损伤力学资料

Effect of manufacturing defects on mechanical properties and failure features of 3D orthogonal woven C/CcompositesAi Shigang a ,Fang Daining b ,⇑,He Rujie b ,1,Pei Yongmao ba Institute of Engineering Mechanics,Beijing Jiaotong University,Beijing 100044,PR ChinabState Key Laboratory of Turbulence and Complex System,College of Engineering,Peking University,Beijing 100871,PR Chinaa r t i c l e i n f o Article history:Received 8September 2014Received in revised form 1November 2014Accepted 3November 2014Available online 10November 2014Keywords:A.Carbon-carbon composites (CCCs)B.DefectsC.Damage mechanics C.Numerical analysisD.Non-destructive testinga b s t r a c tFor high performance 3D orthogonal textile Carbon/Carbon (C/C)composites,a key issue is the manufac-turing defects,such as micro-cracks and voids.Defects can be substantial perturbations of the ideal archi-tecture of the materials which trigger the failure mechanisms and compromise strength.This study presents comprehensive investigations,including experimental mechanical tests,micron-resolution computed tomography (l CT)detection and finite element modeling of the defects in the C/C composite.Virtual C/C specimens with void defects were constructed based on l CT data and a new progressive dam-age model for the composite was proposed.According to the numerical approach,effects of voids on mechanical performance of the C/C composite were investigated.Failure predictions of the C/C virtual specimens under different void fraction and location were presented.Numerical simulation results showed that voids in fiber yarns had the greatest influences on performance of the C/C composite,espe-cially on tensile strength.Ó2014Elsevier Ltd.All rights reserved.1.IntroductionCarbon fiber reinforced carbon composites (C/C)have high ther-mal stability,thermal shock resistance,strength and stiffness in non-oxidizing atmosphere.Due to its superior specific strength and toughness,C/C composites can be considered as favourite materials for highly demanding thermostructural lightweight applications e.g.in aerospace and nuclear industry [1–6].Nowa-days C/C components are leading candidates for applications under extreme conditions.C/C composites are produced by chemical vapor infiltration (CVI)of a textile fiber preform.After the CVI pro-cess and high temperature heart-treatments,generally,manufac-turing defects exist inner the materials.In particular,porosity/voids and micro-cracks are typical defects in C/C composites,and seriously affect the performance of the composites [7–9].So,it is mandatory to account for the effects of defects and their evolution,even in the early stages of the design process.With the increasing use of C/C composites as advanced structural materials,the deter-mination of damage criticality and structural reliability of compos-ites has become an important issue in recent years.Defects–mechanical property relationships of fiber reinforced composites have always been of interest to scientists addressing the composite performance.In Gowayed et al.’s work [10],defects in an as-manufactured oxide/oxide and two non-oxide (SiC/SiNC and MI SiC/SiC)ceramic matrix composites were categorized and their volume fraction quantified using optical imaging and image analysis.Aslan and Sahin [11]investigated the effects of delamin-ations size on the critical buckling load and compressive failure load of E-glass/epoxy composite laminates with multiple large del-aminations by experiments and numerical simulations.In Masoud et al.’s work [12]effects of manufacturing and installation defects on mechanical performance of polymer matrix composites appear-ing in civil infrastructure and aerospace applications were studied.Damage onset and propagation were studied used time-dependent nonlinear regression of the strain field.In Refs.[13–17],the finite element method (FEM)was followed by various authors to study the delamination problems.FEM is preferred than analytical solu-tions because it can handle various laminate configurations and boundary conditions.In recent decades,high-fidelity X-ray micro-computed tomog-raphy (l CT)technology has been used to characterize defects and reconstruct meso-structure of textile composites [18].In Cox et al.’s work [19–21],three-dimensional images of textile com-posites were captured by X-ray l CT on a synchrotron beamline.Based on a modified Markov Chain algorithm and the l CT data,/10.1016/positesb.2014.11.0031359-8368/Ó2014Elsevier Ltd.All rights reserved.⇑Corresponding author.E-mail addresses:sgai@ (F.Daining),rujh@ (H.Rujie).1Co-corresponding author.a computationally efficient method has been demonstrated for generating virtual textile specimens.In Fard et al.’s work [22],manufacturing defects in stitch-bonded biaxial carbon/epoxy composites were studied through nondestructive testing (NDT)and the mechanical performance of the composite structures was investigated using strain mapping technique.In Desplentere et al.’s work [23],X-ray l CT was used to characterize the micro-structural variation of four different 3D warp-interlaced fabrics.And the influence of the variability of the fabric internal geometry on the mechanical properties of the composites was estimated.In Guillaume et al.’s work [24]effects of porosity defects on the interlaminar tensile (ILT)fatigue behavior of car-bon/epoxy tape composites were studied.In that work,CT mea-surements of porosity defects present in specimens were integrated into finite element stress analysis to capture the effects of defects on the ILT fatigue behavior.In Thomas et al.’s work [25]X-ray microtomography technology was adopted to measure the dimensions and orientation of the critical defects in short-fiber reinforced composites.Generally,geometry reconstruction based on l CT data is a huge and complex work,sometimes,virtual specimens explored through this approach are difficult to use for numerical analysis.For 3D fabric composites,because of the 2.Material and experimentsMaterial studied in this article is C/C 3-D orthogonal woven ceramic composite (fabricated by National Key Laboratory of Ther-mostructure Composite Materials,Northwestern Polytechnical University,China)in which T300carbon fiber (Nippon Toray,Japan)tows rigidified by carbon matrix.The C/C composite was prepared using chemical vapor infiltration (CVI)method.T300car-bon fiber was used as reinforcement of the C/C composites with the fiber volume fraction was 56.5%.The fiber preforms,as shown in Fig.1a,were infiltrated with carbon matrix using multiple cycles of infiltration and heat treatment at 1373K,0.03MPa (the thick-ness of the fiber preforms is about 5mm).With increasing cycles,a matrix with near full density can be asymptotically approached,generally,it was about 10cycles (1200h).The C/C specimens are illustrated in Fig.1b (the thickness of the tensile specimen is 5.0mm).However,from the l CT images of the C/C materials,it was found that manufacturing defects such as voids and micro-cracks appeared inner the composites.It is because of the special material preparation process.The manufacturing defects are illus-trated in Fig.1c.Uniaxial tensile experiments were carried out under a Shima-Fig.1.C/C 3-D orthogonal woven composite.Fig.2.Stress–strain curve of the C/C composite under uniaxial tension.114 A.Shigang et al./Composites:Part B 71(2015)113–121In the tensile experiments,five specimens in total were tested and the tensile strengths were217.3,185.1,219.8,176.5and 187.3MPa correspondingly.The average value of the tensile strength was197.2MPa and the dispersion of the experimental results was less than11.5%.Other more,the fracture behaviors of thefive specimens were similar with the failure locations almost all located in the middle of the specimens.From the experiments, deformation of the C/C3-D orthogonal composite under uniaxial tension comprises with three stages:linear elastic stage,damage initiation/evolution stage and the material fracture stage.In the first stage the stress–strain curve increased linearly and in the sec-ond stage the stress–strain curve increased nonlinearly.In the frac-ture stage the stress–strain curve rapidly declined.3.Numerical programmer3.1.3Dfinite element modelFiber tows in the3-D orthogonal architecturesfit together snugly in the woven pattern by a system of periodic motions, and approximately in the same cross-sectional geometry.In this study,cross-sections of the warpfiber yarns and weftfiber yarns werefitted as rectangle.The cross-sections of the z-binder tows werefitted as circular.Geometric parameters of thefiber yarn cross-sections were recorded.For the warp yarns and weft yarns the side lengths of the cross-section rectangle were0.786mm and0.340mm.For the z-binderfiber yarns the diameter of the cross-section circular was0.790mm.The smallest repeatable rep-resentative volume element(RVE)of the textile architecture was constructed and shown in Fig.3.The lengths of the RVE model in X and Y direction both were1.96mm and the height of the RVE model in Z direction was0.76mm.To reveal the internal defects in thefinite element model,l CT technology was used to investigate the meso-structures of the fore,three local coordinates were constructed to identify the mate-rial directions.Then,an interface zone with a constant thickness 0.01mm was generated based on the geometrical model of the fiber yarns,as shown in Fig.3d.Finally,a solid block model with the same size of the composite specimen was constructed.Boolean operation were carried out among the solid block,interfaces and thefiber yarns to generate the geometrical model of the carbon matrix,which is shown in Fig.3b.A whole RVE model of the com-posite is illustrated in Fig.3a.A Monte Carlo algorithm was adopted to choose elements one-by-one randomly as‘‘void defects’’until the volume fraction of the voids satisfied the threshold values in the three zones respectively. For the C/C composite studied in this paper,the void fractions of thefiber yarns,matrix and the interfaces are0.51%,0.47%and 1.94%respectively.It must be noted out that those elements which identified as‘‘void defects’’were not moved away from the FE model,but the stiffness was degenerated by10eÀ6times in the simulation process.The void defects in the three zones are high-light as‘‘red’’,as shown in Fig.3.3.2.Progressive damage modelThe failure criterion proposed here is a strain-based continuum damage formulation with different failure criteria applied for matrix andfiber yarns.A gradual degradation of the material prop-erties is assumed.This gradual degradation is controlled by the individual fracture energies of matrix andfiber yarns,respectively. Thefiber yarn is in the X(1)–Y(2)–Z(3)Cartesian coordinate sys-tem,and the X direction corresponds to thefiber longitudinal direction.For thefiber yarns,two different modes of failure are considered:fiber failure in longitudinal direction and matrix fail-ure in transverse direction.The damage mechanism consists of two ingredients:the damage initiation criteria and the damage evolution law.orthogonal textile C/C composite,(a)RVE model,(b)carbon matrix,(c)fiber yarns and(d)fiber yarns-matrixinterpretation of the references to colour in thisfigure legend,the reader is referred to the web version of thisA.Shigang et al./Composites:Part B71(2015)113–121115failure strains infiber direction in tension and compression,F f;tX and F f;cXare the tensile and compressive strength of thefiberyarns in X direction,respectively.Once the above criterion is sat-isfied,thefiber damage variable,f Xf,evolves according to the fol-lowing equation law:d X f ¼1Àe f;t11f XfeÀC11e f;t11f X fÀe f;t11ðÞL c=G fðÞð2Þwhere L c is the characteristic length associated with the material point.For matrix failure the following failure criterion is used:f Y m ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffie f;t22e f;c22ðe22Þ2þe f;t22Àe f;t222e f;c22B@1C A e22þe f;t22e f;s12!2ðe12Þ2>e f;t22v uu uu tð3Þf Z m ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffie f;t3333ðe33Þ2þe f;t33Àe f;t33233B@1C A e33þe f;t3313!2ðe13Þ2>e f;t33v uu uu tð4Þwhere e f;t22;e f;t33;e f;c22and e f;c33are the failure strains perpendicular to the fiber direction in tension and compression,respectively.The failure strain for shear are e f;s13and e f;s12.Failure occurs when f Y m exceeds its threshold value e f;t22or f Z m exceeds its threshold value e f;t33.The evolu-tion law of the matrix damage variable,d m,is:d Ym¼1Àe f;t22f YmeÀC22e f;t22f Y mÀe f;t22ðÞL c=G mðÞð5Þd Zm¼1Àe f;t33fmeÀC33e f;t33f Z mÀe f;t33ðÞL c=G mðÞð6ÞAs damage progressing,the effective elasticity matrix isreduced as functions of the three damage variables f Xf,d Ymand d Zm, as follows:3.2.2.Failure criterion for matrixDamage in thefiber is initiated when the following criterion is reached:where e f;t and e f;c are the failure strains in tension and compression respectively and e f,t=r f,t/C11,e f,c=r f,c/C11.Once the above criterionis satisfied,thefiber damage variable,f XðY=ZÞm,evolves according to the equation:d XðY=ZÞm¼1Àef;tfmeÀC11e f;t f XðY=ZÞmÀe f;tL c=G mð9ÞThe modulus matrix of the matrix will be reduced according to:In user subroutine UMAT the stresses are updated according to the following equation:C f d ¼1Àd XfC111Àd Xf1Àd YmC121Àd Xf1Àd ZmC130001Àd YmC221Àd Ym1Àd ZmC230001Àd ZmC330001Àd Xf1Àd YmC4400Symmetric1Àd Xf1Àd ZmC5501Àd Ym1Àd ZmC66ð7Þf XðY=ZÞm ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffief;tef;cðe11ð22=33ÞÞ2þe f;tÀðe f;tÞ2ef;c!e11ð22=33Þþef;tef;s2ðe12ð23=13ÞÞ2þef;tef;s2ðe13ð12=23ÞÞ2v uu t>e f;tð8ÞC m d ¼1Àd XmC111Àd Xm1Àd YmC121Àd Xm1Àd ZmC130001Àd YmC221Àd Ym1Àd ZmC230001Àd ZmC330001Àd Xm1Àd YmC4400Symmetric1Àd Xm1Àd ZmC5501Àd Ym1Àd ZmC66ð10Þ116 A.Shigang et al./Composites:Part B71(2015)113–121r ¼C d :eTo improve convergence,a technique based ization (Duvaut–Lions regularization [27])of is implemented in the user subroutine.In this age variables are ‘‘normalized’’via the _d t ;X ðY =Z Þf ðm Þ¼1gd X ðY =Z Þf ðm ÞÀd t ;X ðY =Z Þf ðm Þwhere d X f and d X ðY =Z Þm are the fiber and matrix culated according to the damage evolution d t ;X f and d t ;X ðY =Z Þm are the ‘‘normalized’’the real calculations of the damaged elasticity bian matrix,and g is the viscosity parameter.and d t ;X ðY =Z Þm can be calculated according to the d t ;X ðY =Z Þf ðm Þt 0þD t¼D t t 0þt d X ðY =Z Þf ðm Þ t 0þD t þg g þt dt ;X ðY =f ðm ÞTherefore,for the fiber yarns and matrix,can be further formulated as Eqs.(14)and (15)correspondingly@r e ðf Þ¼C f d þ@C f d@d f:e !@d X f @f f Á@f Xfe!þ@C f d @d Y m :e !@d Y m @f Y m Á@f Y m @e !þ@C f d @d Z m :e !@d Z m @f Zm Á@f Z m@e !ð14Þ@r @e ðm Þ¼C m d þ@C md @d m :e !@d X m @f m Á@f X m@e!þ@C md @d m :e !@d Y m @f m Á@f Y m @e !þ@C m d @d m :e !@d Z m @f m Á@f Z m @e!ð15Þ3.3.Material parameters3D orthogonal C/C composites are composed by T300fiber yarns and carbon matrix.The fiber yarns can be regarded as unidi-rectional fiber-reinforced C/C composites and are assumed to be one transversely isotropic entity in each local material coordinate system.The mechanical properties of the fiber yarns can be calcu-lated using the properties of the component materials (fibers and matrix):E 1¼e E f 11þð1Àe ÞE mE 2¼E 3¼E m1Àffiffie p 1ÀE m =E f 22ðÞG 12¼G 13¼G m 1Àffip 1ÀG m =G f 12ðÞG 23¼G m1Àffip 1ÀG m =G f23ðÞl 12¼l 13¼e l f 12þð1Àe Þl m l 23¼E 222G 23À19>>>>>>>>>>>>=>>>>>>>>>>>>;ð16Þwhere e is the yarn pack factor,for the C/C composite studied in this paper,e =0.81.E f 11,E f 22are the Young’s elastic modulus of the fiberin the principal axis 1and 2,respectively.Axis 1is the longitudinal direction of the fiber yarns.G f 12,G f 23are the shear modulus of the fiber in the 1–2and 2–3plane,respectively.l f 12is the primary Pois-son’s ratio of the fiber,E m ,l m and G m represent the Young’s elastic modulus,Poisson’s ratio and shear modulus of the matrix,respec-tively.Materials parameters are listed in Table 1.It should be noted that the mechanical parameters of the carbon matrix and the T300fibers changed after the CVI process.In particular,strength of the fiber will had a greater decline.The tensile and com-pressive strength of the T300fiber yarns were tested with the values listed in Table 1.The elasticity modular of the carbon matrix was tested by a nanoindentor system,which developed by Fang’s research team from Peking University [28].In the carbon matrix modular tests,the experiments repeated 20times for statistical averaging.The val-ues in the 20measurements were 7.18,9.77,8.58,10.01,11.92,5.30,9.98,8.14,8.63,7.31,6.19,10.69,11.10,13.45,9.15,9.13,11.27,9.20,10.14and 10.06GPa;average value was 9.36GPa.Mate-rial parameters of the fiber/matrix interface are not very clear so far,in this study the Young’s elastic modulus and Poisson’s ratio of the inter-faces were assumed as same as the carbon matrix.G f is one of the key parameters which control the failure pro-gress of the fiber yarns,however,different values were recom-mended in reported articles.In this study,influences of G f on the mechanical properties of the C/C composite were investigated firstly.Based on the values reported in Refs.[29,30],five virtual specimens with different G f values (0.5,2.0,6.0,10.0,14.0)were constructed and numerical tested.Simulation results were com-pared with the experimental result,as illustrated in Fig.4.It was found that G f has influences on tensile strength and fracture strain of the C/C composite.When G f were 0.5,2.0,6.0,10.0and 14.0,ten-sile strengths of the specimens were 200.5,205.1,205.3,214.2and 214.8MPa.When G f were 0.5,2.0,6.0,the failure strains were 0.36%,0.43%and 0.57%correspondingly.When G f is bigger than 10.0,failure strains of the C/C specimens were bigger than 1.0%.So,by the simulation results,in the present study the value of G f was set to 6.0.Table 1Materials parameters.E 11(GPa)E 22(GPa)ˆ12G 12(GPa)G 23(GPa)F t (MPa)F c (MPa)S (MPa)G f (m )(N/mm)gT300fiber 230400.262414.389075650 6.00.001C matrix 9.360.338210050 1.00.001Interface9.360.3382100501.00.001Fig.4.Stress–strain curves of the C/C virtual specimens under different G f .4.Simulation results and discussionThe anisotropic damage model of thefiber yarns and the isotro-damage model of the matrix and the interface were carriedmaterial constitutive equations by User subroutine UMAT ABAQUS nonlinearfinite element codes.Static uniaxial tensile sim-ulations were carried out.In order to keep forces continuity and displacements compatibility of the opposite faces of the unit cell, periodic boundary conditions were imposed in the simulation. Because the opposite faces of the unit cell have the same geomet-rical features,the nodes on the faces were controlled in the same position to form the corresponding nodes in the process of meshing.The periodic BCs were imposed on the corresponding nodes by FORTRAN pre-compiler code,detailed in Ref.[26].The RVE model subjected to a constant displacement load in Y direction and the loading strain is1%.4.1.Effects of the void defectsIn order to investigate the void defects on the mechanical prop-erties and failure behaviors of the C/C composite,two RVE models of the C/C composite were numerical simulated.In one RVE model (FE_D),thefiber yarns,interface and matrix all had void defects with the void fractions are0.51%,1.94%and0.47%respectively. For the other RVE model(FE_Intact),no defect inside.The stress–strain curves of the C/C composite in the simulations and experi-ment are illustrated in Fig.5.By the experimental results,the elas-ticity modular of this C/C composite was58.4GPa.By the numerical simulations,for the intact model,the elasticity modular was56.6GPa;for the‘defected’model the modular was56.3GPa. In the view of modular,the simulation error of the two models were3.1%and3.6%compared with the experimental results.The difference between the two FE models was only0.53%,so,void defects have relatively limited effects on the elastic modular of the C/C composite.The uniaxial tensile strength of the C/C compos-ite was197.2MPa by the experiments.In the simulations,the ten-sile strengths were231.4MPa and205.3MPa corresponding to the intact model and the‘defected’model.It was about17.3%and4.1% difference compared with experimental results.It is clear that,theFig.5.Stress–strain curves of the C/C composite under uniaxial tension.Fig.6.Damage evolution infiber yarns,(a)RVE model with voids defects,(b)intact model.Part B71(2015)113–121yarns are corresponding to the three pictures‘o’,‘p’and‘q’in Fig.6. For the RVE model with defects,it was found that damages were firstly generated besides the defects.During the loading process, damages were growing in several sections in thefiber yarns.How-ever,for the intact model,damages were almost generated in one section in thefiber yarns.Damage evolution in carbon matrix and the interface zone are illustrated in Figs.7and8.From the simulation results,in all of the three zones,damages werefirstly generated in the‘defected’RVE model.For the‘defected’model,when e=0.27%damages appeared in the interface zone,while for the intact model the strain was0.33%.In the matrix zone,the strains in the two models were0.31%and0.33%,respectively,when damages appeared.In fiber yarns,the strains when damages appear for the two models were0.37%and0.44%.So,because of the internal defects,in load-ing progress damages will generate early inner the material.Fail-ure strain of the materials which with defects is comparatively small when compared with the materials without defects.4.2.Influence of void locationBy the l CT images,it is clear that voids and micro cracks exist in fiber yarns,carbon matrix and the interface zones.By statistical analysis for those defects,fraction of the voids in those three zones was calculated.To study the influence of void location on the mechanical properties of the C/C materials,threefinite elementFig.7.Damage evolution in carbon matrix,(a)model with voids defects,(b)intact model.Fig.8.Damage evolution in interface,(a)model with void defects,(b)intact model.models were constructed and numerically analyzed.In the three RVE models,one model has defects only in thefiber yarns(FE_DF) and another model has the defects only in carbon matrix(FE_DM), while the other one has defects only in the interface zone(FE_DI). Simulation results were compared with the experimental results. Stress–strain curves in the numerical simulations and experiments are illustrated in Fig.9.Tensile strength calculated by the simulations were208.5MPa, 229.7MPa and230.1MPa,corresponding to the threefinite ele-ment models:FE_DF,FE_DI and FE_DM.By the simulation results of thefinite element models FE_D and FE_Intact,as mentioned in above section,the tensile strengths were205.3MPa and 231.4MPa.It can give the conclusion that,defects infiber yarns has the biggest effects on the mechanical properties of the C/C composite.If thefiber yarns are perfect and defects only exist in carbon matrix and interfaces,void defects have limited influences on the mechanical properties of the C/C composites under the cur-rent void volume fractions.4.3.Influence of void volume fractionBy the statistical analysis in Section3.1,volume fractions of voids in thefiber yarns,matrix and the interface zones are0.51%, 0.47%and1.94%.Under this defect fraction,as calculated in Section,tensile strength of the C/C composite declined12.7%compared with the material which contains no defects.So,it is important and meaningful that if we can make sure about the mechanical behav-iors of C/C composites when we exactly know the void defect frac-tion.If so,it will be helpful for the performance evaluation of C/C composites and structures.To investigate the influence of the void defect fraction on the mechanical performance of the C/C composite,five RVE models were constructed and the defect fractions of thefiber yarns were 0.25%,0.5%,1.0%,2.0%and4.0%.In this study,void defect was assumed only exist infiber yarns.Because,as calculated in Section 4.2,voids in carbon matrix and interfaces zone had very little effects on the mechanical properties of the C/C composite.Uniaxial tension simulations were carried out and the stress–strain curves of thefive C/C virtual specimens are illustrated in Fig.10.From the simulation results,it is clear that as the defect fraction increased tensile strength of the C/C composite decreased.For the intact FE model,the tensile strength was231.4MPa.For thefive FE models with voids defects,the tensile strengths were214.8MPa, 206.6MPa,197.1MPa,182.3MPa and152.8MPa.For the FE model under the defect density0.25%,tensile strength decreased7.2% compared with the intact model.So,if there exist defects inner the C/C materials,even if the volume fraction of the defects was small,it will has obvious effects on the mechanical performance of the composite,especially on the tensile strength.When the defect density was4.0%,tensile strength of the C/C virtual speci-men declined33.9%compared with the intact specimen.5.ConclusionUniaxial tensile properties and meso-structure of the3D orthogonal C/C composite were studied by experimental approaches.Manufacturing defects inner the C/C composite were investigated though a micron-resolution computed tomography (l CT)approach.From the l CT photos of the3-D orthogonal car-bon/carbon composite,it was found that voids and microcracks are two classic type of manufacture defects inner the C/C materials. Base on the statistical analysis of the l CT data,finite element mod-els of the C/C composite were constructed.According to a new pro-gressive damage model,failure behaviors and mechanical properties of the C/C composites were studied by ABAQUS code. Effects of the void defects on the mechanical performances of the C/C material were numerically investigated.From the numerical simulation results,manufacturing defects such as voids have great effects on the mechanical performance of the carbon/carbon com-posite,especially on the tensile strength.With0.51%void volume fraction,tensile strength of the carbon/carbon composite has 13.2%declines compared with the intact material.When void defects exist infiber yarns,even if the volume fraction of the defects is small it still will has great influence on tensile strength of the C/C composite.However,the defects which exist in carbon matrix and interface have limited effects on the mechanical prop-erties of the C/C materials.So,keep the continuity and improve the density of the carbonfiber yarns in C/C composite manufacture process is the key to improve the mechanical properties of the C/ C composites.AcknowledgementsFinancial support from the National Natural Science Founda-tions of China(Nos.11202007,11232001,11402132)and the Foundation of Beijing Jiaotong University(KCRC14002536)are gratefully acknowledged.Fig.9.Stress–strain curves of the C/C composite in experiment and simulations.10.Stress–strain curves of the virtual specimens with different void defectfraction.Part B71(2015)113–121。