Composite Structures 132 (2015) 290–298

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Composite Structures

journal homepage: www.elsevier .com/locate /compstruct

Delamination prediction in composite laminates under low-velocityimpact

http://dx.doi.org/10.1016/j.compstruct.2015.05.0370263-8223/� 2015 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Tel.: +86 20 87111137.E-mail address: yaoxh@scut.edu.cn (X. Yao).

Shuchang Long, Xiaohu Yao ⇑, Xiaoqing ZhangSchool of Civil Engineering and Transportation, South China University of Technology, Guangzhou, Guangdong 510640, PR China

a r t i c l e i n f o

Article history:Available online 18 May 2015

Keywords:Composite laminatesDelaminationDamage predictionLow-velocity impactNumerical simulation

a b s t r a c t

This paper presents a damage analysis process of composite laminates subjected to low-velocity impact.Drop weight tests were carried out on specimens with two kinds of stacking sequence. Ultrasonic C-Scanwas used to investigate the delamination area of each interface. Numerical models were built based on adamage model where cohesive contact method was involved. The efficiency of delamination modelingwas discussed and the damage model was validated. The results of the FEM were found to agree well withexperimental observation. According to the results, a prediction process of delamination shape was madefor composite laminates under low-velocity impact. The delamination area was found to distribute sym-metrically around the impact point while the shape is related to the ply angles of the layers close to theinterface. The prediction was proved to have good accuracy and efficiency.

� 2015 Elsevier Ltd. All rights reserved.

1. Introduction

Delamination is one of the common failure modes in compositelaminates. It appears in the interface of two adjacent layers and cansignificantly reduce the compression strength of laminated struc-tures. One of the main elements that lead to delamination islow-velocity impact. Impact with low velocity will cause excessivestress cross the interface of layers with different ply angles anddelamination appeared after the failure of interface material.

Since delamination always takes place inside composite layers,it is difficult to characterize it without breaking the laminatedstructure. Therefore, the prediction of delamination in compositelaminates became necessary during the service period of compos-ite structures.

Studies have been done throughout the world to reveal thedelamination damage behavior in composite laminates.Generally, they can be divided into two categories: experimentalanalysis, and numerical analysis.

A large amount of experiments were carried out on the damagebehavior of composite laminates. Tita [1] tested three kinds ofcomposite plates with typical stacking sequences under differentimpact energies. The mechanical behavior of the specimens wasclassified by the ratio of absorbed energy versus impact energy.Matrix crack and delamination were found when the fraction of

absorbed energy was above 35%, while fiber rupture appeared asthe fraction increased to 75%. Schoeppner [2] investigated thedelamination threshold load of composite laminate under lowvelocity impact. The threshold load level was obtained from theload–time history or load–displacement plot, at which a suddenload drop occurs due to specimen stiffness loss as a result of lam-inate level damage. Sebaey [3] and Lopes [4,5] studied the effect ofmismatch angle between plies on the delamination areas of com-posite laminates. Specimens with different stacking sequenceswere subjected to drop weight impact, and damages under differ-ent load levels were gained through C-Scan. The results indicatedthat by reducing the mismatch angle between the adjacent layers,the response of CFRP composites to low velocity impact could beimproved. The experiments made by these researchers weremostly based on drop weight impact machines. Hou [6] and Joshi[7] carried out impact tests using a gas gun. This kind of loadingmethod can avoid repeated loading appeared in drop weight tests,and impact energy can be easily controlled in the experimentprocedure.

Many researchers also focused on the damage detection in com-posite materials. There are mainly two kinds of nondestructiveinspection (NDI) method that are used in delamination analysis.Ultrasonic C-Scan is the most common technique to obtain damagecaused by impact loads. Since the wave impedance of damagedmaterial is different from the original material, the damage areacan be drawn clearly by ultrasonic microscope. The other methodthat is widely used is lamb wave detection. In the research ofKessler [8], Bruno [9], Guo [10] and Su [11], lamb wave is used

S. Long et al. / Composite Structures 132 (2015) 290–298 291

for damage inspection in composite materials. The method iseffective for the determination of the presence and severity ofdamage, but difficult to investigate the damage shape and positiondirectly.

There are also many other techniques for damage detection.Zhu [12] and Zou [13] proposed a vibration-based evaluationmethod to determine the location and size of debonding in com-posite structures. Lahuerta [14] describe a technique for measuringthe delamination length in mode I tests based on video image pro-cessing. In the studies of Jody [15] and Zabala [16], damage visualenhancement technique was used to highlight the damage scope incomposite laminates.

In these experimental studies, delamination scopes obtainedwere superimposed together. Although the damage is character-ized by the total area, it is difficult to distinguish a delaminationarea of an interface from another. In order to study the relationshipof stacking sequence and delamination area, it is necessary toinvestigate the damage behavior between each pair of adjacentlayers.

Due to the big cost of experiments, researchers have paidmore attention to numerical approach. The basis of numericalanalysis is the damage theory models for composite materials.Hinton [17] concluded 12 leading theories for predicting failurein composite laminates. The predictions were compared withexperimental evidence and the effectiveness of each theorywas discussed. Several theories were found to be accurate forintra-laminar damage prediction but few considered the delam-ination behavior. Eijo [18] presented a numerical method basedon the refined zigzag theory to model delamination in compos-ite laminated plates. The quadrilateral QLRZ finite element wasused for predicting the laminate kinematics. Results show thatboth the onset and the evolution of delamination were accu-rately predicted by the QLRZ element. Moura [19] proposed anew double failure criterion based on the combination of failuretheories presented by Tsai-Wu, Hashin, Choi and Becker. Thecriterion identified the matrix rupture and delamination sepa-rately. Liu [20] performed a nonlinear progressive damagemodel to predict the ultimate strength and the failure processedof composite laminates. A three-dimensional strength criterionin terms of strains, which concluded fiber damage, matrix dam-age and delamination, was developed in the analysis model.Martinez [21,22] developed a matrix-reinforced mixing theoryto predict delamination in composite laminates in ply drop-offtest and drop-weight impact test. The method was proved tobe less time consuming and applicable in structures withmulti-plies. Zubillaga [23] considered that delamination wascaused by matrix cracks, and developed a failure criterion basedon the energy release rate and fracture toughness of theinterface.

Among the numerical studies, cohesive elements were widelyused to simulate the delamination behavior of composite lami-nates. These elements were used to connect two surfaces of an

11σ

TX

11ε011ε 11

tε0

ftG

Fig. 1. Stress–strain relationship for fiber tensile damage.

interface whose thickness is taken as zero before the deformationof the body occurs [24]. Delamination was simulated by controllingthe constitutive model of cohesive elements. Recently, many stud-ies have been done to improve the application of cohesive ele-ments. Camanho [25] proposed a mixed-mode criterion for thedelamination model based on cohesive elements. In the criterion,both tensile stress and shear stress are considered to account forthe delamination. In the study of Jalalvand [26], cohesive elementswith a random distribution of strength were embedded betweenthe layers for modeling of delamination. Numerical results werefound to agree well with the experimental observations. Xin [27]and Turon [28] studied how the mesh density of cohesive elementsaffects the delamination area. It was found that more elements willlead to more accurate result.

It can be seen that many methods have been proposed to predictthe delamination behavior in composite laminates. However, few ofthe researchers focused on the shape of delamination area in eachinterlayer of a laminate, since the delamination scopes obtainedfrom the tests were always superimposed together.

This paper presented a damage analysis process for compositelaminates under low-velocity impact. First, a damage model forcomposite materials is proposed which has consideredintra-laminar and inter-laminar damage. Then, drop weight testswere carried out on laminated composite specimens. UltrasonicC-Scan was used to investigate the delamination area in each inter-face and image processing method was applied to characterize thedamage scopes. Based on the damage model, numerical simula-tions were made to study the efficiency of delamination modeling.Validation was also made for the damage model, and numericalresult was found to agree well with experimental observation.Furthermore, the relationship of stacking sequence and delamina-tion shape was summarized. Several conclusions were made andsome future work was listed.

2. Damage criteria and evolution

The damage behavior of composite laminates can be dividedinto two types: intra-laminar damage and inter-laminar damage.The intra-laminar damage consists of fiber damage and matrixdamage, while the inter-laminar damage is mainly contributedby delamination.

2.1. Intra-laminar damage

2.1.1. Damage criteriaHashin damage criteria were used to model the damage

appeared within layers. The criteria were formulated below.Fiber damage:

Ftf ¼

r11

XT

� �2

P 1 ðr11 P 0Þ ð1Þ

Fcf ¼

r11

XC

� �2

P 1 ðr11 6 0Þ ð2Þ

Matrix damage:

Ftm ¼

r22

YT

� �2

þ s12

SL

� �2

P 1 ðr22 P 0Þ ð3Þ

Fcm ¼

r22

YC

� �2

þ s12

SL

� �2

P 1 ðr22 6 0Þ ð4Þ

r11-normal stress in the fiber direction;r22-normal stress in the transverse direction;

a. Mode I b. Mode II c. Mode III

Fig. 2. Three fracture modes for delamination.

t

mδ0mδ

CG

Fig. 3. Traction–separation law for cohesive contact.

292 S. Long et al. / Composite Structures 132 (2015) 290–298

s12-shear stress in the plane of fiber and transverse directions;XT -tensile strength in the fiber direction;XC-compressive strength in the fiber direction;YT -tensile strength in the transverse direction;YC-compressive strength in the transverse direction;SL-shear strength in the fiber and transverse plane.

Both fiber damage and matrix damage were taken into accountin Hashin damage criteria. The normal stress in the fiber directionwas considered to be the only reason that leads to the fiber dam-age, while the normal stress in the transverse direction and theshear stress in the plane of fiber and transverse directions con-tributed to the matrix damage.

2.1.2. Damage evolutionLinear damage evolution law was used after damage appeared

in the composite material. The evolution law of fiber tensile dam-age was presented in Fig. 1.

The stress–strain relationship can be divided into two steps.Before fiber tensile damage appeared, linear elastic behavior wasconsidered for the material along the fiber direction. Once the nor-mal stress met the tensile strength in the fiber direction, the elasticmodule reduces in a linear way. e0

11 represents the initial normalstrain when the initiation criterion was met, and et

11 is the normalstrain when fiber was completely damaged. The area of the triangleformed by the curve and abscissa axis, Gft , represents the fractureenergy of fiber tensile damage.

The evolution laws of the rest three damage modes are similarwith the one proposed above.

It should be noted that in Hashin damage criteria, the compositelayer was considered as an orthotropic homogeneous material.However, the intra-laminar damage took place either in fiber orin matrix. In order to distinguish different damage modes, the prin-ciple axes of material were taken into consideration. The first prin-ciple axis is parallel to the fiber direction while the second one isperpendicular to the direction. The third principle axis is perpen-dicular to the first and second axes. When damage occurred, thecorresponding stiffness along the principle axis will demise. Forexample, once the fiber tensile damage criterion was meet, the

fiber was regarded broken in the element. Both fiber and matrixwill not sustain the tensile load and the tensile stiffness alongthe first principle axis of the material reduced to zero. The equiva-lent method is appropriate because the fiber mainly sustain thelongitudinal load while the matrix sustain the transverse one.

2.2. Inter-laminar damage

The cohesive contact method was used to simulate the delami-nation between layers of composite laminates. The basis of themethod is the cohesive behavior interaction of two adjacent sur-faces. The traction stress and separation displacement of the nodeson the surfaces are governed by traction–separation law. Similarwith the intra-laminar damage models, the traction–separationlaw is composed by damage criterion and damage evolution.

2.2.1. Damage criterionThe interaction area of two adjacent layers in composite lami-

nates can be regarded as matrix material. Therefore, theinter-laminar behavior is considered to be linear elastic beforethe delamination occurred. The traction stress on a surface consistsof 3 components: a normal traction and two shear tractions. Theelastic behavior can be written as:

t ¼tn

ts

tt

264

375 ¼

Kn 0 00 Ks 00 0 Kt

264

375

dn

ds

dt

264

375 ð5Þ

t is the traction stress, d is the separation displacement and K rep-resents the stiffness of interaction. The three directions correspondto the three fracture modes which are shown in Fig. 2.

A quadratic separation law was used to control the damage cri-terion of delamination. In the law, damage is assumed to initiatewhen the quadratic interaction function reaches one, which is pre-sented below.

hdnid0

n

!2

þ ds

d0s

!2

þ dt

d0t

!2

P 1 ð6Þ

d0n; d0

s and d0t represent the peak values of the contact separation,

when the separation is either purely along the contact normal orpurely in the first or the second shear direction, respectively. Inorder to describe the evolution of damage under a combination ofnormal and shear separations across the interface, effective separa-tion dm is introduced.

dm ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffihdni2 þ d2

s þ d2t

qð7Þ

2.2.2. Damage evolutionThe damage evolution law of delamination is similar with the

law of intra-laminar damage discussed above. Before delaminationappeared, the interaction was considered to have a linear behavior.Once the damage criterion was satisfied, the cohesive stiffnessdegrades linearly (see Fig. 3).

Fig. 4. Setup for impact tests.

S. Long et al. / Composite Structures 132 (2015) 290–298 293

GC is the fracture energy of delamination with mixed modes. Itis formed based on the Benzeggagh–Kenane fracture criterion. Theexpression is presented below.

GC ¼ GCn þ GC

s � GCn

� � GCs þ GC

t

GCs þ GC

n

!g

ð8Þ

GCn ; GC

s and GCt are critical fracture energies required to cause failure

in the normal, the first, and the second shear directions while g is acohesive property parameter.

3. Experimental analysis

Drop weight impact tests were carried out based onASTM-D7136. The standard is a test method for evaluating the dam-age resistance of a fiber-reinforced polymer matrix composite to adrop-weight impact event. The laminate plate was manufacturedwith T700/3234 UD carbon/epoxy composite. According to thestandard, the specimen was cut into a plate with a size of150 � 100 mm, and clipped on a rigid supporting structure with arectangular cut of 125 � 75 mm in the center. The low-velocityimpact was made by InstronDynatup 9250HV drop weightmachine. The punch, with a diameter of 16 mm, was made of alu-minum. The impact energy varies with the weight and drop heightof the punch. The setup for impact tests were presented in Fig. 4.

Two specimens were tested under different impact energies.Parameters of the tests are listed in Table 1.

Curves of impact force versus time and displacement wereobtained through the load sensor and the displacement sensor,

Fig. 5. Curves of impact force versus time (a) an

Table 1Test parameters.

Specimenno.

Thickness(mm)

Stacking sequence Impact energy(J)

A 2.5 [�45/0/0/45/0/�45/0/45/0/0]S 11.30 JB 3.25 [45/0/0/0/�45/90/45/0/0/�45/90/

45/0]S

20.09 J

as presented in Fig. 5. After the drop weight tests, the dent depthof the impact point on each specimen was measured using amicro-digital indicator. The visual damage on the surface of speci-men A is presented in Fig. 6.

Matrix crack and fiber failure appeared at the impact point,while small bulges were found on the back surface, which indicatesdelamination of the bottom layer. In order to investigate thedelamination area directly, C-Scan technique was used. The resultsof specimen The specimens were examined under an ultrasonicscanning microscope made in Germany. Delamination areas wereobtained layer by layer along the thickness direction of specimenA (Fig. 7). The experimental results will be discussed more specif-ically in Section 5.

4. Numerical analysis

4.1. Efficiency analysis of delamination modeling

Based on the inter-laminar damage criterion and evolutionintroduced in Section 2.2, the delamination can be simulated bycohesive behavior interaction of two adjacent surfaces. The resultwill be more accurate if we defined cohesive contact in each pairof adjacent layers. However, when a cohesive behavior was intro-duced into an interface, the computational speed would be sloweddown. Therefore, it is necessary to find out how many layersshould be taken into account with cohesive contact.

In the study of Heimbs [29], conclusion was made that moredelamination interfaces in the model will lead to higher accuracyand computational cost. The author suggested that for a 17-plylaminate, a 6-interface model was accurate enough, althoughspecific reasons were not mentioned.

In this paper, five models were built to find the most suitablenumber of cohesive interfaces. Since test results have shown thatdelamination just took place between the layers away from theimpact surface, we introduce cohesive contact into the laminategradually from the bottom. For example, the contact informationof model 3 is presented in Fig. 8. The layers of the laminate are

d displacement (b) obtained from the tests.

Fig. 7. Delamination image of specimen A through C-Scan.

tie

cohesivecontact

layer 8

layer 1

Impact side

layer 2layer 3layer 4layer 5layer 6layer 7

Fig. 8. Interaction in model 3.

a. Impact side b. Back side

Fig. 6. Visual damage on the specimen surface.

294 S. Long et al. / Composite Structures 132 (2015) 290–298

numbered from the bottom to the top. Layers 5 to 8 are tiedtogether, while cohesive contact is introduced between layers 1and 2, layers 2 and 3, layers 3 and 4. The distribution of cohesivecontact in five models was listed in Table 2.

After calculation, the delamination area for each interface wasobtained. The results were listed in Table 3.

It is reliable to regard the result of model 5 as the real delami-nation area. It can be found that the delamination areas of the toptwo interfaces with cohesive contact for model1 to model 4 havegreat differences with the real areas. For example, the delamina-tion area in interlayer 1|2 of model 3 is similar with the one ofmodel 5. However, the areas of interlayer 2|3 and 3|4 in model 3is different from the areas of model 5.

Table 2Distribution of cohesive contact.

Model no. Interlayer with cohesive contact

1 1|22 1|2, 2|33 1|2, 2|3, 3|44 1|2, 2|3, 3|4, 4|55 All

This phenomenon should attribute to the different stiffness oftwo adjacent layers. For model 3, layer 5, 6, 7 and 8 are tiedtogether while layers below are connected by cohesive contact.The 4 layers above form a thick laminate with larger stiffness thana single layer. As a result, the stiffness of the structure changes a lotacross the interlayer of 3|4. Therefore, big delamination will takeplace when the structure is exposed to impact loads.

When cohesive contact was introduced into an interlayer of alaminate, the delamination area of the top two interfaces withcohesive contact are inaccurate. In order to obtain a reliable result,two more interfaces under the concerned one should be taken intoaccount with cohesive contact.

It should be noticed that, as cohesive contact was introducedinto more interfaces, more time was needed to complete the calcu-lation. Additionally, since at least one element was needed for onelayer along the thickness direction, the time step will be dividedinto a very tiny amount in order to avoid numerical instabilities.As a result, the damage model with cohesive contact was not suit-able for structures with too many plies. However, the damagemodel is able to reveal the damage mechanism of delaminationin composite laminates.

4.2. Modeling validation

In order to validate the modeling method proposed in Section 2,numerical models were built based on the drop weight tests inSection 3. The mechanical parameters of the UD composite werelisted in Table 4.

The UD composite was regarded as orthotropic homogeneousmaterial with linear elastic behavior. The intra-laminar damagewas simulated by defining Hashin damage criteria and linear dam-age evolution law on each layer, while the inter-laminar damagewas simulated by introducing cohesive contact between adjacentlayers. When delamination occurred, friction between layers wasconsidered with a coefficient of 0.15.

Table 4Mechanical parameters of T700/3234 UD composite.

Density 1700 kg/m3

Intra-laminar Elasticproperties

E1 = 110 GPa, E2 = 7.8 GPa, m12 = 0.32,G12 = G13 = G23 = 40 GPa

Strength XT = 2093 MPa, XC = 870 MPa,YT = 50 MPa, YC = 198 MPa,SL = 104 MPa

Fractureenergy

Gft = Gfc = 10 N/mm, Gmt = Gmc = 1 N/mm

Inter-laminar Elasticproperties

Kn = Ks = Kt = 850 MPa

Strength Tn = 3.3 MPa, Ts = Tt = 7 MPaFractureenergy

Gn = 0.306 N/mm; Gs = Gt = 0.632 N/mm

Table 3Delamination areas for five models.

Model No.

Delamination area Time Consuming Layer 1│2 Layer 2│3 Layer 3│4 Layer 4│5

1 54min

2 58min

3 63min

4 83min

5 92min

U1=U2=U3=0

U1=U2=U3=0

Fig. 9. Finite element model.

S. Long et al. / Composite Structures 132 (2015) 290–298 295

The finite element model of specimen A was presented in Fig. 9.The model contains 48,000 continuum shell elements and 928solid elements. Each layer contains 2400 elements with 3Simpson integral points. The displacement of the edge was fixedalong X, Y and Z directions. Initial velocity field was defined onthe punch model. Ultrasonic C-Scan presented the delaminationarea in the bottom 3 layers. Therefore, cohesive contact was intro-duced into the bottom 5 layers according to the efficiency ofdelamination modeling discussed in Section 4.1. Since

delamination will not take place between the layers with the sameply angle, the layers were tied together.

The calculation costs 32 h for specimen A and 37 h for specimenB. The results of numerical simulation are presented in Section 5.

5. Results and discussion

5.1. Impact response of composite plates

Time history curves of impact force are shown in Fig. 10. Theblack and red curves represent the experimental and numericalresult respectively. Good agreement can be found in bothspecimens.

The dent depth of the impact point was listed in Table 5. It canbe found that the dent depth obtained from simulation is smallerthan the value measured by the micrometer. This phenomenonshould attribute to the damage model used in numerical simula-tion. In the damage model, only elastic behavior is considered forthe composite material. In order to simulate the real deformationof composite materials, plastic behavior should be taken intoaccount. In the study of Chen [30], a combined elastoplastic dam-age model was proposed to simulate the plastic deformations ofcomposite layers. Irreversible deformations are allowed in themodel which includes the yield criterion, plastic flow rule, harden-ing rule and the hardening law.

5.2. Delamination characteristics

The delamination areas obtained through simulation were com-pared with the image acquired from C-Scan. In order to present thedelamination area more clearly, an image processing methodbased on Matlab and Image Pro was adopted. The accurate correla-tion between experimental and numerical results tends to confirmthe relevance of the damage analysis model.

In the studies before, delamination was found along the fiberdirection of the layer below the interface. This law was provedonce again by the results presented in Figs. 11 and 12. However,it should be noticed that the delamination shapes are not the samefor interlayer 3|4 in specimen A and interlayer 4|5 in specimen B,although the fiber directions of the layers below the interfaces

Fig. 10. Time history curves of impact force.

Table 5Dent depth of the impact point.

Specimen no. Dent depth (mm) Error

Experimental result Numerical result

A 0.85 0.64 24.7%B 1.42 1.04 26.8%

296 S. Long et al. / Composite Structures 132 (2015) 290–298

are both 0�. This phenomenon indicated that the delaminationshape is affected by the fiber direction of both layers close to theinterface.

Table 6Prediction process of delamination shape.

Ply angle Delamination predi

045

°

°

450

°

°

045

°

°−

450

°

°

−

4545

°

°−

900

°

°

B

A

A

B

B

A

A

B

B

A

B

A

Based on the numerical and experimental results, delaminationshape was predicted for two adjacent layers with different plyangles (see Table 6). The prediction process consists of three steps:

a. Draw a line along the fiber direction of the layer above,noted by line A. Draw another line along the fiber directionof the layer below, noted by line B. The two lines intersectat the impact point.

b. Make a projection from line B to line A, forming twotriangles.

ct C-Scan result

Fig. 11. Delamination shapes of the bottom 3 interfaces in specimen A.

Fig. 12. Delamination shapes of the bottom 3 interfaces in specimen B.

S. Long et al. / Composite Structures 132 (2015) 290–298 297

c. Drag the two triangles along line B for a distance equals tothe radius of the punch.

The prediction process was easy to operate for the interfacewith the mismatch ply angle of 45�. As for the interfaces withthe mismatch ply angle of 90�, the prediction process is a little dif-ferent. Since the projection area is 0 when line A is perpendicular toline B, we expand the projection area along line A forming twoisosceles triangles. The delamination shape for interface of45�|�45� is validated by a specimen with the stacking sequenceof [�45/45/0/�45/90/45/0]S. The situation for 90�|0� is validatedby the experimental result of Aymerich [31].

6. Conclusions

A delamination analysis process for composite laminates underlow-velocity impact was presented in this paper. A damage modelwhich considered both intra-laminar and inter-laminar damagewas proposed. Experimental analysis was carried out through dropweight tests. Ultrasonic C-Scan technique was used to reveal thedelamination appeared in the interfaces.

Numerical models were built based on the damage model. Theefficiency of delamination modeling was discussed. It can be con-cluded that when cohesive contact was introduced into an inter-face of a laminate structure, the delamination area of the top twointerfaces with cohesive contact are inaccurate. In order to obtaina reliable delamination area, two more interfaces under the con-cerned one should be taken into account with cohesive contact.

Finite element models were also used to validate the damagemodels. The accurate correlation between experimental and

numerical results tends to confirm the relevance of the damageanalysis model. Based on the results, the relationship of stackingsequence and delamination damage was summarized. The damagearea was found to distribute centrosymmetrically around theimpact point while the shape is related to the ply angles of the lay-ers close to the interface. The prediction was also validated byexperimental results of other researchers.

Future works will focus on the damage models. Since the dentdepth predicted by the damage model proposed in this paperwas inaccurate, plastic behavior should be taken into account inthe future. The stacking sequence of composite laminates studiedin this paper is limited to combinations of 0�, 90� and ±45�. Moreply angles should be taken into account in the prediction of delam-ination area.

Acknowledgments

The financial sponsorship and support from the Natural ScienceFoundation of China (11472110, 11372113), the FundamentalResearch Funds for the Central Universities (2014ZG0033), andNew Century Excellent Talents (NCET-13-0218). This paper is alsosupported by the opening project of State Key Laboratory ofExplosion Science and Technology (Beijing Institute ofTechnology) (KFJJ15-20M, KFJJ14-2M).

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