Finite Element Analysis of Delamination Initiation and Growth in E-Glass/Epoxy Reinforced Laminated Beams under Axial Impact

CAI Zhong-yun,MO Jian-hui,TANG Wen-yong,WANG Gang,ZHANG Sheng-kun( State Key Laboratory of Ocean Engineering,Shanghai Jiao Tong University,Shanghai 0040,China; China Classification Society,Beijing 00007,China)

Finite Element Analysis of Delamination Initiation and Growth in E-Glass/Epoxy Reinforced Laminated Beams under Axial Impact

CAI Zhong-yun1,MO Jian-hui2,TANG Wen-yong1,WANG Gang2,ZHANG Sheng-kun1(1 State Key Laboratory of Ocean Engineering,Shanghai Jiao Tong University,Shanghai 200240,China;2 China Classification Society,Beijing 100007,China)

The initiation and growth of delamination in E-glass/epoxy reinforced laminated beams subjected to axial impact were investigated numerically.Introducing a mixed failure mode which was made up of quadratic nominal stress criterion and BK(Benzeggagt-Kenane)fracture criterion,a finite element model with the cohesive element which was employed to simulate the intra-laminar failure area was established by the commercial software ABAQUS/Explicit.The results show the delamination location and its growth in terms of beam’s ply sequence and impact velocity.An experimental setup was used to investigate the dynamic response and failure behavior of the laminated beams.A good agreement was obtained between numerical simulation and experimental results.

laminated beam;delamination;dynamic response;axial impact;finite element method;ABAQUS

Biography：CAI Zhong-yun(1978-),Male,Ph.D.student of Shanghai Jiao Tong University;Corresponding author

E-mail:wytang@sjtu.edu.cn.

1 Introduction

Due to the high specific stiffness,strength and high fracture strength,fiber reinforced plastic(FRP)laminated composite materials have been increasingly used in modern industrial fields,such as aircraft,civil engineering and marine industry.These materials have high strength-to-weight and stiffness-to-weight ratios.However,laminated composites are susceptible to cause damage in form of matrix cracking,delamination and fiber breakage under impact load like drop tools during their service time.Delaminations are generated by matrix cracks,which are the initial damage[1].In the presence of delamination,the properties of laminated materials may be significantly degenerated,which can result in a severe failure of structure.Therefore,it is particularly important to investigate the mechanism of damage behavior to FRP laminated materials.

Many researchers have made effort to investigate the damage mechanism of laminated composites under impact load.Elder et al[2]reviewed methods for predicting the delamination,including finite element method,boundary element method and cohesive fracture model based on linear elastic fracture mechanics(LEFM).Early research[3-5]focused on finite element method and Collombet et al[5]presented two approaches for modeling damage phenomena:a.averaging models and the contact technique;b.simple criteria for determining damage initiation and growth.Mohammadi et al[6]presented a discrete element method based on contact and a re-mesh method to model an individual crack.Renard et al[7]introduced an intermediate scale between ‘micro’ and ‘macro’,called the ‘meso’ scale,which considered the ply as the basic entity for the description of laminated structures.The continuum damage mechanics model was employed to construct the damage surface[8],and the model has been implemented in a commercial explicit element code[9].Yang et al[10]investigated the delamination growth based on the variational principle of moving boundary and Griffith criteria.Borg et al[11]analyzed delamination initiation and growth by using a discrete cohesive crack model which was derived postulating the existence of a maximum load surface which limited the adhesive forces in the process zone of the crack.

Failure criteria and contact mechanism have been noticed for many researchers in recent studies.Narayana et al[12]established a new failure criterion based on initial failure mechanism，which can be concluded that influence of shear stress on the failure of the lamina is of little consequence as far as prediction of strength in laminates.Luo et al[13]employed maximum stress and quadratic stress failure criteria in three failure modes and the results showed that the shape of impact mass should be considered as an important parameter.Tay et al[14]used the element-failure method and the micromechanics-based failure criterion SIFT to model the damage and its development.Contact mechanism is unnecessary to be defined in this method.Zhang et al[15]brought forward an approach based on contact constraint introduced by penalty function method and the damage areas were considered as cohesive zone.Then the damage model was implemented into a commercial finite element package,ABAQUS,via its user subroutine VUINTER.A linearized contact law has been well applied to the impact analysis and parametric study on contact coefficient and exponent of the contact law was performed by Choi[16].

Experimental investigation is another important approach to study the damage mechanism for laminated composites under impact load by three common impact setups:drop weight impact machine,pendulum impactor and gas-gun impactor.Zhou[17]studied thick glass fiber reinforced laminates of various dimensions subjected to impact with a flat-ended impactor and the influence on impact behavior was found to be generally dependent on the impact force or incident kinetic energy level.Techniques such as cross-sectional fractography,scanning acoustic microscopy and scanning electron microscopy were employed by Sohn et al[18]to assess the internal damage and the results showed that laminates experienced various types of fracture.The effect of ply-up sequence has been studied by Mili[19]and Belingardi[20].The energy absorption capability has been studied with respect to the different ply-ups and it points out that it has no sensitivity to strain-rate effect by the force-displacement curves which are obtained during the conducted tests.Hou et al[21]verified a new delamination criterion by ex-periment results,with consideration of both the inter-laminar shear and through-thickness compression stresses.The investigation conducted by Aslan et al[22]was concerned with evaluation of the in-plane dimensional effect of laminates with(0/90/0/90)soriented cross-ply and three different geometrical dimensions.

The work mentioned above has also considered the damage of laminated plates subjected to transverse impact load.Slender beams as common structural components applied in various engineering fields may be easily buckled and damaged under static or dynamic axial load.Kenny et al[23]presented a numerical investigation for dynamic buckling of an elastic slender beam with initial geometric imperfections modeled by the finite difference and finite element methods.By using a horizontal linear bearing impact setup,Zhang[24]performed the analysis of dynamic damage behavior of FRP laminated beams under axial impulse caused by pendulum impactor,and the results showed that delamination and matrix crack were the primary damage mechanism.

This paper is concerned with dynamic response and damage behavior of E-glass/epoxy reinforced laminated beams under the axial impact.Based on Hashin’s stress failure criterion[25]and BK(Benzeggagt-Kenane)fracture criterion[26],a mixed failure criterion was employed to determine the initial crack and delamination growth.A 3-Dimentional finite element model was established in ABAQUS/Explicit,where the failure field was modeled by cohesive elements.With a gas-gun impactor test system,the dynamic response and damage behavior were investigated experimentally.Compare the time-history curves of strain records and the residual deformations,good agreements were obtained between numerical simulation and experimental observation.The effect of ply sequence and impact velocity were considered principally in the investigation.

2 Numerical model

Finite element method(FEM)was made a wide application in mechanics analysis of structure strength,response and buckling in different materials.Based on appropriate failure criteria,the failure behavior of orthotropic materials can be investigated correctly.

The FRP laminated beam can be considered as a stack of homogeneous,orthotropic laminas with different ply-up sequence.The delamination may occur at interface between any individual neighboring laminas which can be tied together using a ‘sliding contact interface’[15].The interface behaves as an entity with large stiffness but no thickness that can be modeled by cohesive element with traction-separation damage description[26].

The numerical simulation of dynamic response and damage behavior of laminated composite beams are performed using the finite element package ABAQUS/Explicit.The whole beam is considered as an elastic entity and each lamina is discretized into a 100×4 model(see Fig.2)used by 8-node,quadrilateral,first-order interpolation,stress/displacement continuum shell element with reduced integration named SC8R included in ABAQUS.The impact beam is modeled as a homogeneous property block with an initial velocity.The impact block has a same cross-section to the laminated beam,and the general contact interaction is defined between the beam and block’s surfaces.

The 8-node three-dimensional cohesive element COH3D8 in ABAQUS is used to model the initiation and growth of delamination between laminas of the beam.We observed experimentally that the mid-plane and the second interface from bottom surface of the beam were sensitive to damage under axial impact.Based on experimental result,the correlative interfaces were modeled as cohesive elements in numerical simulation.

The time-history strain records,damage initiation and growth were obtained in order to compare with the experimental results.A valuable conclusion was found after the comparison.

3 Failure criterion

Fiber breakage,matrix cracking and delamination are three common failure modes in the laminated composites subjected to dynamic load.In our case,no fiber breakage was observed for all beams after impact.We present in the following paragraphs the failure criteria developed for modeling of matrix cracking and delamination.In fact,delaminations were generated by matrix cracks in interfaces,which were the initial damage[1].A mixed failure criterion,which was made up of quadratic nominal stress criterion and BK(Benzeggagt-Kenane)fracture criterion,was used to model damage initiation in numerical simulation.

3.1 Quadratic nominal stress criterion

The cohesive element in ABAQUS was used to model interaction surface between two fiber plies.The nominal traction stress at this surface includes tn,tsand ttwhich represent the normal and the two shear tractions,respectively(Fig.3).

Damage is assumed to initiate when a quadratic interaction function involving the nominal stress ratios reaches a value of one.This criterion can be represented as[26]

For the current laminated beam subjected to axial impact,the whole beam can be considered as an one-dimensional model,so the normal and one shear stress are ignored as described by the differential equations in Ref.[24].The failure criteria can be described by Ref.[25],

3.2 BK(Benzeggagh-Kenane)fracture criterion

The nominal traction stress at the interaction surface,tn,tsand tt,we define the respective critical strain energy release rateandas follows,which indicate the fracture ModeⅠ,Ⅱ and Ⅲ:

The delamination of laminated materials is not determined by one fracture mode,it is reasonable to calculate a mixed strain energy release rate.In order to accurately account for the variation of fracture toughness as a function of mode ratio in epoxy composites,the mixedmode criterion proposed by Benzeggagh and Kenane is used here[27].

where GS=Gs+Gt,GT=Gn+GS,η is a fitting parameter in equation and its value lies on the material property and can be obtained from Mixed-Mode Bending(MMB)tests[27].

In the above expression the quantities Gn,Gsand Gtrefer to the work done by the traction and its conjugate relative displacement in the normal,the first,and the second shear directions respectively.The quantitiesandrefer to the critical fracture energies required to cause failure in the normal,and the first shear directions respectively.In our simulation,the values ofand η are specified as 120J/m2,1 200J/m2and η=2.6.

3.3 Mixed-mode failure criterion[26]

Fig.4 shows the traction on the vertical axis,the magnitudes of the normal and the shear separations along the two horizontal axes.The unshaded triangles in the two vertical coordinate planes represent the response under pure normal and pure shear deformation,respectively.All intermediate vertical planes that contain the vertical axis represent the damage response under mixed mode conditions with different mode mixes.The dependence of the damage evolution data on the mode mix can be defined either in tabular form or,in the case of an energybased definition,analytically.

4 Results discussion

The name of beams groups A and B represents the experimental test and numerical simulation.Each group has two kinds of beam with different ply-up sequence.The geometric and material properties of beams are listed in Tab.1 and Tab.2.

Tab.1 Geometric properties of the laminated beams

Tab.2 The material property of 45°ply-up sequence

4.1 Strain records

4.1.1 Strain record curves analysis of[(±45)3]sply-up

Fig.5 shows typical time-history of strain values recorded under low impact velocity by two strain gauges mounted on beam’s top and bottom surfaces at the middle length of the beam.When a geometrically imperfect beam is impacted axially,it will vibrate in both axial and transverse directions[24].From Fig.5,we can see that the record curves of top and bottom are overlapped at the beginning,which indicates the beam experiences compressive strain.Subsequently,the curves are bifurcated because the stress wave propagates along the beam,and flexure strain occurs during compressive process.Compared with Fig.6,the same trend of strain record curves is observed in finite element analysis which illustrates that the value of stiffness is low in[(±45)3]sply-up sequence and the beam is sensitive to flexure deformation.

The model of numerical simulation is idealization and the imperfection during manufacture process has been ignored.

4.1.2 Strain analysis of[(0)6]sply-up

Figs.7-8 show the experimental and numerical results of beam with[(0)6]sply sequence under low speed axial impact.The curves are overlapped during the first half sine wave due to both top and bottom surfaces experience compressive strain because of larger value of stiffness contrast to the results of[(±45)3]sply sequence.Then,the beam vibrates in compressive and flexure deformation and the vibration diminishes gradually due to the damping effect.

4.2 Damage analysis

The damage of transverse impacted FRP laminate composites with delamination,fiber breakage and matrix crack mainly occurs at the contact area of the impacted region[1,18].Under axial impact,the damage may occur at the location along the beam length and through the beam thickness that varies depending on the lay-up configurations[24].The beams with initial geometric imperfections deform transversely and axially under axial impact,and the maximum bending strains occur at the outer plies and shear stain mainly takes place at mid-plane due to the higher order shear deformation theory.From the experimental results for all beams,damage in form of delamination dominates beam’s failure behavior and differs in ply-up sequence.The following paragraphs present the details of damage behavior of beams under axial impact according to different ply-up sequence.

4.2.1 Damage analysis of beams with[(±45)3]sply-up

Beams in groups A1 and B1 have low value of material stiffness due to lay up sequence of[(±45)3]s.The maximum flexure deformation occurs at outer plies that induce matrix cracking at that location.Fig.9 shows the residual deformation and damage form of beam A1 after axial impact velocity 11.7m/s.From the figures it is seen that the damage occurs at the location of 1/4L and 1/2L from the fixed support end along the beam length.The damage in form of delamination is observed in beam’s mid-plane near to the fixed support end.The matrix crack is observed at top surface in 1/2L distance and bottom surface in 1/4L along the whole length that is induced by the maximum tension stain.The similar damage in form of delamination is also obtained in numerical simulation by finite element model(see Fig.10),and initial delamination occurs near to the fixed support end and extends towards the middle along beam’s length during the stress wave propagating.Matrix cracking is not considered because it is difficult to set up cohesive element between elements through the beam width at outer ply.

4.2.2 Damage analysis of beams with[(0)6]sply-up

Being different from the beams with [(±45)3]sply-up sequence which the damage in form of delamination and matrix cracking coexisted under axial impact,the damage form of delamination dominated over beams with[(0)6]sply-up sequence.

Fig.11 shows the delamination form of beam A2 after axial impact velocity 23.7m/s.From the illustrated detail,we can see that the delamination appears in the middle surface at the impact side and extends approximatly 1/4L along the beam’s length.Then it is transfered to the neighbor interaction surfaces,and the delamination in the surface between plies 4 and 5 near to bottom extends to the fixed support end.

The finite element analysis shows the same delamination form at the impact side and its growth between plies 4 and 5,see Fig.12.At the fixed-support end,delaminations do not occur in simulation model contrary to the experimental result as shown in Fig.11(B),where delamination occurs in interac

tion surfaces close to beam’s bottom due to the refection of stress wave propagation.

The laminated beam with[(0)6]sply-up sequence has considerable carrying capacity after damage occurs at the impact side,stress wave propagates along the beam and reflects at the fixed end in experimental investigation.The material properties are considered as linear elastic mode and the dynamic stiffness is not described accurately in numerical simulation.The impact energy is transfered to stain energy and is released when failure happened.

5 Conclusions

Dynamic response and damage behavior of E-glass/epoxy reinforced laminated slender beams with geometric imperfection under axial impact were investigated numerically.The time history strain records were used to analysis the dynamic response during the beam subject to impact.Employing mixed failure criteria based on quadratic nominal stress criterion and BK fracture criterion,the delamination phenomenon was modeled by cohesive element in a 3-D finite element model.Some valuable conclusions were obtained as follows:

(1)Damage in form of delamination dominated the behavior of FRP laminated beams un-der axial impact.

(2)Ply-up configuration is a key element that affects the material properties and damage behaviors.The delamination occurred near to fixed support end in beam with[(±45)3]sply-up sequence due to stress wave reflection under low impact velocity.For beam with[(0)6]sply-up sequence,delaminations occurred when impact velocity exceeded 20m/s,tremendous impact energy resulted in damage located in beam’s impact side.

(3)Finite element method is a useful technique to simulate dynamic response and perform damage behavior analysis of laminated composite models due to the agreement of experimental results.Because of the complexity of damage behavior in laminated composite material,the parameters of cohesive elements and the material property in dynamic status should be seriously considered in numerical simulation.

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軸向沖擊作用下玻璃纖維復(fù)合材料層合梁脫層及其擴(kuò)展分析

蔡忠云1，莫鑒輝2，唐文勇1，王 剛2，張圣坤1

（1上海交通大學(xué)海洋工程國(guó)家重點(diǎn)實(shí)驗(yàn)室，上海 200240；2中國(guó)船級(jí)社，北京 100007）

玻璃纖維增強(qiáng)型復(fù)合材料層合梁在受軸向質(zhì)量塊沖擊時(shí)，由于纖維鋪層間的粘結(jié)強(qiáng)度較小，該區(qū)域易出現(xiàn)初始裂紋，進(jìn)而擴(kuò)展為脫層損傷。文章探討了采用有限元數(shù)值模擬對(duì)脫層的產(chǎn)生與擴(kuò)展進(jìn)行建模、計(jì)算分析的方法。針對(duì)發(fā)生在纖維層間的脫層損傷，基于傳統(tǒng)的應(yīng)力失效準(zhǔn)則，結(jié)合斷裂力學(xué)的B-K能量失效準(zhǔn)則，建立了混合失效準(zhǔn)則來(lái)定義界面處的損傷規(guī)律，將發(fā)生脫層的潛在區(qū)域定義為粘結(jié)接觸。計(jì)算結(jié)果與實(shí)驗(yàn)對(duì)比具有較好的一致性。

層合梁；脫層；動(dòng)力響應(yīng)；軸向沖擊；有限元；ABAQUS

O347.3

A

蔡忠云（1978-），男，上海交通大學(xué)博士研究生，中國(guó)船級(jí)社研發(fā)中心工程師；

張圣坤（1942-），男，上海交通大學(xué)船舶海洋與建筑工程學(xué)院教授。

O347.3

A

1007-7294（2010）06-0649-11

date：2009-06-03

莫鑒輝（1961-），男，中國(guó)船級(jí)社總工程師；

唐文勇（1970-），男，上海交通大學(xué)船舶海洋與建筑工程學(xué)院教授；

王 剛（1969-），男，中國(guó)船級(jí)社研發(fā)中心總工程師；