基于连续介质损伤力学的复合材料层合板低速冲击损伤模型
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摘要
基于连续介质损伤力学(CDM)方法,建立了分析复合材料层合板低速冲击问题的三维数值模型。该模型考虑了层内损伤(纤维和基体损伤)、层间分层损伤和剪切非线性行为,采用最大应变失效准则预测纤维损伤的萌生,双线性损伤本构模型表征纤维损伤演化,基于物理失效机制的三维Puck准则判断基体损伤的起始,根据断裂面内等效应变建立混合模式下基体损伤扩展准则。横向基体拉伸强度和面内剪切强度采用基于断裂力学假设的就地强度(in-situ strength)。纤维和基体损伤本构关系中引入单元特征长度,有效降低模型对网格密度的依赖性。层间分层损伤情况由内聚力单元(cohesive element)预测,以二次应力准则为分层损伤的起始准则,B-K准则表征分层损伤演化。分别通过数值分析方法和试验研究方法对复合材料典型铺层层合板四级能量低速冲击下的冲击损伤和冲击响应规律进行分析,数值计算和试验测量的接触力-时间曲线、分层损伤的形状和面积较好吻合,表明该模型能够准确地预测层合板低速冲击损伤和冲击响应。
A novel three-dimensional composite damage model based on continuum damage mechanics(CDM)was developed to investigate low-velocity impact behavior of composite laminates.The maximum strain failure criterion was used to predict the initiation of fiber damage and the fiber damage revolution was evaluated by a bi-linear damage constitutive relation.A physically-based failure theory and three dimensional Puck criterion was employed to capture the onset of matrix damage and the damage evolution was determined by the effective strain on the fracture plane under the particular fracture angle.The in-situ strength of transverse tensile and in-plane shear depended on the assumption of fracture mechanics.The mesh dependency was alleviated effectively by introducing the characteristic length of element in the constitutive model of fiber and matrix damage.The interlaminar delamination damage was simulated by the cohesive element.Quadratic stress criterion and B-K power law was adopted to confirm the damage initiation and damage revolution for the interface element respectively.The impact damage and impact responses of composite laminates under four levels of impact energy were studied by experimental and numerical method.Theagreement between the simulation results and experimental results about impact-force curves,delamination shape and size shows that the finite element analysis model can effectively predict the impact responses and impact damage.
A novel three-dimensional composite damage model based on continuum damage mechanics(CDM)was developed to investigate low-velocity impact behavior of composite laminates.The maximum strain failure criterion was used to predict the initiation of fiber damage and the fiber damage revolution was evaluated by a bi-linear damage constitutive relation.A physically-based failure theory and three dimensional Puck criterion was employed to capture the onset of matrix damage and the damage evolution was determined by the effective strain on the fracture plane under the particular fracture angle.The in-situ strength of transverse tensile and in-plane shear depended on the assumption of fracture mechanics.The mesh dependency was alleviated effectively by introducing the characteristic length of element in the constitutive model of fiber and matrix damage.The interlaminar delamination damage was simulated by the cohesive element.Quadratic stress criterion and B-K power law was adopted to confirm the damage initiation and damage revolution for the interface element respectively.The impact damage and impact responses of composite laminates under four levels of impact energy were studied by experimental and numerical method.Theagreement between the simulation results and experimental results about impact-force curves,delamination shape and size shows that the finite element analysis model can effectively predict the impact responses and impact damage.
引文
[1]沈真,陈普会,刘俊石,等.含缺陷复合材料层压板的压缩破坏机理[J].航空学报,1991,12(3):105-113.SHEN Z,CHEN P H,LIU J S,et al.Experimental study on the compressive failure mechanisms of damaged composite laminates[J].Acta Aeronautica et Astronautica Sinica,1991,12(3):105-113(in Chinese).
[2]张子龙,程小全,益小苏.复合材料冲击损伤及冲击后压缩强度的等效实验方法[J].实验力学,2001,16(3):313-319.ZHANG Z L,CHENG X Q,YI X S.An Effective Test method for characterization of impact damage and gaining the compression properties after impact of composite laminates[J].Journal of Experimental Mechanics,2001,16(3):313-319(in Chinese).
[3]程小全,张子龙,吴学仁.小尺寸试件层合板低速冲击后的剩余压缩强度[J].复合材料学报,2002,19(6):8-12.CHENG X Q,ZHANG Z L,WU X R.Post-impact compressive strength of small composite laminate specimens[J].Acta Materiae Compositae Sinica,2002,19(6):8-12(in Chinese).
[4]CHOI H Y,WU H Y,CHANG F K.Effect of laminate configuration and impactor’s mass on the initial impact damage of graphite/epoxy composite plates due to line-loading impact[J].Journal of Composite Materials,1992,26(6):804-827.
[5]CHOI H Y,DOWNS R J,CHANG F K.A new approach toward understanding damage mechanisms and mechanics of laminated composite due to low-velocity impact part I:Experiments[J].Journal of Composite Materials,1991,25(8):992-1011.
[6]MOURA M D,MARQUES A T.Prediction of low velocity impact damage in carbon-epoxy laminates[J].Composites Part A:Applied Science and Manufacturing,2002,33(3):361-368.
[7]MOURA M F S F D,GONALVES J P M.Modelling the interaction between matrix cracking and delamination in carbon-epoxy laminates under low velocity impact[J].Composites Science&Technology,2004,64(7-8):1021-1027.
[8]TITA V,CARVALHO J D,VANDEPITTE D.Failure analysis of low velocity impact on thin composite laminates:Experimental and numerical approaches[J].Composite Structures,2008,83(4):413-428.
[9]KACHANOV L M.Introduction to continuum damage mechanics[M].Boston:Marinive Nijhoff,1986.
[10]LEMAITRE J,CHABOCHE J L.Mechanics of solid materials[M].Cambridge:Cambridge University Press,1990.
[11]LOPES C S,CAMANHO P P,GURDAL Z,et al.Lowvelocity impact damage on dispersed stacking sequence laminates part II:Numerical simulations[J].Composite Science and Technology,2009,69(7-8):937-947.
[12]PUCK A,SCHRMANN H.Failure analysis of FRP laminates by means of physically based phenomenological models[J].Composites Science&Technology,2002,62(12-13):1633-1662.
[13]FAGGIANI A,FALZON B G.Predicting low-velocity impact damage on a stiffened composite panel[J].Composites Part A:Applied Science and Manufacturing,2010,41(6):737-749.
[14]FALZON B G,APRUZZESE P.Numerical analysis of intralaminar failure mechanisms in composite structures part I:FE implementation[J].Composite Structures,2011,93(2):1039-1046.
[15]FALZON B G,APRUZZESE P.Numerical analysis of intralaminar failure mechanisms in composite structures part II:Applications[J].Composite Structures,2011,93(2):1047-1053.
[16]LONG S,YAO X,ZHANG X.Delamination prediction in composite laminates under low-velocity impact[J].Composite Structures,2015,132:290-298.
[17]BATRA R C,GOPINATH G,ZHENG J Q.Damage and failure in low energy impact of fiber-reinforced polymeric composite laminates[J].Composite Structures,2012,94(2):540-547.
[18]TAN W,FALZON B G,CHIU L N S,et al.Predicting low velocity impact damage and compression-after-impact(CAI)behaviour of composite laminates[J].Composites Part A:Applied Science and Manufacturing,2015,71:212-226.
[19]ABIR M R,TAY T E,RIDHA M,et al.Modelling damage growth in composites subjected to impact and compression after impact[J].Composite Structures,2017,168:13-25.
[20]谭建设,张晓晶,张俊琪,等.复合材料层合板低速冲击的接触力和能量响应仿真[J].复合材料学报,2014,31(4):970-980.TAN J S,ZHANG X J,ZHANG J Q,et al.Simulation of impact force and energy response of composite laminate subjected to low velocity impact[J].Acta Materiae Compositae Sinica,2014,31(4):970-980(in Chinese).
[21]DONADON M V,IANNUCCI L,FALZON B G,et al.A progressive failure model for composite laminates subjected to low velocity impact damage[J].Computers&Structures,2008,86(11-12):1232-1252.
[22]HE W,GUAN Z,LI X,et al.Prediction of permanent indentation due to impact on laminated composites based on an elasto-plastic model incorporating fiber failure[J].Composite Structures,2013,96(4):232-242.
[23]李念,陈普会.复合材料层合板低速冲击损伤分析的连续介质损伤力学模型[J].力学学报,2015,47(3):458-470.LI N,CHEN P H.Continuum damage mechanics model for low-velocity impact damage analysis of composite laminates[J].Chinese Journal of Theoretical and Applied Mechanics,2015,47(3):458-470(in Chinese).
[24]刘向民,姚卫星,陈方.复合材料层合板结构冲击损伤数值模拟的损伤力学模型[J].航空学报,2016,37(10):3054-3063.LIU X M,YAO W X,CHEN F.Damage mechanics model for simulating impact responses of composite laminated structures[J].Acta Aeronautica et Astronauica Sinica,2016,37(10):3054-3063(in Chinese).
[25]SHI Y,SWAIT T,SOUTIS C.Modelling damage evolution in composite laminates subjected to low velocity impact[J].Composite Structures,2012,94(9):2902-2913.
[26]SHI Y,PINNA C,SOUTIS C.Modelling impact damage in composite laminates:A simulation of intra-and inter-laminar cracking[J].Composite Structures,2014,114(1):10-19.
[27]LONGO G.Models and methods to simulate low-energy impact damage on composite aerospace structures[D].Toscana:University of Pisa,2011.
[28]FENG D,AYMERICH F.Finite element modelling of damage induced by low-velocity impact on composite laminates[J].Composite Structures,2014,108(1):161-171.
[29]FENG D,AYMERICH F.Damage prediction in composite sandwich panels subjected to low-velocity impact[J].Composites Part A:Applied Science&Manufacturing,2013,52:12-22.
[30]FANTERIA D,LONGO G,PANETTIERI E.A non-linear shear damage model to reproduce permanent indentation caused by impacts in composite laminates[J].Composite Structures,2014,111:111-121.
[31]LI Z,KHENNANE A,HAZELL P J,et al.Impact behaviour of pultruded GFRP composites under low-velocity impact loading[J].Composite Structures,2017,168:360-371.
[32]ABISSET E,DAGHIA F,SUN X C,et al.Interaction of inter-and intralaminar damage in scaled quasi-static indentation tests part 1:Experiments[J].Composite Structures,2016,136:712-726.
[33]SUN X C,WISNOM M R,HALLETT S R.Interaction of inter-and intralaminar damage in scaled quasi-static indentation tests part 2:Numerical simulation[J].Composite Structures,2016,136:727-742.
[34]ASTM International.Standard test method for measuring the damage resistance of a fiber-reinforced polymer matrix composite to a drop-weight impact event:ASTM D7136M—15[S].West Conshohocken:ASTM International,2015.
[35]PAEPEGEM W V,BAERE I D,LAMKANFI E,et al.Monitoring quasi-static and cyclic fatigue damage in fibre-reinforced plastics by Poisson’s ratio evolution[J].International Journal of Fatigue,2010,32(1):184-196.
[36]HAHN H T,TSAI S W.Nonlinear elastic behavior of unidirectional composite laminae[J].Journal of Composite Materials,1973,7(1):102-118.
[37]KNOPS M.Analysis of failure in fiber polymer laminates[M].Berlin:Springer,2008.
[38]DVORAK G J,LAWS N.Analysis of progressive matrix cracking in composite laminates II:First ply failure[J].Journal of Composite Materials,1987,21(4):309-329.
[39]CAMANHO P P,DVILA C G,PINHO S T,et al.Prediction of in situ strengths and matrix cracking in composites under transverse tension and in-plane shear[J].Composites Part A:Applied Science&Manufacturing,2006,37(2):165-176.
[40]WIEGAND J,PETRINIC N,ELLIOTT B.An algorithm for determination of the fracture angle for the three-dimensional Puck matrix failure criterion for UD composites[J].Composites Science&Technology,2008,68(12):2511-2517.
[41]SCHIRMAIER F J,WEILAND J,KRGER L,et al.A new efficient and reliable algorithm to determine the fracture angle for Puck’s 3D matrix failure criterion for UD composites[J].Composites Science&Technology,2014,100(3):19-25.
[42]BENZEGGAGH M L,KENANE M.Measurement of mixedmode delamination fracture toughness of unidirectional glass/epoxy composites with mixed-mode bending apparatus[J].Composites Science&Technology,1996,56(4):439-449.
[2]张子龙,程小全,益小苏.复合材料冲击损伤及冲击后压缩强度的等效实验方法[J].实验力学,2001,16(3):313-319.ZHANG Z L,CHENG X Q,YI X S.An Effective Test method for characterization of impact damage and gaining the compression properties after impact of composite laminates[J].Journal of Experimental Mechanics,2001,16(3):313-319(in Chinese).
[3]程小全,张子龙,吴学仁.小尺寸试件层合板低速冲击后的剩余压缩强度[J].复合材料学报,2002,19(6):8-12.CHENG X Q,ZHANG Z L,WU X R.Post-impact compressive strength of small composite laminate specimens[J].Acta Materiae Compositae Sinica,2002,19(6):8-12(in Chinese).
[4]CHOI H Y,WU H Y,CHANG F K.Effect of laminate configuration and impactor’s mass on the initial impact damage of graphite/epoxy composite plates due to line-loading impact[J].Journal of Composite Materials,1992,26(6):804-827.
[5]CHOI H Y,DOWNS R J,CHANG F K.A new approach toward understanding damage mechanisms and mechanics of laminated composite due to low-velocity impact part I:Experiments[J].Journal of Composite Materials,1991,25(8):992-1011.
[6]MOURA M D,MARQUES A T.Prediction of low velocity impact damage in carbon-epoxy laminates[J].Composites Part A:Applied Science and Manufacturing,2002,33(3):361-368.
[7]MOURA M F S F D,GONALVES J P M.Modelling the interaction between matrix cracking and delamination in carbon-epoxy laminates under low velocity impact[J].Composites Science&Technology,2004,64(7-8):1021-1027.
[8]TITA V,CARVALHO J D,VANDEPITTE D.Failure analysis of low velocity impact on thin composite laminates:Experimental and numerical approaches[J].Composite Structures,2008,83(4):413-428.
[9]KACHANOV L M.Introduction to continuum damage mechanics[M].Boston:Marinive Nijhoff,1986.
[10]LEMAITRE J,CHABOCHE J L.Mechanics of solid materials[M].Cambridge:Cambridge University Press,1990.
[11]LOPES C S,CAMANHO P P,GURDAL Z,et al.Lowvelocity impact damage on dispersed stacking sequence laminates part II:Numerical simulations[J].Composite Science and Technology,2009,69(7-8):937-947.
[12]PUCK A,SCHRMANN H.Failure analysis of FRP laminates by means of physically based phenomenological models[J].Composites Science&Technology,2002,62(12-13):1633-1662.
[13]FAGGIANI A,FALZON B G.Predicting low-velocity impact damage on a stiffened composite panel[J].Composites Part A:Applied Science and Manufacturing,2010,41(6):737-749.
[14]FALZON B G,APRUZZESE P.Numerical analysis of intralaminar failure mechanisms in composite structures part I:FE implementation[J].Composite Structures,2011,93(2):1039-1046.
[15]FALZON B G,APRUZZESE P.Numerical analysis of intralaminar failure mechanisms in composite structures part II:Applications[J].Composite Structures,2011,93(2):1047-1053.
[16]LONG S,YAO X,ZHANG X.Delamination prediction in composite laminates under low-velocity impact[J].Composite Structures,2015,132:290-298.
[17]BATRA R C,GOPINATH G,ZHENG J Q.Damage and failure in low energy impact of fiber-reinforced polymeric composite laminates[J].Composite Structures,2012,94(2):540-547.
[18]TAN W,FALZON B G,CHIU L N S,et al.Predicting low velocity impact damage and compression-after-impact(CAI)behaviour of composite laminates[J].Composites Part A:Applied Science and Manufacturing,2015,71:212-226.
[19]ABIR M R,TAY T E,RIDHA M,et al.Modelling damage growth in composites subjected to impact and compression after impact[J].Composite Structures,2017,168:13-25.
[20]谭建设,张晓晶,张俊琪,等.复合材料层合板低速冲击的接触力和能量响应仿真[J].复合材料学报,2014,31(4):970-980.TAN J S,ZHANG X J,ZHANG J Q,et al.Simulation of impact force and energy response of composite laminate subjected to low velocity impact[J].Acta Materiae Compositae Sinica,2014,31(4):970-980(in Chinese).
[21]DONADON M V,IANNUCCI L,FALZON B G,et al.A progressive failure model for composite laminates subjected to low velocity impact damage[J].Computers&Structures,2008,86(11-12):1232-1252.
[22]HE W,GUAN Z,LI X,et al.Prediction of permanent indentation due to impact on laminated composites based on an elasto-plastic model incorporating fiber failure[J].Composite Structures,2013,96(4):232-242.
[23]李念,陈普会.复合材料层合板低速冲击损伤分析的连续介质损伤力学模型[J].力学学报,2015,47(3):458-470.LI N,CHEN P H.Continuum damage mechanics model for low-velocity impact damage analysis of composite laminates[J].Chinese Journal of Theoretical and Applied Mechanics,2015,47(3):458-470(in Chinese).
[24]刘向民,姚卫星,陈方.复合材料层合板结构冲击损伤数值模拟的损伤力学模型[J].航空学报,2016,37(10):3054-3063.LIU X M,YAO W X,CHEN F.Damage mechanics model for simulating impact responses of composite laminated structures[J].Acta Aeronautica et Astronauica Sinica,2016,37(10):3054-3063(in Chinese).
[25]SHI Y,SWAIT T,SOUTIS C.Modelling damage evolution in composite laminates subjected to low velocity impact[J].Composite Structures,2012,94(9):2902-2913.
[26]SHI Y,PINNA C,SOUTIS C.Modelling impact damage in composite laminates:A simulation of intra-and inter-laminar cracking[J].Composite Structures,2014,114(1):10-19.
[27]LONGO G.Models and methods to simulate low-energy impact damage on composite aerospace structures[D].Toscana:University of Pisa,2011.
[28]FENG D,AYMERICH F.Finite element modelling of damage induced by low-velocity impact on composite laminates[J].Composite Structures,2014,108(1):161-171.
[29]FENG D,AYMERICH F.Damage prediction in composite sandwich panels subjected to low-velocity impact[J].Composites Part A:Applied Science&Manufacturing,2013,52:12-22.
[30]FANTERIA D,LONGO G,PANETTIERI E.A non-linear shear damage model to reproduce permanent indentation caused by impacts in composite laminates[J].Composite Structures,2014,111:111-121.
[31]LI Z,KHENNANE A,HAZELL P J,et al.Impact behaviour of pultruded GFRP composites under low-velocity impact loading[J].Composite Structures,2017,168:360-371.
[32]ABISSET E,DAGHIA F,SUN X C,et al.Interaction of inter-and intralaminar damage in scaled quasi-static indentation tests part 1:Experiments[J].Composite Structures,2016,136:712-726.
[33]SUN X C,WISNOM M R,HALLETT S R.Interaction of inter-and intralaminar damage in scaled quasi-static indentation tests part 2:Numerical simulation[J].Composite Structures,2016,136:727-742.
[34]ASTM International.Standard test method for measuring the damage resistance of a fiber-reinforced polymer matrix composite to a drop-weight impact event:ASTM D7136M—15[S].West Conshohocken:ASTM International,2015.
[35]PAEPEGEM W V,BAERE I D,LAMKANFI E,et al.Monitoring quasi-static and cyclic fatigue damage in fibre-reinforced plastics by Poisson’s ratio evolution[J].International Journal of Fatigue,2010,32(1):184-196.
[36]HAHN H T,TSAI S W.Nonlinear elastic behavior of unidirectional composite laminae[J].Journal of Composite Materials,1973,7(1):102-118.
[37]KNOPS M.Analysis of failure in fiber polymer laminates[M].Berlin:Springer,2008.
[38]DVORAK G J,LAWS N.Analysis of progressive matrix cracking in composite laminates II:First ply failure[J].Journal of Composite Materials,1987,21(4):309-329.
[39]CAMANHO P P,DVILA C G,PINHO S T,et al.Prediction of in situ strengths and matrix cracking in composites under transverse tension and in-plane shear[J].Composites Part A:Applied Science&Manufacturing,2006,37(2):165-176.
[40]WIEGAND J,PETRINIC N,ELLIOTT B.An algorithm for determination of the fracture angle for the three-dimensional Puck matrix failure criterion for UD composites[J].Composites Science&Technology,2008,68(12):2511-2517.
[41]SCHIRMAIER F J,WEILAND J,KRGER L,et al.A new efficient and reliable algorithm to determine the fracture angle for Puck’s 3D matrix failure criterion for UD composites[J].Composites Science&Technology,2014,100(3):19-25.
[42]BENZEGGAGH M L,KENANE M.Measurement of mixedmode delamination fracture toughness of unidirectional glass/epoxy composites with mixed-mode bending apparatus[J].Composites Science&Technology,1996,56(4):439-449.