Composite Structures 94 (2012) 2902–2913

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Composite Structures

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Modelling damage evolution in composite laminates subjected to lowvelocity impact

Y. Shi, T. Swait, C. Soutis ⇑Department of Mechanical Engineering (Aerospace), The University of Sheffield, Mappin Street, Sheffield S1 3JD, UK

a r t i c l e i n f o

Article history:Available online 10 April 2012

Keywords:Composite laminatesImpact behaviourFinite element analysisDelaminationNon-linear behaviourCohesive zone elements

0263-8223/$ - see front matter � 2012 Elsevier Ltd. Ahttp://dx.doi.org/10.1016/j.compstruct.2012.03.039

⇑ Corresponding author.E-mail address: c.soutis@sheffield.ac.uk (C. Soutis)

a b s t r a c t

In this paper, the impact damage of composite laminates in the form of intra- and inter-laminar crackingwas modelled using stress-based criteria for damage initiation, and fracture mechanics techniques tocapture its evolution. The nonlinear shear behaviour of the composite was described by the Soutis shearstress–strain semi-empirical formula. The finite element (FE) method was employed to simulate thebehaviour of the composite under low velocity impact. Interface cohesive elements were insertedbetween plies with appropriate mixed-mode damage laws to model delamination. The damage modelwas implemented in the FE code (Abaqus/Explicit) by a user-defined material subroutine (VUMAT).Numerical results in general gave a good agreement when compared to experimentally obtained curvesof impact force and absorbed energy versus time. The various damage mechanisms introduced during theimpact event were observed by non-destructive technique (NDT) X-ray radiography and were success-fully captured numerically by the proposed damage evolution model.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction studies [2–6]. It is important when constructing and meshing the

Advanced composite structures offer many advantages com-pared to conventional materials, especially where high strengthand stiffness to weight ratio is concerned. Thus, composites havebeen used widely in many applications such as aerospace, sportequipment, pressure vessels and automotive parts. However, whenloaded under static or fatigue conditions they exhibit a relativelybrittle behaviour with extensive matrix cracking and delamination,which leads to loss of stiffness and load-carrying capability; theyalso show poor damage resistance and low impact strength. Mod-elling the progressive damage of thin laminates under low velocityimpact is an important area, especially in the fabrication of aircraftstructural components where barely visible impact damage (BVID)can be a critical issue [1]. The damage mechanisms for a thin plateare different for low and high velocity scenarios; in a high velocityimpact of a thin plate perforation is more likely to occur, while fora low velocity impact, there is a sufficiently long contact durationto introduce internal matrix cracking, delamination and fibrebreakage that spreads over a larger area [2].

Considering the time and cost of physical testing, finite element(FE) techniques offer the opportunity to develop a numerical mod-el, which could accurately describe the impact and predict thecomplex internal damage mechanisms in a relatively short time.The complicated composite material behaviour can be simulatedbased on the constitutive models provided by several analytical

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model to follow the experimental conditions as closely as possiblealthough in some cases it is also necessary to make some assump-tions to simplify the model and speed up the analysis. An appropri-ate balance in terms of factors such as model complexity and meshsize and shape must be struck between reducing the calculationtime and increasing the precision of the results. FE methods arethus convenient and efficient tools to use for engineering researchwhen used with a strong knowledge background of the finite ele-ment theory [3].

Recent research, based on continuum damage mechanics(CDMs), on modelling the damage of composite laminates sub-jected to impact has been reported [4–7]. This was initiated bythe work of Kachanov [8] and Rabotnov [9]. In addition, Kashtalyanand Soutis [10,11] developed the equivalent constraint model(ECM) [12] of damaged lamina to successfully predict the effectof matrix cracking and matrix crack induced delamination on stiff-ness degradation.

In this paper, a user-defined 3D damage model (VUMAT) withsolid elements was developed and implemented into the finite ele-ment code Abaqus/Explicit to predict the type and extent of dam-age through the laminate thickness. Interface cohesive elementswere inserted between plies of the modelled laminate to simulatedelamination. An effective approach developed by Soutis et al.[13,14] was also used to describe the nonlinear shear behaviourof the laminate. The general contact algorithm in Abaqus was usedto simulate the contact between impactor and composite plate sur-face, and the contact between layers by defining appropriate con-tact pair properties. The numerical results from the simulation

Y. Shi et al. / Composite Structures 94 (2012) 2902–2913 2903

were evaluated by comparing with experimental measurementsand observations and this demonstrated the ability of the proposeddamage modelling approach to predict the type and extent of im-pact induced damage.

Fig. 1. Fracture plane for matrix compressive failure relative to material coordinatesystem.

2. Composite damage model for impact

Composite laminated structures, which are made from the con-tinuous carbon fibres and a polymeric resin, usually show a com-plicated damage pattern that develops internally and becomesdifficult to detect [15,16]. In general, this damage can be character-ised by two main failure categories: (i) Intra-laminar failure thatoccurs within a ply and can be expressed by modes such as: fibretensile and compressive breakage, matrix tensile and compressivedamage and damage between the fibre and matrix interface and(ii) Inter-laminar failure or delamination that occurs betweenneighbouring plies.

Large tensile loads introduced during impact finally lead to fibrerupture. This damage mode releases large amounts of energy andthe load in the composites cannot be redistributed. Thus this kindof damage can result in a catastrophic failure of the structure. Com-pression load in the fibre direction, causes fibre micro-bucklingand leads to the formation of fibre kinking [13,14]. The resin shearbehaviour and initial fibre misalignment have a crucial influenceon this type of failure mode. Matrix cracking in the composite re-sults from the load in the transverse direction. Tensile loading ofthe matrix can cause transverse ply cracks (TPCs) and/or can leadto fibre/matrix interfacial failure or splitting. This interfacial failureis also called fibre/matrix debonding and can occur when a resincrack meets a fibre or when a fibre fractures and the crack is direc-ted along the fibre-matrix interface. Matrix compression failurehas been observed but experimental evidence has shown that itis actually dominated by the shear matrix failure with a fractureplane in the through-thickness direction [17].

Delamination is a common damage mechanism in compositelaminated structures. Delamination seldom occurs on its ownand in many cases is initiated due to intra-laminar failures suchas transverse ply cracking [10–12]. The stiffness of the structureis decreased depending on the amount of delamination and this in-duces further intra-laminar damage which then prompts propaga-tion of the delamination under high transverse shear loadingand additional deterioration of stiffness and strength properties[18–20].

2.1. Damage initiation

Damage modelling in composites can be studied either by astress or strain-based failure criteria approach or following damagemechanics concepts. The polynomial failure criteria, such as theTsai-Wu or Tsai-Hill, based on the equivalent stress or strain areusually employed to describe the failure envelope of any givenmultidirectional laminate subjected to multi-axial loading. How-ever, the damage mechanisms as different modes cannot be clearlycharacterised using the polynomial failure criteria, unless they areapplied at the ply level. Hence a ply-by-ply method has beenwidely used to model the progressive failure in composites. Hashinproposed a failure criterion for a unidirectional composite to sepa-rately model four distinct failure modes: fibre damage in tensionand compression and matrix tensile and compressive failure[21,22]. Hashin failure criterion has been used extensively inindustry, although it cannot accurately predict the matrix com-pressive failure initiation. Thus, in the present study, Hashin crite-rion is used to estimate the fibre and tensile matrix damageinitiation, while the damage model developed by Puck and Schur-mann [23] is used to model matrix compressive failure, i.e.

Fibre tensile failure (br11 P 0):

Fft ¼r11

XT

� �2

þ jr12

S12

� �2

¼ 1 ð1Þ

Fibre compressive failure (br11 < 0):

Ffc ¼br11

XC

� �2

¼ 1 ð2Þ

Matrix tensile failure (br22 P 0):

Fmt ¼br22

YT

� �2

þbr12

S12

� �2

þbr23

S23

� �2

¼ 1 ð3Þ

Matrix compressive failure (br22 < 0):

Fmc ¼rTN

SA23 þ lTNrNN

!2

þ rLN

S12 þ lLNrNN

� �2

¼ 1 ð4Þ

In Eqs. (1)–(4), brij (i, j = 1, 2, 3) is the effective stress tensor, XT

and XC denote the tensile and compressive strengths of the unidi-rectional composite laminate in the fibre direction, YT and YC arethe tensile and compressive strengths in the transverse direction,Si,j (i, j = 1, 2, 3) denotes the longitudinal and transverse shearstrengths of the composite, respectively. The coefficient j in Eq.(1) accounts for the contribution of shear stress on fibre tensilefailure, which is ignored in the present study. In Eq. (4) rij ( i,j = L, T, N) is the stress tensor rij (i, j = 1, 2, 3) rotated to the fractureplane by using the transformation matrix T(a):

rLTN ¼ TðaÞr123TðaÞT ð5Þ

SA23 is the transverse shear strength in the fracture plane, which

can be determined by the transverse compression strength and theangle of fracture plane. The key concept of Puck’s failure criterion isto determine the inclination or orientation of the fracture plane bycalculating the angle, a, as shown in Fig. 1. Generally it has beenexperimentally observed that matrix compressive damage occursalong a fracture plane oriented at a = 53� with respect to thethrough-thickness direction [23], although this angle was deter-mined under uniaxial compressive loading rather than impact.The angle of the fracture plane can be evaluated by the finite ele-ment method where Fmc is estimated at various angles between0� and 180�, the angle of the fracture plane will be that wherethe value of Fmc is maximum.

2.2. Damage evolution

In order to predict damage development in the laminate, a stiff-ness degradation rule needs to be defined. Tita et al. [20] reduced

2904 Y. Shi et al. / Composite Structures 94 (2012) 2902–2913

the material moduli by using appropriate factors with respect tothe various failure modes observed. For instance, to account fortransverse ply cracking Young’s modulus E2 and Poisson’s ratiom12 were reduced to zero. For delamination the degradation stiff-ness parameters were given a value equal to 0.01. Although thisprocess was straightforward to apply, the method was unable toaccurately predict the size of the damage area. In this paper, thedamage evolution procedure described in the following sectionsis used and is based on a strain failure criterion where the straintensor is continuously updated with increasing load for each mate-rial point associated with each different failure mechanism.

2.2.1. Tensile failure modesAccording to previous work [4–6], the stresses in the fibre direc-

tion are predominantly carried by the fibres because of their highstiffness and strength. When the damage initiation criterion ismet, Eqs. (1) and (3), the material properties are gradually de-graded, by using the following damage variable where for fibreand matrix tensile failure is expressed as:

dT1;2 ¼

efT1;2

efT1;2 � e0T

1;2

1�e0T

1;2

e1;2

!ð6Þ

where the subscript 1 and 2 denote the fibre and transverse direc-tion, respectively; e0T

1;2 is the tensile strain for damage initiation. Dueto the irreversibility of the damage variable, the strain calculated ateach time step is defined as e1;2 ¼ maxðe1;2; e0T

1;2Þ in Eq. (6). In order toavoid zero or negative energy absorption due to damage, the finalfailure strain needs to be greater than the initial failure strain, i.e.efT

1;2 > e0T1;2.

The failure initiation strain is given by the following equations:

e0T1 ¼

XT

E01

ð7aÞ

e0T2 ¼

YT

E02

ð7bÞ

where E01;2 is the undamaged elastic modulus and XT and YT are the

tensile strengths of the material in either the fibre or transversedirection. efT

1;2 denotes the tensile strain at final failure at whichthe damage variable is equal to one. The efT

1;2 is derived from thefracture toughness GT

1;2C associated with fibre (1) or matrix (2) ten-sile failure, the failure strength of the material (XT or YT) and thecharacteristic length l⁄:

efT1 ¼

2GT1C

XT l�ð8aÞ

efT2 ¼

2GT2C

YT l�ð8bÞ

where l⁄ is the characteristic length that would keep a constant en-ergy release rate per unit area of crack and make the final resultsindependent of FE mesh size. In this work the approach developedby Bazant and Oh [24] was used and for a solid element l⁄ is given by

l� ¼ffiffiffiffiffiffiAIPp

cos hjhj 6 45� ð9Þ

The AIP area is associated with an integration point and the h an-gle between the mesh line and the crack direction. This method hasbeen shown to be computationally efficient and to work reason-ably well for solid elements [25].

2.2.2. Compressive failure modesSimilarly, the compressive damage variable in the fibre direc-

tion can be expressed:

dC1 ¼

efC1

efC1 � e0C

1

1� e0C1

e1

� �ð10Þ

The strain at failure initiation and the strain at final failure areobtained by a similar approach described in Section 2.2.1.

e0C1 ¼

XC

E01

ð11aÞ

efC1 ¼

2GC1C

XCl�ð11bÞ

In order to account for matrix crushing and fragment interac-tion effects within the damage zone, the stress value at final failureis not completely degraded but is reduced to the transverse com-pressive strength of the material system YC.For matrix compressivefailure, the damage evolution can be effectively predicted by defin-ing the fracture plane and the corresponding transformed strain,i.e.,

dC2 ¼

efCmat

efCmat � e0C

mat

1� e0Cmat

emat

� �ð12Þ

where emat is the strain calculated at each time step, transformed to

the fracture plane and defined by emat ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffie2

TN þ e2LN

q. eij (i, j = L, T, N)

is the strain eij (i, j = 1, 2, 3) rotated to the fracture plane and givenby:

eTN ¼ �e2 cosðaÞ sinðaÞ þ e3 cosðaÞ sinðaÞ þ c23ð2 cos2ðaÞ � 1Þð13Þ

eLN ¼ c12 cosðaÞ þ c13 sinðaÞ ð14Þ

The e0Cmat is the failure onset strain and is recorded by the pro-

gram once the damage initiation criterion for matrix compressivefailure has been satisfied, Eq. (4). The a parameter is the fractureplane angle discussed earlier, see Fig. 1. The final failure strain isdefined in terms of the fracture toughness for matrix compressivefailure GC

2C , the damage initiation stress r0Cmat and the characteristic

length, l⁄:

efCmat ¼

2GC2C

r0Cmatl

� ð15Þ

2.3. Delamination

In work by Camanho and Dávila [26] a stress failure criterionwas developed to predict damage initiation while delaminationpropagation was based on fracture mechanics concepts where aninterface element was introduced between each ply of the compos-ite laminate. The stress failure criterion used to estimate thedelamination onset is given by:

rn

N

� �2þ rs

S

� �2þ rt

T

� �2¼ 1 ð16Þ

where ri (i = n, s, t) denotes the traction stress vector in the normal nand shear directions, s and t, respectively, while N, S and T are de-fined as the corresponding inter-laminar normal and two shearstrengths.

The traction stress ri can be calculated as given in the Abaqusmanual [27] using the stiffness in Modes I, II and III and the open-ing and/or sliding displacements di:

ri ¼ Kidi; i ¼ n; s; t ð17Þ

Once the damage initiation criterion has been reached, thematerial stiffness is gradually degraded in terms of a damage var-iable d. Its values range from zero when damage initiates to one

Fig. 2. Typical traction-opening or sliding displacement.

Y. Shi et al. / Composite Structures 94 (2012) 2902–2913 2905

(d = 1) when complete delamination has occurred in the interfaceelement. The failure criterion to predict delamination propagationunder mixed-mode loading is expressed in terms of the energy re-lease rates associated with Modes I, II and III. For a linear softeningprocess the damage variable d for delamination evolution is de-fined as:

d ¼ dfmðd

maxm � d0

mÞdmax

m ðdfm � d0

mÞð18Þ

where dmaxm refers to the maximum value of the mixed-mode dis-

placement attained during the loading history. The dm parametercorresponds to the total mixed-mode displacement (normal, sliding,tearing) given by:

dm ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffid2

n þ d2s þ d2

t

qð19Þ

In Eq. (18) dfm is the mixed-mode displacement at complete fail-

ure and d0m is the effective displacement at damage initiation. A

Benzeggagh–Kenane (BK) fracture energy based criterion [26] canbe used to define the mixed-mode displacement for complete fail-ure, df

m:

dfm ¼

2Kd0

m½GIC þ ðGIIC � GICÞng� dn > 0ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðdf

sÞ2 þ ðdf

t Þ2

qdn 6 0

8<: ð20Þ

where g is the B–K power law parameter that can be determinedusing a least-square fit from a set of mixed-mode bending experi-

mental data; n ¼ b2

1þb2 with n taking values between zero and one.

When n = 0 fracture is mode I driven, while as n ? 1 is mode II dom-inated (and this is also the case when g = 0). b is the mode mixityratio (¼ ds

dn).A typical linear traction-separation model used for frac-

ture Modes I, II and III is shown in Fig. 2. Initially, the linear elastic

Fig. 3. Nonlinear shear behaviour using the Soutis model: (a) Experimental and analyticafor the present composite system.

response is represented using the stiffness Ki (i = n, s, t). Once thenormal or shear tractions reach the corresponding inter-laminarnormal and shear strengths, delamination will be initiated and thenthe stiffness will start to degrade linearly according to the damageevolution variable d given by Eq. (18).

2.4. Nonlinear shear behaviour

According to experimental observations, composite laminatesgenerally show a nonlinear and irreversible shear behaviour. Thereare two different mechanisms to describe the nonlinear shearbehaviour: matrix plasticity, matrix cracking and fibre/matrixinterfacial failure that progressively cause stiffness degradationleading eventually to fibre breakage and catastrophic failure. Anumber of approaches to model the nonlinear shear behaviour ofthe composite laminate have been published in the literature suchas continuum theories of plasticity [28], continuum damagemechanics [29], or combination of these two methods [30]. In thispaper, a semi-empirical expression developed by Soutis et al.[13,14] is used to represent the nonlinear shear response. A goodagreement between the experimental and analytical results is ob-tained as shown in Fig. 3a. The nonlinear shear stress–strain rela-tions are expressed by Eq. (21):

si;j ¼ Si;j 1� exp �G0

i;jcSi;j

!" #; i; j ¼ 1;2;3 ð21Þ

The ultimate shear strength Si,j and the elastic shear modulusG0

i;j, both of which are composite materials constants and readilymeasurable, are required for implementation in the FE programthat models the nonlinear shear behaviour of the composite.Thenonlinear shear damage is successfully simulated using a strainbased damage initiation and evolution criterion as shown inFig. 3b. The strain in this nonlinear shear model is decomposed intotwo parts: elastic strain ce

i;j and inelastic strain cini;j. The inelastic

strain is defined as:

cini;j ¼ ci;j � ce

i;j ¼ ci;j �si;j

G0i;j

ð22Þ

where si,j is the nonlinear shear stress corresponding to the differ-ent shear planes; G0

i;j is the original shear modulus. The criterionof initiation of shear failure is expressed in terms of the nonlinearshear stress and maximum shear strength:

FSi;j ¼jsi;jjSi;j¼ 1; i; j ¼ 1;2;3 ð23Þ

where si,j is the shear stress at the given shear plane and Si,j indi-cates the relative ultimate shear strength in that plane.

l results [13,14] and (b) numerical s�c curve with non-linear shear damage variable

z

y

x Fixed edge

Contact between surfaces of impactor and top laminate surface

Impactor: Fixed except z axis Initial velocity along z

Ø= 75 mm

Ø= 15 mm

Fig. 4. FE model used for the numerical simulation of the impact event; the generalcontact algorithm in Abaqus/Explicit is used while the boundary condition (BC) forthe laminate edge is fixed.

2906 Y. Shi et al. / Composite Structures 94 (2012) 2902–2913

The damage evolution law for the nonlinear shear modes is ex-pressed by the damage variable di,j:

di;j ¼cf

i;j½2ðci;j � cini;j;0Þ � cf

i;j�ðcf

i;j þ cini;j;0 � ci;jÞðci;j � cin

i;j;0Þð24Þ

where cfi;j is the shear strain at complete failure and is related to the

shear fracture toughness (varies with mode of fracture) GS, shearstrengths of the material Si,j and the characteristic length l⁄:

cfi;j ¼

2GS

Si;jl� ð25Þ

cini;j;0 denotes the inelastic strain at shear damage initiation

which can be stored and employed automatically when the mate-rial model is implemented into the FE software.

3. Experiment and simulation of impact events

3.1. Impact test

Composite laminates, 2 mm thick, were fabricated from carbonfibre/epoxy resin prepreg with a stacking sequence of [0/90]2s. Theprepreg was made from continuous unidirectional high tensilestrength carbon fibres (Tenax HTS40 12 K 300) impregnated withCycom� 977-2 epoxy resin, which is a typical high temperaturecuring aerospace grade system. The laminates were autoclave

Table 1Material properties of the carbon fibre/epoxy unidirectional laminate [5,32].

Density (kg/m3) 1600Orthotropic properties E0

1 ¼ 153 GPa; E02 ¼ E0

3 ¼ 10:3 GPa; m12 = m13 = 0.3;

m23 = 0.4; G012 ¼ G0

13 ¼ 6 GPa; G023 ¼ 3:7 GPa

Strength (MPa) XT = 2537; XC = 1580; YT = 82; YC = 236; S12 = 90;S23 = 40

In-plane fracturetoughness (kJ/m2)

GT1C ¼ 91:6; GC

1C ¼ 79:9; GT2C ¼ 0:22; GC

2C ¼ 1:1;GS ¼ 0:7

Table 2Material parameters used in the interface cohesive element [33,34].

Mode I Mode II Mode III

Normalised elastic modulus (GPa/mm) 1373.3 493.3 493.3Inter-laminar strength (MPa) 62.3 92.3 92.3Inter-laminar fracture toughness (kJ/m2) 0.28 0.79 0.79

cured following the manufacturer’s recommended schedule andcut into specimens measuring 100 mm � 100 mm.

The impact testing followed the guidelines given by the ASTMD7136/D7136M-07 standard [31]. The dart impactor used had ahemispherical head 15 mm in diameter, while the tested panelswere clamped between two steel plates with a circular exposedarea of 75 mm in diameter. A drop height of 0.75 m was usedthroughout the test program, the mass of the impactor was equalto 1, 1.5 and 2 kg resulting in impact energies of 7.35, 11.03 and14.7 J, respectively. Force data were logged from the impactorusing a high speed data acquisition unit. At least three specimenswere tested for each energy level.

3.2. Simulation of impact event

The Abaqus/Explicit code was used to run the numerical FEmodel where the proposed failure initiation and fracture criteriawere implemented together with the shear damage materialmodel described in the earlier sections. Appropriate geometricalmodels were built and kinematic and loading boundary conditionswere defined to represent the experimental set up.

3.2.1. Geometrical modelling and boundary conditionsA 3D FE model was built for the impactor and the circular plate

and appropriate boundary conditions were defined as shown inFig. 4. In the FE analysis the unsupported circular plate of 75 mmin diameter was modelled with a fully clamped edge. The 2 mmthick laminate consisted of eight plies with a ply thickness of0.25 mm in the stacking sequence [0/90]2s. Global and local coordi-nates were defined to account for ply orientations and correctly de-scribe the laminate and material behaviour. All the nodes of theplate edge were fixed in all directions (x, y, z) to simulate theexperimental clamped conditions, Fig. 4.

The impactor was modelled as a rigid body; the impact eventswere performed for the three energies mentioned earlier and a pre-scribed initial velocity of 3.83 ms�1 was assigned to the impactor.

3.2.2. Types of finite element used and mesh densityIn the circular composite plate examined, each ply was repre-

sented by two eight-node linear brick element, C3D8. The comput-ing time was reduced by introducing different mesh size/density indifferent regions of the FE model, from 1 mm � 1 mm elements inthe impacted zone, in Fig. 4, up to a coarser mesh size elementsaway from the impact where damage was not expected to occur,which is in agreement with experimental observations. The local-ised stiffness reduction due to internal damage can cause an exces-sive element distortion that could lead to difficulties in numericalconvergence, run slowly or even abort the solution. To resolve thisnumerical issue, the ‘distortion control’ was activated in Abaqusand the damage variables were limited to a maximum value of0.99, which helps to maintain some residual stiffness. At each plyinterface, COH3D8 cohesive elements were inserted with a thick-ness of 0.0075 mm and were used to model delamination initiationand growth with the failure criteria discussed in Section 2.3. Thedegradation parameters were again set to a value of 0.99 and thefailed elements were removed from the FE model once the failurecriteria were satisfied. In this damage simulation process, a smallstable time increment was required, which increased the comput-ing time. The elastic modulus assigned to the cohesive zone ele-ment, Table 2, was normalised by its thickness (mass scaling) toreduce the calculation time.

3.2.3. Material propertiesThe detailed material properties are listed in Table 1 [5,32].

The values of fracture toughness for the various intra- and inter-laminar damage modes were taken from the Refs. [33,34]. The

Fig. 5. Experimental and numerical impact force–time histories: (a) Impact energyof 7.35 J; (b) Impact energy of 11.03 J; (c) Impact energy of 14.7 J.

Fig. 6. Experimental and numerical impact force–displacement histories: (a)Impact energy of 7.35 J; (b) Impact energy of 11.03 J; (c) Impact energy of 14.7 J.

Table 3Experimental and numerical values of absorbed impact energy.

Impact energy (J) Absorbed energy Difference between test and simulation (%)

Experimental (J) Numerical (J)

7.35 5.5 4.49 18.3611.03 7.1 6.02 15.2114.7 9.52 9.08 4.62

Y. Shi et al. / Composite Structures 94 (2012) 2902–2913 2907

properties assigned to the cohesive elements are also listed inTable 2, which includes values for the elastic modulus, strength

Fig. 7. Experimental and numerical impact energy–time histories: (a) Impactenergy of 7.35 J; (b) Impact energy of 11.03 J; (c) Impact energy of 14.7 J.

2908 Y. Shi et al. / Composite Structures 94 (2012) 2902–2913

and fracture energy; the stiffness properties were normalised bythe element thickness. Damage evolution under mixed-mode load-ing was predicted by the Benzeggagh–Kenane fracture energy law[26] where factor g = 1.45 was experimentally obtained. As men-tioned previously the fracture energy should be kept independentof the FE mesh size, thus the characteristic length l⁄, Eq. (9), needsto be defined to correctly predict damage growth.

3.2.4. Contact algorithmContact between the impactor and impacted plate and among

each contacted ply of the laminate, were defined by the generalcontact algorithm within Abaqus/Explicit. This algorithm gener-ated the contact forces based on the penalty enforcement contactmethod. A tangential interaction was defined between the surfacesof adjacent layers in terms of a Coulomb friction model. The fric-tion coefficient, l, is used to account for the shear stress s of thesurface traction with contact pressure p, which can be representedas s = lp.

Generally, the friction coefficient is mainly determined by thematerial property and the surface quality. Various researchers haveinvestigated the friction between composite surfaces and severaleffective methods exist to obtain the friction coefficient [35–37].The friction coefficient between contacted layers is defined as afunction of fibre orientation. So for a 0�/0� interface the value ofl = 0.2 was reported, while a value of 0.8 was suggested for theinterface between neighbouring 90� plies. Thus, in the presentanalysis an average friction coefficient of 0.5 was used betweenthe 0�/90� interface of the cross ply laminate. In addition, a similarcontact algorithm was applied between the surface of the metalimpactor and the composite plate and a friction coefficient valueof l = 0.3 was used. It needs to be said that these assumed l valuesdo have an effect on energy absorbed prediction, so ideally shouldbe measured for the system examined.

4. Results and discussion

Experimental and predicted impact force and energy versustime curves were compared to assess the accuracy of the proposedmodel that attempts to estimate the impact resistance of the cross-ply laminate.

4.1. Impact force

In Fig. 5a the force-time history for the 7.35 J impact test isshown. In the initial phase of contact some oscillations can be seenin the time interval of 0 ms to approximate 0.7 ms due to the elas-tic vibration induced by the initial contact between the impactorand the composite laminate. After that, intense oscillations occurnear the peak force value that indicates initiation of damage. Theimpactor then bounces back and the load is reduced to zero. A goodagreement is obtained between the numerical result and experi-ment, especially while the load is increasing. The maximum forceof 3230 N obtained experimentally closely matches the predictedvalue of 3116 N. After the peak load is reached and the impactorstarts to rebound the numerical result shows a slightly higher va-lue of load than the experimental and takes a longer time to reachzero. This phenomenon may be due to contact forces between thedelaminated plies after the cohesive elements have been removedfrom the simulation as the composite plate returns to its originalshape. The force-time for the 11.03 J impact test is plotted inFig. 5b, where the important features are accurately captured bythe numerical modelling although the maximum force is stillslightly under predicted at 3338 N compared to 3765 N measuredin the experiment. Fig. 5c shows the force-time response under a14.7 J impact. The numerical analysis gives a good prediction dur-ing the load phase and the estimated maximum force is 3917 N,only slightly lower than that of the test value (4605 N). More in-tense oscillations, highs and drops of force are experimentally ob-served near the peak, and at approximately 2.2 ms the larger forcereduction seen can be attributed to the fibre breakage. Due to thehigher impact energy, more contact time is recorded that intro-duces more extensive damage in the composite.

The F–t results presented in Fig. 5 are translated into force–dis-placement curves shown in Fig. 6; experimental and numerically

Fig. 8. X-ray radiographs and superposition of numerically predicted delamination area: (a and b) Impact energy of 7.35 J; (c and d) Impact energy of 11.03 J; (e and f) Impactenergy of 14.7 J.

Table 4Measured and numerically predicted delamination area.

Impact energy (J) Delamination area (mm2)

Experiment Simulation

Complete failure (d P 1) Delamination evolution (0 < d 6 1)

7.35 80.36 48 28811.03 190.46 141 46614.7 314 251 698

Y. Shi et al. / Composite Structures 94 (2012) 2902–2913 2909

predicted curves are compared. In the initial phase of the impactevent, there is a similar slope until the maximum impact force isreached and this is in better agreement with increasing impact en-ergy. However, during the unloading phase the composite plate re-turns back to its original state more slowly and less completelythan simulated, especially in the case of the lowest energy, 7.35 Jimpact, Fig. 6a. It should be noted that in the experiment the dis-placement measured corresponds to that of the rebounding impac-tor, while the numerical value is obtained from the mid-point ofthe plate’s back face. This difference and factors like the assumedfriction coefficient between the projectile and plate may have aneffect that lead to numerical predictions which show a faster platerecovery than the one measured experimentally. Also in Fig. 6c thepredicted force is not reduced to zero since at this impact energy

(14.7 J) the element in the FE model has completely failed and ‘re-moved’ so no force value is recorded.

4.2. Impact energy

The impact energy-time relationship is presented in Fig. 7. InFig. 7a the initial kinetic energy of the impactor (7.35 J) is trans-ferred to the composite plate once contact is made. During the im-pact event, part of this energy is the absorbed energy by the platein the form of elastic deformation (elastic energy), while a largeramount is dissipated in the form of intra-laminar damage, delam-ination and the friction between projectile/laminate and amongneighbouring ply within the laminate. The kinetic energy of theimpactor is completely transferred to the plate when its velocity

3rd interface - 0o/90o 4th interface - 90o/90o

5th interface - 90o/0o 6th interface - 0o/90o

7th interface - 90o/0o

1st interface - 0o/90o2nd interface - 90o/0o

Fig. 9. Predicted delamination area at each interface under the impact energy of 14.7 J.

2910 Y. Shi et al. / Composite Structures 94 (2012) 2902–2913

reaches zero. After this point, the elastic energy stored by the plateis transferred back to the impactor which causes it to rebound. Fi-nally, the energy absorbed by the composite reaches a stable valueresulting from the damage and friction. Compared to the experi-mental result in Fig. 7a, the initial impact energy is captured veryaccurately by the numerical model. However, the inaccuracy inmodelling of the rebound phase of the impact leads to inaccuracyin the final value of energy absorbed. The final absorbed energywith different impact energies is listed in Table 3. It shows that

the final absorbed energy predicted by the numerical model isabout 4.49 J for the impact energy of 7.35 J, approximately 18%lower than the experimental result (5.5 J). Fig. 7b and c shows im-pact energy-time histories for 11.03 and 14.7 J impacts respec-tively. A better prediction is obtained for these two cases as seenin Table 3; for the 11.03 J impact the final energy absorbed bythe composite in the form of damage and friction is 7.1 J obtainedexperimentally compared to 6.02 J predicted, while for the case of14.7 J, the predicted value of 9.08 J comes closer to the measured

Fig. 10. Numerically predicted damage in the form of matrix tensile failure, (a, c and e) and nonlinear shear damage, (b, d and f): (a and b) Impact energy of 7.35 J; (c and d)Impact energy of 11.03 J; (e and f) Impact energy of 14.7 J; (g) Predicted fibre breakage for impact energy of 14.7 J.

1 For interpretation of color in Figs. 2,3,5–10, the reader is referred to the webversion of this article.

Y. Shi et al. / Composite Structures 94 (2012) 2902–2913 2911

value of 9.52 J, an error of 15% and 4.6% respectively. It appears thatthe difference between experimental and numerical values getssmaller with increasing impact energy, especially less than 5% forthe 14.7 J case, suggesting that the assumptions made in the failurecriteria can represent relatively accurately the experimental set up,at least in the case of higher energy impacts.

4.3. Experimentally detected and numerically predicted damage

Visually, it was observed that a shallow dent (of the order of0.25 mm) was created on the front face and slight fibre/matrixsplitting on the back face. Non-destructive evaluation (NDE) of

the composite panel by penetrant-enhanced X-ray radiography,showed transverse ply cracking, splitting and almost ‘‘peanut’’shaped delaminations, as illustrated in Fig. 8a. The predicted over-all damage is shown for comparison in Fig. 8b, where all the delam-inations are represented in rainbow colour (while in print indifferent shades of grey); dark regions (red)1 indicate that thematerial has failed completely while in the lighter grey areas thematerial comes closer to failure (failure criterion has not yet beenreached). The delaminated region shown in Fig. 8a is larger than

Fig. 11. Permanent indentation and delamination damage predicted by thenumerical model that accounts for the nonlinear shear behaviour: (a) Impactedface and (b) delamination locations through the thickness of the laminate.

2912 Y. Shi et al. / Composite Structures 94 (2012) 2902–2913

that predicted, which indicates the damage model underestimatedthe energy absorbed shown in Fig. 7a. Similar radiographs and pre-dicted damage patterns are shown in Fig. 8c–f for the other twoimpact cases (11.03 and 14.7 J). The amount of damage introducedis more extensive with increasing impact energy, as expected. Thedamage area obtained experimentally and numerically has beencalculated and is presented in Table 4. The predicted area of com-plete failure is always smaller than that of the measured delamina-tion area for all impact energies. However, the delaminationevolution area which includes the complete and partially failed re-gion is larger than the experiment. The images shown by Fig. 8b, d,and f illustrates the severity of damage by different colours (orshades of grey); very dark corresponds to the complete delamina-tion region while lighter shade of grey indicates the interface hasnot yet delaminated but the material has been locally weakenedthat contributes to the energy dissipation. Fig. 9 shows the pre-dicted delamination at each ply interface for the case of 14.7 J im-pact energy. It can be seen that the largest area of completedelamination is found to occur at the 90�/90� mid-plane interface,something that could change if axial splitting (fibre/matrix inter-face) was taken explicitly into account in the analysis.

Matrix tensile and shear damage are also important damagemechanisms that absorb energy and can be predicted as shownin Fig. 10a–f; in these images, the matrix tensile failure and in-plane shear damage of each ply are superimposed. The matrixtensile failure in Fig. 10a is initially small and gets larger underincreased impact energy, Fig. 10c and e. In-plane shear damagein each ply is superimposed in Fig. 10b and develops at approxi-mately ±45� to the 0� fibre direction. A larger amount of sheardamage is introduced at a high impact energy level, Fig. 10d andf. This damage might lead to a small permanent indentation afterthe impact event. Moreover, fibre breakage in Fig. 10g was pre-dicted by the damage model when the load in the fibre directionis exceeding its strength, like in the case of the 14.7 J impact. Fibrebreakage was also observed experimentally and can be seen inFig. 8c and e as the darker regions (zinc iodide solution has com-pletely penetrated the damaged plate).

Fig. 11a shows the permanent indentation predicted by thenumerical model with the delamination at different ply interfaces.The predicted post-impact indentation is similar in depth to the ac-tual damage observed after the impact test. The permanent inden-tation is formed due to the nonlinear shear damage behaviour of

the polymer matrix, where the inelastic shear strain results in apermanent indentation and this indentation could play animportant role on the performance of the compression after impactevent. In addition, delamination predicted at different plyinterfaces can be seen in Fig. 11b that shows a through-thicknesssection of the simulated laminate.

5. Concluding remarks

In this paper the impact response and impact induced damagefor a simple cross-ply [0/90]2s composite laminate have beeninvestigated experimentally and numerically under three differentimpact energy levels. A stress based failure criterion was used topredict damage initiation while damage propagation in the formof intra- and inter-laminar cracking (delamination) was simulatedby energy based criteria. The method was implemented via theuser subroutine VUMAT of the Abaqus/Explicit commercially avail-able code. Delamination is considered as one of the critical failuremechanisms that can substantially reduce the residual strength ofthe composite plate, especially under compression [38,39], whichmakes its accurate prediction crucial in the design of compositestructures. In this analysis, delamination was modelled by insert-ing cohesive element layers between all plies where an appropriatetraction law and damage initiation and evolution criteria were ap-plied. The nonlinear shear response of the composite was also con-sidered by using the Soutis et al. shear model [14] and damageprogression compared favourably with the experimental resultsand observations. While the peak force, energy and displacementwere all accurately captured in the numerical simulations, thematerial behaviour during the projectile rebound was less accu-rately predicted. The model under-predicted the energy absorbedby the laminate and the degree of permanent deformation duringthe 7.35 J impact, but the discrepancy kept decreasing withincreasing impact energy. This discrepancy is most likely to bedue to material properties variability, specimen quality/imperfec-tions introduced during the manufacturing process and/or inaccu-racies in the friction coefficient assumed between the projectileand plate or between individual plies. The type, location and extentof damage were also identified by the model and overall damagearea was in good agreement with observations and X-ray radiogra-phy images. At higher energy levels, especially at 14.7 J, a verygood agreement was found between the experimental and numer-ically predicted delaminated area. In addition, the permanentindentation on the impacted face and fibre breakage were also suc-cessfully predicted for the 14.7 J impact case, further supportingthe modelling approach and assumptions made. In the near futureother multi-directional lay-ups will be attempted, especially thicklaminates where a volume effect (scaling effect) may be an issue[40,41]. In addition, residual strength prediction under uniaxialcompressive loading and compression after impact (CAI), often alimiting design parameter in the aircraft construction with com-posites [42,43], will be studied. Also, the X-ray radiography in thiswork was performed after the impact event, when the plate wasunloaded. This of course implies that many of the resin cracksand delaminations, especially at the lower impact levels, mightclose making it difficult for the zinc iodide solution to penetrateand reveal the real extent of damage, which resulted in overesti-mating the size of the weakened (delaminated) region, Table 4.Real time structural health monitoring techniques [15,16] will berequired for more accurate comparisons between damage sizes ofprediction and measurement.

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