激光熔覆颗粒增强复合涂层的力学性能及损伤破坏机理研究
|
摘要
激光熔覆颗粒增强复合涂层材料，由于其高硬度、耐磨损、耐高温等优越和特殊的性能，在机械制造、石油化工、核工程、汽车工业、航空航天等恶劣和特殊环境下工作的机械零件和元件中得到了越来越广泛的应用。然而复合涂层在受到不同形式的载荷作用时，内部会发生颗粒断裂、颗粒与基体的界面开裂等各种形式的损伤；另外，涂层的微孔洞、微裂纹等缺陷是激光熔覆过程中很容易出现的一个质量问题，这些缺陷的存在会加剧涂层的开裂破坏行为，因此需要对激光熔覆复合涂层的力学性能以及损伤机制作进一步深入系统的研究。
本文以激光熔覆H13-TiC复合涂层为研究对象，研究了复合涂层的宏观力学性能和微观损伤机理；借助纳米压痕仪测量复合涂层的微区力学性能，并结合弹塑性有限元方法计算颗粒的断裂强度；以细观力学理论为基础，结合损伤力学、塑性力学和实验研究结果等，提出一种颗粒增强复合涂层材料损伤本构模型，以有限元软件ABAQUS子程序UMAT为基础，研究分析细观结构对颗粒增强涂层材料力学性能以及损伤破坏的影响。研究工作为提高复合涂层的强度分析水平以及优化激光熔覆工艺奠定理论和实验上的基础。本文的主要工作和成果如下：
1.利用合适的激光加工工艺，在模具钢（H13）表面制备H13-TiC复合涂层。测试了不同TiC颗粒体积分数下H13-TiC复合涂层的力学性能，并结合扫描电镜（SEM）分析复合涂层的微结构演化。结果显示复合涂层在制备过程中产生许多微气孔，涂层的失效形式以颗粒断裂为主，在拉伸后期出现一些颗粒和基体界面开裂的现象，这对复合涂层的损伤本构模型提出奠定了实验基础。
2.采用纳米压痕仪，测得复合涂层TiC颗粒以及H13基体的弹性模量及硬度，研究分析了压痕位置与颗粒中心的距离、压入深度以及颗粒形貌对压痕结果的影响。建立颗粒压痕的有限元模型，结合压痕实验结果，计算TiC颗粒的断裂强度，实现利用纳米压痕技术表征陶瓷颗粒断裂强度的测试方法。
3.基于Mori-Tanaka均匀场理论，计算分析不同颗粒体积分数下复合涂层的弹塑性性能。另外，基于WeiBull损伤准则，描述颗粒在拉伸过程中的损伤状态，结合实验数据，计算WeiBull参数。
4.通过耦合Gologanu–Leblond–Devaux (GLD)细观损伤模型与Mori–Tanaka（M-T）均匀化方法，建立颗粒增强复合涂层材料损伤破坏的分析模型。把涂层制备过程中产生的微气孔作为损伤模型的初始孔洞，数值模拟分析孔洞形状、尺寸、分布、颗粒密度以及颗粒损伤等对复合涂层拉伸应力应变曲线以及断裂韧性的影响。最后对模型预测与拉伸实验结果进行比较，结果表明该模型能很好地描述激光熔覆复合涂层的损伤演化特征。
Due to its high strength, high temperature resistance and good wear resistance, the lasercladding composite coatings has been widely used as mechanical parts and components in thespecial and harsh field such as machinery manufacturing, petrochemical, nuclear engineering,automotive industry, aerospace. However, some kind damages of composite coatings suchparticle broken and particle/matrix interface debonding will occur under different loadingconditions. On the other hand, the defects of composite coatings such as micro-void introducedduring preparation will accelerate the failure of material. Further and deeper researches on themechanical properties and damage mechanism of laser cladding composite coatings werenecessarily required.
In this dissertation, macro-mechanical properties and micro-damage mechanism of lasercladding H13-TiC composite coatings has been studied. The mechanical properties of particleand matrix phases at the microscopic scales were measured by nanoindentation. The particlecracking induced by nanoindentation was observed and the critical fracture strength of particlewas obtained by the combination of experiment and finite element analysis. Based on themicromechanics, elastic-plastic mechanics and experimental results, a new damage constitutivemodel of composite coatings was presented. The model was embedded in the finite elementsoftware ABAQUS subroutine UMAT, focusing on investigation of damage and failurebehavior of composite coatings. The research work will provide theoretical, numerical andexperimental support for the preparation of laser cladding composite coatings. The main workand achievements are as follows:
1. With appropriate laser processing, the H13-TiC composite coatings was cladded on the H13die steel. The mechanical properties of composite coatings containing different particlevolume were obtained by uniaxial tensile experiment. The initial and evolution microstructureof material as well as damage mechanism were observed by scanning electron microscopy(SEM). The results showed that micro-defects such as micro-void were introduced duringpreparation, particle fractures was the main reason of crack formation in the composite coatings,the particle/matrix interface debonding appeared in the later tensile experiment. Such resultsprovided the experimental basis of damage model.
2. The mechanical properties such as hardness and modulus of TiC particle and H13matrixwere measured by nanoindentation. In addition, the influence of distance between indentationposition and particle center, indentation depth and the particle morphology on the indentationresults were investigated; The critical fracture stress of TiC particle was obtained by thecombination of experiment and finite element analysis characterizing of the strengthmeasurement of ceramic particle.
3. The elastic-plastic properties of composite coatings with different particle volume werestudied by Mori-Tanaka mean-field homogenization scheme. Based on the experimental results,the parameters of Weibull damage principal, which characterized the damage mode of particle,were obtained.
4.Coupling Mori-Tanaka(M-T) mean-field homogenization scheme with theGologanu–Leblond–Devaux (GLD) yield criterion, the damage model accounting for theeffect of void shape, void size, void volume and particle damage on tensile behavior oflaser-processed composite coatings was developed. At last, the prediction results of this modelwas compared with experimental results, and the consistence demonstrated that the model welldescribed the damage process of laser cladding composite coatings.
本文以激光熔覆H13-TiC复合涂层为研究对象，研究了复合涂层的宏观力学性能和微观损伤机理；借助纳米压痕仪测量复合涂层的微区力学性能，并结合弹塑性有限元方法计算颗粒的断裂强度；以细观力学理论为基础，结合损伤力学、塑性力学和实验研究结果等，提出一种颗粒增强复合涂层材料损伤本构模型，以有限元软件ABAQUS子程序UMAT为基础，研究分析细观结构对颗粒增强涂层材料力学性能以及损伤破坏的影响。研究工作为提高复合涂层的强度分析水平以及优化激光熔覆工艺奠定理论和实验上的基础。本文的主要工作和成果如下：
1.利用合适的激光加工工艺，在模具钢（H13）表面制备H13-TiC复合涂层。测试了不同TiC颗粒体积分数下H13-TiC复合涂层的力学性能，并结合扫描电镜（SEM）分析复合涂层的微结构演化。结果显示复合涂层在制备过程中产生许多微气孔，涂层的失效形式以颗粒断裂为主，在拉伸后期出现一些颗粒和基体界面开裂的现象，这对复合涂层的损伤本构模型提出奠定了实验基础。
2.采用纳米压痕仪，测得复合涂层TiC颗粒以及H13基体的弹性模量及硬度，研究分析了压痕位置与颗粒中心的距离、压入深度以及颗粒形貌对压痕结果的影响。建立颗粒压痕的有限元模型，结合压痕实验结果，计算TiC颗粒的断裂强度，实现利用纳米压痕技术表征陶瓷颗粒断裂强度的测试方法。
3.基于Mori-Tanaka均匀场理论，计算分析不同颗粒体积分数下复合涂层的弹塑性性能。另外，基于WeiBull损伤准则，描述颗粒在拉伸过程中的损伤状态，结合实验数据，计算WeiBull参数。
4.通过耦合Gologanu–Leblond–Devaux (GLD)细观损伤模型与Mori–Tanaka（M-T）均匀化方法，建立颗粒增强复合涂层材料损伤破坏的分析模型。把涂层制备过程中产生的微气孔作为损伤模型的初始孔洞，数值模拟分析孔洞形状、尺寸、分布、颗粒密度以及颗粒损伤等对复合涂层拉伸应力应变曲线以及断裂韧性的影响。最后对模型预测与拉伸实验结果进行比较，结果表明该模型能很好地描述激光熔覆复合涂层的损伤演化特征。
Due to its high strength, high temperature resistance and good wear resistance, the lasercladding composite coatings has been widely used as mechanical parts and components in thespecial and harsh field such as machinery manufacturing, petrochemical, nuclear engineering,automotive industry, aerospace. However, some kind damages of composite coatings suchparticle broken and particle/matrix interface debonding will occur under different loadingconditions. On the other hand, the defects of composite coatings such as micro-void introducedduring preparation will accelerate the failure of material. Further and deeper researches on themechanical properties and damage mechanism of laser cladding composite coatings werenecessarily required.
In this dissertation, macro-mechanical properties and micro-damage mechanism of lasercladding H13-TiC composite coatings has been studied. The mechanical properties of particleand matrix phases at the microscopic scales were measured by nanoindentation. The particlecracking induced by nanoindentation was observed and the critical fracture strength of particlewas obtained by the combination of experiment and finite element analysis. Based on themicromechanics, elastic-plastic mechanics and experimental results, a new damage constitutivemodel of composite coatings was presented. The model was embedded in the finite elementsoftware ABAQUS subroutine UMAT, focusing on investigation of damage and failurebehavior of composite coatings. The research work will provide theoretical, numerical andexperimental support for the preparation of laser cladding composite coatings. The main workand achievements are as follows:
1. With appropriate laser processing, the H13-TiC composite coatings was cladded on the H13die steel. The mechanical properties of composite coatings containing different particlevolume were obtained by uniaxial tensile experiment. The initial and evolution microstructureof material as well as damage mechanism were observed by scanning electron microscopy(SEM). The results showed that micro-defects such as micro-void were introduced duringpreparation, particle fractures was the main reason of crack formation in the composite coatings,the particle/matrix interface debonding appeared in the later tensile experiment. Such resultsprovided the experimental basis of damage model.
2. The mechanical properties such as hardness and modulus of TiC particle and H13matrixwere measured by nanoindentation. In addition, the influence of distance between indentationposition and particle center, indentation depth and the particle morphology on the indentationresults were investigated; The critical fracture stress of TiC particle was obtained by thecombination of experiment and finite element analysis characterizing of the strengthmeasurement of ceramic particle.
3. The elastic-plastic properties of composite coatings with different particle volume werestudied by Mori-Tanaka mean-field homogenization scheme. Based on the experimental results,the parameters of Weibull damage principal, which characterized the damage mode of particle,were obtained.
4.Coupling Mori-Tanaka(M-T) mean-field homogenization scheme with theGologanu–Leblond–Devaux (GLD) yield criterion, the damage model accounting for theeffect of void shape, void size, void volume and particle damage on tensile behavior oflaser-processed composite coatings was developed. At last, the prediction results of this modelwas compared with experimental results, and the consistence demonstrated that the model welldescribed the damage process of laser cladding composite coatings.
引文
[1]徐滨士,朱绍华,刘世参.表面工程与维修[M].1996.
[2]关成君,陈再良.机械产品的磨损,磨粒磨损失效分析[J].理化检验:物理分册,2006,42(1):50-54.
[3] Sundararajan G, Prasad K, Rao D, et al. A comparative study of tribological behavior of plasma andD-gun sprayed coatings under different wear modes[J]. Journal of Materials Engineering andPerformance,1998,7(3):343-351.
[4] Nerz J, Kushner B,Rotolico A. Microstructural evaluation of tungsten carbide-cobalt coatings[J].Journal of Thermal Spray Technology,1992,1(2):147-152..
[5]李强.激光熔覆耐磨涂层的研究现状与展望[J].宇航材料工艺,1999,1(1):13-17.
[6]黄瑞芬,罗建民,王春琴.激光熔覆技术的应用及其发展[J].兵器材料科学与工程,2005,28(4):57-59.
[7]刘其斌,李绍杰.航空发动机叶片铸造缺陷激光熔覆修复的研究[J].金属热处理,2006,31(3):52-55.
[8]王晓荣,王新洪,杜宝帅,等.激光熔覆Fe-Ti-V-Cr-C合金涂层的微观组织和性能[J].材料工程,201111(3):50-54.
[9]符跃春,杨智成,王国华,等. Al3Ti和TiC/Al3Ti激光熔覆涂层的高温氧化和浸泡腐蚀性能[J].重庆大学学报,201033(7):12-16..
[10]曹凤国.激光加工技术[M].北京科学技术出版社,2007.
[11]李军. Cr12MoV模具钢激光熔覆Ni基/WC合金工艺及性能研究[D].华东交通大学,2008.
[12] Gnanamuthu D S. Laser surface treatment[J]. Optical Engineering,1980,19(5):783-792.
[13]汤光平,黄文荣,杨家林. Cr12MoV模具钢的激光熔覆[J].金属热处理,200227(4):13-19.
[14]汤光平,黄文荣,杨家林.模具钢的激光表面改性研究[J].材料保护,200235(2):37-40.
[15]宋仁国,王晶,林鑫,等.γ-TiAI金属间化合物合金表面激光熔覆TiC-Ti-AI涂层研究[J].稀有金属材料与工程,200837(12):2191-2194.
[16] Wang A H,Yue T M. YAG laser cladding of an Al-Si alloy onto an Mg/SiC composite for theimprovement of corrosion resistance[J]. Composites Science and Technology,61(11):1549-1554.
[17]钱兆勇,钟敏霖,刘文今,等.瓦楞辊高耐磨激光熔覆颗粒增强铁基复合涂层[J].中国激光,200835(8):1271-1276.
[18]陈宁,周立志,徐桂梅. Cr12MoV模具钢激光熔覆Ni60/WC复合涂层的组织与性能[J].热加工工艺,2009,38(8):87-88.
[19] VanAcker K, Vanhoyweghen D, Persoons R, et al. Influence of tungsten carbide particle size anddistribution on the wear resistance of laser clad WC/Ni coatings[J]. Wear,2005,258(1-4):194-202.
[20]郭绍义,李兴俊,杨秋合,等.激光熔覆WC-Ni/TiC涂层的组织和摩擦磨损性能研究[J].材料工程,2008,6(7):72-75.
[21]楼白杨,徐斌,白万金,等.激光熔覆制备SiC/Ni基复合涂层及其耐冲蚀性能[J].中国激光,2008,35(1):147-150.
[22] Li R, Shi Y, Liu J, et al. Selective laser melting W–10wt.%Cu composite powders[J]. TheInternational Journal of Advanced Manufacturing Technology,2010,48(5):597-605.
[23]刘富荣,高谦,高登攀,等.激光熔覆WC增强复合涂层开裂行为分析[J].材料工程,20035:37-39.
[24] Müller S, Pries H, Dilger K, et al., Applying Functionally Graded Materials by Laser Cladding: acost-effective way to improve the Lifetime of Die-Casting DiesGlocalized Solutions for Sustainabilityin Manufacturing. Springer Berlin Heidelberg,2011,3(6):235-239.
[25] Liu Y, Koch J, Mazumder J, et al. processing microstructure and properties of laser-clad Ni-alloy FP-5on Al-alloy AA333[J]. Metallurgical and Materials Transactions B-Process Metallurgy and MaterialsProcessing Science,1994,25(3):425-434.
[26] Mazumder J, Choi J, Nagarathnam K, et al. The direct metal deposition of H13tool steel for3-Dcomponents[J]. Jom-Journal of the Minerals Metals&Materials Society,1997,49(5):55-60.
[27] Chai T,Chou C K. Mechanical properties of laser-welded cast titanium joints under differentconditions[J]. The Journal of Prosthetic Dentistry,1998,79(4):477-483.
[28] Gu D,Shen Y. Influence of reinforcement weight fraction on microstructure and properties ofsubmicron WC–Cop/Cu bulk MMCs prepared by direct laser sintering[J]. Journal of Alloys andCompounds,2007,431(1-2):112-120.
[29] Vreeling J A, Hamstra G A, et al. In-situ microscopy investigation of failure mechanisms in Al/SiCpmetal matrix composite produced by laser embedding[J]. Scripta Materialia,2000,42(3):589–595.
[30] Liu D, Zhang S Q, Li A, et al. Microstructure and tensile properties of laser melting depositedTiC/TA15titanium matrix composites[J]. Journal of Alloys and Compounds,2009,485(1-2):156-162.
[31] Liu D, Zhang S Q, Li A, et al. Creep rupture behaviors of a laser melting deposited TiC/TA15in situtitanium matrix composite[J]. Materials& Design,2010,31(6):3127-3133.
[32] ISO14577. Metallic materials—instrumented indentation test for hardness and materials parameters.[S].2002.
[33] Cui C, Guo Z, Wang H, et al. In situ TiC particles reinforced grey cast iron composite fabricated bylaser cladding of Ni–Ti–C system[J]. Journal of Materials Processing Technology,2007,183(2–3):380-385.
[34] Rabe U, Amelio S, Kopycinska M, et al. Imaging and measurement of local mechanical materialproperties by atomic force acoustic microscopy[J]. Surface and Interface Analysis,2002,33(2):65-70.
[35] Ho E, Marcolongo M. Effect of coupling agents on the local mechanical properties of bioactive dentalcomposites by the nano-indentation technique[J]. Dental Materials,2005,21(7):656-664.
[36] Volodin A, Ahlskog M, Seynaeve E, et al. Imaging the Elastic Properties of Coiled Carbon Nanotubeswith Atomic Force Microscopy[J]. Physical Review Letters,2000,84(15):3342-3345.
[37] Vinckier A, Semenza G. Measuring elasticity of biological materials by atomic force microscopy[J].FEBS Letters,1998,430(1–2):12-16.
[38] Saha R, Nix W D. Effects of the substrate on the determination of thin film mechanical properties bynanoindentation[J]. Acta Materialia,2002,50(1):23-38..\
[39] Durst K, Goken M,Vehoff H. Finite element study for nanoindentation measurements on two-phasematerials[J]. J mater Res,2004,191(85-93).
[40] Kim H S, Bush M B,Estrin Y. A phase mixture model of a particle reinforced composite with finemicrostructure[J]. Materials Science and Engineering: A,2000,276(1–2):175-185.
[41] Hryha E, Zubko P, Dudrová E, et al. An application of universal hardness test to metal powderparticles[J]. Journal of Materials Processing Technology,2009,209(5):2377-2385.
[42] Ulm F J, Vandamme M, Jennings H M, et al. Does microstructure matter for statistical nanoindentationtechniques?[J]. Cement and Concrete Composites,2010,32(1):92-99.
[43] Xia S, Qi Y, Perry T, et al. Strength characterization of Al/Si interfaces: A hybrid method ofnanoindentation and finite element analysis[J]. Acta Materialia,2009,57(3):695-707.
[44] Besterci M, Pe ek L, Zubko P, et al. Mechanical properties of phases in Al–Al4C3mechanicallyalloyed material measured by depth sensing indentation technique[J]. Materials Letters,2005,59(16):1971-1975.
[45] Desaeger M,Verpoest I. On the use of the micro-indentation test technique to measure the interfacialshear strength of fibre-reinforced polymer composites[J]. Composites Science and Technology,1993,48(1–4):215-226..
[46]杨敏.采用纳米压痕测试技术对碳/碳复合材料微观性能的研究[D].上海大学,2008.
[47] Eshelby J D. The determination of the elastic field of an ellipsoidal inclusion and related problems[J].Proceedings of the Royal Society of London,1957,241(3):376-396.
[48] Hill R. Theory of mechanical properties of fiber-strengthened materials:elastic behavior.[J]. Journal ofMechanical of Physics and Solids,1964,12(5):199-212.
[49] Hill R. Continuum micro-mechanics of elastoplastic polycrystals[J]. Journal Mechanics of Physics andSolids,1965,13(8):89-101.
[50] Hill R. A self-consistent mechanics of composite materials[J]. Journal of the Mechanics and Physics ofSolids,1965,13(4):213-222.
[51] Hashin Z,Shtrikman S. On some variational principles in anisotropic and nonhomogeneous elasticity[J].Journal of the Mechanics and Physics of Solids,10(4):335-342.
[52] Hashin Z,Shtrikman S. A variational approach to the theory of the elastic behaviour of multiphasematerials[J]. Journal of the Mechanics and Physics of Solids,11(2):127-140.
[53] Budiansky B. On the elastic moduli of some heterogeneous materials[J]. Journal of the Mechanics andPhysics of Solids,1965,13(4):223-227.
[54] Levin V M. On the coefficients of thermal expansion of heterogeneous materials[J]. Mechanics ofsolids,1967,11(5):58-61.
[55] Hutchinson J W. Elastic-Plastic Behaviour of Polycrystalline Metals and Composites[J]. Preceeding ofthe Royal Society of London,1970,319(1537):247-272.
[56] Mori T,Tanaka K. Average stress in matrix and average elastic energy of materials with misfittinginclusions[J]. Acta Metallurgica,1973,21(5):571-574.
[57] McLaughlin R A. study of the differential scheme for composite materials[J]. International Journal ofEngineering Science,1977,15(4):237-244.
[58] Aboundi J. Mechanics of composite materials: Unified micromechanical approach[J]. Volume29ofstudies in Applied Mechanics. Elsevier,1991,45(4):
[59] Duschlbauer D, B hm H J,Pettermann H E. Computational Simulation of Composites Reinforced byPlanar Random Fibers: Homogenization and Localization by Unit Cell and Mean Field Approaches[J].Journal of Composite Materials2006,40(20):2217-2234.
[60]杨庆生,陈浩然.杂问题中的自洽有限元法和复合材料的平均弹性性能[J].复合材料学报,1992,9(1):67-71.
[61]陈浩然,苏晓风,郑长良.广义自洽有限元迭代平均化方法[J].复合材料学报,1992,9(1):52-56.
[62] Cheng J, Jordan E H,Walker K P. A simple accurate method for calculating local stresses aroundindividual fibers in periodic composites[J]. Composites Part B: Engineering,1999,30(5):453-463.
[63] Ghosh S, Mukhopadhyay S N. A material based finite element analysis of heterogeneous mediainvolving Dirichlet tessellations[J]. Computer Methods in Applied Mechanics and Engineering,1993,104(2):211-247.
[64] Gurson A L. Continuum theory of ductile rupture by void nucleation and growth: Part I—yield criteriaand flow rules for porous ductile media[J]. Journal of Engineering Materials and Technology,1977,99(1-15.
[65] Tvergaard V, Needleman A. Analysis of the cup-cone fracture in a round tensile bar[J]. ActaMetallurgica,1984,32(1):157-169.
[66] Argon A, Im J,Safoglu R. Cavity formation from inclusions in ductile fracture[J]. Metallurgical andMaterials Transactions A,1975,6(4):825-837.
[67] Babout L, Brechet Y, Maire E, et al. On the competition between particle fracture and particledecohesion in metal matrix composites[J]. Acta Materialia,2004,52(15):4517-4525.
[68] Kroon M, Faleskog J. Micromechanics of cleavage fracture initiation in ferritic steels by carbidecracking[J]. Journal of the Mechanics and Physics of Solids,2005,53(1):171-196.
[69] Needleman A. A continuum model for void nucleation by inclusion debonding[J]. Journal of AppliedMechanics,1987,54(3):525-532.
[70] Cho Y T. Incremental damage mechanics of particle or short-fiber reinforced composites includingcracking damage[J]. Journal of Mechanical Science and Technology,2002,16(2):192-202.
[71] Fitoussi J, Bourgeois N, Guo G, et al. Prediction of the anisotropic damaged behavior of compositematerials: introduction of multilocal failure criteria in a micro-macro relationship[J]. ComputationalMaterials Science,1996,5(1-3):87-100.
[72] Brockenbrough J R,Zok F W. On the role of particle cracking in flow and fracture of metal matrixcomposites[J]. Acta Metallurgica et Materialia,1995,43(1):11-20.
[73] Gonzalez C, Llorca J. Prediction of the tensile stress-strain curve and ductility in Al/SiC composites[J].Scripta Materialia,1996,35(1):91-97.
[74] Poza P, Llorca J. Mechanical behavior of Al Li/SiC composites: Part III. Micromechanical modeling[J].Metallurgical and Materials Transactions A,1999,30(13):869-878.
[75] Llorca J,González C. Microstructural factors controlling the strength and ductility of particle-reinforcedmetal-matrix composites[J]. Journal of the Mechanics and Physics of Solids,1998,46(1):1-28.
[76] Dvorak G J, Zhang J. Transformation field analysis of damage evolution in composite materials[J].Journal of the Mechanics and Physics of Solids,2001,49(11):2517-2541.
[77] Ghosh S, Moorthy S. Particle fracture simulation in non-uniform microstructures of metal–matrixcomposites[J]. Acta Materialia,1998,46(3):965-982.
[78] Ibnabdeljalil M, Curtin W A. Strength and reliability of notched fiber-reinforced composites[J]. ActaMaterialia,1997,45(9):3641-3652.
[79] B hm H J, Eckschlager A,Han W. Multi-inclusion unit cell models for metal matrix composites withrandomly oriented discontinuous reinforcements[J]. Computational Materials Science,2002,25(1-2):42-53.
[80] Segurado J,Llorca J. Computational micromechanics of composites: The effect of particle spatialdistribution[J]. Mechanics of Materials,2006,38(8-10):873-883.
[81] Ghosh S, Bai J, Paquet D. Homogenization-based continuum plasticity-damage model for ductilefailure of materials containing heterogeneities[J]. Journal of the Mechanics and Physics of Solids,2009,57(7):1017-1044.
[82] Lee H K, Pyo S H. An elastoplastic multi-level damage model for ductile matrix compositesconsidering evolutionary weakened interface[J]. International Journal of Solids and Structures,2008,45(6):1614-1631.
[83] Tekog C, Pardoen T. A micromechanics based damage model for composite materials[J]. InternationalJournal of Plasticity,2010,26(4):549-569.
[84] Thomason P F. Ductile fracture of metals[D]. Oxford: Pergamon Press,1990..
[85]鲁燕,孔凡志,姚建华,等.半导体激光熔覆TiC/H13涂层的抗回火性能[J].应用激光2010,30(6):451-455.
[86]张群莉,姚建华,骆芳.热作模具H13钢表面激光堆焊类高速钢的实验研究[J].材料热处理学报,2005,26(4):95-97.
[87]汤晓丹,姚建华,孔凡志,等. TiC对激光熔覆H13-TiC复合涂层组织和性能的影响[J].热加工工艺,200938(14):92-96.
[88] Li Q, Lei T C,Chen W Z. Microstructural characterization of WCp reinforced Ni–Cr–B–Si–Ccomposite coatings[J]. Surface and Coatings Technology,1999,114(2–3):285-291.
[89] Li Q, Lei T C,Chen W Z. Microstructural characterization of laser-clad TiCp-reinforced Ni–Cr–B–Si–Ccomposite coatings on steel[J]. Surface and Coatings Technology,1999,114(2–3):278-284.
[90] Ariely S, Shen J, Bamberger M, et al. Laser surface alloying of steel with TiC[J]. Surface and CoatingsTechnology,1991,45(1–3):403-408.
[91]黄尚猛. Cr12模具钢激光熔覆技术的研究[D].天津：天津大学,2008.
[92] Jiang W H,Kovacevic R. Laser deposited TiC/H13tool steel composite coatings and their erosionresistance[J]. Journal of Materials Processing Technology,2007,186(1–3):331-338.
[93] Sun R L, Yang D Z, Guo L X, et al. Laser cladding of Ti-6Al-4V alloy with TiC and TiC+NiCrBSipowders[J]. Surface and Coatings Technology,2001,135(2–3):307-312.
[94] TaeWon K. Heterogeneous void distribution in aluminum metal matrix composites and its effect ondeformation-failure processes[J]. Scripta Materialia,2006,55(12):1115-1118.
[95] Little J E, Yuan X, Jones M I. Characterisation of voids in fibre reinforced composite materials[J]. NDT& E International,2012,46(0):122-127.
[96]毛小南,张廷杰,张小明. TiC颗粒增强钛基复合材料的形变[J].稀有金属材料与工程,2001,35(4):245-248.
[97] Ramesh C S, Keshavamurthy R, Channabasappa B H, et al. Microstructure and mechanical propertiesof Ni–P coated Si3N4reinforced Al6061composites[J]. Materials Science and Engineering: A,2009,502(1–2):99-106.
[98] Wang Q. Microstructural effects on the tensile and fracture behavior of aluminum casting alloysA356/357[J]. Metallurgical and Materials Transactions A,2003,34(12):2887-2899.
[99] V V Bhanuprasad, M A Staley, P Ramakrishnan, et al. Fractography of Metal Matrix Composites[J].Key Engineering Materials,1995,104-107(495-506.
[100] da Silva A A M, Meyer A, Santos J F d, et al. Mechanical and metallurgical properties offriction-welded TiC particulate reinforced Ti–6Al–4V[J]. Composites Science and Technology,2004,64(10–11):1495-1501..
[101] Srivatsan T S, Al-Hajri M, Smith C, et al. The tensile response and fracture behavior of2009aluminum alloy metal matrix composite[J]. Materials Science and Engineering: A,2003,346(1–2):91-100.
[102] Maziasz P J, Payzant E A, Schlienger M E, et al. Residual stresses and microstructure of H13steelformed by combining two different direct fabrication methods[J]. Scripta Materialia,1998,39(10):1471-1476.
[103] Hauert A, Rossoll A,Mortensen A. Ductile-to-brittle transition in tensile failure of particle-reinforcedmetals[J]. Journal of the Mechanics and Physics of Solids,2009,57(3):473-499..
[104] Furnémont Q, Kempf M, Jacques P J, et al. On the measurement of the nanohardness of theconstitutive phases of TRIP-assisted multiphase steels[J]. Materials Science and Engineering: A,2002,328(1–2):26-32.
[105] William D N. Elastic and plastic properties of thin films on substrates: nanoindentation techniques[J].Materials Science and Engineering: A,1997,234–236(0):37-44.
[106] Bhowmick S, Jayaram V,Biswas S K. Deconvolution of fracture properties of TiN films on steelsfrom nanoindentation load–displacement curves[J]. Acta Materialia,2005,53(8):2459-2467.
[107] Oliver W, Pharr G. An improved technique for determining hardness and elastic modulus using loadand displacement sensing indentation[J]. Joumai of Materials Research,1992,7(6):1564–1583.
[108] Seshadri S, Srinivasan M,King L. indentation fracture testing of ceramics[[J]. Ceramic Eng. Sci. Proc.,1983,4(9-10):853-863.
[109] Hysitron TI900. nanoindentaion system operation guide[Z].2008.
[110] Ure a A, Rams J, Escalera M D, et al. Characterization of interfacial mechanical properties in carbonfiber/aluminium matrix composites by the nanoindentation technique[J]. Composites Science andTechnology,2005,65(13):2025-2038.
[111] Pour H A, Lieblich M, López A J, et al. Assessment of tensile behaviour of an Al–Mg alloy compositereinforced with NiAl and oxidized NiAl powder particles helped by nanoindentation[J]. CompositesPart A: Applied Science and Manufacturing,2007,38(12):2536-2540.
[112] Mussert K M, Vellinga W P, Bakker A, et al. A nano-indentation study on the mechanical behaviour ofthe matrix material in an AA6061-Al<sub>2</sub>O<sub>3</sub> MMC[J].Journal of Materials Science,2002,37(4):789-794.
[113] Walter C, Antretter T, Daniel R, et al. Finite element simulation of the effect of surface roughness onnanoindentation of thin films with spherical indenters[J]. Surface and Coatings Technology,2007,202(4–7):1103-1107.
[114] Kim J-Y, Kang S-K, Lee J-J, et al. Influence of surface-roughness on indentation size effect[J]. ActaMaterialia,2007,55(10):3555-3562.
[115] Bouzakis K D, Michailidis N, Hadjiyiannis S, et al. The effect of specimen roughness and indenter tipgeometry on the determination accuracy of thin hard coatings stress–strain laws by nanoindentation[J].Materials Characterization,2002,49(2):149-156.
[116] Fischer-Cripps A C. Nanoindentation[M]. NewYork: Spring-Verlag,2002.
[117] Johnson K L. Contact Mechanics[M]. Cambridge:Cambridge University Press,1985.
[118]张泰华.微/纳米力学测试技术及其应用[M].机械工业出版社,2005.
[119] Lin S, Hills D A,Warren P D. A theoretical investigation of sharp indentation testing of a nearly-brittlematerial, with some experimental results[J]. Journal of the Mechanics and Physics of Solids,2000,48(10):2057-2075.
[120] Lawn B R,Evans A G. A model for crack initiation in elastic/plastic indentation fields[J]. Journal ofMaterials Science,1977,12(11):2195-2199.
[121] Larsson P-L,E. Giannakopoulos A. Tensile stresses and their implication to cracking at pyramidindentation of pressure-sensitive hard metals and ceramics[J]. Materials Science and Engineering: A,1998,254(1–2):268-281.
[122] Sun Y, Bell T,Zheng S. Finite element analysis of the critical ratio of coating thickness to indentationdepth for coating property measurements by nanoindentation[J]. Thin Solid Films,1995,258(1–2):198-204.
[123] Lichinchi M, Lenardi C, Haupt J, et al. Simulation of Berkovich nanoindentation experiments on thinfilms using finite element method[J]. Thin Solid Films,1998,312(1–2):240-248.
[124] Shan Z,Sitaraman S K. Elastic–plastic characterization of thin films using nanoindentationtechnique[J]. Thin Solid Films,2003,437(1–2):176-181.
[125] Antunes J M, Fernandes J V, Menezes L F, et al. A new approach for reverse analyses indepth-sensing indentation using numerical simulation[J]. Acta Materialia,2007,55(1):69-81..
[126] H. Buckle. Metallurgical Reviews4[M]. London, Institute of Metals,1959.
[127] Babu J S S,Kang C G. Nanoindentation behaviour of aluminium based hybrid composites withgraphite nanofiber/alumina short fiber[J]. Materials& Design,2010,31(10):4881-4885.
[128] Guemmaz M, Mosser A, Boudoukha L, et al. Ion beam synthesis of non-stoichiometric titaniumcarbide: composition structure and nanoindentation studies[J]. Nuclear Instruments and Methods inPhysics Research Section B: Beam Interactions with Materials and Atoms,1996,111(3–4):263-270.
[129] Mencin P, Van Tyne C,Levy B. A Method for Measuring the Hardness of the Surface Layer on HotForging Dies Using a Nanoindenter[J]. Journal of Materials Engineering and Performance,2009,18(8):1067-1072.
[130] Li M. Characterization and modeling of damage in metal matrix composite microstructures[D]. TheOhio State University,1998.
[131] Mahesh M. Plasma spray processing of TiC-based coatings for sliding wear resistance[D]. DrexelUniversity,1997.
[132]秦庆华,杨庆生.非均匀材料多场耦合行为的宏细观理论[M].北京：高等教育出版社,2006.
[133] Eshelby J D. The determination of the elastic field of an ellipsoidal inclusion and related problems[J].Mathematical and Physical Sciences,1957,241(7):376-396.
[134] Benveniste Y. A new approach to the application of Mori–Tanaka’s theory in composite materials[J].Mechanics of Materials,1987,6(2):147–157.
[135] Doghri I,Ouaar A. Homogenization of two-phase elasto-plastic composite materials and structures:Study of tangent operators, cyclic plasticity and numerical algorithms[J]. International Journal ofSolids and Structures,2003,40(7):1681-1712.
[136] González C,Llorca J. A self-consistent approach to the elasto-plastic behaviour of two-phase materialsincluding damage[J]. Journal of the Mechanics and Physics of Solids,2000,48(4):675-692.
[137] Segurado J, Llorca J,González C. On the accuracy of mean-field approaches to simulate the plasticdeformation of composites[J]. Scripta Materialia,2002,46(7):525-529.
[138] Doghri I,Tinel L. Micromechanical modeling and computation of elasto-plastic materials reinforcedwith distributed-orientation fibers[J]. International Journal of Plasticity,2005,21(10):1919-1940.
[139] McClintock F A. A Criterion for Ductile Fracture by the Growth of Holes[J]. Journal of AppliedMechanics1968,135(363-371.
[140] Rice J R,Tracey D M. On the ductile enlargement of voids in triaxial stress fields[J]. Journal of theMechanics and Physics of Solids,1969,17(3):201-217.
[141]余寿文,冯桥西.损伤力学[M].北京：清华大学出版社,1997.
[142] Faleskog J, Gao X,Shih C. Cell model for nonlinear fracture analysis–I. Micromechanicscalibration[J]. International Journal of Fracture,1998,89(4):355-373.
[143] Leblond J B, Perrin G,Devaux J. An improved Gurson-type model for hardenable ductile metals[J].European journal of mechanics,1995,14(5):499-527.
[144] Li Z, Wang C,Chen C. The influence of matrix yield stress gradient on the growth and coalescence ofspheroidal voids[J]. International Journal of Solids and Structures,2002,39(3):601-616..
[145] Li Z, Wang C,Chen C. The evolution of voids in the plasticity strain hardening gradient materials[J].International Journal of Plasticity,2003,19(2):213-234.
[146]王自强,秦嘉亮.含孔洞非线性材料的本构势和孔洞扩展率[J].固体力学学报,1989,2(5):127-141.
[147] Yi S,Duo W. A lower bound approach to the yield loci of porous materials[J]. Acta Mechanica Sinica,1989,5(3):237-243.
[148] Huang Y. Accurate dilatation rates for spherical voids in triaxial stress fields[J]. Journal of AppliedMechanics,1991,58(4):1084-1086.
[149] Zhang K S, Bai J B,Fran ois D. Numerical analysis of the influence of the Lode parameter on voidgrowth[J]. International Journal of Solids and Structures,2001,38(32–33):5847-5856.
[150] Becker R, Smelser R E,Richmond O. The effect of void shape on the development of damage andfracture in plane-strain tension[J]. Journal of the Mechanics and Physics of Solids,1989,37(1):111-129.
[151] Becker R, Smelser R, Richmond O, et al. The effect of void shape on void growth and ductility inaxisymmetric tension tests[J]. Metallurgical and Materials Transactions A,1989,20(5):853-861.
[152] Yee K C,Mear M E. Effect of void shape on the macroscopic response of non-linear porous solids[J].International Journal of Plasticity,1996,12(1):45-68.
[153] Gologanu M, Leblond J-B, Devaux J. Approximate models for ductile metals containingnon-spherical voids—Case of axisymmetric prolate ellipsoidal cavities[J]. Journal of the Mechanicsand Physics of Solids,1993,41(11):1723-1754.
[154] Gologanu M, Leblond J-B, Devaux J. Approximate Models for Ductile Metals ContainingNonspherical Voids---Case of Axisymmetric Oblate Ellipsoidal Cavities[J]. Journal of EngineeringMaterials and Technology,1994,116(3):290-297.
[155] Kim J, Gao X. A generalized approach to formulate the consistent tangent stiffness in plasticity withapplication to the GLD porous material model[J]. International Journal of Solids and Structures,2005,42(1):103-122.
[156] Huber G, Brechet Y, Pardoen T. Predictive model for void nucleation and void growth controlledductility in quasi-eutectic cast aluminium alloys[J]. Acta Materialia,2005,53(9):2739-2749.
[157] Brunet M, Morestin F,Walter-Leberre H. Failure analysis of anisotropic sheet-metals using a non-localplastic damage model[J]. Journal of Materials Processing Technology,2005,170(1–2):457-470.
[158] Croix P, Lauro F, Oudin J, et al. Improvement of damage prediction by anisotropy of microvoids[J].Journal of Materials Processing Technology,2003,143–144(0):202-208.
[159] Pardoen T,Hutchinson J W. An extended model for void growth and coalescence[J]. Journal of theMechanics and Physics of Solids,2000,48(12):2467-2512.
[160] Lassance D, Fabrègue D, Delannay F, et al. Micromechanics of room and high temperature fracture in6xxx Al alloys[J]. Progress in Materials Science,2007,52(1):62-129.
[161] Tohgo K, Mochizuki M,Ishii H. Incremental damage theory and its application toglass-particle-reinforced nylon66composites[J]. International Journal of Mechanical Sciences,1998,40(2/3):199-213.
[162] Tan H, Huang Y, Liu C, et al. The Mori–Tanaka method for composite materials with nonlinearinterface debonding[J]. International Journal of Plasticity,2005,21(10):1890-1918.
[163] Thomason P F. A three-dimensional model for ductile fracture by the growth and coalescence ofmicrovoids[J]. Acta Metallurgica,1985,33(6):1087-1095.
[164]米厚天.土的半隐式图形返回算法研究及土坡稳定分析[D].大连理工大学,2005.
[165]王晓荣,王新洪,杜宝帅,等.激光熔覆Fe-Ti-V-Cr-C合金涂层的微观组织和性能[J].材料工程,201111(3):50-55..
[2]关成君,陈再良.机械产品的磨损,磨粒磨损失效分析[J].理化检验:物理分册,2006,42(1):50-54.
[3] Sundararajan G, Prasad K, Rao D, et al. A comparative study of tribological behavior of plasma andD-gun sprayed coatings under different wear modes[J]. Journal of Materials Engineering andPerformance,1998,7(3):343-351.
[4] Nerz J, Kushner B,Rotolico A. Microstructural evaluation of tungsten carbide-cobalt coatings[J].Journal of Thermal Spray Technology,1992,1(2):147-152..
[5]李强.激光熔覆耐磨涂层的研究现状与展望[J].宇航材料工艺,1999,1(1):13-17.
[6]黄瑞芬,罗建民,王春琴.激光熔覆技术的应用及其发展[J].兵器材料科学与工程,2005,28(4):57-59.
[7]刘其斌,李绍杰.航空发动机叶片铸造缺陷激光熔覆修复的研究[J].金属热处理,2006,31(3):52-55.
[8]王晓荣,王新洪,杜宝帅,等.激光熔覆Fe-Ti-V-Cr-C合金涂层的微观组织和性能[J].材料工程,201111(3):50-54.
[9]符跃春,杨智成,王国华,等. Al3Ti和TiC/Al3Ti激光熔覆涂层的高温氧化和浸泡腐蚀性能[J].重庆大学学报,201033(7):12-16..
[10]曹凤国.激光加工技术[M].北京科学技术出版社,2007.
[11]李军. Cr12MoV模具钢激光熔覆Ni基/WC合金工艺及性能研究[D].华东交通大学,2008.
[12] Gnanamuthu D S. Laser surface treatment[J]. Optical Engineering,1980,19(5):783-792.
[13]汤光平,黄文荣,杨家林. Cr12MoV模具钢的激光熔覆[J].金属热处理,200227(4):13-19.
[14]汤光平,黄文荣,杨家林.模具钢的激光表面改性研究[J].材料保护,200235(2):37-40.
[15]宋仁国,王晶,林鑫,等.γ-TiAI金属间化合物合金表面激光熔覆TiC-Ti-AI涂层研究[J].稀有金属材料与工程,200837(12):2191-2194.
[16] Wang A H,Yue T M. YAG laser cladding of an Al-Si alloy onto an Mg/SiC composite for theimprovement of corrosion resistance[J]. Composites Science and Technology,61(11):1549-1554.
[17]钱兆勇,钟敏霖,刘文今,等.瓦楞辊高耐磨激光熔覆颗粒增强铁基复合涂层[J].中国激光,200835(8):1271-1276.
[18]陈宁,周立志,徐桂梅. Cr12MoV模具钢激光熔覆Ni60/WC复合涂层的组织与性能[J].热加工工艺,2009,38(8):87-88.
[19] VanAcker K, Vanhoyweghen D, Persoons R, et al. Influence of tungsten carbide particle size anddistribution on the wear resistance of laser clad WC/Ni coatings[J]. Wear,2005,258(1-4):194-202.
[20]郭绍义,李兴俊,杨秋合,等.激光熔覆WC-Ni/TiC涂层的组织和摩擦磨损性能研究[J].材料工程,2008,6(7):72-75.
[21]楼白杨,徐斌,白万金,等.激光熔覆制备SiC/Ni基复合涂层及其耐冲蚀性能[J].中国激光,2008,35(1):147-150.
[22] Li R, Shi Y, Liu J, et al. Selective laser melting W–10wt.%Cu composite powders[J]. TheInternational Journal of Advanced Manufacturing Technology,2010,48(5):597-605.
[23]刘富荣,高谦,高登攀,等.激光熔覆WC增强复合涂层开裂行为分析[J].材料工程,20035:37-39.
[24] Müller S, Pries H, Dilger K, et al., Applying Functionally Graded Materials by Laser Cladding: acost-effective way to improve the Lifetime of Die-Casting DiesGlocalized Solutions for Sustainabilityin Manufacturing. Springer Berlin Heidelberg,2011,3(6):235-239.
[25] Liu Y, Koch J, Mazumder J, et al. processing microstructure and properties of laser-clad Ni-alloy FP-5on Al-alloy AA333[J]. Metallurgical and Materials Transactions B-Process Metallurgy and MaterialsProcessing Science,1994,25(3):425-434.
[26] Mazumder J, Choi J, Nagarathnam K, et al. The direct metal deposition of H13tool steel for3-Dcomponents[J]. Jom-Journal of the Minerals Metals&Materials Society,1997,49(5):55-60.
[27] Chai T,Chou C K. Mechanical properties of laser-welded cast titanium joints under differentconditions[J]. The Journal of Prosthetic Dentistry,1998,79(4):477-483.
[28] Gu D,Shen Y. Influence of reinforcement weight fraction on microstructure and properties ofsubmicron WC–Cop/Cu bulk MMCs prepared by direct laser sintering[J]. Journal of Alloys andCompounds,2007,431(1-2):112-120.
[29] Vreeling J A, Hamstra G A, et al. In-situ microscopy investigation of failure mechanisms in Al/SiCpmetal matrix composite produced by laser embedding[J]. Scripta Materialia,2000,42(3):589–595.
[30] Liu D, Zhang S Q, Li A, et al. Microstructure and tensile properties of laser melting depositedTiC/TA15titanium matrix composites[J]. Journal of Alloys and Compounds,2009,485(1-2):156-162.
[31] Liu D, Zhang S Q, Li A, et al. Creep rupture behaviors of a laser melting deposited TiC/TA15in situtitanium matrix composite[J]. Materials& Design,2010,31(6):3127-3133.
[32] ISO14577. Metallic materials—instrumented indentation test for hardness and materials parameters.[S].2002.
[33] Cui C, Guo Z, Wang H, et al. In situ TiC particles reinforced grey cast iron composite fabricated bylaser cladding of Ni–Ti–C system[J]. Journal of Materials Processing Technology,2007,183(2–3):380-385.
[34] Rabe U, Amelio S, Kopycinska M, et al. Imaging and measurement of local mechanical materialproperties by atomic force acoustic microscopy[J]. Surface and Interface Analysis,2002,33(2):65-70.
[35] Ho E, Marcolongo M. Effect of coupling agents on the local mechanical properties of bioactive dentalcomposites by the nano-indentation technique[J]. Dental Materials,2005,21(7):656-664.
[36] Volodin A, Ahlskog M, Seynaeve E, et al. Imaging the Elastic Properties of Coiled Carbon Nanotubeswith Atomic Force Microscopy[J]. Physical Review Letters,2000,84(15):3342-3345.
[37] Vinckier A, Semenza G. Measuring elasticity of biological materials by atomic force microscopy[J].FEBS Letters,1998,430(1–2):12-16.
[38] Saha R, Nix W D. Effects of the substrate on the determination of thin film mechanical properties bynanoindentation[J]. Acta Materialia,2002,50(1):23-38..\
[39] Durst K, Goken M,Vehoff H. Finite element study for nanoindentation measurements on two-phasematerials[J]. J mater Res,2004,191(85-93).
[40] Kim H S, Bush M B,Estrin Y. A phase mixture model of a particle reinforced composite with finemicrostructure[J]. Materials Science and Engineering: A,2000,276(1–2):175-185.
[41] Hryha E, Zubko P, Dudrová E, et al. An application of universal hardness test to metal powderparticles[J]. Journal of Materials Processing Technology,2009,209(5):2377-2385.
[42] Ulm F J, Vandamme M, Jennings H M, et al. Does microstructure matter for statistical nanoindentationtechniques?[J]. Cement and Concrete Composites,2010,32(1):92-99.
[43] Xia S, Qi Y, Perry T, et al. Strength characterization of Al/Si interfaces: A hybrid method ofnanoindentation and finite element analysis[J]. Acta Materialia,2009,57(3):695-707.
[44] Besterci M, Pe ek L, Zubko P, et al. Mechanical properties of phases in Al–Al4C3mechanicallyalloyed material measured by depth sensing indentation technique[J]. Materials Letters,2005,59(16):1971-1975.
[45] Desaeger M,Verpoest I. On the use of the micro-indentation test technique to measure the interfacialshear strength of fibre-reinforced polymer composites[J]. Composites Science and Technology,1993,48(1–4):215-226..
[46]杨敏.采用纳米压痕测试技术对碳/碳复合材料微观性能的研究[D].上海大学,2008.
[47] Eshelby J D. The determination of the elastic field of an ellipsoidal inclusion and related problems[J].Proceedings of the Royal Society of London,1957,241(3):376-396.
[48] Hill R. Theory of mechanical properties of fiber-strengthened materials:elastic behavior.[J]. Journal ofMechanical of Physics and Solids,1964,12(5):199-212.
[49] Hill R. Continuum micro-mechanics of elastoplastic polycrystals[J]. Journal Mechanics of Physics andSolids,1965,13(8):89-101.
[50] Hill R. A self-consistent mechanics of composite materials[J]. Journal of the Mechanics and Physics ofSolids,1965,13(4):213-222.
[51] Hashin Z,Shtrikman S. On some variational principles in anisotropic and nonhomogeneous elasticity[J].Journal of the Mechanics and Physics of Solids,10(4):335-342.
[52] Hashin Z,Shtrikman S. A variational approach to the theory of the elastic behaviour of multiphasematerials[J]. Journal of the Mechanics and Physics of Solids,11(2):127-140.
[53] Budiansky B. On the elastic moduli of some heterogeneous materials[J]. Journal of the Mechanics andPhysics of Solids,1965,13(4):223-227.
[54] Levin V M. On the coefficients of thermal expansion of heterogeneous materials[J]. Mechanics ofsolids,1967,11(5):58-61.
[55] Hutchinson J W. Elastic-Plastic Behaviour of Polycrystalline Metals and Composites[J]. Preceeding ofthe Royal Society of London,1970,319(1537):247-272.
[56] Mori T,Tanaka K. Average stress in matrix and average elastic energy of materials with misfittinginclusions[J]. Acta Metallurgica,1973,21(5):571-574.
[57] McLaughlin R A. study of the differential scheme for composite materials[J]. International Journal ofEngineering Science,1977,15(4):237-244.
[58] Aboundi J. Mechanics of composite materials: Unified micromechanical approach[J]. Volume29ofstudies in Applied Mechanics. Elsevier,1991,45(4):
[59] Duschlbauer D, B hm H J,Pettermann H E. Computational Simulation of Composites Reinforced byPlanar Random Fibers: Homogenization and Localization by Unit Cell and Mean Field Approaches[J].Journal of Composite Materials2006,40(20):2217-2234.
[60]杨庆生,陈浩然.杂问题中的自洽有限元法和复合材料的平均弹性性能[J].复合材料学报,1992,9(1):67-71.
[61]陈浩然,苏晓风,郑长良.广义自洽有限元迭代平均化方法[J].复合材料学报,1992,9(1):52-56.
[62] Cheng J, Jordan E H,Walker K P. A simple accurate method for calculating local stresses aroundindividual fibers in periodic composites[J]. Composites Part B: Engineering,1999,30(5):453-463.
[63] Ghosh S, Mukhopadhyay S N. A material based finite element analysis of heterogeneous mediainvolving Dirichlet tessellations[J]. Computer Methods in Applied Mechanics and Engineering,1993,104(2):211-247.
[64] Gurson A L. Continuum theory of ductile rupture by void nucleation and growth: Part I—yield criteriaand flow rules for porous ductile media[J]. Journal of Engineering Materials and Technology,1977,99(1-15.
[65] Tvergaard V, Needleman A. Analysis of the cup-cone fracture in a round tensile bar[J]. ActaMetallurgica,1984,32(1):157-169.
[66] Argon A, Im J,Safoglu R. Cavity formation from inclusions in ductile fracture[J]. Metallurgical andMaterials Transactions A,1975,6(4):825-837.
[67] Babout L, Brechet Y, Maire E, et al. On the competition between particle fracture and particledecohesion in metal matrix composites[J]. Acta Materialia,2004,52(15):4517-4525.
[68] Kroon M, Faleskog J. Micromechanics of cleavage fracture initiation in ferritic steels by carbidecracking[J]. Journal of the Mechanics and Physics of Solids,2005,53(1):171-196.
[69] Needleman A. A continuum model for void nucleation by inclusion debonding[J]. Journal of AppliedMechanics,1987,54(3):525-532.
[70] Cho Y T. Incremental damage mechanics of particle or short-fiber reinforced composites includingcracking damage[J]. Journal of Mechanical Science and Technology,2002,16(2):192-202.
[71] Fitoussi J, Bourgeois N, Guo G, et al. Prediction of the anisotropic damaged behavior of compositematerials: introduction of multilocal failure criteria in a micro-macro relationship[J]. ComputationalMaterials Science,1996,5(1-3):87-100.
[72] Brockenbrough J R,Zok F W. On the role of particle cracking in flow and fracture of metal matrixcomposites[J]. Acta Metallurgica et Materialia,1995,43(1):11-20.
[73] Gonzalez C, Llorca J. Prediction of the tensile stress-strain curve and ductility in Al/SiC composites[J].Scripta Materialia,1996,35(1):91-97.
[74] Poza P, Llorca J. Mechanical behavior of Al Li/SiC composites: Part III. Micromechanical modeling[J].Metallurgical and Materials Transactions A,1999,30(13):869-878.
[75] Llorca J,González C. Microstructural factors controlling the strength and ductility of particle-reinforcedmetal-matrix composites[J]. Journal of the Mechanics and Physics of Solids,1998,46(1):1-28.
[76] Dvorak G J, Zhang J. Transformation field analysis of damage evolution in composite materials[J].Journal of the Mechanics and Physics of Solids,2001,49(11):2517-2541.
[77] Ghosh S, Moorthy S. Particle fracture simulation in non-uniform microstructures of metal–matrixcomposites[J]. Acta Materialia,1998,46(3):965-982.
[78] Ibnabdeljalil M, Curtin W A. Strength and reliability of notched fiber-reinforced composites[J]. ActaMaterialia,1997,45(9):3641-3652.
[79] B hm H J, Eckschlager A,Han W. Multi-inclusion unit cell models for metal matrix composites withrandomly oriented discontinuous reinforcements[J]. Computational Materials Science,2002,25(1-2):42-53.
[80] Segurado J,Llorca J. Computational micromechanics of composites: The effect of particle spatialdistribution[J]. Mechanics of Materials,2006,38(8-10):873-883.
[81] Ghosh S, Bai J, Paquet D. Homogenization-based continuum plasticity-damage model for ductilefailure of materials containing heterogeneities[J]. Journal of the Mechanics and Physics of Solids,2009,57(7):1017-1044.
[82] Lee H K, Pyo S H. An elastoplastic multi-level damage model for ductile matrix compositesconsidering evolutionary weakened interface[J]. International Journal of Solids and Structures,2008,45(6):1614-1631.
[83] Tekog C, Pardoen T. A micromechanics based damage model for composite materials[J]. InternationalJournal of Plasticity,2010,26(4):549-569.
[84] Thomason P F. Ductile fracture of metals[D]. Oxford: Pergamon Press,1990..
[85]鲁燕,孔凡志,姚建华,等.半导体激光熔覆TiC/H13涂层的抗回火性能[J].应用激光2010,30(6):451-455.
[86]张群莉,姚建华,骆芳.热作模具H13钢表面激光堆焊类高速钢的实验研究[J].材料热处理学报,2005,26(4):95-97.
[87]汤晓丹,姚建华,孔凡志,等. TiC对激光熔覆H13-TiC复合涂层组织和性能的影响[J].热加工工艺,200938(14):92-96.
[88] Li Q, Lei T C,Chen W Z. Microstructural characterization of WCp reinforced Ni–Cr–B–Si–Ccomposite coatings[J]. Surface and Coatings Technology,1999,114(2–3):285-291.
[89] Li Q, Lei T C,Chen W Z. Microstructural characterization of laser-clad TiCp-reinforced Ni–Cr–B–Si–Ccomposite coatings on steel[J]. Surface and Coatings Technology,1999,114(2–3):278-284.
[90] Ariely S, Shen J, Bamberger M, et al. Laser surface alloying of steel with TiC[J]. Surface and CoatingsTechnology,1991,45(1–3):403-408.
[91]黄尚猛. Cr12模具钢激光熔覆技术的研究[D].天津：天津大学,2008.
[92] Jiang W H,Kovacevic R. Laser deposited TiC/H13tool steel composite coatings and their erosionresistance[J]. Journal of Materials Processing Technology,2007,186(1–3):331-338.
[93] Sun R L, Yang D Z, Guo L X, et al. Laser cladding of Ti-6Al-4V alloy with TiC and TiC+NiCrBSipowders[J]. Surface and Coatings Technology,2001,135(2–3):307-312.
[94] TaeWon K. Heterogeneous void distribution in aluminum metal matrix composites and its effect ondeformation-failure processes[J]. Scripta Materialia,2006,55(12):1115-1118.
[95] Little J E, Yuan X, Jones M I. Characterisation of voids in fibre reinforced composite materials[J]. NDT& E International,2012,46(0):122-127.
[96]毛小南,张廷杰,张小明. TiC颗粒增强钛基复合材料的形变[J].稀有金属材料与工程,2001,35(4):245-248.
[97] Ramesh C S, Keshavamurthy R, Channabasappa B H, et al. Microstructure and mechanical propertiesof Ni–P coated Si3N4reinforced Al6061composites[J]. Materials Science and Engineering: A,2009,502(1–2):99-106.
[98] Wang Q. Microstructural effects on the tensile and fracture behavior of aluminum casting alloysA356/357[J]. Metallurgical and Materials Transactions A,2003,34(12):2887-2899.
[99] V V Bhanuprasad, M A Staley, P Ramakrishnan, et al. Fractography of Metal Matrix Composites[J].Key Engineering Materials,1995,104-107(495-506.
[100] da Silva A A M, Meyer A, Santos J F d, et al. Mechanical and metallurgical properties offriction-welded TiC particulate reinforced Ti–6Al–4V[J]. Composites Science and Technology,2004,64(10–11):1495-1501..
[101] Srivatsan T S, Al-Hajri M, Smith C, et al. The tensile response and fracture behavior of2009aluminum alloy metal matrix composite[J]. Materials Science and Engineering: A,2003,346(1–2):91-100.
[102] Maziasz P J, Payzant E A, Schlienger M E, et al. Residual stresses and microstructure of H13steelformed by combining two different direct fabrication methods[J]. Scripta Materialia,1998,39(10):1471-1476.
[103] Hauert A, Rossoll A,Mortensen A. Ductile-to-brittle transition in tensile failure of particle-reinforcedmetals[J]. Journal of the Mechanics and Physics of Solids,2009,57(3):473-499..
[104] Furnémont Q, Kempf M, Jacques P J, et al. On the measurement of the nanohardness of theconstitutive phases of TRIP-assisted multiphase steels[J]. Materials Science and Engineering: A,2002,328(1–2):26-32.
[105] William D N. Elastic and plastic properties of thin films on substrates: nanoindentation techniques[J].Materials Science and Engineering: A,1997,234–236(0):37-44.
[106] Bhowmick S, Jayaram V,Biswas S K. Deconvolution of fracture properties of TiN films on steelsfrom nanoindentation load–displacement curves[J]. Acta Materialia,2005,53(8):2459-2467.
[107] Oliver W, Pharr G. An improved technique for determining hardness and elastic modulus using loadand displacement sensing indentation[J]. Joumai of Materials Research,1992,7(6):1564–1583.
[108] Seshadri S, Srinivasan M,King L. indentation fracture testing of ceramics[[J]. Ceramic Eng. Sci. Proc.,1983,4(9-10):853-863.
[109] Hysitron TI900. nanoindentaion system operation guide[Z].2008.
[110] Ure a A, Rams J, Escalera M D, et al. Characterization of interfacial mechanical properties in carbonfiber/aluminium matrix composites by the nanoindentation technique[J]. Composites Science andTechnology,2005,65(13):2025-2038.
[111] Pour H A, Lieblich M, López A J, et al. Assessment of tensile behaviour of an Al–Mg alloy compositereinforced with NiAl and oxidized NiAl powder particles helped by nanoindentation[J]. CompositesPart A: Applied Science and Manufacturing,2007,38(12):2536-2540.
[112] Mussert K M, Vellinga W P, Bakker A, et al. A nano-indentation study on the mechanical behaviour ofthe matrix material in an AA6061-Al<sub>2</sub>O<sub>3</sub> MMC[J].Journal of Materials Science,2002,37(4):789-794.
[113] Walter C, Antretter T, Daniel R, et al. Finite element simulation of the effect of surface roughness onnanoindentation of thin films with spherical indenters[J]. Surface and Coatings Technology,2007,202(4–7):1103-1107.
[114] Kim J-Y, Kang S-K, Lee J-J, et al. Influence of surface-roughness on indentation size effect[J]. ActaMaterialia,2007,55(10):3555-3562.
[115] Bouzakis K D, Michailidis N, Hadjiyiannis S, et al. The effect of specimen roughness and indenter tipgeometry on the determination accuracy of thin hard coatings stress–strain laws by nanoindentation[J].Materials Characterization,2002,49(2):149-156.
[116] Fischer-Cripps A C. Nanoindentation[M]. NewYork: Spring-Verlag,2002.
[117] Johnson K L. Contact Mechanics[M]. Cambridge:Cambridge University Press,1985.
[118]张泰华.微/纳米力学测试技术及其应用[M].机械工业出版社,2005.
[119] Lin S, Hills D A,Warren P D. A theoretical investigation of sharp indentation testing of a nearly-brittlematerial, with some experimental results[J]. Journal of the Mechanics and Physics of Solids,2000,48(10):2057-2075.
[120] Lawn B R,Evans A G. A model for crack initiation in elastic/plastic indentation fields[J]. Journal ofMaterials Science,1977,12(11):2195-2199.
[121] Larsson P-L,E. Giannakopoulos A. Tensile stresses and their implication to cracking at pyramidindentation of pressure-sensitive hard metals and ceramics[J]. Materials Science and Engineering: A,1998,254(1–2):268-281.
[122] Sun Y, Bell T,Zheng S. Finite element analysis of the critical ratio of coating thickness to indentationdepth for coating property measurements by nanoindentation[J]. Thin Solid Films,1995,258(1–2):198-204.
[123] Lichinchi M, Lenardi C, Haupt J, et al. Simulation of Berkovich nanoindentation experiments on thinfilms using finite element method[J]. Thin Solid Films,1998,312(1–2):240-248.
[124] Shan Z,Sitaraman S K. Elastic–plastic characterization of thin films using nanoindentationtechnique[J]. Thin Solid Films,2003,437(1–2):176-181.
[125] Antunes J M, Fernandes J V, Menezes L F, et al. A new approach for reverse analyses indepth-sensing indentation using numerical simulation[J]. Acta Materialia,2007,55(1):69-81..
[126] H. Buckle. Metallurgical Reviews4[M]. London, Institute of Metals,1959.
[127] Babu J S S,Kang C G. Nanoindentation behaviour of aluminium based hybrid composites withgraphite nanofiber/alumina short fiber[J]. Materials& Design,2010,31(10):4881-4885.
[128] Guemmaz M, Mosser A, Boudoukha L, et al. Ion beam synthesis of non-stoichiometric titaniumcarbide: composition structure and nanoindentation studies[J]. Nuclear Instruments and Methods inPhysics Research Section B: Beam Interactions with Materials and Atoms,1996,111(3–4):263-270.
[129] Mencin P, Van Tyne C,Levy B. A Method for Measuring the Hardness of the Surface Layer on HotForging Dies Using a Nanoindenter[J]. Journal of Materials Engineering and Performance,2009,18(8):1067-1072.
[130] Li M. Characterization and modeling of damage in metal matrix composite microstructures[D]. TheOhio State University,1998.
[131] Mahesh M. Plasma spray processing of TiC-based coatings for sliding wear resistance[D]. DrexelUniversity,1997.
[132]秦庆华,杨庆生.非均匀材料多场耦合行为的宏细观理论[M].北京：高等教育出版社,2006.
[133] Eshelby J D. The determination of the elastic field of an ellipsoidal inclusion and related problems[J].Mathematical and Physical Sciences,1957,241(7):376-396.
[134] Benveniste Y. A new approach to the application of Mori–Tanaka’s theory in composite materials[J].Mechanics of Materials,1987,6(2):147–157.
[135] Doghri I,Ouaar A. Homogenization of two-phase elasto-plastic composite materials and structures:Study of tangent operators, cyclic plasticity and numerical algorithms[J]. International Journal ofSolids and Structures,2003,40(7):1681-1712.
[136] González C,Llorca J. A self-consistent approach to the elasto-plastic behaviour of two-phase materialsincluding damage[J]. Journal of the Mechanics and Physics of Solids,2000,48(4):675-692.
[137] Segurado J, Llorca J,González C. On the accuracy of mean-field approaches to simulate the plasticdeformation of composites[J]. Scripta Materialia,2002,46(7):525-529.
[138] Doghri I,Tinel L. Micromechanical modeling and computation of elasto-plastic materials reinforcedwith distributed-orientation fibers[J]. International Journal of Plasticity,2005,21(10):1919-1940.
[139] McClintock F A. A Criterion for Ductile Fracture by the Growth of Holes[J]. Journal of AppliedMechanics1968,135(363-371.
[140] Rice J R,Tracey D M. On the ductile enlargement of voids in triaxial stress fields[J]. Journal of theMechanics and Physics of Solids,1969,17(3):201-217.
[141]余寿文,冯桥西.损伤力学[M].北京：清华大学出版社,1997.
[142] Faleskog J, Gao X,Shih C. Cell model for nonlinear fracture analysis–I. Micromechanicscalibration[J]. International Journal of Fracture,1998,89(4):355-373.
[143] Leblond J B, Perrin G,Devaux J. An improved Gurson-type model for hardenable ductile metals[J].European journal of mechanics,1995,14(5):499-527.
[144] Li Z, Wang C,Chen C. The influence of matrix yield stress gradient on the growth and coalescence ofspheroidal voids[J]. International Journal of Solids and Structures,2002,39(3):601-616..
[145] Li Z, Wang C,Chen C. The evolution of voids in the plasticity strain hardening gradient materials[J].International Journal of Plasticity,2003,19(2):213-234.
[146]王自强,秦嘉亮.含孔洞非线性材料的本构势和孔洞扩展率[J].固体力学学报,1989,2(5):127-141.
[147] Yi S,Duo W. A lower bound approach to the yield loci of porous materials[J]. Acta Mechanica Sinica,1989,5(3):237-243.
[148] Huang Y. Accurate dilatation rates for spherical voids in triaxial stress fields[J]. Journal of AppliedMechanics,1991,58(4):1084-1086.
[149] Zhang K S, Bai J B,Fran ois D. Numerical analysis of the influence of the Lode parameter on voidgrowth[J]. International Journal of Solids and Structures,2001,38(32–33):5847-5856.
[150] Becker R, Smelser R E,Richmond O. The effect of void shape on the development of damage andfracture in plane-strain tension[J]. Journal of the Mechanics and Physics of Solids,1989,37(1):111-129.
[151] Becker R, Smelser R, Richmond O, et al. The effect of void shape on void growth and ductility inaxisymmetric tension tests[J]. Metallurgical and Materials Transactions A,1989,20(5):853-861.
[152] Yee K C,Mear M E. Effect of void shape on the macroscopic response of non-linear porous solids[J].International Journal of Plasticity,1996,12(1):45-68.
[153] Gologanu M, Leblond J-B, Devaux J. Approximate models for ductile metals containingnon-spherical voids—Case of axisymmetric prolate ellipsoidal cavities[J]. Journal of the Mechanicsand Physics of Solids,1993,41(11):1723-1754.
[154] Gologanu M, Leblond J-B, Devaux J. Approximate Models for Ductile Metals ContainingNonspherical Voids---Case of Axisymmetric Oblate Ellipsoidal Cavities[J]. Journal of EngineeringMaterials and Technology,1994,116(3):290-297.
[155] Kim J, Gao X. A generalized approach to formulate the consistent tangent stiffness in plasticity withapplication to the GLD porous material model[J]. International Journal of Solids and Structures,2005,42(1):103-122.
[156] Huber G, Brechet Y, Pardoen T. Predictive model for void nucleation and void growth controlledductility in quasi-eutectic cast aluminium alloys[J]. Acta Materialia,2005,53(9):2739-2749.
[157] Brunet M, Morestin F,Walter-Leberre H. Failure analysis of anisotropic sheet-metals using a non-localplastic damage model[J]. Journal of Materials Processing Technology,2005,170(1–2):457-470.
[158] Croix P, Lauro F, Oudin J, et al. Improvement of damage prediction by anisotropy of microvoids[J].Journal of Materials Processing Technology,2003,143–144(0):202-208.
[159] Pardoen T,Hutchinson J W. An extended model for void growth and coalescence[J]. Journal of theMechanics and Physics of Solids,2000,48(12):2467-2512.
[160] Lassance D, Fabrègue D, Delannay F, et al. Micromechanics of room and high temperature fracture in6xxx Al alloys[J]. Progress in Materials Science,2007,52(1):62-129.
[161] Tohgo K, Mochizuki M,Ishii H. Incremental damage theory and its application toglass-particle-reinforced nylon66composites[J]. International Journal of Mechanical Sciences,1998,40(2/3):199-213.
[162] Tan H, Huang Y, Liu C, et al. The Mori–Tanaka method for composite materials with nonlinearinterface debonding[J]. International Journal of Plasticity,2005,21(10):1890-1918.
[163] Thomason P F. A three-dimensional model for ductile fracture by the growth and coalescence ofmicrovoids[J]. Acta Metallurgica,1985,33(6):1087-1095.
[164]米厚天.土的半隐式图形返回算法研究及土坡稳定分析[D].大连理工大学,2005.
[165]王晓荣,王新洪,杜宝帅,等.激光熔覆Fe-Ti-V-Cr-C合金涂层的微观组织和性能[J].材料工程,201111(3):50-55..