颗粒增强复合材料细观力学研究
|
摘要
颗粒增强复合材料在当今工程界得到越来越广泛的应用。随着增强颗粒尺寸的减小，复合材料的一系列宏观性能会发生显著的改变。深刻理解其内在的颗粒尺寸效应将对复合机理的认识和工艺设计起到重要作用。本论文着重开展以下研究工作：
(1)利用有限元方法研究非均匀界面相对复合材料有效剪切模量的影响。着重研究界面相厚度，界面性能变化规律，边界条件和颗粒体积含量对有效剪切模量的影响。
(2)基于Mori-Tanaka方法，提出一个可研究规则分布颗粒增强复合材料有效弹性性能的力学模型。在模型中，考虑粒子间相互作用及其特征分布，利用几何对称性求解应变格林函数，并通过引入双夹杂理论来描述界面相效应，从而得到等效弹性常量的显式表达，并与上一章的有限元数值结果对比，以验证该模型的准确性。
(3)从一个全新的角度来解释颗粒尺寸效应对聚合物基复合材料力学性能的影响。基于分子链网络理论，将颗粒看作分子链之间的缠结，类似聚合物分子链中的物理缠结或化学交联，从而提出一个可用于研究聚合物基复合材料颗粒尺寸效应的分析模型。
(4)基于Eshelby等效夹杂理论和Mori Tanaka方法，建立一个高弹性基复合材料的细观力学模型。该模型基于单一分子链模型建立，可分析纯橡胶材料和复合材料的力学特性，并通过与实验数据进行比较来验证模型的准确性。
(5)提出一个可描述颗粒增强复合材料的渐进式脱粘损伤、基体塑性及颗粒尺寸效应的本构模型。采用双夹杂模型将脆性界面相嵌入到增量损伤理论模型，用界面分离的能量平衡式来描述渐进式脱粘损伤。该模型可研究颗粒尺寸效应和界面性能对复合材料应力-应变关系的影响，并可解释界面相对复合材料力学性能的颗粒尺寸效应的影响。
(6)在增量损伤理论中考虑韧性界面的作用，研究颗粒尺寸对颗粒增强复合材料弹塑性损伤行为的影响，并应用场波动方法确定基体与界面的等效应力。该模型可研究渐进性脱粘损伤、颗粒尺寸效应及界面相性能对颗粒增强复合材料的有效应力-应变关系的影响。由于韧性界面相的存在，颗粒增强复合材料中应力传递和屈服起始变得更加复杂，则应用有限元方法研究韧性界面对应力传递和和屈服起始的影响。
The thesis is to interpret the particle size effect on the equivalent stiffness and plasticbehaviors of composites from different point of views. Based on the inherentmicrostructures of composites, some innovative methods are developed. The basicresearch contents are as follows.
(1) Numerical studies on the effective shear modulus of particle reinforced composites withan inhomogeneous interphase are systematically performed. The influences ofinterphase thickness, variation laws of interphase properties, boundary conditions andparticle volume fraction on the equivalent shear modulus are carefully investigated, andthe accuracy of the existing models is verified.
(2) A micro-mechanics model is developed to study the effective elastic properties ofcomposites reinforced by regularly distributed particles. Particle interaction anddistribution are simultaneously taken into account by using strain Green’s function,which is determined by utilizing the conditions of geometric symmetry. TheDouble-Inclusion configuration is introduced to describe the role of the interphase.The overall elastic properties are described by three independent elastic constantsexpressed in the explicit form.
(3) Particle size effect is attributed to the synergism mechanism between particles andthe host matrix. A molecular-chain-network based micromechanics model waspresented for exploring particle size effect on the effective modulus. In the presentmodel, particles are regarded as junctions among molecular chains, which areequivalent to the cross-links pre-existing in the polymer. At a certain particleconcentration, the smaller the particle size, the higher is the cross-link density in thecomposites, and the higher is the effective stiffness of the resulting composites.Therefore, particle size effect would be clearly demonstrated from a new point ofview, which is different from all the existing explanations.
(4) A micromechanics–based model is proposed for the finite strain deformation offilled elastomers based on generalized Eshelby’s tensor and Mori Tanaka’s method.The present formulation leads to a clear explanation of the constraint effect ofrubber–like matrix on the inclusions. Comparisons with experiments and other micromechanics models are conducted. It is observed that an improvement inpredictive capability for the composite with randomly dispersed particles wasachieved by the present method. Based on the latest experiment of single molecularchain, a compact network model is fatherly developed to reflect the microstructureeffect on the stress–strain relations of rubbery polymer and the resultingcomposites.
(5) An incremental damage model of PRC has been extended to three-phase compositesfor interpreting particle size effect. The interphase was perfectly incorporated as athird phase with the help of double-inclusion model. Progressive damage wascontrolled by a critical energy criterion. Based on the developed model, particle sizeeffect on the mechanical behaviors of composites was clearly interpreted from therole of the interphase, which is different from all the existing researches.
(6) A new micromechanics model of particulate reinforced composites was proposedto describe the evolution of debonding damage, matrix plasticity and particle sizeeffect on the deformation. A ductile interphase was involved to analyze thedependence of elastic plastic damage behavior on particle size. The equivalentstresses of the two constituents were determined by field fluctuation method.Furthermore, a unit cell (UC) based FEM was used to understand their evolutionand demonstrate the role of the interphase.
(1)利用有限元方法研究非均匀界面相对复合材料有效剪切模量的影响。着重研究界面相厚度，界面性能变化规律，边界条件和颗粒体积含量对有效剪切模量的影响。
(2)基于Mori-Tanaka方法，提出一个可研究规则分布颗粒增强复合材料有效弹性性能的力学模型。在模型中，考虑粒子间相互作用及其特征分布，利用几何对称性求解应变格林函数，并通过引入双夹杂理论来描述界面相效应，从而得到等效弹性常量的显式表达，并与上一章的有限元数值结果对比，以验证该模型的准确性。
(3)从一个全新的角度来解释颗粒尺寸效应对聚合物基复合材料力学性能的影响。基于分子链网络理论，将颗粒看作分子链之间的缠结，类似聚合物分子链中的物理缠结或化学交联，从而提出一个可用于研究聚合物基复合材料颗粒尺寸效应的分析模型。
(4)基于Eshelby等效夹杂理论和Mori Tanaka方法，建立一个高弹性基复合材料的细观力学模型。该模型基于单一分子链模型建立，可分析纯橡胶材料和复合材料的力学特性，并通过与实验数据进行比较来验证模型的准确性。
(5)提出一个可描述颗粒增强复合材料的渐进式脱粘损伤、基体塑性及颗粒尺寸效应的本构模型。采用双夹杂模型将脆性界面相嵌入到增量损伤理论模型，用界面分离的能量平衡式来描述渐进式脱粘损伤。该模型可研究颗粒尺寸效应和界面性能对复合材料应力-应变关系的影响，并可解释界面相对复合材料力学性能的颗粒尺寸效应的影响。
(6)在增量损伤理论中考虑韧性界面的作用，研究颗粒尺寸对颗粒增强复合材料弹塑性损伤行为的影响，并应用场波动方法确定基体与界面的等效应力。该模型可研究渐进性脱粘损伤、颗粒尺寸效应及界面相性能对颗粒增强复合材料的有效应力-应变关系的影响。由于韧性界面相的存在，颗粒增强复合材料中应力传递和屈服起始变得更加复杂，则应用有限元方法研究韧性界面对应力传递和和屈服起始的影响。
The thesis is to interpret the particle size effect on the equivalent stiffness and plasticbehaviors of composites from different point of views. Based on the inherentmicrostructures of composites, some innovative methods are developed. The basicresearch contents are as follows.
(1) Numerical studies on the effective shear modulus of particle reinforced composites withan inhomogeneous interphase are systematically performed. The influences ofinterphase thickness, variation laws of interphase properties, boundary conditions andparticle volume fraction on the equivalent shear modulus are carefully investigated, andthe accuracy of the existing models is verified.
(2) A micro-mechanics model is developed to study the effective elastic properties ofcomposites reinforced by regularly distributed particles. Particle interaction anddistribution are simultaneously taken into account by using strain Green’s function,which is determined by utilizing the conditions of geometric symmetry. TheDouble-Inclusion configuration is introduced to describe the role of the interphase.The overall elastic properties are described by three independent elastic constantsexpressed in the explicit form.
(3) Particle size effect is attributed to the synergism mechanism between particles andthe host matrix. A molecular-chain-network based micromechanics model waspresented for exploring particle size effect on the effective modulus. In the presentmodel, particles are regarded as junctions among molecular chains, which areequivalent to the cross-links pre-existing in the polymer. At a certain particleconcentration, the smaller the particle size, the higher is the cross-link density in thecomposites, and the higher is the effective stiffness of the resulting composites.Therefore, particle size effect would be clearly demonstrated from a new point ofview, which is different from all the existing explanations.
(4) A micromechanics–based model is proposed for the finite strain deformation offilled elastomers based on generalized Eshelby’s tensor and Mori Tanaka’s method.The present formulation leads to a clear explanation of the constraint effect ofrubber–like matrix on the inclusions. Comparisons with experiments and other micromechanics models are conducted. It is observed that an improvement inpredictive capability for the composite with randomly dispersed particles wasachieved by the present method. Based on the latest experiment of single molecularchain, a compact network model is fatherly developed to reflect the microstructureeffect on the stress–strain relations of rubbery polymer and the resultingcomposites.
(5) An incremental damage model of PRC has been extended to three-phase compositesfor interpreting particle size effect. The interphase was perfectly incorporated as athird phase with the help of double-inclusion model. Progressive damage wascontrolled by a critical energy criterion. Based on the developed model, particle sizeeffect on the mechanical behaviors of composites was clearly interpreted from therole of the interphase, which is different from all the existing researches.
(6) A new micromechanics model of particulate reinforced composites was proposedto describe the evolution of debonding damage, matrix plasticity and particle sizeeffect on the deformation. A ductile interphase was involved to analyze thedependence of elastic plastic damage behavior on particle size. The equivalentstresses of the two constituents were determined by field fluctuation method.Furthermore, a unit cell (UC) based FEM was used to understand their evolutionand demonstrate the role of the interphase.
引文
[1] B Maruyama. Promise and Progress in Aluminum Composites. Adwanced Materials Processes,1999,6:47~50.
[2]崔岩.碳化硅颗粒增强复合材料的航空航天应用[J].材料工程.2002,6：
[3]陈亚莉.美国F-22先进战斗机选材分析[R].航空信息研究报告，1995,7:15~16.
[4]丁立铭,饶勤,陈亚莉,任小华.F-22战斗机选材与制造技术[R].航空信息研究报告,1996,6:25~26.
[5] B M Daniel.2ndAnnual Aluminum Metal Matrix Composites Meeting,1997,75.
[6]李成功,傅恒志,于翘．航空航天材料[M].北京：国防工业出版社,2002:7.
[7] Geiger A L, Walker J A. The processing and properties of discontinuously reinforcedaluminum composites[J]．JOM,1991(8):8~15.
[8] A.C. Balazs, T. Emrick, T.P. Russell. Nanoparticle-polymer Composites: Where two smallworlds meet. Science2006,314:1107~1110.
[9] J. Jordan, K.I. Jacob, R. Tannenbaum, M.A. Sharaf, I. Jasiuk. Experimental trends in polymernanocomposites—a review. Mater Sci Eng A2005,393(1-2):1~11.
[10] L. Jiang, Y.C. Lam, K.C. Tam, T.H. Chua, G.W. Sim, L.S. Ang. Strengtheningacrylonitrile-butadiene-styrene (ABS) with nano-sized and micron-sized calcium carbonate.Polymer2005,46:243~252.
[11] P.H.T. Vollenberg, D. Heikens. Particle size dependence of the Young's modulus of filledpolymers:1. Preliminary experiments. Polymer1989,30:1656~1662.
[12] P.H.T. Vollenberg, J.W. Haan, L.J.M. van de Ven, D. Heikens. Particle size dependence of theYoung's modulus of filled polymers:2. Annealing and solid-state nuclear magnetic resonanceexperiments. Polymer1989,30:1663~1667.
[13] J. Cho, M.S. Joshi, C.T. Sun. Effect of inclusion size on mechanical properties of polymericcomposites with micro and nano particles. Compos Sci Technol2006,66:1941~1952.
[14] A. Adnan, C.T. Sun, H. Mahfuz. A molecular dynamics simulation study to investigate theeffect of filler size on elastic properties of polymer nanocomposites. Compos Sci Technol2007,67:348~356.
[15] G.M. Odegard, T.C. Clancy, T.S. Gates. Modeling of the mechanical properties ofnanoparticle/polymer composites. Polymer2005,46:553~562.
[16] S. Yu, S. Yang, M. Cho. Multi-scale modeling of cross-linked epoxy nanocomposites. Polymer2009,50:945~952.
[17] G.J. Papakonstantopoulos, K. Yoshimoto, M. Doxastakis, P.F. Nealey, J.J. Pablo. Localmechanical properties of polymeric nanocomposites. Phys Rev E2005,72:031801.
[18] K. Masenelli-Varlot, E. Reynaud, G. Vigier, J. Varlet. Mechanical Properties ofClay-Reinforced Polyamide. J Polym Sci B2002,40:272~283.
[19] E. Tadd, A. Zeno, M. Zubris, N. Dan, R. Tannenbaum. Adsorption and polymer film formationon metal nanoclusters. Macromolecules2003,36:6497~6502.
[20] S. Boutaleb, F. Za ri, A. Mesbah, M. Na t-Abdelaziz, J.M. Gloaguen, T. Boukharouba, J.M.Lefebvre. Micromechanics-based modelling of stiffness and yield stress for silica/polymernanocomposites. Int J Solids Struct2009,46:1716~1726.
[21] Y.P. Jiang, K. Tohgo, Y. Shimamura. A micro-mechanics model for composites reinforced byregularly distributed particles with an inhomogeneous interphase. Comput Mater Sci2009,46:507~515.
[22] H.T. Liu, L.Z. Sun. A micromechanics-based elastoplastic model for amorphous compositeswith nanoparticle interactions. ASME J Appl Mech2008,75:310091~3100910.
[23] P. Sharma, A. Dasgupt. Average elastic fields and scale-dependent overall properties ofheterogeneous micropolar materials containing spherical and cylindrical inhomogeneities.Phys Rev B2002,66(22):224110~2241120.
[24] X. Zhang, P. Sharma. Inclusions and inhomogeneities in strain gradient elasticity with couplestresses and related problems. Int J Solids Struct2005,42:3833~3851.
[25] F. Xun, G.K. Hu, Z.P. Huang. Effective in plane moduli of composites with a micropolar matrixand coated fibers. Int J Solids Struct2004,41:247~265.
[26] H.L. Duan, J. Wang, Z.P. Huang, Z.Y. Luo. Stress concentration tensors of inhomogeneitieswith interface effects. Mech Mater2005,37:723~736.
[27] H.L. Duan, X. Yi, Z.P. Huang, J. Wang. A unified scheme for prediction of effective moduli ofmultiphase composites with interface effects: Part II—Application and scaling laws. MechMater2007,39:94~103.
[28] M. Lagache, A. Agbossou, J. Pastor, D. Muller. Role of interphase on the elastic behavior ofcomposite materials: theoretical and experimental analysis. J Compos Mater1994,28:1140~1157.
[29] A. Al-Ostaz, I. Jasiuk. The influence of interface and arrangement of inclusions on localstresses in composite materials. Acta Mater1997,45:4131~4143.
[30] V. Nassehi, J. Dhillon, L. Mascia. Finite element simulation of the micromechanics ofinterlayered polymer/fibre composites: A study of the interactions between the reinforcingphases. Compos Sci Technol1993,47:349~358.
[31] J.L. Wang, S.L. Crouch, S.G. Mogilevskay. Numerical modeling of the elastic behavior offiber-reinforced composites with inhomogeneous interphases. Compos Sci Technol2006,66:1~18.
[32] E. Bugnicourt, J. Galy, J.F. Gerard, H. Barthel. Effect of sub-micron silica fillers on themechanical performances of epoxy-based composites. Polymer2007,48:1596~1605.
[33]张洪武，王鲲鹏．弹塑性复合材料多尺度计算的模型与算法研究[J]．复合材料学报，2003，20(1)：60~66．
[34]段慧玲，王建祥，黄筑平等．颗粒增强复合材料的界面模型与界面相模型的关系[J]．复合材料学报,2004,21(3):102~109．
[35]周储伟.高体积含量颗粒增强复合材料的一个细观力学模型I:弹性分析与等效模量[J].复合材料学报,2005,22(4):125~130.
[36] S.Y Fu, X.Q Feng, B. Lauke, Y.M. Mai. Effects of particle size, particle/matrix interfaceadhesion and particle loading on mechanical properties of particulate-polymer composites.Compos Part B2008,39:933~961.
[37] P.H.T. Vollenberg, J.W. Haan, L.J.M. van de Ven, D. Heikens. Particle size dependence of theYoung's modulus of filled polymers:2. Annealing and solid-state nuclear magnetic resonanceexperiments. Polymer1989,30:1663~1667.
[38] S. Boutaleb, F. Za ri, A. Mesbah, M. Na t-Abdelaziz, J.M Gloaguen, T. Boukharouba, J.M.Lefebvre. Micromechanics based modeling of stiffness and yield stress for silica/polymernanocomposites. Int J Solids Struct2009,46:1716~1726.
[39] V. Marcadon, E. Herve, A. Zaoui. Micromechanical modeling of packing and size effects inparticulate composites. Int J Solids Struct2007,44:8213~8228.
[40] W.X. Zhang, L.X. Li, T.J. Wang. Interphase effect on the strengthening behavior ofparticle-reinforced metal matrix composites. Comput Mater Sci2007,41:145~155.
[41] N. Esmaeili, Y. Tomita. Micro-to macroscopic responses of a glass particle-blended polymer inthe presence of an interphase layer. Int J Mech Sci2006,48:1186~1195.
[42] L.P. Canal, J. Segurado, J. LLorca. Failure surface of epoxy-modified fiber-reinforcedcomposites under transverse tension and out-of-plane shear. Int J Solids Struct2009,46:2265~2274.
[43] C.F Niordson, V. Tvergaard. Nonlocal plasticity effects on the tensile properties of a metalmatrix composite. Euro J Mech A/Solid2001,20:601~613.
[44] Z. Xue, Y. Huang, M. Li. Particle size effect in metallic materials: a study by the theory ofmechanism-based strain gradient plasticity. Acta Mater2002,50:149~160.
[45] N.A Fleck, G.M Muller, M.F Ashby, J.W Hutchinson. Strain gradient plasticity: theory andexperiment. Acta Metall Mater1994,42:475~487.
[46] C.W. Nan, D.R Clarke. The influence of particle size and particle fracture on the elastic/plasticdeformation of metal matrix composites. Acta Mater1996,44:3801~3811.
[47] G.K. Hu, X.N. Liu, T.J. Lu. A variational method for nonlinear micropolar composites. MechMater2005,37:407~425.
[48] X.N. Liu, G.K. Hu. A continuum micromechanical theory of overall plasticity for particulatecomposites including particle size effect. Int J Plasticity,2005,21:777~799.
[49] E. Demir, D. Raabe, N. Zaafarani, S. Zaefferer. Investigation of the indentation size effectthrough the measurement of the geometrically necessary dislocations beneath small indents ofdifferent depths using EBSD tomography. Acta Mater2009,57(2):559~569.
[50] Swadener J G, George E P, Pharr G M. The correlation of the indentation size effect measuredwith indenters of various shapes.2002(04)0022-5096(01)00103-X.
[51] F. Xun, G.K. Hu, Z.P. Huang. Effective in plane moduli of composites with a micropolar matrixand coated fibers. Int J Solids Struct2004,41(1):247~265.
[52] K. Tohgo, T. Itoh. Elastic and elastic-plastic singular fields around a crack-tip inparticulate-reinforced composites with progressive. Int J Solids Struct2005,42:6566~6585.
[53] K. Tohgo, G.J. Weng. A progressive damage mechanics in particle-reinforced metal-matrixcomposites under high triaxial tension. ASME J Eng Mater Technol1994,116:414~420.
[54] J.D. Eshelby. The determination of the elastic field of an ellipsoidal inclusion, and relatedproblems. Proc R Soc London1957, A241:376~396.
[55] T. Mori, K. Tanaka. Average stress in matrix and average elastic energy of materials withmisfitting inclusions. Acta Metall1973,21:571~574.
[56] Y.T. Cho, K. Tohgo, H. Ishii. Load carrying capacity of a broken ellipsoidal inhomogeneity.Acta Mater1997,45:4787~4795.
[57] K. Tohgo, Y.T. Cho. Theory of reinforcement damage in discontinuously reinforced compositesand its application. JSME Int J Series A1999,42:521~529.
[58] K. Tohgo, Y. Itoh, Y. Shimamura. A constitutive model of particulate-reinforced compositestaking account of particle size effects and damage evolution. Compos Part A2010,41(2):313~321.
[59] H.T. Liu, L.Z. Sun. Multi-scale modeling of elastoplastic deformation and strengtheningmechanisms in aluminum-based amorphous nanocomposites. Acta Mater2005,53(9):2693~2701.
[60] K. Ding, G.J. Weng. Plasticity of particle-reinforced composites with a ductile interphase.ASME J Applied Mech1998,65:596~604.
[61] J. Llorca, A. Martin, J. Ruiz and M. Elices. Particulate fracture during deformation of a sprayformed metal-matrix composite. Metall Trans A (1993),24:1575~1588.
[62] J.C. Shao, B.L. Xiao, Q.Z. Wang, Z.Y. Ma and K. Yang. An enhanced FEM model for particlesize dependent flow strengthening and interface damage in particle reinforced metal matrixcomposites. Compos Sci Tech2011,71:39~45.
[63] M. Kouzeli and A. Mortensen. Size dependent strengthening in particle reinforced aluminium.Acta Mater2002,50:39~51.
[64]张亚芳,唐春安,梁正召.单颗粒增强复合材料破裂过程的数值模拟[J].广州大学学报(自然科学版),2005,4(2):152~155.
[65]张亚芳,唐春安,梁正召,张娟霞.颗粒增强脆性基复合材料的尺寸效应[J].武汉理工大学学报,2006,3(28):22~28.
[66] A.A. Needleman. Continuum model for void nucleation by inclusion debonding. ASME J ApplMech1987,54:525~531.
[67] G. Bao. Damage due to fracture of brittle reinforcements in a ductile matrix. Acta Metall Mater1992,40:2547~2555.
[68] M. Finot, Y.L. Shen, A. Needleman, S. Suresh. Micromechanical modeling of reinforcementfracture in particle-rainforced metal-matrix composites. Metall Mater Trans A1994,25:2403~2420.
[69] J.R. Brockenbrough, F.W. Zok. On the role of particle cracking in flow and fracture of metalmatrix composites. Acta Metall Mater1995,43(1):11~20.
[70] J. Llorca, J. Segurado. Three-dimensional multiparticle cell simulations of deformation anddamage in sphere-reinforced composites. Mater Sci Eng A2004,365(1-2):267~274.
[71] A. Eckschlager, W. Han, H.J. B hm. A unit cell model for brittle fracture of particles embeddedin a ductile matrix. Comput Mater Sci2002,25(1-2):85~91.
[72] J. Segurado, J. Llorca. A computational micromechanics study of the effect of interfacedecohesion on the mechanical behavior of composites. Acta Mater2005,53(18):4931~4942.
[73]杨卫.细观力学和细观损伤力学.力学进展,1992,22:1~9.
[74] K. Tohgo, T.W. Chou. Incremental theory of particulate-reinforced composites includingdebonding damage. Int J JSME1996,39:389~397.
[75] Y.H. Zhao, G.J. Weng. Transversely isotropic moduli of two partially debonded composites. IntJ Solids Struct1997,34(4):493~507.
[76] J.W. Ju, H.K. Lee. A micromechanical damage model for effective elastoplastic behavior ofpartially debonded ductile matrix composites. Int J Solids Struct2001,38:6307~6332.
[77] L.Z. Sun, J.W. Ju, H.T. Liu. Elastoplastic modeling of metal matrix composites withevolutionary particle debonding. Mech Mater2003,35(3-6):559~569.
[78]张国定.金属基复合材料界面问题.材料研究学报[J].1977,11(6):649-657.
[79] W.H Wang, K. Sadeghipour, G. Baran. Finite element analysis of the effect of an interphase ontoughening of a particle reinforced polymer composite. Compos Part A2008,39:956~964.
[80]闻荻江．复合材料原理[M]．武汉：武汉工业大学出版社.1998．
[81] B. Lauke. Determination of adhesion strength between a coated particle and polymer matrix.Compos Sci Technol2006,66:3153~3160.
[82] J.C. Wang, G.C. Yang. The energy dissipation of particle-reinforced metal-matrix compositewith ductile interphase. Mater Sci Eng A2001,303:77~81.
[83] R. Paskaramoorthy, S. Bugarin, R. Reid. Effect of an interphase layer on the dynamic stressconcentration in an Mg-matrix surrounding SiC particle. Compos Struct2009,91:451~460.
[84] Z.J. Wu, J.M. Davies. Effect of interphase on fiber-bridging toughness of a unidirectional FRPcomposite thin plate. Compos Struct2005,69:510~515.
[85] G.C. Papanicolaou, A.S. Bouboulas, N.K. Anifantis. Thermal expansion in fibrous compositesincorporating hybrid interphase regions. Compos Struct2009,88:542~547.
[86] H. Liu, L.C. Brinson. A hybrid numerical-analytical method for modeling the ViscoelasticProperties of polymer nanocomposites. J Appl Mech2006,73(5):758~768.
[87] H.K. Schmid, M. Aslan, S. Assmann, R. Na, H. Schmidt. Microstructural characterization ofAl2O3-SiC nanocopmosites. J Eur Ceram Soc1998,18:39~49.
[88] L. Carroll, M. Sternitzke, B. Derby. Silicon carbide particle size effects in alumina basednanocomposites. Acta mater1996,44:4543~4552.
[89] M.Z. Rong, M.Q. Zhang, Y.X. Zheng, H.M. Zeng, R. Walter, K. Friedrich. Structure-propertyrelationships of irradiation grafted nano-inorganic particle filled polypropylene composites.Polymer2001,42(1):167~183.
[90] S.J.V. Frankland, A. Caglar, D.W. Brenner, M. Griebel. Molecular Simulation of the Influenceof Chemical Cross-Links on the Shear Strength of carbon nanotube-polymer interfaces. J PhysChem B2002,106:3046~3048.
[91] M. Wong, M. Paramsothy, X.J. Xu, Y. Ren, S. Li, K. Liao. Physical Interactions at CarbonNanotube–Polymer Interface. Polymer2003,44:7757~7764.
[92] K. Liao and S. Li, Interfacial Characteristics of Carbon Nanotube-Polystyrene CompositeSystem. Appl. Phys. Lett.2001,79:4225~4227.
[93] Y.L. Wu, Z.F. Dong. Three-dimensional finite element analysis of composites with coatedspherical inclusions. Mater Sci Eng A1995,203(2):314~323.
[94] J.C. Wang, G.C. Yang. The energy dissipation of particle-reinforced metal-matrix compositewith ductile interphase. Mater Sci Eng A2001,303(1):77~81.
[95] H. Zhang, Z. Zhang, K. Friedrich, C. Egger. Property improvements of in situ epoxynanocomposites with reduced interparticle distance at high nanosilica content. Acta Mater2006,54(7):1833~1842.
[96] V. Marcadon, E. Herve, A. Zaoui. Micromechanical modelling of packing and size effects inparticulate composites. Int J Solids Struct2007,44(25):8213~8228.
[97] S.H. Nie, C. Basaran. A micromechanical model for effective elastic properties of particulatecomposites with imperfect interfacial bonds. Int J Solids Struct2005,42(14):4179~4191.
[98] A.S. Sarvestani. On the overall elastic moduli of composites with spherical coated fillers. Int JSolids Struct2003,40(26):7553~7566.
[99] H.T. Liu, L.Z. Sun. A micromechanics-based elastoplastic model for amorphous compositeswith nanoparticle interactions. ASME J Appl Mech2008,75:031009~1.
[100] E.H. Barhdadi, P. Lipinski, M. Cherkaoui. Micromechanical modeling of an arbitraryellipsoidal multi-coated inclusion. ASME J Eng Mater Technol2007,129(22):313~320.
[101] A.V. Hershey. The plasticity of an isotropic aggregate of anisotropic face centered cubiccrystals, Trans. ASME J Appl Mech1954,2:226~240.
[102] R. M. Christensen, K.H. Lo. Solutions for effective shear properties in three phase sphere andcylinder models. J Mech Phys Solids1979,27:315~330.
[103] M. Hori, S. Nemat-Nasser. Double-inclusion model and overall moduli of multi-phasecomposites. Mech Mater1993,14(3):189~206.
[104] P.P. Castaneda, J.R. Willis. The effect of spatial distribution on the effective behavior ofcomposite materials and cracked media. J Mech Phys Solids1995,43(12):1919~1951.
[105] Q.S. Zheng, D.X. Du. An explicit and universally applicable estimate for the effectiveproperties of multiphase composites which accounts for inclusion distribution. J Mech PhysSolids2001,49(11):2765~2788.
[106] Z.Q. Cheng, L.H. He. Micropolar elastic fields due to a spherical inclusion. Int J Engng Sci1995,33(33):389~397.
[107] H.A. Luo, G.J. Weng. On eshelby's-tensor in a three-phase cylindrically concentric solid, andthe elastic moduli of fiber-reinforced composites. Mech Mater1989,8(2-3):77~88.
[108] J. Schj dt-Thomsen, R. Pyrz, The Mori–Tanaka stiffness tensor: diagonal symmetry, complexfibre orientations and non-dilute volume fractions. Mech Mater2001,33(10):531~544.
[109] M. P. Lutz, R. W. Zimmerman. Effect of an inhomogeneous interphase zone on thebulkmodulus and conductivity of a particulate composite. Int J Solids Struct2005,42:429~437.
[110] Z. Hashin. The elastic moduli of heterogeneous materials. ASME J Appl Mech1962,29:143~150.
[111] W. Wang, I. Jasiuk. Effective elastic constants of particulated composites with inhomogeneousinterphases. J Compos Mater1998,32(5):1391~1424.
[112] W. Huang and S.I. Rokhlin. Generalized self-consistent model for composites with functionallygraded and multilayered interphases. Transfer matrix approach. Mech Mater1996,22:219~247.
[113] S. K. Kanaun, L. T. Kudriavtseva, Spherically layered inclusions in a homogeneous elasticmedium. Appl Math Mech1986,50:483~491.
[114] S. K. Kanaun, L. T. Kudriavtseva. Elastic and thermoelastic characteristics of compositesreinforced with unidirectional fibre layers. Appl Math Mech1989,53:628~636.
[115] L. X. Shen, J. Li. Effective elastic moduli of comp of plates with various distributions and sizesof cracks. Int J Solids Struct2003,40(6):1393~1409.
[116] L. X. Shen, S. Yi. An effective inclusion model for effective moduli of heterogeneous materialswith ellipsoidal inhomogeneities. Int J Solids Struct2001,38(32-33):5789~5805.
[117] I. Sevostianov, M. Kachanov. Effect of interphase layers on the overall elastic and conductiveproperties of matrix composites. Int J Solids Struct2007,44:1304~1315.
[118] L. Mullins, N.R. Tobin. Stress softenings in rubber vulcanizates. J Appl Polymer Sci1965,9:2993~3009.
[119] H.J. Qi, M.C. Boyce. Constitutive model for stretch-induced softening of the stress–stretchbehavior of elastomeric materials. J Mech Phys Solids2004,52:2187~2205.
[120] J.S. Bergstrom, M.C. Boyce. Mechanical Behavior of Particle Filled Elastomers. Rubber ChemTech1999,72:633~656.
[121] P. Ponte Casta eda, Second-order homogenization estimates for nonlinear compositesincorporating field fluctuations. I–Theory. J Mech Phys Solids2002,50:737~757.
[122] O. Lopez-Pamies, P. Ponte-Casta eda. Homogenization-based constitutive models for porouselastomers and implications for macroscopic instabilities: I—Analysis. J Mech Phys Solids2007,55:1677~1701.
[123] V. Bouchart, M. Brieu, D. Kondo, M. Na t Abdelaziz. Implementation and numericalverification of a non-linear homogenization method applied to hyperelastic composites.Computat Mater Sci2008,43:670~680.
[124] V. Bouchart, M. Brieu, N. Bhatnagar, D. Kondo. A multiscale approach of nonlinearcomposites under finite deformation: Experimental characterization and numerical modeling.Int J Solids Struct2010,47:1737~1750.
[125] H.M. Yin, L.Z. Sun, J.S. Chen. Micromechanics-based hyperelastic constitutive modeling ofmagnetostrictive particle-filled elastomers. Mech Mater2002,34:505~516.
[126] Sia Nemat-Nasser. Multi-inclusion method for finite deformations: exact results andapplications. Mater Science Eng A2000,285:239~245.
[127] Sia Nemat-Nasser. Averaging theorems in finite deformation plasticity. Mech Mater1999,31:493~523.
[128] W.H. Wang, K.A. Kistler, K. Sadeghipour, G. Baran. Molecular dynamics simulation of AFMstudies of a single polymer chain.Physics Letters A2008,372:7007~7010.
[129] C. Miehe, S. Goktepe, F. Lu lei. A micro-macro approach to rubber-like materials—Part I: thenon-affine micro-sphere model of rubber elasticity. J Mechanics Phys Solids2004,52:2617~2660.
[130] M. B l, S. Reese. Finite element modelling of rubber-like polymers based on chain statistics.Int J Solids Struct2006,43:2~26.
[131] A.D. Drozdov, A. Dorfmann. A micro-mechanical model for the response of filledelastomers at finite strains. Int J Plasticity2003,19:1037~1067.
[132] M. Brieu, F. Devries. Micro-mechanical approach and algorithm for the study of damageappearance in elastomer composites. Compos Struct1999,46:309~319.
[133] M.T. Abadi. Characterization of heterogeneous materials under shear loading at finite strain.Compos Struct2010,92:578~584.
[134] Y. Zhong, J. Wang, Y. M. Wu, Z.P. Huang. Effective moduli of particle-filled composite withinhomogeneous interphase Part II: mapping method and evaluation. Compos Sci Tech2004,64:1353~1362.
[135] C. P. Tsui, D. Z. Chen, C.Y. Tang, P. S. Uskokovic, J. P. Fan. Prediction for debonding damageprocess of glass beads-reinforced modified polyphenylene oxide under simple shear. J MaterProc Tech2005,167:429~437.
[136] L.G. Zhao, N.A. Warrior, A.C. Long. A micromechanical study of residual stress and its effecton transverse failure in polymer–matrix composites. Int J Solids Struct2006,43:5449~5467.
[137] L.G. Zhao, N.A. Warrior, A.C. Long. A thermo-viscoelastic analysis of process-inducedresidual stress in fibre-reinforced polymer–matrix composites. Mater Sci Eng A2007,452~453:483~498.
[138] Z.H. Xia, Y. F. Zhang, F. Ellyin. An unified periodical boundary conditions for presentativevolume elements of composites and applications. Int J Solids Struct2003,40:1907~1721.
[139] Y.L. Wu, Z. F. Dong. Three-dimensional finite element analysis of composites with coatedspherical inclusions. Mater Sci Eng A1995,203:314~323.
[140] J.C. Wang, G.C. Yang. The energy dissipation of particle-reinforced metal-matrix compositewith ductile interphase. Mater Sci Eng A2001,303(1):77~81.
[141] V.P. Privalko, V. F. Shumsky, E. G. Privalko. Viscoelasticity and flow behavior of irradiationgrafted nano-inorganic particle filled polypropylene composites in the melt state. J Mater ProcTech2003,137(1-3):208~213.
[142] C.T. Sun, R.S. Vaidya. Prediction of composite properties from a representative volumeelement. Compos Sci Tech1990,56:171~179.
[143] R.A. Naik, J.H. Crews. Micromechanical Analysis of fibermatrix Interface Stresses underThermo mechanical Loadings. Composite Materials: Testing and Design1993,1206:205~219.
[144] J.R. Brockenbrough, S. Suresh, H.A.Wienencke. Deformation of metal-matrix composites withcontinuous fibers: Geometrical effects of fiber distribution and shaper. Acta Metall Mater1991,39(5):735~752.
[145] P. Potluri, A. Manan. Mechanics of non-orthogonally interlaced textile composites. Compos A2007,38:1216~1226.
[146] Z.A. Moshovidis, T. Mura. Two ellip-tical inhomogeneities by the equivalent inclusion method.ASME J Appl Mech1975,42:847~852.
[147] P. Ganguly, W.J. Poole. Influence of reinforcement arrangement on the local reinforcementstresses in composite materials. J Mech Phys Solids2004,52(6):1355~1377.
[148]严鹏,蒋持平.考虑周期微结构分布特征的Mori-Tanaka方法.复合材料学报2007,24(4):178~184.
[149]徐耀玲.含双周期夹杂复合材料细观力学研究[D].北京:北京航空航天大学,2003.
[150] P.B. Bowden. The elastic modulus of an amorphous glassy polymer. Polymer1968,9:449~454.
[151] V.A. Kuznetsov. Influence of the stress jump condition at the porous-medium/clear-fluidinterface on a flow at a porous wall. Compos Mater1973,9:401~404.
[152] I.V. Yannas, R.R. Luise. Distinction between two molecular mechanisms for deformation ofglassy amorphous polymers. J Macromolecular Sci B1982,21:443~474.
[153] Y. Tomita, S. Tanaka. Prediction of deformation behavior of glassy polymers based onmolecular chain network model. Int J Solids Struct1995,32:3423~3434.
[154] E.M. Arruda, M.C. Boyce. A three-dimensional constitutive model for the large stretchbehavior of rubber elastic materials. J Mech Phys Solids1993,41:389~412.
[155] G.K. Hu, G. Guo, D. Baptiste. A micromechanical model of influence of particle fracture andparticle cluster on mechanical properties of metal matrix composites. Comput Mater Sci1998,9:420~430.
[156] B. Bittmann, F. Haupert, A.K. Schlarb, Preparation of TiO2/epoxy nanocomposites byultrasonic dispersion and their structure property relationship.The6thAsin-AustralasianConference on Composite Materials, Kumamoto, Japan,2008,9~12.
[157] D. Gersappe, Molecular mechanisms of failure in polymer nanocomposites. Phys Rev Lett2002,89:058301.
[158] O.H. Yeoh. Some Forms of the Strain Energy Function for Rubber. Rubber Chem Tech1993,66:754~771.
[159] Y. Benveniste. A new approach to the application of Mori-Tanaka's theory in compositematerials. Mech Mater1987,6:147~157.
[160] D.J. Lloyd. Particle reinforced aluminium and magnesium matrix composites. Int Mater Rev1994,39(1):1~23.
[161] B.C. Kima, S.W. Parka, D.G. Lee. Fracture toughness of the nano-particle reinforced epoxycomposite. Compos Struct2008,86:69~77.
[162] J.J. Williams, Z Flom, A.A. Amell, N Chawla, X Xiao, F De Carlo. Damage evolution in SiCparticle reinforced Al alloy matrix composites by X-ray synchrotron tomography. Acta Mater2010,58(18):6194~6205.
[163] A. Brara, F. Camborde, J.R. Klepaczko, C. Mariotti. Experimental and numerical study ofconcrete at high strain rates in tension. Mech Mater2001,33(1):33~45.
[164] G.K. Hu. A method of plasticity for general aligned spherical void or fiber-reinforcedcomposites. Int J Plasticity1996,12:439~449.
[165] Y.P. Qiu, G.J. Weng. A theory of plasticity for porous mate-rials and particle-reinforcedcomposites. ASME J Appl Mech1992,59:261~268.
[166] R. Lakes. Continuum models for materials with microstructure, ed. H. Mühlhaus, J. Wiley, N. Y.Ch.1995,1:1~22.
[167] H.J. Gao, B.H. Ji, I.L. Jager, E. Arz and P. Fratzl. Materials become insensitive to flaws atnanoscale: Lessons from nature. PNAS2003,100:5597~5600.
[168] J. Segurado, J. LLorca. Computational micromechanics of composites: The effect of particlespatial distribution. Mech Mater2006,38:873~883.
[169] J. Segurado, C. González, J. LLorca. A numerical investigation of the effect of particleclustering on the mechanical properties of composites. Acta Mater2003,51:2355~2369.
[170] T. Mura, Micromechanics of Defects in Solids. Martinus Nijhoff Publication, The Hague1987.
[2]崔岩.碳化硅颗粒增强复合材料的航空航天应用[J].材料工程.2002,6：
[3]陈亚莉.美国F-22先进战斗机选材分析[R].航空信息研究报告，1995,7:15~16.
[4]丁立铭,饶勤,陈亚莉,任小华.F-22战斗机选材与制造技术[R].航空信息研究报告,1996,6:25~26.
[5] B M Daniel.2ndAnnual Aluminum Metal Matrix Composites Meeting,1997,75.
[6]李成功,傅恒志,于翘．航空航天材料[M].北京：国防工业出版社,2002:7.
[7] Geiger A L, Walker J A. The processing and properties of discontinuously reinforcedaluminum composites[J]．JOM,1991(8):8~15.
[8] A.C. Balazs, T. Emrick, T.P. Russell. Nanoparticle-polymer Composites: Where two smallworlds meet. Science2006,314:1107~1110.
[9] J. Jordan, K.I. Jacob, R. Tannenbaum, M.A. Sharaf, I. Jasiuk. Experimental trends in polymernanocomposites—a review. Mater Sci Eng A2005,393(1-2):1~11.
[10] L. Jiang, Y.C. Lam, K.C. Tam, T.H. Chua, G.W. Sim, L.S. Ang. Strengtheningacrylonitrile-butadiene-styrene (ABS) with nano-sized and micron-sized calcium carbonate.Polymer2005,46:243~252.
[11] P.H.T. Vollenberg, D. Heikens. Particle size dependence of the Young's modulus of filledpolymers:1. Preliminary experiments. Polymer1989,30:1656~1662.
[12] P.H.T. Vollenberg, J.W. Haan, L.J.M. van de Ven, D. Heikens. Particle size dependence of theYoung's modulus of filled polymers:2. Annealing and solid-state nuclear magnetic resonanceexperiments. Polymer1989,30:1663~1667.
[13] J. Cho, M.S. Joshi, C.T. Sun. Effect of inclusion size on mechanical properties of polymericcomposites with micro and nano particles. Compos Sci Technol2006,66:1941~1952.
[14] A. Adnan, C.T. Sun, H. Mahfuz. A molecular dynamics simulation study to investigate theeffect of filler size on elastic properties of polymer nanocomposites. Compos Sci Technol2007,67:348~356.
[15] G.M. Odegard, T.C. Clancy, T.S. Gates. Modeling of the mechanical properties ofnanoparticle/polymer composites. Polymer2005,46:553~562.
[16] S. Yu, S. Yang, M. Cho. Multi-scale modeling of cross-linked epoxy nanocomposites. Polymer2009,50:945~952.
[17] G.J. Papakonstantopoulos, K. Yoshimoto, M. Doxastakis, P.F. Nealey, J.J. Pablo. Localmechanical properties of polymeric nanocomposites. Phys Rev E2005,72:031801.
[18] K. Masenelli-Varlot, E. Reynaud, G. Vigier, J. Varlet. Mechanical Properties ofClay-Reinforced Polyamide. J Polym Sci B2002,40:272~283.
[19] E. Tadd, A. Zeno, M. Zubris, N. Dan, R. Tannenbaum. Adsorption and polymer film formationon metal nanoclusters. Macromolecules2003,36:6497~6502.
[20] S. Boutaleb, F. Za ri, A. Mesbah, M. Na t-Abdelaziz, J.M. Gloaguen, T. Boukharouba, J.M.Lefebvre. Micromechanics-based modelling of stiffness and yield stress for silica/polymernanocomposites. Int J Solids Struct2009,46:1716~1726.
[21] Y.P. Jiang, K. Tohgo, Y. Shimamura. A micro-mechanics model for composites reinforced byregularly distributed particles with an inhomogeneous interphase. Comput Mater Sci2009,46:507~515.
[22] H.T. Liu, L.Z. Sun. A micromechanics-based elastoplastic model for amorphous compositeswith nanoparticle interactions. ASME J Appl Mech2008,75:310091~3100910.
[23] P. Sharma, A. Dasgupt. Average elastic fields and scale-dependent overall properties ofheterogeneous micropolar materials containing spherical and cylindrical inhomogeneities.Phys Rev B2002,66(22):224110~2241120.
[24] X. Zhang, P. Sharma. Inclusions and inhomogeneities in strain gradient elasticity with couplestresses and related problems. Int J Solids Struct2005,42:3833~3851.
[25] F. Xun, G.K. Hu, Z.P. Huang. Effective in plane moduli of composites with a micropolar matrixand coated fibers. Int J Solids Struct2004,41:247~265.
[26] H.L. Duan, J. Wang, Z.P. Huang, Z.Y. Luo. Stress concentration tensors of inhomogeneitieswith interface effects. Mech Mater2005,37:723~736.
[27] H.L. Duan, X. Yi, Z.P. Huang, J. Wang. A unified scheme for prediction of effective moduli ofmultiphase composites with interface effects: Part II—Application and scaling laws. MechMater2007,39:94~103.
[28] M. Lagache, A. Agbossou, J. Pastor, D. Muller. Role of interphase on the elastic behavior ofcomposite materials: theoretical and experimental analysis. J Compos Mater1994,28:1140~1157.
[29] A. Al-Ostaz, I. Jasiuk. The influence of interface and arrangement of inclusions on localstresses in composite materials. Acta Mater1997,45:4131~4143.
[30] V. Nassehi, J. Dhillon, L. Mascia. Finite element simulation of the micromechanics ofinterlayered polymer/fibre composites: A study of the interactions between the reinforcingphases. Compos Sci Technol1993,47:349~358.
[31] J.L. Wang, S.L. Crouch, S.G. Mogilevskay. Numerical modeling of the elastic behavior offiber-reinforced composites with inhomogeneous interphases. Compos Sci Technol2006,66:1~18.
[32] E. Bugnicourt, J. Galy, J.F. Gerard, H. Barthel. Effect of sub-micron silica fillers on themechanical performances of epoxy-based composites. Polymer2007,48:1596~1605.
[33]张洪武，王鲲鹏．弹塑性复合材料多尺度计算的模型与算法研究[J]．复合材料学报，2003，20(1)：60~66．
[34]段慧玲，王建祥，黄筑平等．颗粒增强复合材料的界面模型与界面相模型的关系[J]．复合材料学报,2004,21(3):102~109．
[35]周储伟.高体积含量颗粒增强复合材料的一个细观力学模型I:弹性分析与等效模量[J].复合材料学报,2005,22(4):125~130.
[36] S.Y Fu, X.Q Feng, B. Lauke, Y.M. Mai. Effects of particle size, particle/matrix interfaceadhesion and particle loading on mechanical properties of particulate-polymer composites.Compos Part B2008,39:933~961.
[37] P.H.T. Vollenberg, J.W. Haan, L.J.M. van de Ven, D. Heikens. Particle size dependence of theYoung's modulus of filled polymers:2. Annealing and solid-state nuclear magnetic resonanceexperiments. Polymer1989,30:1663~1667.
[38] S. Boutaleb, F. Za ri, A. Mesbah, M. Na t-Abdelaziz, J.M Gloaguen, T. Boukharouba, J.M.Lefebvre. Micromechanics based modeling of stiffness and yield stress for silica/polymernanocomposites. Int J Solids Struct2009,46:1716~1726.
[39] V. Marcadon, E. Herve, A. Zaoui. Micromechanical modeling of packing and size effects inparticulate composites. Int J Solids Struct2007,44:8213~8228.
[40] W.X. Zhang, L.X. Li, T.J. Wang. Interphase effect on the strengthening behavior ofparticle-reinforced metal matrix composites. Comput Mater Sci2007,41:145~155.
[41] N. Esmaeili, Y. Tomita. Micro-to macroscopic responses of a glass particle-blended polymer inthe presence of an interphase layer. Int J Mech Sci2006,48:1186~1195.
[42] L.P. Canal, J. Segurado, J. LLorca. Failure surface of epoxy-modified fiber-reinforcedcomposites under transverse tension and out-of-plane shear. Int J Solids Struct2009,46:2265~2274.
[43] C.F Niordson, V. Tvergaard. Nonlocal plasticity effects on the tensile properties of a metalmatrix composite. Euro J Mech A/Solid2001,20:601~613.
[44] Z. Xue, Y. Huang, M. Li. Particle size effect in metallic materials: a study by the theory ofmechanism-based strain gradient plasticity. Acta Mater2002,50:149~160.
[45] N.A Fleck, G.M Muller, M.F Ashby, J.W Hutchinson. Strain gradient plasticity: theory andexperiment. Acta Metall Mater1994,42:475~487.
[46] C.W. Nan, D.R Clarke. The influence of particle size and particle fracture on the elastic/plasticdeformation of metal matrix composites. Acta Mater1996,44:3801~3811.
[47] G.K. Hu, X.N. Liu, T.J. Lu. A variational method for nonlinear micropolar composites. MechMater2005,37:407~425.
[48] X.N. Liu, G.K. Hu. A continuum micromechanical theory of overall plasticity for particulatecomposites including particle size effect. Int J Plasticity,2005,21:777~799.
[49] E. Demir, D. Raabe, N. Zaafarani, S. Zaefferer. Investigation of the indentation size effectthrough the measurement of the geometrically necessary dislocations beneath small indents ofdifferent depths using EBSD tomography. Acta Mater2009,57(2):559~569.
[50] Swadener J G, George E P, Pharr G M. The correlation of the indentation size effect measuredwith indenters of various shapes.2002(04)0022-5096(01)00103-X.
[51] F. Xun, G.K. Hu, Z.P. Huang. Effective in plane moduli of composites with a micropolar matrixand coated fibers. Int J Solids Struct2004,41(1):247~265.
[52] K. Tohgo, T. Itoh. Elastic and elastic-plastic singular fields around a crack-tip inparticulate-reinforced composites with progressive. Int J Solids Struct2005,42:6566~6585.
[53] K. Tohgo, G.J. Weng. A progressive damage mechanics in particle-reinforced metal-matrixcomposites under high triaxial tension. ASME J Eng Mater Technol1994,116:414~420.
[54] J.D. Eshelby. The determination of the elastic field of an ellipsoidal inclusion, and relatedproblems. Proc R Soc London1957, A241:376~396.
[55] T. Mori, K. Tanaka. Average stress in matrix and average elastic energy of materials withmisfitting inclusions. Acta Metall1973,21:571~574.
[56] Y.T. Cho, K. Tohgo, H. Ishii. Load carrying capacity of a broken ellipsoidal inhomogeneity.Acta Mater1997,45:4787~4795.
[57] K. Tohgo, Y.T. Cho. Theory of reinforcement damage in discontinuously reinforced compositesand its application. JSME Int J Series A1999,42:521~529.
[58] K. Tohgo, Y. Itoh, Y. Shimamura. A constitutive model of particulate-reinforced compositestaking account of particle size effects and damage evolution. Compos Part A2010,41(2):313~321.
[59] H.T. Liu, L.Z. Sun. Multi-scale modeling of elastoplastic deformation and strengtheningmechanisms in aluminum-based amorphous nanocomposites. Acta Mater2005,53(9):2693~2701.
[60] K. Ding, G.J. Weng. Plasticity of particle-reinforced composites with a ductile interphase.ASME J Applied Mech1998,65:596~604.
[61] J. Llorca, A. Martin, J. Ruiz and M. Elices. Particulate fracture during deformation of a sprayformed metal-matrix composite. Metall Trans A (1993),24:1575~1588.
[62] J.C. Shao, B.L. Xiao, Q.Z. Wang, Z.Y. Ma and K. Yang. An enhanced FEM model for particlesize dependent flow strengthening and interface damage in particle reinforced metal matrixcomposites. Compos Sci Tech2011,71:39~45.
[63] M. Kouzeli and A. Mortensen. Size dependent strengthening in particle reinforced aluminium.Acta Mater2002,50:39~51.
[64]张亚芳,唐春安,梁正召.单颗粒增强复合材料破裂过程的数值模拟[J].广州大学学报(自然科学版),2005,4(2):152~155.
[65]张亚芳,唐春安,梁正召,张娟霞.颗粒增强脆性基复合材料的尺寸效应[J].武汉理工大学学报,2006,3(28):22~28.
[66] A.A. Needleman. Continuum model for void nucleation by inclusion debonding. ASME J ApplMech1987,54:525~531.
[67] G. Bao. Damage due to fracture of brittle reinforcements in a ductile matrix. Acta Metall Mater1992,40:2547~2555.
[68] M. Finot, Y.L. Shen, A. Needleman, S. Suresh. Micromechanical modeling of reinforcementfracture in particle-rainforced metal-matrix composites. Metall Mater Trans A1994,25:2403~2420.
[69] J.R. Brockenbrough, F.W. Zok. On the role of particle cracking in flow and fracture of metalmatrix composites. Acta Metall Mater1995,43(1):11~20.
[70] J. Llorca, J. Segurado. Three-dimensional multiparticle cell simulations of deformation anddamage in sphere-reinforced composites. Mater Sci Eng A2004,365(1-2):267~274.
[71] A. Eckschlager, W. Han, H.J. B hm. A unit cell model for brittle fracture of particles embeddedin a ductile matrix. Comput Mater Sci2002,25(1-2):85~91.
[72] J. Segurado, J. Llorca. A computational micromechanics study of the effect of interfacedecohesion on the mechanical behavior of composites. Acta Mater2005,53(18):4931~4942.
[73]杨卫.细观力学和细观损伤力学.力学进展,1992,22:1~9.
[74] K. Tohgo, T.W. Chou. Incremental theory of particulate-reinforced composites includingdebonding damage. Int J JSME1996,39:389~397.
[75] Y.H. Zhao, G.J. Weng. Transversely isotropic moduli of two partially debonded composites. IntJ Solids Struct1997,34(4):493~507.
[76] J.W. Ju, H.K. Lee. A micromechanical damage model for effective elastoplastic behavior ofpartially debonded ductile matrix composites. Int J Solids Struct2001,38:6307~6332.
[77] L.Z. Sun, J.W. Ju, H.T. Liu. Elastoplastic modeling of metal matrix composites withevolutionary particle debonding. Mech Mater2003,35(3-6):559~569.
[78]张国定.金属基复合材料界面问题.材料研究学报[J].1977,11(6):649-657.
[79] W.H Wang, K. Sadeghipour, G. Baran. Finite element analysis of the effect of an interphase ontoughening of a particle reinforced polymer composite. Compos Part A2008,39:956~964.
[80]闻荻江．复合材料原理[M]．武汉：武汉工业大学出版社.1998．
[81] B. Lauke. Determination of adhesion strength between a coated particle and polymer matrix.Compos Sci Technol2006,66:3153~3160.
[82] J.C. Wang, G.C. Yang. The energy dissipation of particle-reinforced metal-matrix compositewith ductile interphase. Mater Sci Eng A2001,303:77~81.
[83] R. Paskaramoorthy, S. Bugarin, R. Reid. Effect of an interphase layer on the dynamic stressconcentration in an Mg-matrix surrounding SiC particle. Compos Struct2009,91:451~460.
[84] Z.J. Wu, J.M. Davies. Effect of interphase on fiber-bridging toughness of a unidirectional FRPcomposite thin plate. Compos Struct2005,69:510~515.
[85] G.C. Papanicolaou, A.S. Bouboulas, N.K. Anifantis. Thermal expansion in fibrous compositesincorporating hybrid interphase regions. Compos Struct2009,88:542~547.
[86] H. Liu, L.C. Brinson. A hybrid numerical-analytical method for modeling the ViscoelasticProperties of polymer nanocomposites. J Appl Mech2006,73(5):758~768.
[87] H.K. Schmid, M. Aslan, S. Assmann, R. Na, H. Schmidt. Microstructural characterization ofAl2O3-SiC nanocopmosites. J Eur Ceram Soc1998,18:39~49.
[88] L. Carroll, M. Sternitzke, B. Derby. Silicon carbide particle size effects in alumina basednanocomposites. Acta mater1996,44:4543~4552.
[89] M.Z. Rong, M.Q. Zhang, Y.X. Zheng, H.M. Zeng, R. Walter, K. Friedrich. Structure-propertyrelationships of irradiation grafted nano-inorganic particle filled polypropylene composites.Polymer2001,42(1):167~183.
[90] S.J.V. Frankland, A. Caglar, D.W. Brenner, M. Griebel. Molecular Simulation of the Influenceof Chemical Cross-Links on the Shear Strength of carbon nanotube-polymer interfaces. J PhysChem B2002,106:3046~3048.
[91] M. Wong, M. Paramsothy, X.J. Xu, Y. Ren, S. Li, K. Liao. Physical Interactions at CarbonNanotube–Polymer Interface. Polymer2003,44:7757~7764.
[92] K. Liao and S. Li, Interfacial Characteristics of Carbon Nanotube-Polystyrene CompositeSystem. Appl. Phys. Lett.2001,79:4225~4227.
[93] Y.L. Wu, Z.F. Dong. Three-dimensional finite element analysis of composites with coatedspherical inclusions. Mater Sci Eng A1995,203(2):314~323.
[94] J.C. Wang, G.C. Yang. The energy dissipation of particle-reinforced metal-matrix compositewith ductile interphase. Mater Sci Eng A2001,303(1):77~81.
[95] H. Zhang, Z. Zhang, K. Friedrich, C. Egger. Property improvements of in situ epoxynanocomposites with reduced interparticle distance at high nanosilica content. Acta Mater2006,54(7):1833~1842.
[96] V. Marcadon, E. Herve, A. Zaoui. Micromechanical modelling of packing and size effects inparticulate composites. Int J Solids Struct2007,44(25):8213~8228.
[97] S.H. Nie, C. Basaran. A micromechanical model for effective elastic properties of particulatecomposites with imperfect interfacial bonds. Int J Solids Struct2005,42(14):4179~4191.
[98] A.S. Sarvestani. On the overall elastic moduli of composites with spherical coated fillers. Int JSolids Struct2003,40(26):7553~7566.
[99] H.T. Liu, L.Z. Sun. A micromechanics-based elastoplastic model for amorphous compositeswith nanoparticle interactions. ASME J Appl Mech2008,75:031009~1.
[100] E.H. Barhdadi, P. Lipinski, M. Cherkaoui. Micromechanical modeling of an arbitraryellipsoidal multi-coated inclusion. ASME J Eng Mater Technol2007,129(22):313~320.
[101] A.V. Hershey. The plasticity of an isotropic aggregate of anisotropic face centered cubiccrystals, Trans. ASME J Appl Mech1954,2:226~240.
[102] R. M. Christensen, K.H. Lo. Solutions for effective shear properties in three phase sphere andcylinder models. J Mech Phys Solids1979,27:315~330.
[103] M. Hori, S. Nemat-Nasser. Double-inclusion model and overall moduli of multi-phasecomposites. Mech Mater1993,14(3):189~206.
[104] P.P. Castaneda, J.R. Willis. The effect of spatial distribution on the effective behavior ofcomposite materials and cracked media. J Mech Phys Solids1995,43(12):1919~1951.
[105] Q.S. Zheng, D.X. Du. An explicit and universally applicable estimate for the effectiveproperties of multiphase composites which accounts for inclusion distribution. J Mech PhysSolids2001,49(11):2765~2788.
[106] Z.Q. Cheng, L.H. He. Micropolar elastic fields due to a spherical inclusion. Int J Engng Sci1995,33(33):389~397.
[107] H.A. Luo, G.J. Weng. On eshelby's-tensor in a three-phase cylindrically concentric solid, andthe elastic moduli of fiber-reinforced composites. Mech Mater1989,8(2-3):77~88.
[108] J. Schj dt-Thomsen, R. Pyrz, The Mori–Tanaka stiffness tensor: diagonal symmetry, complexfibre orientations and non-dilute volume fractions. Mech Mater2001,33(10):531~544.
[109] M. P. Lutz, R. W. Zimmerman. Effect of an inhomogeneous interphase zone on thebulkmodulus and conductivity of a particulate composite. Int J Solids Struct2005,42:429~437.
[110] Z. Hashin. The elastic moduli of heterogeneous materials. ASME J Appl Mech1962,29:143~150.
[111] W. Wang, I. Jasiuk. Effective elastic constants of particulated composites with inhomogeneousinterphases. J Compos Mater1998,32(5):1391~1424.
[112] W. Huang and S.I. Rokhlin. Generalized self-consistent model for composites with functionallygraded and multilayered interphases. Transfer matrix approach. Mech Mater1996,22:219~247.
[113] S. K. Kanaun, L. T. Kudriavtseva, Spherically layered inclusions in a homogeneous elasticmedium. Appl Math Mech1986,50:483~491.
[114] S. K. Kanaun, L. T. Kudriavtseva. Elastic and thermoelastic characteristics of compositesreinforced with unidirectional fibre layers. Appl Math Mech1989,53:628~636.
[115] L. X. Shen, J. Li. Effective elastic moduli of comp of plates with various distributions and sizesof cracks. Int J Solids Struct2003,40(6):1393~1409.
[116] L. X. Shen, S. Yi. An effective inclusion model for effective moduli of heterogeneous materialswith ellipsoidal inhomogeneities. Int J Solids Struct2001,38(32-33):5789~5805.
[117] I. Sevostianov, M. Kachanov. Effect of interphase layers on the overall elastic and conductiveproperties of matrix composites. Int J Solids Struct2007,44:1304~1315.
[118] L. Mullins, N.R. Tobin. Stress softenings in rubber vulcanizates. J Appl Polymer Sci1965,9:2993~3009.
[119] H.J. Qi, M.C. Boyce. Constitutive model for stretch-induced softening of the stress–stretchbehavior of elastomeric materials. J Mech Phys Solids2004,52:2187~2205.
[120] J.S. Bergstrom, M.C. Boyce. Mechanical Behavior of Particle Filled Elastomers. Rubber ChemTech1999,72:633~656.
[121] P. Ponte Casta eda, Second-order homogenization estimates for nonlinear compositesincorporating field fluctuations. I–Theory. J Mech Phys Solids2002,50:737~757.
[122] O. Lopez-Pamies, P. Ponte-Casta eda. Homogenization-based constitutive models for porouselastomers and implications for macroscopic instabilities: I—Analysis. J Mech Phys Solids2007,55:1677~1701.
[123] V. Bouchart, M. Brieu, D. Kondo, M. Na t Abdelaziz. Implementation and numericalverification of a non-linear homogenization method applied to hyperelastic composites.Computat Mater Sci2008,43:670~680.
[124] V. Bouchart, M. Brieu, N. Bhatnagar, D. Kondo. A multiscale approach of nonlinearcomposites under finite deformation: Experimental characterization and numerical modeling.Int J Solids Struct2010,47:1737~1750.
[125] H.M. Yin, L.Z. Sun, J.S. Chen. Micromechanics-based hyperelastic constitutive modeling ofmagnetostrictive particle-filled elastomers. Mech Mater2002,34:505~516.
[126] Sia Nemat-Nasser. Multi-inclusion method for finite deformations: exact results andapplications. Mater Science Eng A2000,285:239~245.
[127] Sia Nemat-Nasser. Averaging theorems in finite deformation plasticity. Mech Mater1999,31:493~523.
[128] W.H. Wang, K.A. Kistler, K. Sadeghipour, G. Baran. Molecular dynamics simulation of AFMstudies of a single polymer chain.Physics Letters A2008,372:7007~7010.
[129] C. Miehe, S. Goktepe, F. Lu lei. A micro-macro approach to rubber-like materials—Part I: thenon-affine micro-sphere model of rubber elasticity. J Mechanics Phys Solids2004,52:2617~2660.
[130] M. B l, S. Reese. Finite element modelling of rubber-like polymers based on chain statistics.Int J Solids Struct2006,43:2~26.
[131] A.D. Drozdov, A. Dorfmann. A micro-mechanical model for the response of filledelastomers at finite strains. Int J Plasticity2003,19:1037~1067.
[132] M. Brieu, F. Devries. Micro-mechanical approach and algorithm for the study of damageappearance in elastomer composites. Compos Struct1999,46:309~319.
[133] M.T. Abadi. Characterization of heterogeneous materials under shear loading at finite strain.Compos Struct2010,92:578~584.
[134] Y. Zhong, J. Wang, Y. M. Wu, Z.P. Huang. Effective moduli of particle-filled composite withinhomogeneous interphase Part II: mapping method and evaluation. Compos Sci Tech2004,64:1353~1362.
[135] C. P. Tsui, D. Z. Chen, C.Y. Tang, P. S. Uskokovic, J. P. Fan. Prediction for debonding damageprocess of glass beads-reinforced modified polyphenylene oxide under simple shear. J MaterProc Tech2005,167:429~437.
[136] L.G. Zhao, N.A. Warrior, A.C. Long. A micromechanical study of residual stress and its effecton transverse failure in polymer–matrix composites. Int J Solids Struct2006,43:5449~5467.
[137] L.G. Zhao, N.A. Warrior, A.C. Long. A thermo-viscoelastic analysis of process-inducedresidual stress in fibre-reinforced polymer–matrix composites. Mater Sci Eng A2007,452~453:483~498.
[138] Z.H. Xia, Y. F. Zhang, F. Ellyin. An unified periodical boundary conditions for presentativevolume elements of composites and applications. Int J Solids Struct2003,40:1907~1721.
[139] Y.L. Wu, Z. F. Dong. Three-dimensional finite element analysis of composites with coatedspherical inclusions. Mater Sci Eng A1995,203:314~323.
[140] J.C. Wang, G.C. Yang. The energy dissipation of particle-reinforced metal-matrix compositewith ductile interphase. Mater Sci Eng A2001,303(1):77~81.
[141] V.P. Privalko, V. F. Shumsky, E. G. Privalko. Viscoelasticity and flow behavior of irradiationgrafted nano-inorganic particle filled polypropylene composites in the melt state. J Mater ProcTech2003,137(1-3):208~213.
[142] C.T. Sun, R.S. Vaidya. Prediction of composite properties from a representative volumeelement. Compos Sci Tech1990,56:171~179.
[143] R.A. Naik, J.H. Crews. Micromechanical Analysis of fibermatrix Interface Stresses underThermo mechanical Loadings. Composite Materials: Testing and Design1993,1206:205~219.
[144] J.R. Brockenbrough, S. Suresh, H.A.Wienencke. Deformation of metal-matrix composites withcontinuous fibers: Geometrical effects of fiber distribution and shaper. Acta Metall Mater1991,39(5):735~752.
[145] P. Potluri, A. Manan. Mechanics of non-orthogonally interlaced textile composites. Compos A2007,38:1216~1226.
[146] Z.A. Moshovidis, T. Mura. Two ellip-tical inhomogeneities by the equivalent inclusion method.ASME J Appl Mech1975,42:847~852.
[147] P. Ganguly, W.J. Poole. Influence of reinforcement arrangement on the local reinforcementstresses in composite materials. J Mech Phys Solids2004,52(6):1355~1377.
[148]严鹏,蒋持平.考虑周期微结构分布特征的Mori-Tanaka方法.复合材料学报2007,24(4):178~184.
[149]徐耀玲.含双周期夹杂复合材料细观力学研究[D].北京:北京航空航天大学,2003.
[150] P.B. Bowden. The elastic modulus of an amorphous glassy polymer. Polymer1968,9:449~454.
[151] V.A. Kuznetsov. Influence of the stress jump condition at the porous-medium/clear-fluidinterface on a flow at a porous wall. Compos Mater1973,9:401~404.
[152] I.V. Yannas, R.R. Luise. Distinction between two molecular mechanisms for deformation ofglassy amorphous polymers. J Macromolecular Sci B1982,21:443~474.
[153] Y. Tomita, S. Tanaka. Prediction of deformation behavior of glassy polymers based onmolecular chain network model. Int J Solids Struct1995,32:3423~3434.
[154] E.M. Arruda, M.C. Boyce. A three-dimensional constitutive model for the large stretchbehavior of rubber elastic materials. J Mech Phys Solids1993,41:389~412.
[155] G.K. Hu, G. Guo, D. Baptiste. A micromechanical model of influence of particle fracture andparticle cluster on mechanical properties of metal matrix composites. Comput Mater Sci1998,9:420~430.
[156] B. Bittmann, F. Haupert, A.K. Schlarb, Preparation of TiO2/epoxy nanocomposites byultrasonic dispersion and their structure property relationship.The6thAsin-AustralasianConference on Composite Materials, Kumamoto, Japan,2008,9~12.
[157] D. Gersappe, Molecular mechanisms of failure in polymer nanocomposites. Phys Rev Lett2002,89:058301.
[158] O.H. Yeoh. Some Forms of the Strain Energy Function for Rubber. Rubber Chem Tech1993,66:754~771.
[159] Y. Benveniste. A new approach to the application of Mori-Tanaka's theory in compositematerials. Mech Mater1987,6:147~157.
[160] D.J. Lloyd. Particle reinforced aluminium and magnesium matrix composites. Int Mater Rev1994,39(1):1~23.
[161] B.C. Kima, S.W. Parka, D.G. Lee. Fracture toughness of the nano-particle reinforced epoxycomposite. Compos Struct2008,86:69~77.
[162] J.J. Williams, Z Flom, A.A. Amell, N Chawla, X Xiao, F De Carlo. Damage evolution in SiCparticle reinforced Al alloy matrix composites by X-ray synchrotron tomography. Acta Mater2010,58(18):6194~6205.
[163] A. Brara, F. Camborde, J.R. Klepaczko, C. Mariotti. Experimental and numerical study ofconcrete at high strain rates in tension. Mech Mater2001,33(1):33~45.
[164] G.K. Hu. A method of plasticity for general aligned spherical void or fiber-reinforcedcomposites. Int J Plasticity1996,12:439~449.
[165] Y.P. Qiu, G.J. Weng. A theory of plasticity for porous mate-rials and particle-reinforcedcomposites. ASME J Appl Mech1992,59:261~268.
[166] R. Lakes. Continuum models for materials with microstructure, ed. H. Mühlhaus, J. Wiley, N. Y.Ch.1995,1:1~22.
[167] H.J. Gao, B.H. Ji, I.L. Jager, E. Arz and P. Fratzl. Materials become insensitive to flaws atnanoscale: Lessons from nature. PNAS2003,100:5597~5600.
[168] J. Segurado, J. LLorca. Computational micromechanics of composites: The effect of particlespatial distribution. Mech Mater2006,38:873~883.
[169] J. Segurado, C. González, J. LLorca. A numerical investigation of the effect of particleclustering on the mechanical properties of composites. Acta Mater2003,51:2355~2369.
[170] T. Mura, Micromechanics of Defects in Solids. Martinus Nijhoff Publication, The Hague1987.