u. barberis, a. hassim, c. ravera* & g. vanderborck* · 2014. 5. 14. · u. barberis*, a....

Impact-induced damage analysis tools for

laminated composites

U. Barberis*, A. Hassim*, C. Ravera* & G. Vanderborck*Ansaldo Ricerche s.r.l., Genova, Italy, Inria, Rocquencourt, France,^Thomson Marconi Sonar, Sophia-Antipolis, France.

Abstract

The aim of the present work is to produce a validated set of design/analysissoftware tools called ADANIDEC, in the shape of finite element programs, forthe selection and impact-induced damage evaluation of laminated compositestructures for engineering design.

The first part of this paper summarises our previous work[l] on the impact-induced damage analysis of laminated composites which includes:• the formulation of material model, based on phenomenological continuum

damage mechanics for a number of selected laminated composites, andexperimental tests to evaluate the constants in the damage evolution law;

• development of algorithms and of a computer program to represent theabove material models and their incorporation into the dynamic analysiscodes using three-dimensional finite element techniques;

# the design of a multi-level (component, lamina, laminate) material databaseto accumulate and to retrieve information on specific composite materials.

A Graphical User Interface has been developed and pull-down menus lead theuser to multi-level material selection from the database which when combinedwith the use of finite element based numerical tools enables the rapididentification of the optimum materials for a specific design. In the second part,the structural analysis scheme and the general view on the use of theADANIDEC program is described. To illustrate the ability of the numericalprocedure, the damage accumulation and the global displacement calculations forlaminates subjected to local and global impact loads were performed andcompared with experimental observations.

Advances in Composite Materials and Structures VII, C.A. Brebbia, W.R. Blain & W.P. De Wilde (Editors) © 2000 WIT Press, www.witpress.com, ISBN 1-85312-825-2

Advances in Composite Materials and Structures Vll

1 Introduction

Damage development in composite laminates under impact loading is a com-plicated process. Such damage which often are undetectable includes matrixcracks, fiber breakages, and fiber-matrix debonding. Although it does not tocatastrofic failure, its presence causes stiffness reduction. Hence the studiesof the initiation and of the growth of the matrix crack in composites lami-nates under impact have received considerable attention in recent years [2].The objectives of the current work are : (1) to develop design tools capableof predicting the gradual development of damage in laminates compositessubjected to low-velocity transverse impact, (2) to demonstrate the designtools by comparing numerical results with experimental tests, (3) to consol-idate experimental and computational data by constructing a data base ofconstants associated with each damage model implemented into the designtools, (4) to interface this database with various structural dynamic codes.Because of the wide variety of compositions with which composites can beproduced, it is difficult to produce a single material model that will faith-fully reproduce the responses of all these composites, not even if they areall subjected to only one type of loading. We have chosen to concentrateon a few composite materials of immediate interest and to produce genericmodels for these composites. A programme of tests have been carryingout to characterize the composites under low rates of loading. To buildup an understanding of the physical processes involved in the growth andaccumulation of a variety of damage (e.g. fiber-breakage, matrix crack-ing, fiber-matrix debonding) in the composite test-specimens, the extend ofdamage has been assessed by visual and ultrasonic inspection both duringand post-test. In order to be fitted to mathematical damage model, eachlayer of a laminate have been tested separately so that its elastic propertiesas well as the degradation of these properties are obtained. Thus a largenumber of tests have been performed on each material specimen involv-ing loading and unloading loops to obtain the required information. Thesetests have been carried out to a very high standard. Formulations, basedon Kachanov's concept [1, 3], have been produced, to simulate the observedexperimental phenomena and to correctly model the underlying physicalprocess that cause cumulative damage in the selected composite materials.The approach relates the damage parameters introduced to describe thecollective effect of such cracks, to reductions of the elastic constants. Themathematics of these models is based on broad fundamental principles thatallows the extension of these models to reasonably similar other compositematerials. Global half sine acceleration using a free fall shock test ma-chines as well as local acceleration using a height falling tower system havebeen imposed on composite laminate specimens and the consequent onsetof damage have been investigated during the impact. The non-linear tran-sient dynamic response of the same laminate specimen using the same testconfigurations have been performed by analytical and numerical methods.


Advances in Composite Materials and Structures I'll 2&3

Three-dimensional finite elements have been used to get accurate informa-tion for the transient stress and strain distributions through the laminate.Damage based on the above model have been investigated at any instantin the dynamic simulation. Experimental and parametric computationalinvestigations of the nonlinear structural behavior have been compared. Adatabase that contain the relevant elastic and damage-dependent propertiesof the materials and typical experimental results as well as the results ofany analysis have been produced. This database has been interfaced withselected dynamic structural analysis codes.

2 Progressive damage modelling of composites

Material models based on phenomenological continuum damage mechanics(CDM) approaches [3] have being developed and introduced in existing finiteelement code to predict progressive damage growth in laminated composites.These models are applicable at the layer scale : i.e. the laminated compositeis divided in a stacked homogeneous plies and each layer is treated as asimple homogeneous (fictitious) material [4].

2.1 Damage model of a single layer

By damage is meant any reduction of the mechanical properties of the fic-titious continuous material. Two non-observable damage variable d and d'with (d, d'} £ [0,1] are introduced in the constitutive equations of the fic-titious layer to express the reduction of the elastic constants. Each damagevariable varies from 0 (undamaged material) to unity (damage is complete).Evolution laws for the damage variables are obtained from phenomenologi-cal observations and the general framework of thermodynamics. The stateof the material at a particular instant of time can be completely defined bythe value of those internal variables at this instant of time. Described hereis the damage model for a layer reinforced by unidirectional fibers and inwhat follow subscript 1,2, and 3 designate respectively the fiber direction,the transverse direction and the normal direction to the ply. The damagehas little or no effect on E\ and 1/12 and :

#2 = #2(l-d') ; z/21 = i(l-d')(1)

^2 , z/2i ? O^2 5 Oig are the values for the undamaged material. The otherconstants Ei,v-2i and G^ maintain their undamaged value. The elasticstrain energy in the damaged state is :

G23


904 Advances in Composite Materials and Structures Vll

where the reduced values of the elastic constants have to be used, if neces-

sary. The rate of change of this elastic energy is :

" "~ dtrij • V ' dd • « r

W = £ij . ff\j + Yd . d + Y^ . d'

where :V -eW _ i r ^ _L f;J- d — o j

(4)V — ^ M^ __ !_ ( 22) +

are internal variables associated with damage in the same way as strain isassociated with stress. They are expressed in Joules. < . >+ = 0 if (...)is negative, to take into account that the cracks close on compression (£"22 —£§ upon compression). Now define one more variable :

Y(t) = supr<t ( (r) + b Y,, (r) ) (5)

The symbol supr means that the highest value must be taken which r has

taken at any time preceding the instant t. b is a material constant. Then the

following equations are used to compute the value of the damage variables :

d = <-~y°>+ if d <1 and Y_ < Y , else d = 1

(6)d' = <-~> >+ if d' < 1 and Y_ < Y', , else d' = I

* c

YO, YC, YQ, YCJ b and Y/ are material constants of the layer : YO and Yjare threshold values, YC and Y^ represent damage toughness, 6 is a couplingconstant of the material, and Y* is the breaking threshold value of thefiber-matrix. The identification of these constants can be carried out fromtensile-tensile tests on laminates composed of several plies of the materialconcerned, with particular orientations of the plies [1]. The computation atthe instant t of d and d' requires the knowledge of the stress at this instant.

2.2 Structural analysis formulation

This damage evolution at the ply level have been implemented in the designsoftware tool based on a three-dimensional finite elements method. Eachlayer were considered homogeneous and orthotropic. Because of the nonlin-ear nature of the damage-dependent constitutive equation, this analysis isperformed in a stepwise manner [5] .Equations governing the dynamic response of a composite laminate sub-jected to transverse low-velocity impact loading can be derived by using the


Advances in Composite Materials and Structures 111 no<r

principle of virtual work, which states for any compatible displacements thetotal internal work is equal to the total work done by external loads. Usingthe finite element formulations together with the principle of virtual work,yields the spatially discretized system of FE equations :

[M}{U}n+i + [K(d,d')]{U}n+i = {F}n+i at time tn+i = (n+l)At (7)

where [M] is the consistent mass matrix, [K (d, d')] is the nonlinear stiffnessmatrix, and [F] is the applied force vector. {U} is the vector of nodaldisplacement and the over-dot indicates differentiation with respect to time(acceleration vector). Using the Newmark's method for time integration [5],the nodal displacement solution £/„+! at time tn+i is obtained from :

l (8)

where

(9)„ + ! + [M] (^ {{/}„ + & {U}n + (U}n)

2.3 Structural analysis scheme

The numerical solution of the above equations proceeds in the followingsteps (repeated at each time step) and illustrated in the following structuralanalysis scheme :

• First, calculate [K(d, d'}] and {F}n+i at time t + At from eqn (9).• Once the value of [K(d, d')] and {F}n+1 is known, the displacement

vector solution {[/} at time t 4- At is calculated from eqn (8), and thevelocity and acceleration vector at time t -j- At are calculated from theNewmark scheme [5].

• From the known displacements, transient dynamic strains and stresseswithin each layer as a function of time, are calculated. The damageevolution investigated and mechanical properties reduced appropri-ately, according to eqn (1,4,5,6).

3 The Adanidec software

ADANIDEC software is a set of design/analysis tools for the selection andimpact-induced damage evaluation of laminated composite materials forengineering design. Adanidec uses a multi-level (component, lamina, lami-nate) interactive database designed to accumulate and to retrieve informa-tion on composite materials. A Graphical User Interface have been devel-oped and a pull-down menus lead the user to multi-level material selectionfrom the database which when combined with the use of finite element basednumerical tools enable the rapid identification of the optimum materials fora specific design.


286 Advances in Composite Materials and Structures 111

The ADANIDEC SOFTWARE consists of :• a material database which contains for a number of composite lam-

inates : (1) at the laminate scale : material description and typicalexperimental results and the predictions of any numerical analysis,(2) at the layer scale : effective properties, strengths, relevant dam-age parameters and experimental details, (3) at the component scale(whenever possible) : the moduli of the constituents (fiber, matrix)and the parameters describing the microscopic geometrical layout.

• a suite of software tools : (1) at the laminate scale : IMPACT to ac-curately predict the development of damage induced by low velocityimpact in laminated composite and the associated strength reduction,(2) at the layer scale : CoMEP to compute the effective properties ofa lamina when its construction is based on the component level andVISUA to compute and visualize stresses at component scale from av-eraged stresses in a finite element of a layer, and (3) to interface thematerial database with selected dynamic structural analysis code.

3.1 Execution of the adanidec program

After Adanidec is invoked, a menu like the one in Figure 1 appears.

Figure 1: Adanidec Multi-level Dialog Boxes

The help button links with an hypertext version of the User Man-ual of Adanidec Software. The gen ar ray button generates spreadsheetfile array.xls containing an array with materials in lines and properties incolumns, to be used with Excel or any spreadsheet program. The threebasic levels are laminate, lamina and component. Under each level, anew case study or a new simulation can be entered at any time or one canuse a previously defined example. These examples can be saved at differentlevels and ready to be extracted as information for use elsewhere.Click on component button bring up the display like to the one shown forthe lamina level (Figure 2). This is the most basic level where the materialcould be either fiber or matrix. This level in effect provides information tothe lamina level where the construction of a lamina is based on the com-ponent level. The new menu asks for the designation, manufacture andmaterial properties information. When the cursor is placed on the individ-ual components button that are already existed in the database, a click


Advances in Composite Materials and Structures VII 987

provides direct access to the actual components properties.Click on lamina button produces a dialog box, like to the one shown in Fig-ure 2. The new menu asks for the designation of the lamina, manufactureand effective mechanical properties and damage parameters.

Figure 2: Lamina level

When the construction of the lamina is known at the component level,The effective properties of the laminate may then be computed by usingthe software tool COMEP (button run simulation) based on a two-scaleasymptotic homogenization [?].Click on laminate button produces the dialog box, like to the one shown forcomponents and laminates (Figure 2). The new command is particularlyuseful when constructing a new laminate. Along with the building-laminate,select the appropriate layer's name by clicking on it allows users to checkmaterial properties. After the laminate was specified, the next step is tomake experimental tests or numerical simulation of impact on this laminateby constructing a new case study. The IMPACT software is invoked bya click on the Run simulation button which will transform the problemdescription to an input data file suitable for impact software.

4 Numerical and experimental examples

The effective properties, strengths and damage parameters of the GlassFabric Reinforced Epoxy (THsi] used in this study are :Mass Density p = 1905 Kgjrr?Young modulus E\ - 21100 MPa ; E^ - 21100 MPaShear modulus Gi2 — 5700 MPa ; Poisson's ratio 1/12 = .094Damage variable % = 1326\/CPa) ; Yo = 56\/(Pa) ; 6 = l.E-3Damage variable = l.E + Gi/fPa) ; ^ = 0.\/(Pa)Ultimate tensile stress &IR = 515 MPa ; a^R — 515 MPaUltimate tensile strain SIR - 0.023 ; SIR = 0.023

4.1 Local impact bend tests

A height falling tower was employed for the low-velocity impact tests. Theimpactor used are steel cylinders with a tip radius of 10 mm. The impact


288 Advances in Composite Materials and Structures Vll

measurement system includes an optical system which provides a signalfrom which the displacement of the impactor can be obtained as a functionof time. The specimens (dimensions : 21 * 120 mm) made of 13 plies ofTHsi and of a total thickness of 3.5 mm, clamped on two opposite sideswith a free span of 80 mm have been impacted. The plies orientationswas (0° — 90°) and the steel impactor mass, radius and initial velocity wasrespectively 100 g, 10 mm and 10 m/s. Numerous fine matrix cracksnormal to the longitudinal direction of the specimen, have been observednear the impacted area, extending over one third of the thickness.

2.5

0-10 f 1 ~ "1-

0 0.4,. 0.8 1.2Time (ms)

Figure 3: Impactor Deflection (mm) Figure 4: Impactor Velocity (m/s)

0 0.4. 0.8 1.2rime (ms)

1600

1200

800 4- --

a) impactor mass = 100 gTop layer

b) impactor mass = 100Bottom layer

400HWIH-I -H — — —

0 0.4. Q.8 1.2lime (ms)

Figure 5: Contact Force (N) Figure 6: Damage d level


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Figures 3 and 4 illustrate impactor deflection and velocity historiesobtained from theoretical analysis (dotted line) and the experimental tests(solid line). Figures 5 illustrates the numerical and experimental contactforce histories. Figure 6 show the isovalues of the damage parameter d. Themap a) and b) show the level of damage parameter d on the top and thebottom layer (dmax — 0.158).

4.2 Global impact bend tests

The impact generation system for the global imposed acceleration is a freefall shock test machine which produces in our cases global half sine acceler-ation of amplitude 200 G to laminates (dimensions : 520 * 520 mm) madeof 34 plies of THsi and of a total thickness of 8 mm, clamped on the foursides with a free span of 400*400 mm.

Figure 7: Half Sine Acceleration.

0.0008

Figure 8: Experimental strain.

0.0004

-0.0004

-0.0008-2 0 _. 2 , 4 6

Time (ms)

Figure 9: Computed strain. Figure 10: Damage d level


9QQ Advances in Composite Materials and Structures VII

Strain histories obtained from theoretical analysis and the experimentalresults at strain-gage location (center of the plate) have been compared.From the computed strain distributions across the laminate thickness, thedamage initiation and progression during the shock have been predicted.Figures 7 and 8 illustrate experimental imposed global half sine accelerationand the strain response at gage location (center of top layer). Figure 9illustrates the computed strain at gage location, and Figure 10 shows thelevel of damage parameter d (dmax = 0.131) on the top layer.

5 Conclusions

Material model based on damage mechanics approaches have been developedto simulate the behavior of a number of selected composite laminates. Avalidated set of design/analysis tools called ADANIDEC, in the shape offinite element programs has been produced. ADANIDEC will be very usefulto those concerned with the analyze and the prediction of the behavior ofcomposite material. The experience so far accumulated in the AdanidecMaterial Database will help to reduce and optimize the number of teststo a minimum. It has great potential to expand and could be used as astorehouse of a vast amount of data concerned with composites.

Acknowledgements

The authors would like to acknowledge the support of the Commission ofthe European Communities (Brite Project BRE2-CT94-0953).

References

[1] Hassim, A.; G. Vanderborck, G., Damage tolerance of laminated com-posites subjected to low-velocity impact, Proc. of the 68th Shock &Vibration Symposium,,, Baltimore, pp 313-321.

[2] Mackerle, J., Structural response to impact, blast and shock loadings.A FE/BE bibliography (1993-1995), Finite Elements in Analysis anddesign, 24, pp. 295-110, 1996.

[3] Ladeveze, P., (D. Baptiste Ed.) Mechanics and Mechanisms of Dam-age in Composites and Multi-materials, Computational MechanicsPublications, Southampton and Boston, pp. 129-158, 1993.

[4] Hassim, A., Characterization of Composite Materials using a two-scaleAsymptotic Homogenization Method, Proc. of the Conf. on SmartStructures and Materials, 14-16 fevrier 1994) Orlando (Floride)- U.S.A.

[5] Bathe, K.J, Finite Element Procedures in Engineering Analysis, Printice-Hall 1982.


u. barberis*, a. hassim*, c. ravera* & g. vanderborck* · 2014. 5. 14. · u. barberis*, a....

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u. barberis, a. hassim, c. ravera* & g. vanderborck* · 2014. 5. 14. · u. barberis*, a....