracy factors.
The key findings are discussed in more detail in the following three paragraphs.
7.1 Numerical analysis A closed-form model was developed that predicts peel stresses in adhesively bonded
joints and was successfully used to better understand the singularity of the stress field
at the discontinuity. Using FE models, different run-out termination schemes were
compared and the first estimations of the geometrical effects were made. It was shown
that the peeling stresses could be reduced by using stiffener run-outs with tapered web
and widened flange.
A parametric analysis based on the strain energy release rates for debonding and
delamination successfully predicted the failure loads for the three different specimen
types. The behaviour of the models was analysed for different parametric values and
the best combination was used in order to select on the best design and proceed in
manufacturing.
Also, the variation of energy release rate across the width of the stiffener was taken
into account. The predictions were more accurate when the maximum strain energy
release rate across the width was used. It can be concluded that the variation of the
energy release rate across the width should be considered when stiffener run-outs are
designed.
7.2 The manufacturing and testing processes The manufacturing process used in this study led to sound skin-stiffener run-outs
whose design was validated against a numerical study. The material characterisation
was the first step in order to obtain inputs for the FE models to be created. The
aluminium moulds led to specimens with accurate dimensions. Special attention was
given to the manufacturing of the filler, since this is a very critical region in the
Page | 154
Chapter 7 - Conclusions
failing procedure of the specimen. The good bonding of the stiffener on the skin was
achieved with the usage of wooden moulds that also ensured the centred positioning
of the stiffener on the skin.
DIC captured well the strain field in the area around the stiffeners tip but could not
provide significant information at the skin interface area. AE data recorded during
skin-stiffener run-out compression tests proved useful to analyse the failure processes
which take place in these specimens and detected the failure modes experienced by
the specimens. The classification of the failure modes, that the AE provided, gave an
insight into the damage that occurred and the damage tolerance for each design.
According to the AE results, it was concluded that the Compliant design exhibited the
best damage tolerance.
The experimental program provided all the appropriate data needed for failure
investigation and the FE modelling. The predicted failure loads were confirmed by
the tests, especially when the maximum release rate across the width was used for the
prediction. Also, the results show that in the design of skin-stiffener run-outs it is
important to consider the possibility of failure modes other than debonding, and that
compliant termination schemes offer the possibility of improved damage tolerance.
7.3 Detail modeling of run-out stiffeners The delamination of the Tapered stiffener as well as the debonding from the skin were
investigated by using different damage models. Firstly, this was investigated by using
the cohesive contact. This model showed that delamination at the interface of the 00
and 450 plies of the stiffener happened across the 00 plies and stopped at a point along
filler region.
Moving to the Hashin damage models, the lack of the possibility to remove elements
when one of the four failure modes is completed proved a drawback in the analysis.
Despite this, these models helped to understand the intralaminar failure modes of
initiation and the following sequence. Following the findings with the Hashin model,
the failure in/around the filler was investigated with precisely located cohesive
models for modelling intralaminar failure. A good correlation of the failure load was
Page | 155
Chapter 7 - Conclusions
achieved but the cracking plane in the filler at a lower location to the one observed
experimentally.
Moving to the XFEM method, the damage sequence was captured but with an over-
prediction of the failure load. The failure started by debonding of the stiffener from
the skin, moved to failure in/around the filler area that resulted in delamination
starting from the filler area. When the LaRC05 was used, the same failure sequence
was predicted but the failure load was closer to the experimental one.
Page | 156
Chapter 8
Future work
8 Future work
8.1 Using this study in other structures In this study, the failure of bonded stiffener run-outs was investigated. Considering
the complexity of the specimens, the findings of this research could also be used in
other bonded structures with simpler geometries such as bonded joints or panels with
multiple stiffeners. Also the merits of the manufacturing procedure could be used for
stiffeners with more than 5 plies.
8.2 Other parameters in the parametric study The full capabilities of laminated composites could be exploited by performing a
parametric study on the influence of different stacking sequences in the damage
procedure. A stacking sequence study could be performed by using the parametric
model described in paragraph 4.4.1. Parameters for the stacking sequence of the plies
can be added to the model, not only for the stiffener but also for the skin. Also, the
effects of different boundary conditions could be investigated.
8.3 Study in fatigue From the AE data and the test results it was concluded that the Compliant design had
increased strength and damage tolerance compared to other designs and especially to
Chapter 8 - Future work
the Baseline. It is worth testing the performance of the specimens in fatigue and
include AE monitoring. This way, a clearer view of the performance of its design can
be extracted and a comparison for each design can be made.
8.4 Exploiting further the Python script, the manufacturing
method and the test results The Python script generated can be used as part of other studies in skin stiffner run-
outs. As an example, the script was already adapted in the framework of an Airbus
funded project at Imperial College to generate multiaxial failure envelopes for runouts
and also to generate runout models for global/local analyses.
In addition, the test results of this study were used for validating alternative modelling
methods for runouts at Imperial College, and the manufacturing method was used to
manufacture runouts with different layups and termination schemes.
8.5 Obtain failure data for damage models Finally, a problem faced in this study was obtaining reliable material properties for
the different damage models. Despite the material characterization performed in this
study and the available data in the literature, a complete series of data is still missing.
The development of testing procedures to accurately measure the input required to the
failure models investigated would be a worthwhile activity.
Page | 158
References [ 102-104] [ 105]
List of references
1. http://www.specialchem4adhesives.com. last visited 04/10/2008. 2. www.airlines.net. last visited in 2010. 3. Sousa, J.R.C., Final Numerical Analysis: Predict Skin/Stiffener Separation at
Stiffener Run-outs. CASA, 2000. CASA.T2.TR.5(1). 4. Simulia, Rising Sun Mills, 166 Valley Street, Providence, RI 02909-2499,
USA, ABAQUS 6.10, 2011. 5. Python, Python Software Foundation (PSF). Wolfeboro Falls, NH 03896-
0037, PO Box 37, USA, Python 2.6.2, 2010. 6. Beaumont, P.W.R., J.M. Schultz, and K. Friedrich, eds. Failure analysis of
composite materials. Delaware composites design encyclopedia, ed. G.J.W. Carlsson L.A. Vol. 4. 1990, Technomic Publishing Co. 206.
7. Paris, F., A study of failure criteria of fibrous composite materials. NASA/CR-2001-210661, 2001.
8. Sun, C.T. and J. Tao, Prediction of failure envelopes and stress/strain behaviour of composite laminates. Composites Science and Technology, 1998. 58: p. 1125-1136.
9. Hashin, Z., Failure Criteria for Unidirectional Fiber Composites. Journal of Applied Mechanics, 1980. 47: p. 329-334.
10. Rotem, A., Prediction of laminate failure with the Rotem failure criterion. Composites Science and Technology, 1998. 58: p. 1083-1094.
11. Hinton, M.J.S., P.D., Predicting failure in composite laminates: the background to the exercise. Composites Science and Technology, 1998. 58: p. 1001-1010.
12. Liu, K.S. and S.W. Tsai, A progressive quadratic failure criterion for a laminate. Composites Science and Technology, 1998. 58: p. 1023-1032.
13. Puck A., S.H., Failure analysis of FRP laminates by means of physically based pjenomenological models. Composites Science and Technology, 1998. 58: p. 1045-1067.
14. Soden, P.D., M.J. Hinton, and A.S. Kaddor, A comparison of the predictive capabilities of current failure theories for composite laminates. Composites Science and Technology, 1998. 58: p. 1225-1254.
15. Edge, E.C., Stress-based Grant-Sanders method for predicting failure of composite laminates. Composites Science and Technology, 1998. 58: p. 1033-1041.
References - List of references
16. Gotsis, P.K., C.C. Chamis, and L. Minnetyan, Prediction of composite laminate fracture: Micromechanics and progressive fracture. Composites Science and Technology, 1998. 58: p. 1137-1149.
17. Hart-Smith, L.J., Predictions of a generalized maximum-shear-stress failure criterion for certain fibrous composite laminates. Composites Science and Technology, 1998. 58: p. 1179-1208.
18. Hinton M.J., S.P.D., Predicting failure in composite laminates: the background to the exercise. Composites Science and Technology, 1998. 58: p. 1001-1010.
19. Puck, A. and H. Schurmann, Failure analysis of FRP laminates by means of physically based pjenomenological models. Composites Science and Technology, 1998. 58: p. 1045-1067.
20. Davila, C.G., P.P. Camanho, and C.A. Rose, Failure Criteria for FRP Laminates. Journal of composite materials, 2005. 39(4): p. 323-345.
21. Pinho, S.T., et al., Failure models and criteria for FRP under in-plane or three-dimensional stress states including shear non-linearity. 2005, NASA. p. 69.
22. Pinho, S.T., L. Iannucci, and R. P., Physically based failure models and criteria for laminated fibre-reinforced composites with emphasis on fibre kinking. Part II: FE implementation. Composites Part A: Applied Science and Manufacturing, 2006. 37, 766-777.
23. Pinho, S.T., L. Iannucci, and R. P., Physically based failure models and criteria for laminated fibre-reinforced composites with emphasis on fibre kinking. Part I: Development. Composites Part A: Applied Science and Manufacturing, 2006. 37, 63-73.
24. Greenhalgh, E., Evaluation of IM7/F3900 CFRP skin-stringer panels designed for damage tolerance. Technical report, 2002.
25. Noh, J. and J. Whitcomb, Prediction of delamination growth and opening near intersection oftransverse matrix cracks and delamination. 44th AIAA/ASME/ASCE/AHS Structures, Structural Dynamics, and Materials Conference, 2003. volume 2003-1602.
26. Kachanov, M., Elastic solids with many cracks: a simple method of analysis. International Journal of Solids and Structures, 1987. 23(1): p. 23-43.
27. Rabotnov, Y.N., Creep rupture. Proc. XII Int. Cong. Appl. Mech., 1968. 28. Ladeveze, P. and E.L. Dantec, Damage modelling of the elementary ply for
laminated composites. . Composite Science and Technology, 1992. 43:257–267.
29. Crisfield, M.A., Y. Mi, and G.A.O. Davies, Progressive delamination using interface elements. J. Compos. Mater., 1998. 32(14):1247–1271.
30. Daudeville, L. and P. Ladeveze, A damage mechanics tool for laminate delamination. Composite Structures, 1993. 25:547–555.
31. Barsoum, R.S., On the use of isoparametric finite elements in linear fracture mechanics. International Journal for Numerical Methods in Engineering, 1976. 10.
32. Lim, L.L., I.W. Johnston, and S.K. Choi, Application of singular quadratic distorted isoparametric elements in linear fracture mechanics. International Journal for Numerical Methods in Engineering, 1993. 36: p. 2473-2499.
33. R. Wisnom, M. and F.-K. Chang, Modelling of splitting and delamination in notched cross-ply laminates. Composites Science and Technology, 2000. 60(15): p. 2849-2856.
Page | 160
References - List of references
34. Pierron, F., B. Green, and M.R. Wisnom, Full-field assessment of the damage process of laminated composite open-hole tensile specimens. Part I: Methodology. Composites Part A: Applied Science and Manufacturing, 2007. 38(11): p. 2307-2320.
35. Pierron, F., et al., Full-field assessment of the damage process of laminated composite open-hole tensile specimens. Part II: Experimental results. Composites Part A: Applied Science and Manufacturing, 2007. 38(11): p. 2321-2332.
36. Yashiro, S., et al., Monitoring damage in holed CFRP laminates using embedded chirped FBG sensors. International Journal of Solids and Structures, 2007. 44(2): p. 603-613.
37. Hu, F.Z., C. Soutis, and E.C. Edge, Interlaminar stresses in composite laminates with a circular hole. Composite Structures, 1997. 37(2): p. 223-232.
38. Ko, C.-C., C.-C. Lin, and H. Chin, Prediction for delamination initiation around holes in symmetric laminates. Composite Structures, 1992. 22(4): p. 187-191.
39. Iarve, E.V., Spline variational three dimensional stress analysis of laminated composite plates with open holes. International Journal of Solids and Structures, 1996. 33(14): p. 2095-2118.
40. Lee, J. and C. Soutis, Measuring the notched compressive strength of composite laminates: Specimen size effects. Composites Science and Technology. In Press, Corrected Proof.
41. Green, B.G., M.R. Wisnom, and S.R. Hallett, An experimental investigation into the tensile strength scaling of notched composites. Composites Part A: Applied Science and Manufacturing, 2007. 38(3): p. 867-878.
42. Pandey, P.C. and S. Narasimhan, Three-dimensional nonlinear analysis of adhesively bonded lap joints considering viscoplasticity in adhesives. Computers & Structures, 2001. 79(7): p. 769-783.
43. Edlund, U. and A. Klarbring, A geometrically nonlinear model of the adhesive joint problem and its numerical treatment. Computer Methods in Applied Mechanics and Engineering, 1992. 96(3): p. 329-350.
44. Oterkus, E., et al., Bonded lap joints of composite laminates with tapered edges. International Journal of Solids and Structures, 2006. 43(6): p. 1459-1489.
45. Osnes, H. and A. Andersen, Computational analysis of geometric nonlinear effects in adhesively bonded single lap composite joints. Composites Part B: Engineering, 2003. 34(5): p. 417-427.
46. F M da Silva, L. and R. D Adams, Techniques to reduce the peel stresses in adhesive joints with composites. International Journal of Adhesion and Adhesives, 2007. 27(3): p. 227-235.
47. Dobbs, M.W. and R.B. Nelson, Minimum weight design of stiffened panels with fracture constraints. Computers & Structures, 1978. 8(6): p. 753-759.
48. Gόrdal, Z. and R.T. Haftka, Design of stiffened composite panels with a fracture constraint. Computers & Structures, 1985. 20(1-3): p. 457-465.
49. Hyer, M.W. and D. Cohen, Calculation of stresses in stiffened composite panels. AIAA Journal, 1988. 26(7): p. 852-857.
50. Cohen, D. and M.W. Hyer, Influence of geometric nonlinearities on skin-stiffener interface stresses. AIAA Journal, 1992. 30(4): p. 1055-62.
Page | 161
References - List of references
51. Kassapoglou, C. and A.J. DiNicola, Efficient stress solutions at skin stiffener interfaces of composite stiffened panels. AIAA Journal, 1992. 30(7): p. 1833-1839.
52. Todoroki, A. and M. Sekishiro, Stacking sequence optimization to maximize the buckling load of blade-stiffened panels with strength constraints using the iterative fractal branch and bound method. Composites Part B: Engineering, 2008. 39(5): p. 842-850.
53. Jaunky, N., N.F. Knight, and D.R. Ambur, Formulation of an improved smeared stiffener theory for buckling analysis of grid-stiffened composite panels. Composites Part B: Engineering, 1996. 27(5): p. 519-526.
54. Kong, C.-W., et al., Postbuckling and failure of stiffened composite panels under axial compression. Composite Structures, 1998. 42(1): p. 13-21.
55. Stevens, K.A., R. Ricci, and G.A.O. Davies, Buckling and postbuckling of composite structures. Composites, 1995. 26(3): p. 189-199.
56. Nemeth, M.P., Buckling and Postbuckling Behavior of Square Compression-Loaded Graphite-Epoxy Plates with Circular Cutouts. 1990: United States. p. 33p.
57. Falzon, B.G., K.A. Stevens, and G.O. Davies, Postbuckling behaviour of a blade-stiffened composite panel loaded in uniaxial compression. Composites Part A: Applied Science and Manufacturing, 2000. 31(5): p. 459-468.
58. Falzon, B.G. and G.P. Steven, Buckling mode transition in hat-stiffened composite panels loaded in uniaxial compression. Composite Structures, 1997. 37(2): p. 253-267.
59. Zhuk, Y., I. Guz, and C. Soutis, Compressive behaviour of thin-skin stiffened composite panels with a stress raiser. Composites Part B: Engineering, 2001. 32(8): p. 697-709.
60. Greenhalgh, E., et al., The effect of defects on the performance of post-buckled CFRP stringer-stiffened panels. Composites Part A: Applied Science and Manufacturing, 2003. 34(7): p. 623-633.
61. Meeks, C., E. Greenhalgh, and B.G. Falzon, Stiffener debonding mechanisms in post-buckled CFRP aerospace panels. Composites Part A: Applied Science and Manufacturing, 2005. 36(7): p. 934-946.
62. Greenhalgh, E. and M.H. Garcia, Fracture mechanisms and failure processes at stiffener run-outs in polymer matrix composite stiffened elements. Composites Part A: Applied Science and Manufacturing, 2004. 35(12): p. 1447-1458.
63. Falzon, B.G. and G.A.O. Davies, The Behavior of Compressively Loaded Stiffener Runout Specimens – Part I:Experiments. Journal of composite materials, 2002. 37(No. 5/2003).
64. Falzon, B.G. and D. Hitchings, The Behavior of Compressively Loaded Stiffener Runout Specimens – Part II: Finite Element Analysis. Journal of composite materials, 2002. 37(No. 5/2003).
65. Faggiani, A. and B.G. Falzon, Numerical Analysis of Stiffener Runout Sections. Appl Compos Mater, 2007. 14: p. 145–158.
66. Hosseini-Toudeshky, H., et al., Analysis of composite skin/stiffener debounding and failure under uniaxial loading. Composite Structures, 2006. 75(1-4): p. 428-436.
67. Greenhalgh, E., S. Singh, and K.-F. Nilsson, Mechanisms and modeling of delamination growth and failure of carbon-fiber reinforced skin-stringer panels. ASTM Special Technical Publication, 2000(1383): p. 49-71.
Page | 162
References - List of references
68. Falzon, B.G., D. Hitchings, and T. Besant, Fracture mechanics using a 3D composite element. Composite Structures, 1999. 45(1): p. 29-39.
69. Falzon, B.G., G.A.O. Davies, and E. Greenhalgh, Failure of thick-skinned stiffener runout sections loaded in uniaxial compression. Composite Structures, 2001. 53(2): p. 223-233.
70. Cosentino, E. and P.M. Weaver, Approximate Nonlinear Analysis Method for Debonding of Skin/Stringer Composite Assemblies. AIAA Journal, 2008. 46(5): p. 1144-1159.
71. Zhang, H., et al., Experimental and finite element analyses on the post-buckling behaviour of repaired composite panels. Composites Part A: Applied Science and Manufacturing, 1998. 29(11): p. 1463-1471.
72. Mahdi, S., et al., The mechanical performance of repaired stiffened panels. Part II. Finite element modelling. Composites Part B: Engineering, 2002. 33(5): p. 355-366.
73. Mahdi, S., et al., The mechanical performance of repaired stiffened panels. Part I. Experimental characterisation. Composites Part B: Engineering, 2002. 33(5): p. 343-354.
74. Krueger, R., J.G. Ratcliffe, and P.J. Minguet, Panel stiffener debonding analysis using a shell/3D modeling technique. Composites Science and Technology, 2009. 69(14): p. 2352-2362.
75. 3039-00, A.D.D., Standard Test Method for Tensile Properties of Polymer Matrix Composite Materials,. ASTM International, 2000.
76. Häberle, J.G., Technical Memo TM 99/03: The Imperial College Method for Testing Composite Materials in Compression. Imperial College of Science, Technology and Medicine, Centre for Composite Materials. , 1999.
77. D3518/D3518M-94, A.S., Standard test method for in-plane shear response of polymer matrix composite materials by tensile test of a +/-45 laminate. 2001.
78. 01, A.D., Standard Test Method for Mode I Interlaminar Fracture Toughness of Unidirectional Fiber-Reinforced Polymer Matrix Composites. ASTM International, 2001.
79. Martin, R.H. and B.D. Davidson, Mode II fracture toughness evaluation using four point bend, end notched flexure test. Plastics, Rubber and Composites, 1999. 28 (8): p. 401–406.
80. D6671-01, A.S., Standard test method for mixed mode I-mode II interlaminar fracture toughness of unidirectional fiber reinforced polymer matrix composites. 2001.
81. Gutkin, R., et al., On acoustic emission for failure investigation in CFRP. Mechanical Systems and Signal Processing 25, 2011. 1393–1407.
82. Tracy Elms Roderick, H.M.a.S.B., Characterisation of mode ii delamination using the 4enf. Proceedings of the 4th European Conference on Composites:Testing and Standardisation, Lisbon Portugal,, 1998.
83. Martin, R.H., T. Elms, and S. Bowron, Characterisation of mode II delamination using the 4ENF. Proceedings of 4th European Conference on Composites: Testing and Standardisation. , 1998. Inst. Mater: Lisbon, Portugal. p. 161-70.
84. Kim, H. and J. Lee, Stress Analysis of Generally Asymmetric Single Lap Adhesively Bonded Joints. The Journal of Adhesion, 2005(443-472).
85. Raju, I.S., R. Sistla, and T. Krishnamurthy, Fracture mechanics analyses for skin-stiffener debonding. Engineering Fracture Mechanics, 1996. 54(3): p. 371-385.
Page | 163
References - List of references
86. Hitchings, D., Finite element modelling of composite materials and structures. Cambridge (UK): WOODHEAD PUBLISHING LIMITED, 2009.
87. Psarras, S., S.T. Pinho, and B.G. Falzon, Design of composite stiffener run-outs for damage tolerance. Finite Elements in Analysis and Design, 2011. 47(8): p. 949-954.
88. Benzeggagh, M.K. and M. Kenane, Measurement of mixed-mode delamination fracture toughness of unidirectional class/epoxy with mixed-mode bending apparatus. Composites Science and Technology, 1996. 56: p. 439-449.
89. Benzeggagh, M.L. and M. Kenane, Measurement of mixed-mode delamination fracture toughness of unidirectional glass/epoxy composites with mixed-mode bending apparatus. Composites Science and Technology, 1996. 56(4): p. 439-49.
90. Faggiani, A. and B.G. Falzon, Numerical analysis of stiffener runout sections. Applied Composite Materials, 2007. 14(2): p. 145-58.
91. Falzon, B.G. and G.A.O. Davies, The behavior of compressively loaded stiffener runout specimens - Part I: Experiments. Journal of Composite Materials, 2003. 37(5): p. 381-400.
92. Falzon, B.G. and D. Hitchings, The behavior of compressively loaded stiffener runout specimens - Part II: Finite element analysis. Journal of Composite Materials, 2003. 37(6): p. 481-501.
93. Falzon, B.G., K.A. Stevens, and G.O. Davies, Postbuckling behaviour of a blade-stiffened composite panel loaded in uniaxial compression. Composites Part A (Applied Science and Manufacturing), 2000. 31A(5): p. 459-68.
94. Greenhalgh, E. and M.H. Garcia, Fracture mechanisms and failure processes at stiffener run-outs in polymer matrix composite stiffened elements. Composites Part A (Applied Science and Manufacturing), 2004. 35A(12): p. 1447-58.
95. Mahdi, S., et al., The mechanical performance of repaired stiffened panels. Part II. Finite element modelling. Composites Part B:Engineering, 2002. 33(5): p. 355-366.
96. Krueger, R. and P.J. Minguet, Analysis of composite skin-stiffener debond specimens using a shell/3D modeling technique. Composite Structures, 2007. 81(1): p. 41-59.
97. mBH, G., Aramis 5.4 User Manual. 2005. 98. Maimi, P., et al., A continuum damage model for composite laminates: Part I-
Constitutive model. Mechanics of Materials, 2007. 99. Maimi, P., et al., A continuum damage model for composite laminates: Part II-
Computational implementation and validation. Mechanics of Materials, 2007. 100. Camanho, P.P., P. Maimí, and C.G. Dávila, Prediction of size effects in
notched laminates using continuum damage mechanics. Composites Science and Technology, 2007. 67(13): p. 2715-2727.
101. Vyas, G.M. and S.T. Pinho, Computational implementation of a novel constitutive model for multidirectional composites. Computational Materials Science, 2012. 51(1): p. 217-224.
102. Pinho, S.T., Modelling failure of laminated composites using physically-based failure models. Imperial College London, 2005.
103. Hodgkinson, J.M., Mechanical Testing of Advanced Fibre Composites. 1st ed. Woodhead Publishing Limited, Cambridge, England. , 2000.
Page | 164
References - List of references
104. Häberle, J.G., The Imperial College Method for Testing Composite Materials in Compression. mperial College of Science, Technology and Medicine, Centre for Composite Materials. , 1999.
105. Soutis, C. and P.T. Curtis, A method for predicting the fracture toughness of CFRP laminates failing by fibre microbuckling. Composites Part A: Applied Science and Manufacturing, 2000. 31(7): p. 733-740.
106. Greenhalgh, E., et al., Evaluation of toughening concepts at structural features in CFRP--Part I: Stiffener pull-off. Composites Part A: Applied Science and Manufacturing, 2006. 37(10): p. 1521-1535.
Page | 165
Appendix
Appendix A
Study Material stiffener
type Panel lay-up Stiffener Lay-up
Stiffener
Dimensions
(mm)
Data
Reduction Objective Comments
Z Gόrdal [48] Aluminum
2026-T3
Aluminum
7075-T6
general
purpose
mathematical
optimization
algorithm
automated procedure for designing minimum-weight composite panels subject to a local damage constraint under tensile loading
-Panel fracture
toughness was obtained
by using a strain based
criterion.
-results for both tinstiffened and stiffened plates
K. A. Stevens [55] T300/914C T (45/-45/0"2/45/
-45/90 "2) s
(45/-45/0/45/-45/
0"2/45/-45/0 "2) s
865x43/
30x32
shadow Moire
photography
FE
The postbuckling
behaviour of a flat,
stiffened, carbon
fibre composite
compression panel
delaminate under the stiffener web at points in the panel where the web bending moment is a maximum,
N. Jaunky [53] I [45/-452/45/0/90]s
[45/-45/90/0]s
[45/90/-45]s
[45/-452/45/0]s 51x0.5x5 FE approach to incorporate the effects of local skin-stiffener interaction into a smeared stiffener theory
Rayleigh-Ritz method
B.G. Falzon[58] Hy-E
3034K
Π [45/-45/0/90]s
[45/-45/0/90]s
strain gauges
linear voltage differential transducers (LVDTs)
buckling mode
transition
C.W. Kong [54] T I Π [O/90/45/0/-45] [O/90/45/- 45]s. 280x24 shadow Moire
photography
FE
The postbuckling
behavior of
graphite-epoxy
laminated stiffened
panels
The stiffeners were fabricated by the continuous plies of the skin and cocured with the skin. Therefore, separation between the stiffener
Appendix - Appendix A
and skin did not occur
even after final failure.
Zhang [71] T300/914 I uni uni 274x25 rosette strain
gauges
FE
investigations on
the performance of
repaired thin-
skinned, blade-
stiffened composite
panels in the post-
buckling range
repair scheme is
capable of restoring the
general load path as
well as recovering both
buckling and failure
loads
B. G Falzon [57] T800/924C J I Π [90/02/90/+-45/
0/90/+-45/0]s
[90/0/90/0
/+-45/90/02/90/
+45/+-45/90]s
728x55x45 strain gauge
three-point
bending test
LVDT
The postbuckling
behaviour of a
panel with blade-
stiffeners
incorporating
tapered flanges
the failure mechanism
was an interlaminar
shear stress failure
arising from the
combination of
compressive loading on
the postbuckled
stiffener blade and the
twisting induced at the
node-line of the
buckled stiffener.
Y. Zhuk et. al. [59] T800/924 T [45/−45/0/90]4s [−45/+45/0]2s
[+45/−45/0]2s ,
300x30x30 the Soutis–
Fleck fracture
model,
FE analysis
The in-plane
compressive
behaviour of thin-
skin stiffened
composite panels
with a stress
concentrator in the
form of an open
hole
The influence of the
stiffener on the
compressive strength of
the thin-skin panel is
examined and included
in the analysis
B.G Falzon [63, 64] AS4-8552 I
runout
[45/-45/0/90/
02/-45/45/02/90/
02/45/-45/0]S
[45/45/90/02/45
/-45/03/45/-45/
0/45/0/90]S
[45/-45/90/03/ -45/0/452/_45/ 90/0/45/0/45/ -45/0/90/0/ -45/45/-45/45
[0/90/02/-45/45/04/
-45/45/02/
90/03/90/0]
[_45/02/45/02/
90/02/45/0/90
/02/90/0
/-45/02/90/02
/45/02/-452/45]
[-45/02/45/02/90/
400x120x61 thick shell element is used in conjuction with the Virtual Crack Closure Technique (VCCT) to predict the crack growth characteristics of the modelled specimens
investigating the failure of thick-sectioned stiffener runout specimens loaded in uniaxial compression
-failure in itiated at the edge of the runout and propagated across the skin–stiffener interface -the failure load of each specimen was greatly influenced by intentional changes in the geometric features -some of the observed behavior was unexpected
Page | 167
Appendix - Appendix A
/90/-45]s 02/45/0/90/02/90
/0/-45/02/90/02/
45/02/-452/45]
S. Mahdi [72, 73] T300/914C I [45/−45/0/90]4s [−45/+45/0]2s 400x30x30 Strain gauges
were used for
the
determination
of surface
strains
FE method
develop a simple
FE method that
could be used for
the design of repairs
to I-stiffened panels
-bending occurs as the
applied displacement is
increased
-failure may have
initiated at a crack in
the skin, with the init ial
crack growing
perpendicularly to the
applied stress and
leading to stiffener
debonds, and ultimately
to collapse of the skin
and the stiffeners
E. Greenhalgh [60] HTA/6376C T [+45/−45/0/90]3S [+45/−45/03/90
/03/−45/+45]
450x45x55 fractographic
analysis
the testing and
failure analysis of
wing relevant skin-
stringer panels
containing defects
-a secondary
mechanis m occurred
prior to skin/stringer
detachment developing
-the panel failed in
compression, from the
impact site, before
skin/stringer debonding
could initiate
- the effect of the
defects on the panel
strength was related to
how they influenced
skin/stiffener
debonding
E. Greenhalgh [62] AS4/8552 I
runout
[+45/−45/0/90/−45/
+45/0/+45/−45/0]S
[+45/−45/0/0/0/90]S deflections and
strains
monitored
C-scan
fractographic
analysis
deduce the failu re
processes in the
elements, and to
characterise the
effect of local
geometry of the
stringer run-out on
the failure process
-Tension
- the development and
migration of
delaminations via ply
splits plays an
important role and
needs to be modelled
C. Meeks[61] HTA/6376C T [+45/−45/0/90]3S [+45/−45/03/90
/03/−45/+45]
450x48x45 Ultrasonic
ABAQUS
The detailed
damage
mechanis ms for
skin/stiffener
detachment in an
- provides an insight
into the processes that
control post-buckled
performance of
Page | 168
Appendix - Appendix A
undamaged panel
were characterised
and related to the
stress conditions
during post-
buckling
stiffened panels
- 2D models and
element tests do not
capture the true physics
of skin/stiffener
detachment: a fu ll 3D
approach is required
E. Greenhalgh [106] T800/M21 T [+45/0/−452/0/+45/90/
+45/0/ −452/0/+45]S
[+45/−45/0/0/90/0]S 40x40x66.5 Strain gauges evaluate two
damage tolerance
concepts; improved
toughness matrix
and Z-pinning
Hosseini-
Toudeshky[66]
ASNA 4197 skin and
flange
assembly
[0/45/90/−45/45/−45/0]s
[45/−45/0/0/45/90/−45]s
[90/45/0/0/−45/45/−45/90]s
[45/0/45/0/45/0/45/0/45]
[45/90/−45/0/90]s
[45/90/−45/0/90]s
[45/90/−45/0/90]s
[45/0/45/0/45/0/45/0/45]
50x25 a digital
camera
loads-
displacements
recorded by
the machine
FE
damage
mechanis ms in the
composite bounded
skin/stiffener
constructions under
monotonic tension
loading
- matrix crack init iation
and propagation in the
skin and near the flange
tip, causing the flange
to almost fully debound
from the skin
- interlaminar
debounding and fiber
breakage up to the
failure
A. Faggiani [65] AS4-8552 I
runout
[45/−45/0/90/02/−45 /45/02/90/02/45/−45/0]S
[45/−45/02/90/02/45/−45/
03/45/−45/0/90/02/45/−45 /0/90/02/45/−45]S
[0/90/02/−45/45/04/ −45/45/02/90/03/90/0]
[−45/02/45/02/90/
02/45/0/90/02/90
/0/−45/02/90/02
/45/ 02/−452/45]
400x120x61 strain gauges
Linear voltage differential transducers (LVDTs) fractographic analysis FE
present the experimental results of tests conducted on different stiffener runout specimens, and to show how their behaviour and failure mode can be predicted by the use of high-fidelity fin ite element (FE) analyses incorporating cohesive elements to predict delamination
-thinner skin, showed sudden crack propagation leading to collapse -thicker skin, had initially unstable crack growth followed by stable crack growth
A. Todoroki [52] AS4/3502 I 40 plies 68 plies 762X62x93 FEM analyses optimization of the
stacking sequences
in these composites
is indispensable
The new method is
applied to the buckling
load maximization of a
blade-stiffened
composite panel, in
which the strength
constraint is
demonstrated as a
feasibility study
Page | 169
Appendix - Appendix B
Appendix B
Table. A1 The list of inputs for LaRC'05 failure model
No Name Notation Value 1 Longitudinal Young's modulus (MPa) E1 171420 2 Transverse Young's modulus (MPa) E2 9080 3 Major Poisson's ratio υ12 0.34 4 Major transverse Poisson's ratio υ23 0.5 5 In-plane shear modulus (MPa) G12 4480 6 Longitudinal tensile strength (MPa) Xt 2260 7 Longitudinal compressive strength (MPa) Xc 1573 8 Transverse tensile strength (MPa) Yt 62 9 Transverse compressive strength (MPa) Yc 255 10 In-plane shear strength (MPa) SL 101.2 11 α0 53 12 φ0 0.01 13 Transverse shear strength (MPa) St 112.793 14 Slope coefficient for longitudinal shear strength ηL 0.351575 15 Slope coefficient for transverse shear strength ηt 0.286745 16 Slope coefficient for Young's modulus ηE 16 17 Slope coefficient for shear modulus ηg 0.2 18 Critical energy release rate in fibre tension (mJ/mm2) enft 97.8 19 Critical energy release rate of 2nd failure process in fibre
tension (mJ/mm2) enftii 35.5
20 Ratio strength over 2nd failure process strength rft 0.084 21 Critical energy release rate in kinking (mJ/mm2) enkink 106.3 22 Critical energy release rate of 2nd failure process in kinking
(mJ/mm2) enkinkii 20
23 Ratio strength over 2nd failure process strength rkink 0.3 24 Critical energy release rate of matrix in mode I (mJ/mm2) enb or GIc 0.256 25 Critical energy release rate of 2nd failure process matrix in
mode I (mJ/mm2) enbii 1.37
26 Ratio strength over 2nd failure process strength rb 0.0108 27 Critical energy release rate of matrix in mode II (mJ/mm2) ent or GIIc 0.7874 28 Critical energy release rate of 2nd failure process matrix in
mode II (mJ/mm2) entii 1
29 Ratio strength over 2nd failure process strength rt 0.01 30 Critical energy release rate of matrix in mode II (mJ/mm2) enl or GIIc 0.7874 31 Critical energy release rate of 2nd failure process matrix in
mode II (mJ/mm2) enlii 1
32 Ratio strength over 2nd failure process strength rl 0.01
Page | 170
Appendix - Appendix B
33 Saturation crack density crackdens 5.48008 34 Material orientation (°) beta 0 35 Flag for micro or meso scale (matrix propagation) flagscale 0 36 Flag for UD / outer / embedded ply flagplytype 1 37 Flag for bilinear or trilinear damage law for matrix flaglawmat 1 38 Flag for bilinear or trilinear damage law for fibre tension flaglawft 1 39 Flag for bilinear or trilinear damage law for kinking flaglawkink 0 40 Flag for element deletion after matrix failure delmatflag 1 41 Flag for element deletion after kinking failure delkinkflag 1 42 Flag for element deletion after splitting failure delsplitflag 1 43 Flag for element deletion after fibre tension failure delftflag 1 44 ***** delgap 2 45 ***** delsteps 100 46 Failure propagation flag faipropflag 1 47 Failure initiation flag findexflag 1 48 Non-linearity flag nlf 7 49 First order coefficient in the shear curve polynomial c1ym 5019.25 50 Second order coefficient in the shear curve polynomial c2ym -87839.9 51 Third order coefficient in the shear curve polynomial c3ym 490339 52 First order coefficient in the transverse curve polynomial c1g 9996.22 53 Scnd order coefficient in the transverse curve polynomial c2g -189894 54 Third order coefficient in the transverse curve polynomial c3g 1440960
Table A2 Post-history outputs
Post-history variable number
Name Description
1 k 2 eps1pl longitudinal plastic strain 3 eps2pl transverse plastic strain 4 eps3pl through-thickness plastic strain 5 eps12pl shear plastic strain 6 eps23pl shear plastic strain 7 eps31pl shear plastic strain 8 kfmat Matrix failure index 9 kfkink Kinking failure index 10 kfsplit Splitting failure index 11 kfft Fibre-tension failure index 12 dmat matrix failure damage variable 13 dkink kinking failure damage variable 14 dft fibre tension damage variable 15 epsmato matrix failure initiation strain 16 sigmato matrix failure initiation stress 17 epsmatf matrix failure final strain 18 epsmati matrix failure intermediate strain 19 epskinko kinking failure initiation strain 20 sigkinko kinking failure initiation stress
Page | 171
Appendix - Appendix B
21 epskinki kinking failure intermediate strain 22 epskinkf kinking failure final strain 23 epsfto fibre tension failure initiation strain 24 epsftf fibre tension failure final strain 25 epsfti fibre tension intermediate strain 26 phimem*radtodeg Φ in degrees 27 psimem*radtodeg Ψ in degrees 28 alphamem*radtodeg α in degrees 29 omega*radtodeg Ω in degrees 30 lambda*radtodeg λ in degrees 31 lmat characteristic length of matrix-failed
element 32 lkink characteristic length of kinking-failed
element 33 lftf characteristic length of fibre-tension-failed
element 34 delcount 35 eps1 longitudinal strain 36 eps2 transverse strain 37 eps3 through-thickness strain 38 eps12 shear strain 39 eps23 shear strain 40 eps31 shear strain 41 thick thickness 42 curcdens current crack density 43 failels Failed elements
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