基于断裂韧性预报复合材料层合板的开孔拉伸强度
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摘要
开孔层合板的强度预报往往取决于孔边的临界长度,它不仅与材料性能,而且与铺层、孔径都有关。本文基于线弹性断裂力学,提出了一种预报对称铺层层合板开孔拉伸强度的新方法,只需提供正交层合板的断裂韧性和无缺口层合板的拉伸强度,显著降低对实验数据的依赖性。首先,将临界长度表作为层合板断裂韧性和无缺口拉伸强度的函数,再通过正交层合板[90/0]_(8s)的紧凑拉伸试验和虚拟裂纹闭合技术,确定出0°层断裂韧性,进而计算得到任意对称铺层层合板的断裂韧性。本文测试了T300/7901层合板[0/±45/90]_(2s)和[0/±30/±60/90]_s的开孔拉伸强度,孔径分别为3mm、6mm和9mm。理论预报结果与试验值吻合较好,最大误差为15.2%,满足工程应用需求。
Strength prediction of a laminate with a hole generally depends on a characteristic length of the hole which is not only related to the properties of its constituent materials but also depends on the laminate lay-up and the hole diameter.In this paper,a new method based on linear elastic fracture mechanics was proposed to predict the tensile strength of a symmetric laminate with hole,which only needs the fracture toughness of a cross-ply composite plate and the tensile strength of the un-notched laminate,and which can significantly reduce the requirement on composite data.In this method,the characteristic length was first expressed as a function of the fracture toughness and the un-notched tensile strength of the laminate.Then,the fracture toughness of a 0°ply(i.e.unidirectional laminate)was determined by a compact tension test on the cross-ply laminate[90/0]_(8s)and the virtual crack closure technique.Further,the fracture toughness of laminates with arbitrary symmetric lay-up angles can be calculated from that of the 0°ply.Tensile tests on T300/7901 notched laminates with lay-ups of[0/±45/90]_(2s)and[0/±30/±60/90]_s have been done in this work.Three kinds of hole diameters,i.e.3 mm,6 mm and 9 mm,were assigned for each of the laminates.The theoretical predictions for the tensile strengths are in good agreement with the measured values.The maximum difference is 15.2%,which is acceptable in engineering applications.
Strength prediction of a laminate with a hole generally depends on a characteristic length of the hole which is not only related to the properties of its constituent materials but also depends on the laminate lay-up and the hole diameter.In this paper,a new method based on linear elastic fracture mechanics was proposed to predict the tensile strength of a symmetric laminate with hole,which only needs the fracture toughness of a cross-ply composite plate and the tensile strength of the un-notched laminate,and which can significantly reduce the requirement on composite data.In this method,the characteristic length was first expressed as a function of the fracture toughness and the un-notched tensile strength of the laminate.Then,the fracture toughness of a 0°ply(i.e.unidirectional laminate)was determined by a compact tension test on the cross-ply laminate[90/0]_(8s)and the virtual crack closure technique.Further,the fracture toughness of laminates with arbitrary symmetric lay-up angles can be calculated from that of the 0°ply.Tensile tests on T300/7901 notched laminates with lay-ups of[0/±45/90]_(2s)and[0/±30/±60/90]_s have been done in this work.Three kinds of hole diameters,i.e.3 mm,6 mm and 9 mm,were assigned for each of the laminates.The theoretical predictions for the tensile strengths are in good agreement with the measured values.The maximum difference is 15.2%,which is acceptable in engineering applications.
引文
[1]WHITNEY J M,NUISMER R J.Stress fracture criteria for laminated composites containing stress concentrations[J].Journal of Composite Materials,1974,8(3):253-265.
[2]NUISMER R J,WHITNEY J M.Uniaxial failure of composite laminates containing stress concentrations[J].Fracture Mechanics of Composites,1975:117-142.
[3]KIM J K,KIM D S,TAKEDA N.Notched strength and fracture criterion on fabric composite plates containing a circular hole[J].Journal of Composite Materials,1995,29(7):982-998.
[4]SRIVASTAVA V K,KUMAR D.Prediction of notched strength of laminated fibre composites under tensile loading conditions[J].Journal of Composite Materials,2002,36(9):1121-1133.
[5]HWAN C L,TSAI K H,CHEN W L,et al.Strength prediction of braided composite plates with a center hole[J].Journal of Composite Materials,2011,45(19):1991-2002.
[6]PIPES R B,WETHERHOLD R C,Macroscopic fracture of fibrous composites[J].Materials Science and Engineering,1980,45(3):247-253.
[7]ERIKSSON I,ARONSSON C G.Strength of tensile loaded graphite/epoxy laminates containing cracks,open and filled holes[J].Journal of Composite Materials,1990,24(5):456-482.
[8]WADDOUPS M E,EISENMANN J R,KAMINSKI B E.Macroscopic fracture mechanics of advanced composite materials[J].Journal of Composite Materials,1971,5(4):446-454.
[9]CAMANHO P P,ERCIN G H,CATALANOTTI G.A finite fracture mechanics model for the prediction of the openhole strength of composite laminates[J].Composites Part A,2012,43(8):1219-1225.
[10]LEGUILLON D.Strength or toughness?a criterion for crack onset at a notch[J].European Journal of Mechanics A:Solids,2002,21(1):61-72.
[11]TAN S C.A progressive failure model for composite laminates containing openings[J].Journal of Composite Materials,1991,25(5):556-577.
[12]CHANG K Y,SHENG L,CHANG F K.Damage tolerance of laminated composites containing an open hole and subjected to tensile loadings[J].Journal of Composite Materials,1991,25(3):2-43.
[13]MAA R H,CHENG J H.A CDM-based failure model for predicting strength of notched composite laminates[J].Composites Part B:Engineering,2002,33(6):479-489.
[14]CAMANHO P P,MAIMI P,DAVILA C G.Prediction of size effects in notched laminates using continuum damage mechanics[J].Composites Science and Technology,2007,67(13):2715-2727.
[15]BOWIE O L.Analysis of an infinite plate containing radial cracks at the boundary of an internal circular hole[J].Studies in Applied Mathematics,1956,35(1-4):60-71.
[16]PARIS P C,SIH G C,Stress analysis of cracks.in:fracture toughness testing and its applications[S]ASTM STP 381.Philadelphia:American Society for Testing and Materials.1965,30-81.
[17]TADA H,PARIS P C,IRWIN G R.The stress analysis of crack handbook[M].Hellertown,Pensylvania:Del Research Corporation,1973.
[18]TAN S C.Finite-width correction factors for anisotropic plate containing a central opening[J].Journal of Composite Materials,1988,22(11):1080-1097.
[19]RYBICKI E F,KANNINEN M F.A finite element calculation of stress intensity factors by a modified crack closure integral[J].Engineering Fracture Mechanics,1977,9(4):931-938.
[20]KRUEGER R.Virtual crack closure technique:history,approach and applications[J].Applied Mechanics Reviews,2002,57(1):109-143.
[21]PINHO S T,ROBINSON P,IANNUCCI L.Fracture toughness of the tensile and compressive fibre failure modes in laminated composites[J].Composites Science &Technology,2006,66(13):2069-2079.
[22]RAJU I S.Calculation of strain energy release rates with higher order singularity finite elements[J].Engineering Fracture Mechanics,1987,28(3):251-74.
[23]JOSE S,KUMAR R R,JANA M K,et al.Intralaminar fracture toughness of a cross-ply laminate and its constituent sub-laminates[J].Composites Science &Technology,2001,61(8):1115-1122.
[24]American Society for Testing and Materials International.Standard test method for plane-strain fracture toughness of metallic materials:ASTM E399—90[S].US:ASTM International,1993.
[25]HUANG Zhengming.Simulation of the mechanical properties of fibrous composites by the bridging micromechanics model[J].Composites Part A:Applied Science &Manufacturing,2001,32(2):143-172.
[26]HUANG Zhengming,ZHOU Yexin.Strength of fibrous composites[M].Zhejiang:Zhejiang University Press,2011:149-152.
[27]CAMANHO P P,CATALANTTI G.On the relation between the model I fracture toughness of a composite laminate and that of a 0°ply:Analytical model and experimental validation[J].Engineering Fracture Mechanics,2011,78(13):2535-2546.
[28]VAIDYA R S,SUN C T.Fracture criterion for notched thin composite laminates[J].AIAA Journal,1997,35(2):311-316.
[29]BAO G,HO S,SUO Z,et al.The role of material orthotropy in fracture specimens for composites[J].International Journal of Solids and Structures,1992,29(9):1105-1116.
[30]KAGEYAMA K.Fracture mechanics of notched carbon/epoxy laminates.In:Friedrich K,editor.Application of fracture mechanics to composite materials[M].Elsevier Science Publishers B.V,1989.
[31]American Society for Testing and Materials International.Standard test method for tensile properties of polymer matrix composite materials:ASTM D3039/D3039 M-00[S].West Conshohocken:ASTM International,2000.
[32]American Society for Testing and Materials International.Standard test method for open-hole tensile strength of polymer matrix composite laminates:ASTM D5766/D5766M-02a[S].West Conshohocken:ASTM International,2002.
[2]NUISMER R J,WHITNEY J M.Uniaxial failure of composite laminates containing stress concentrations[J].Fracture Mechanics of Composites,1975:117-142.
[3]KIM J K,KIM D S,TAKEDA N.Notched strength and fracture criterion on fabric composite plates containing a circular hole[J].Journal of Composite Materials,1995,29(7):982-998.
[4]SRIVASTAVA V K,KUMAR D.Prediction of notched strength of laminated fibre composites under tensile loading conditions[J].Journal of Composite Materials,2002,36(9):1121-1133.
[5]HWAN C L,TSAI K H,CHEN W L,et al.Strength prediction of braided composite plates with a center hole[J].Journal of Composite Materials,2011,45(19):1991-2002.
[6]PIPES R B,WETHERHOLD R C,Macroscopic fracture of fibrous composites[J].Materials Science and Engineering,1980,45(3):247-253.
[7]ERIKSSON I,ARONSSON C G.Strength of tensile loaded graphite/epoxy laminates containing cracks,open and filled holes[J].Journal of Composite Materials,1990,24(5):456-482.
[8]WADDOUPS M E,EISENMANN J R,KAMINSKI B E.Macroscopic fracture mechanics of advanced composite materials[J].Journal of Composite Materials,1971,5(4):446-454.
[9]CAMANHO P P,ERCIN G H,CATALANOTTI G.A finite fracture mechanics model for the prediction of the openhole strength of composite laminates[J].Composites Part A,2012,43(8):1219-1225.
[10]LEGUILLON D.Strength or toughness?a criterion for crack onset at a notch[J].European Journal of Mechanics A:Solids,2002,21(1):61-72.
[11]TAN S C.A progressive failure model for composite laminates containing openings[J].Journal of Composite Materials,1991,25(5):556-577.
[12]CHANG K Y,SHENG L,CHANG F K.Damage tolerance of laminated composites containing an open hole and subjected to tensile loadings[J].Journal of Composite Materials,1991,25(3):2-43.
[13]MAA R H,CHENG J H.A CDM-based failure model for predicting strength of notched composite laminates[J].Composites Part B:Engineering,2002,33(6):479-489.
[14]CAMANHO P P,MAIMI P,DAVILA C G.Prediction of size effects in notched laminates using continuum damage mechanics[J].Composites Science and Technology,2007,67(13):2715-2727.
[15]BOWIE O L.Analysis of an infinite plate containing radial cracks at the boundary of an internal circular hole[J].Studies in Applied Mathematics,1956,35(1-4):60-71.
[16]PARIS P C,SIH G C,Stress analysis of cracks.in:fracture toughness testing and its applications[S]ASTM STP 381.Philadelphia:American Society for Testing and Materials.1965,30-81.
[17]TADA H,PARIS P C,IRWIN G R.The stress analysis of crack handbook[M].Hellertown,Pensylvania:Del Research Corporation,1973.
[18]TAN S C.Finite-width correction factors for anisotropic plate containing a central opening[J].Journal of Composite Materials,1988,22(11):1080-1097.
[19]RYBICKI E F,KANNINEN M F.A finite element calculation of stress intensity factors by a modified crack closure integral[J].Engineering Fracture Mechanics,1977,9(4):931-938.
[20]KRUEGER R.Virtual crack closure technique:history,approach and applications[J].Applied Mechanics Reviews,2002,57(1):109-143.
[21]PINHO S T,ROBINSON P,IANNUCCI L.Fracture toughness of the tensile and compressive fibre failure modes in laminated composites[J].Composites Science &Technology,2006,66(13):2069-2079.
[22]RAJU I S.Calculation of strain energy release rates with higher order singularity finite elements[J].Engineering Fracture Mechanics,1987,28(3):251-74.
[23]JOSE S,KUMAR R R,JANA M K,et al.Intralaminar fracture toughness of a cross-ply laminate and its constituent sub-laminates[J].Composites Science &Technology,2001,61(8):1115-1122.
[24]American Society for Testing and Materials International.Standard test method for plane-strain fracture toughness of metallic materials:ASTM E399—90[S].US:ASTM International,1993.
[25]HUANG Zhengming.Simulation of the mechanical properties of fibrous composites by the bridging micromechanics model[J].Composites Part A:Applied Science &Manufacturing,2001,32(2):143-172.
[26]HUANG Zhengming,ZHOU Yexin.Strength of fibrous composites[M].Zhejiang:Zhejiang University Press,2011:149-152.
[27]CAMANHO P P,CATALANTTI G.On the relation between the model I fracture toughness of a composite laminate and that of a 0°ply:Analytical model and experimental validation[J].Engineering Fracture Mechanics,2011,78(13):2535-2546.
[28]VAIDYA R S,SUN C T.Fracture criterion for notched thin composite laminates[J].AIAA Journal,1997,35(2):311-316.
[29]BAO G,HO S,SUO Z,et al.The role of material orthotropy in fracture specimens for composites[J].International Journal of Solids and Structures,1992,29(9):1105-1116.
[30]KAGEYAMA K.Fracture mechanics of notched carbon/epoxy laminates.In:Friedrich K,editor.Application of fracture mechanics to composite materials[M].Elsevier Science Publishers B.V,1989.
[31]American Society for Testing and Materials International.Standard test method for tensile properties of polymer matrix composite materials:ASTM D3039/D3039 M-00[S].West Conshohocken:ASTM International,2000.
[32]American Society for Testing and Materials International.Standard test method for open-hole tensile strength of polymer matrix composite laminates:ASTM D5766/D5766M-02a[S].West Conshohocken:ASTM International,2002.
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