金属的强烈塑性变形与考虑尺寸效应的细观本构关系
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摘要
材料经受强烈塑性变形时其微观结构有很大的改变,导致材料的力学性质发生很大的变化。然而,其中的演化内在机制及其模型描述至今人们仍然没有很好解决。为了研究强烈塑性变形对材料性质的影响,本文结合等通道转角挤压(ECAP)试验和多晶塑性理论,对韧性材料的力学行为开展研究。
作者自行设计调试了ECAP模具,完成了金属材料铜、铝的ECAP试验。发现经ECAP处理后,材料屈服强度大幅提高和极限强度小幅度提高。研究经ECAP不同路径处理后材料的均匀性问题。采用试验与数值模拟技术分析了ECAP过程中压头压力的分布规律。编写了反映材料位错滑移变形物理机制的晶体塑性模型计算子程序。多晶塑性模型中通过引入背应力考虑循环载荷下材料力学行为响应,而且,在滑移阻力函数中考虑了材料的尺寸效应。利用多晶塑性模型分析ECAP过程中局部的应力应变分布规律。
本文研究工作的成果主要有：
1.完成了90°和120°两种转角角度的ECAP模具设计与调试,用这些模具可连续挤压出长达90mm的圆棒试件。
2.完成了经ECAP处理前后材料拉伸性能的测试与数据分析。试验发现：(1)材料经ECAP处理后,在不同挤压路径中屈服强度提高比例最大为312.5%,而极限强度提高比例为最大26.3%。(2)1道次处理对屈服强度提高最显著,多道次挤压中1道次强度提高贡献约为70%。(3)ECAP处理造成材料的塑性性能大幅降低,未挤压材料的延伸率约30%,而1道次挤压后约为7%。(4)在后续道次挤压过程中,材料塑性性能会略有提高。
3.经A、Ba、Bc、C路径以及8道次45。路径挤压的T3紫铜,在同一挤压试件不同部位截取试样进行了拉伸试验。发现无论何采用种路径挤压,材料拉伸性质均表现出有规律的不均匀现象,同一试件不同部位试样的截而强度不均匀系数最高可达24.6%。
4.利用ECAP试验研究了不同路径、不同道次挤压对于压头压力的影响规律,发现压头压力在不同路径与不同挤压道次条件下具有显著差异。
5.研究了多晶塑性分析模型,结合晶体滑移率表达形式的本构关系,编写了与ABAQUS接口的用户材料子程序(VUMAT)。模型考虑了背应力及其演化,考虑了材料单元中晶粒结构的尺寸信息,可以反映材料的屈服、流动过程中的晶粒尺寸效应,特别是可以反映应变循环过程的材料晶粒尺寸效应。
6.采用数值模拟,考虑不同模具参数、多试样连续挤压、材料参数、挤压试件长度、摩擦因子等方面对ECAP试验过程中压头压力变化规律的影响；并结合试验与数值模拟拟合了ECAP过程最大压头压力估算公式。
7.分析了经ECAP处理后挤压试件中头部效应的影响范围。采用应变不变量为参数分析了ECAP过程中挤压试件的变形状态和挤压试件通过模具转角过程中不均匀压缩现象。通过定义截面不均匀系数,分析ECAP过程中挤压试件的不均匀变形状态,与试验中同一挤压试件不同部位的拉伸强度的差异性吻合较好。
8.通过ECAP过程中应力状态分析,合理解释了试验过程中试件表面出现横裂纹的现象。
9.通过多晶塑性模型分析了ECAP过程中应力分布特征,计算显示了材料单元的应力是一定数量各向异性晶粒作用平均化的结果。在材料计算单元中因晶粒取向的差异在不同晶粒之间其应力具有较大的变化；这种差异性对于材料损伤演化与破坏具有重要影响。
Microstructure alteration of material subjected to severe plastic deformation brings on great changes of mechanical property. However, the evolution of intrinsic mechanism and model description on which still haven't been well resolved until now. In order to research mechanical property changes of material subjected to severe plastic deformation, ductile material were researched by the experiment of equal channel angular pressing (ECAP) and theoretical analysis of polycrystalline plasticity.
Moulds of ECAP were designed and complied. Extrusion experiments of copper and aluminum were completed in these moulds. Research indicates that there are dramatic increase in the yield strength of materials subjected to extrusion of ECAP and small scale increase in ultimate strength of that. Non-homogeneity of materials subjected to extrusion with different routes of ECAP was researched. Distribution regularities of pressure head's force during the process of ECAP were studied using experiment and numerical simulation. User material subroutine of polycrystalline plasticity model was compiled which can reflect the physical mechanisms of crystal lattice slipping. In order to describe mechanical property of materials subjected to cyclic loading, the back stress was introduced in polycrystalline plasticity model. Furthermore, size effect was considered through slide resistance evolution function. Distribution regularities of local stress and strain were analyzed using polycrystalline plasticity model during the process of ECAP.
The main results of the paper are as below:
1. The ECAP moulds including90degree and120degree angle were designed and compiled. Round bar specimens with90mm length were successfully extruded through these moulds.
2. Completed tensile test of materials subjected to extrusion of ECAP or not. Experiments indicate that:(1) The increase proportion of the yield strength of materials subjected to different routes of ECAP is up to312.5%and that of ultimate strength is26.3%;(2) Increase of yield stress of pass-one-extrusion is the most significant and the contribution percentage is up to70%during the multi-pass extrusion;(3) Plastic properties of materials subjected to process of ECAP are decreased sharply. Unit extension of non-extrusion materials is30%and that of materials subjected to pass-one-extrusion is7%;(4) Plastic properties of materials during the process of subsequent extrusion are increased slightly.
3. Completed the mechanical properties experiment of test piece interception from different location of the same specimen of T3copper subjected to extrusion of route A, Ba, Bc, C and45-degree-pass-eight. Experiments indicate that:(1) Regular non-homogeneity can be found from tensile test nothing to do with extrusion routes;(2) The maximum of non-uniformity coefficient of section strength during the four test pieces in different location of the same specimen is24.6%among the above routes.
4. Distribution regularities of pressure head's force were researched under different routes and extrusion times during the ECAP experiment. There is remarkable difference for pressure head's force during different routes and extrusion times.
5. Analytical model of polycrystalline plasticity was researched and user material subroutine (VUMAT) interface with ABAQUS was compiled in which constitutive relation were described by rate type of grain slide. Evolution of the back stress was taken in the model and material element was endued with grain characteristic size information which could describe grain size effect during the process of materials'yield and flow. Especially, it could describe grain size effect under the condition of strain cycling.
6. Adopting numerical simulation, distribution regularities of pressure head's force were relative to the factors of mould parameters, continuous extrusion of multi-specimen, material properties, length of specimen and fraction coefficients etc during the process of ECAP. The estimated formula of maximum pressure head's force was presented based on experiment and numerical simulation during the process of ECAP.
7. Influence range of head-effect in the specimen subjected to ECAP treatment was researched. Regarding strain invariant as analysis parameters, deformation state and non-homogeneity compression regularity in the specimen were researched during the ECAP processes. Non-homogeneity state was quantitatively analyzed by the definition of non-homogeneity coefficients of the section during the ECAP processes, which were in accord with experiment results.
8. By the analysis of tensile stress components during the ECAP process, the phenomenon of presenting transverse crack along ordinate axis of specimen in the experiment was reasonably interpreted.
9. Stress distribution during the ECAP process was researched using polycrystalline plasticity model, in which stress in material element was average effect of a certain amount of anisotropic grain. Discrepancy of stress among the grains with different orientations in material element was prominent, which have important effect on damage evolution and rupture in material.
作者自行设计调试了ECAP模具,完成了金属材料铜、铝的ECAP试验。发现经ECAP处理后,材料屈服强度大幅提高和极限强度小幅度提高。研究经ECAP不同路径处理后材料的均匀性问题。采用试验与数值模拟技术分析了ECAP过程中压头压力的分布规律。编写了反映材料位错滑移变形物理机制的晶体塑性模型计算子程序。多晶塑性模型中通过引入背应力考虑循环载荷下材料力学行为响应,而且,在滑移阻力函数中考虑了材料的尺寸效应。利用多晶塑性模型分析ECAP过程中局部的应力应变分布规律。
本文研究工作的成果主要有：
1.完成了90°和120°两种转角角度的ECAP模具设计与调试,用这些模具可连续挤压出长达90mm的圆棒试件。
2.完成了经ECAP处理前后材料拉伸性能的测试与数据分析。试验发现：(1)材料经ECAP处理后,在不同挤压路径中屈服强度提高比例最大为312.5%,而极限强度提高比例为最大26.3%。(2)1道次处理对屈服强度提高最显著,多道次挤压中1道次强度提高贡献约为70%。(3)ECAP处理造成材料的塑性性能大幅降低,未挤压材料的延伸率约30%,而1道次挤压后约为7%。(4)在后续道次挤压过程中,材料塑性性能会略有提高。
3.经A、Ba、Bc、C路径以及8道次45。路径挤压的T3紫铜,在同一挤压试件不同部位截取试样进行了拉伸试验。发现无论何采用种路径挤压,材料拉伸性质均表现出有规律的不均匀现象,同一试件不同部位试样的截而强度不均匀系数最高可达24.6%。
4.利用ECAP试验研究了不同路径、不同道次挤压对于压头压力的影响规律,发现压头压力在不同路径与不同挤压道次条件下具有显著差异。
5.研究了多晶塑性分析模型,结合晶体滑移率表达形式的本构关系,编写了与ABAQUS接口的用户材料子程序(VUMAT)。模型考虑了背应力及其演化,考虑了材料单元中晶粒结构的尺寸信息,可以反映材料的屈服、流动过程中的晶粒尺寸效应,特别是可以反映应变循环过程的材料晶粒尺寸效应。
6.采用数值模拟,考虑不同模具参数、多试样连续挤压、材料参数、挤压试件长度、摩擦因子等方面对ECAP试验过程中压头压力变化规律的影响；并结合试验与数值模拟拟合了ECAP过程最大压头压力估算公式。
7.分析了经ECAP处理后挤压试件中头部效应的影响范围。采用应变不变量为参数分析了ECAP过程中挤压试件的变形状态和挤压试件通过模具转角过程中不均匀压缩现象。通过定义截面不均匀系数,分析ECAP过程中挤压试件的不均匀变形状态,与试验中同一挤压试件不同部位的拉伸强度的差异性吻合较好。
8.通过ECAP过程中应力状态分析,合理解释了试验过程中试件表面出现横裂纹的现象。
9.通过多晶塑性模型分析了ECAP过程中应力分布特征,计算显示了材料单元的应力是一定数量各向异性晶粒作用平均化的结果。在材料计算单元中因晶粒取向的差异在不同晶粒之间其应力具有较大的变化；这种差异性对于材料损伤演化与破坏具有重要影响。
Microstructure alteration of material subjected to severe plastic deformation brings on great changes of mechanical property. However, the evolution of intrinsic mechanism and model description on which still haven't been well resolved until now. In order to research mechanical property changes of material subjected to severe plastic deformation, ductile material were researched by the experiment of equal channel angular pressing (ECAP) and theoretical analysis of polycrystalline plasticity.
Moulds of ECAP were designed and complied. Extrusion experiments of copper and aluminum were completed in these moulds. Research indicates that there are dramatic increase in the yield strength of materials subjected to extrusion of ECAP and small scale increase in ultimate strength of that. Non-homogeneity of materials subjected to extrusion with different routes of ECAP was researched. Distribution regularities of pressure head's force during the process of ECAP were studied using experiment and numerical simulation. User material subroutine of polycrystalline plasticity model was compiled which can reflect the physical mechanisms of crystal lattice slipping. In order to describe mechanical property of materials subjected to cyclic loading, the back stress was introduced in polycrystalline plasticity model. Furthermore, size effect was considered through slide resistance evolution function. Distribution regularities of local stress and strain were analyzed using polycrystalline plasticity model during the process of ECAP.
The main results of the paper are as below:
1. The ECAP moulds including90degree and120degree angle were designed and compiled. Round bar specimens with90mm length were successfully extruded through these moulds.
2. Completed tensile test of materials subjected to extrusion of ECAP or not. Experiments indicate that:(1) The increase proportion of the yield strength of materials subjected to different routes of ECAP is up to312.5%and that of ultimate strength is26.3%;(2) Increase of yield stress of pass-one-extrusion is the most significant and the contribution percentage is up to70%during the multi-pass extrusion;(3) Plastic properties of materials subjected to process of ECAP are decreased sharply. Unit extension of non-extrusion materials is30%and that of materials subjected to pass-one-extrusion is7%;(4) Plastic properties of materials during the process of subsequent extrusion are increased slightly.
3. Completed the mechanical properties experiment of test piece interception from different location of the same specimen of T3copper subjected to extrusion of route A, Ba, Bc, C and45-degree-pass-eight. Experiments indicate that:(1) Regular non-homogeneity can be found from tensile test nothing to do with extrusion routes;(2) The maximum of non-uniformity coefficient of section strength during the four test pieces in different location of the same specimen is24.6%among the above routes.
4. Distribution regularities of pressure head's force were researched under different routes and extrusion times during the ECAP experiment. There is remarkable difference for pressure head's force during different routes and extrusion times.
5. Analytical model of polycrystalline plasticity was researched and user material subroutine (VUMAT) interface with ABAQUS was compiled in which constitutive relation were described by rate type of grain slide. Evolution of the back stress was taken in the model and material element was endued with grain characteristic size information which could describe grain size effect during the process of materials'yield and flow. Especially, it could describe grain size effect under the condition of strain cycling.
6. Adopting numerical simulation, distribution regularities of pressure head's force were relative to the factors of mould parameters, continuous extrusion of multi-specimen, material properties, length of specimen and fraction coefficients etc during the process of ECAP. The estimated formula of maximum pressure head's force was presented based on experiment and numerical simulation during the process of ECAP.
7. Influence range of head-effect in the specimen subjected to ECAP treatment was researched. Regarding strain invariant as analysis parameters, deformation state and non-homogeneity compression regularity in the specimen were researched during the ECAP processes. Non-homogeneity state was quantitatively analyzed by the definition of non-homogeneity coefficients of the section during the ECAP processes, which were in accord with experiment results.
8. By the analysis of tensile stress components during the ECAP process, the phenomenon of presenting transverse crack along ordinate axis of specimen in the experiment was reasonably interpreted.
9. Stress distribution during the ECAP process was researched using polycrystalline plasticity model, in which stress in material element was average effect of a certain amount of anisotropic grain. Discrepancy of stress among the grains with different orientations in material element was prominent, which have important effect on damage evolution and rupture in material.
引文
[1]师吕绪.中国材料科学技术现状与展望[J].中国材料进展,2009,28(1)：1-2
[2]白以龙,汪海英,柯孚久,等.从“哥伦比亚”号悲剧看多尺度力学问题[J].力学与实践,2005,27(3)：1-6
[3]杨卫.微纳米尺度的力学行为[J].世界科技研究与发展,2001,26(4)：2-6
[4]白以龙,汪海英,夏蒙棼,等.固体的统计细观力学—连接多个耦合的时空尺度[J].力学进展,2006,36(2)：286-305
[5]王亚勇.概论汶川地震后我国建筑抗震设计标准的修订[J].土木工程学报,2009,42(5)：1-12
[6]黄克智,黄永刚.固体本构关系[M].北京：清华大学出版社,1999,1-36,150-156
[7]程素玲,杨根仓,樊建锋,等.Ca,Y对AZ91镁合金显微组织和力学性能的影响[J].稀有金属材料与工程,2006,35(9)：1400-1403
[8]王卓琳,林峰,顾祥林.基于离散单元法的混凝土细观力学模型研究进展[J].结构工程师,2007,23(5)：79-85
[9]Reihanian M, Ebrahimi R, Moshksar M M, et al. Microstructure quantification and correlation with flow stress of ultrafine grained commercially pure Al fabricated by equal channel angular pressing [J]. Materials Characterization,2008,59(9):1312-1323
[10]马怀发,陈厚群,黎保琨.细观结构不均匀性对混凝土动弯拉强度的影响[J].水利学报,2005,36(7)：846-852
[11]黄修山，尹小涛,陈厚群,等.不同粒组骨料对混凝土力学性质的影响[J].武汉理工大学学报,2010,32(19)：50-54
[12]杨卫.宏微观断裂力学[M].北京：国防工业出版社,1995,1-11
[13]戚力,董立峰,程华,等.高压条件下Pd-Ni合金熔体非晶形成过程及微观结构演化的分子动力学研究[J].金属学报,2008,44(2)：233-236
[14]Lugo N, Llorca N, Cabrera J M, et al. Microstructures and mechanical properties of pure copper deformed severely by equal-channel angular pressing and high pressure torsion [J]. Materials Science and Engineering A,2008,477(25):366-371
[15]Zhilyaev A P, Gimazov A A, Raab G I, et al. Using high-pressure torsion for the cold-consolidation of copper chips produced by machining [J]. Materials Science and Engineering,2008,486:123-126
[16]Segal V M. Materials processing by simple shear [J]. Materials Science and Engineering,1995, A197:157-164
[17]王自强,段祝平.塑性细观力学[M].科学出版社,北京,1995,28-31,90-91
[18]Hall E O. The deformation and ageing of mild steel:Ⅲ. Discussion of results [J]. Proceedings of the Physical Society,1951, B64:747-753
[19]Petch N J. The cleavage strength of polycrystals [J]. Journal of the Iron and Steel Institute,1953,174: 25-28
[20]Segal V M. Equal channel angular extrusion:from macromechanics to structure formation [J]. Material Science and Engineering,1999, A271:322-333
[21]Valiev R Z, Alexandrov I V. Nanostructured materials from severe plastic deformation [J]. Nanostructured Materials,1999,12:35-40
[22]Nishida Y, Arima H, Kim J C et al. Rotary-die equal-channel angular pressing of an Al-7 mass% Si-0.35 mass% Mg alloy [J]. Scripta Materialia,2001,45:261-266
[23]郝南海,王全聪.等径侧向挤压变形均匀程度的有限元分析[J].中国有色金属学报,2001,11(S2)：230-233
[24]Raab G I. Plastic flow at equal channel angular processing in parallel channels [J]. Materials Science and Engineering A,2005,410-411:230-233
[25]Lee J C, Seok H K, Suh J Y. Microstructural evolutions of the Al strip prepared by cold rolling and continuous equal channel angular pressing [J]. Acta Materialia,2002,50:4005-4019
[26]Lapovok R, Tomus D, Muddle B C. Low-temperature compaction of Ti-6Al-4V powder using equal channel angular extrusion with back pressure [J]. Materials Science and Engineering A,2008, 490(25):171-180
[27]Segal V M. Equal channel angular extrusion of flat products [J]. Materials Science and Engineering A,2008,476:178-185
[28]刘祖岩,梁国宪,王尔德,等.平面纯剪切大变形应变分析[J].塑性工程学报,1997,4(1)：42-46
[29]郝南海,刘祖岩.平面纯剪切大变形等效应变分析[J].塑性工程学报,2000,7(1)：4-5
[30]Iwahashi Y, Wang J, Horita Z. Principle of equal channel angular pressing for the processing of ultrafine-grained materials [J]. Scripta Mater,1996,35(2):143-146
[31]Segal V M, Hartwig K T, Goforth R E. In situ composites processed by simple shear [J]. Materials Science and Engineering A,1997,224:107-115
[32]Beyerlein I J, Tome C N. Modeling compression reloads in copper pre-strained by equal channel angular extrusion [J]. Materials Science and Engineering Technology,2005,26 (10):541-545
[33]Kim H S, Ryu W S, Janecek M, et al. Effect of equal channel angular pressing on microstructure and mechanical properties of if steel [J]. Advanced Engineering Materials,2005,7(1-2):43-46
[34]El-Danaf E A. Mechanical properties and microstructure evolution of 1050 aluminum severely deformed by ECAP to 16 passes [J]. Material Science and Engineering A,2008,487 (25):189-200
[35]Garcia-Infanta J M, Zhilyaev A P, Cepeda-Jimenez C M, et al. Effect of the deformation path on the ductility of a hypoeutectic Al-Si casting alloy subjected to equal-channel angular pressing by routes A, Ba, Bc and C [J]. Scripta Materialia.2008,58:138-141
[36]Purcek G, Saray O, Karaman I, et al. Effect of severe plastic deformation on tensile properties and impact toughness of two-phase Zn-40Al alloy [J]. Materials Science and Engineering A,2008, 490(25):403-410
[37]Hamu G B, Eliezer D, Wagner L. The relation between severe plastic deformation microstructure and corrosion behavior of AZ31 magnesium alloy [J]. Journal of Alloys and Compounds,2009, 468(22):222-229
[38]Chinh N Q, Gubicza J, Czeppe T, et al. Developing a strategy for the processing of age-hardenable alloys by ECAP at room temperature [J]. Materials Science and Engineering A,2009,516:248-252
[39]Chun Y B, Ahn S H, Shin D H, et al. Combined effects of grain size and recrystallization on the tensile properties of cryorolled pure vanadium [J]. Materials Science and Engineering A,2009,508: 253-258
[40]李永霞,张永刚,陈吕麒.等截面通道角形挤压对高纯铝微观组织及力学性能的影响[J].航空材料学报,2001,21(3)：33-38
[41]郑立静.北京航空航天大学博士后研究工作报告,2004
[42]郑立静,李树索,李焕喜,等.7050铝合金等通道转角挤压过程中显微结构和力学性能演化的小角X射线散射研究[J].物理学报,2005,54(4)：1665-1670
[43]王锦程,田景来,张忠明,等.等通道转角挤压对L2工业纯铝力学性能的影响[J].热加工工艺,2004,(8)：1-2
[44]王素梅,孙康宁,毕见强,等.等径角挤压法制备亚微米2A12铝合金块体材料[J].机械工程材料,2006,30(1)：42-45
[45]Fang Daran, Zhang Peng, Duan Qiqiang, et al. Fatigue behavior of Al-Cu alloy subjected to different numbers of ECAP passes [J]. Advanced Engineering Materials,2007,9(10):860-866
[46]Wang Xi-shu, Jin Li, Li Ying, et al. Effect of equal channel angular extrusion process on deformation behaviors of Mg-3Al-Zn alloy [J]. Materials Letters,2008,62:1856-1858
[47]Luis Perez C J, Gonzalez P, Garces Y. Equal channel angular extrusion in a commercial Al-Mn alloy [J]. Journal of Materials Processing Technology,2003,143-144:506-511
[48]Kim H S, Seo M H, Hong S I. Finite element analysis of equal channel angular pressing of strain rate sensitive metals [J]. Journal of Materials Processing Technology,2002,130-131:497-503
[49]Yang Y L, Lee S. Finite element analysis of strain condition after equal channel angular extrusion [J]. Journal of Materials Processing Technology,2003,140:583-587
[50]Li S Y, Bourke M A M, Beyerlein I J, et al. Finite element analysis of the plastic deformation zone and working load in equal channel angular extrusion [J]. Materials Science and Engineering A,2004, 382:217-236
[51]Yoon S C, Quang P, Hong S I, et al. Die design for homogeneous plastic deformation during equal channel angular pressing [J]. Journal of Materials Processing Technology,2007,187-188:46-50
[52]Chaboche J L, Jung O. Application of a kinematic hardening viscoplasticity model with thresholds to the residual stress relaxation [J]. International Journal of Plasticity,1998,13(10):785-807
[53]Chaboche J L. A review of some plasticity and viscoplasticity constitutive theories [J]. International Journal of Plasticity,2008,24:1642-1693
[54]Ohno N. Constitutive modeling of cyclic plasticity with emphasis on ratcheting. International Journal of Mechanical Sciences,1998,40(2-3):251-261
[55]Nakane K, Ohno N, Tsuda M, et al. Thermal ratcheting of solder-bonded elastic and elastoplastic layers [J]. International Journal of Plasticity,2008,24:1819-1836
[56]Kuroda M. Interpretation of the behavior of metals under large plastic shear deformation: comparison of macroscopic predictions to physically based predictions [J]. International Journal of Plasticity,1999,15:1217-1236
[57]冯露,张克实,张光.Hill屈服准则与晶体塑性模型对FCC单晶材料塑性各向异性描述能力的比较[J].计算力学学报,2003,20(5)：535-540
[58]Singh S B, Ray S. Modeling the anisotropy and creep in orthotropic aluminum-silicon carbide composite rotating disc [J]. Mechanics of Materials,2002,34:363-372
[59]Taylor G I, Elam C F. The distortion of an aluminum crystal during a tension test [J]. Proceedings of the Royal Society of London A,1923,102:643-667
[60]王亚男,陈树江,董希淳.位错理论及其应用[M].北京：冶金工业出版社,2007,1-2
[61]Taylor G L. Plastic strain in metals [J]. Journal Institute of Metals,1938,62:307-324
[62]Hill R. Generalized constitutive relations for incremental deformation of metals crystals by multi-slip [J]. Journal of the Mechanics and Physics of Solids,1966,14:95-102
[63]Hill R, Rice J R. Constitutive analysis of elastic-plastic crystals at arbitrary strain [J]. Journal of the Mechanics and Physics of Solids,1972,20:401-413
[64]Asaro R J, Rice J R. Strain localization in ductile single crystals [J]. Journal of the Mechanics and Physics of Solids,1977,25:309-338
[65]Pierces D, Asaro R J, Needleman A. A Material rate dependence and localized deformation in crystalline solids [J]. Acta Metallurgica,1983,31:1951-1976
[66]Hutchinson J M. Bounds and self-consistent estimates for creep of polycrystalline materials [J]. Proceedings of the Royal Society of London A:Mathematical Physical and Engineering Sciences, 1976,348:101-127
[67]Kalidindi S R. Incorporation of deformation twinning in crystal plasticity models [J]. Journal of the Mechanics and Physics of Solids,1998,46(2):267-290
[68]Kalidindi S R. Modeling anisotropic strain hardening and deformation textures in low stacking fault energy FCC metals [J]. International Journal of Plasticity,2001,17:837-860
[69]Kalidindi S R, Duvvru H K, Knezevic M. Spectral calibration of crystal plasticity models [J]. Acta Materialia,2006,54:1795-1804
[70]Cailletaud G. Micromechanical approach to inelastic behaviour of metal [J]. International Journal of Plasticity,1992,8(1):55-73
[71]Cailletaud G, Forest S, Jeulin D, et al. Some elements of microstructural mechanics [J]. Computational Materials Science,2003,27:351-374.
[72]张克实,张光,冯露.单晶体塑性滑移有限变形下的应力计算[J].力学学报,2002,34(4)：636-644
[73]Zhang K S, Wu M S, Feng R. Simulation of microplasticity-induced deformation in uniaxially strained ceramics by 3-D Voronoi polycrystal modeling [J]. International Journal of Plasticity,2005, 21(5):801-834
[74]Li S Y. Orientation stability in equal channel angular extrusion. Part Ⅰ:Face-centered cubic and body-centered cubic materials [J]. Acta Materialia,2008,56:1018-1030
[75]Li S Y. Orientation stability in equal channel angular extrusion. Part Ⅱ:Hexagonal close-packed materials [J]. Acta Materialia,2008,56:1031-1043
[76]Cailletaud G, Sai K. A polycrystalline model for the description of ratcheting:Effect of intergranular and intragranular hardening [J]. Materials Science and Engineering A,2008,480:24-39
[77]Chen Y P, Lee W B, Nakamachi E. Cystallographic homogenization finite element method and its application on simulation of evolution of plastic deformation induced texture [J]. Acta Mechanica Solida Sinica,2010,23(1):36-48
[78]Cheong K S, Busso E P, Arsenlis A. A study of microstructural length scale effects on the behaviour of FCC polycrystals using strain gradient concepts [J]. International Journal of Plasticity,2005,21: 1797-1714
[79]Starink M J, Wang S C. A model for the yield strength of overaged AL-Zn-Mg-Cu alloys [J]. Acta Materialia,2003,51:5153-5150
[80]Starink M J, Deschamps A, Wang S C. The strength of friction stir welded and friction stir processed aluminium alloys [J]. Scripta Materialia,2008,58:377-382
[81]耿小亮.晶粒尺度的金属微成形过程：试验与模拟研究[D].西安：西北工业大学,2008
[82]张光,张克实,冯露.硬化模型对多晶织构预测的影响[J].机械科学与技术,2004,23(8)：988-994
[83]冯露.晶体连续滑移理论的本构研究：计算方法和数值分析[D].西安：西北工业大学,2002
[84]Feng L, Zhang K S, Zhang G, et al. Anisotropic damage model under continuum slip crystal plasticity theory for single crystals [J]. International Journal of Solids and Structures,39(20): 5279-5293 OCT 2002
[85]Zhang M, McDowell D L, Neu R W. Microstructure sensitivity of fretting fatigue based on computational crystal plasticity [J]. Tribology International,2009,42:1286-1296
[86]Janssen P J M, Keijser T H, Geers M G D. An experimental assessment of grain size effects in the uniaxial straining if thin Al sheet with a few grains across the thickness [J]. Materials Science and Engineering A,2006,419:238-248
[87]Valiev R Z, Langdon T G. Principles of equal-channel angular pressing as a processing tool for grain refinement [J]. Progress in Materials Science,2006,51:881-981
[88]Segal V M. Engineering and commercialization of equal channel angular extrusion [J]. Materials Science and Engineering A,2004,386:269-276
[89]Yoon S C, Seo M H, Krishnaiah A, et al. Finite element analysis of rotary-die equal channel angular pressing [J]. Materials Science and Engineering A,2008,490:289-292
[90]张忠明,王锦程,唐文亭,等.等通道转角挤压工艺的研究现状[J].铸造技术,2004,25(1)：10-12
[91]Zhang Jing, Zhang Ke-shi, Wu Hwai-Chung, et al. Experimental and numerical investigation on pure aluminum by ECAP [J]. Transactions of Nonferrous Metals Society of China,2009,19(5):1303-131
[92]毛卫民,任学平,张建勋,等.金属材料成形与加工[M].北京：清华大学出版社,2008,86-88
[93]李文翔.ECAP制器的不同晶粒尺寸的纯铜可性质研究[D].南宁：广西大学,2009
[94]Koiter W T. Stress-strain relations uniqueness and variational theorems for elastic-plastic materials with a singular yield surface [J]. Quarterly of Applied Mathematics,1953,11:350-54
[95]Asaro R J. Crystal plasticity [J]. Journal of Applied Mechanics,1983,50:921-934
[96]Bassani J L, Wu T Y. Latent hardening in single crystals II:Analytical characterization and predictions [J]. Proceedings of the Royal Society of London A,1991,435:21-41
[97]Lee E H. Elastic-plastic deformation at finite strains [J]. Journal of Applied Mechanics Transactions of the ASME,1969,36:1-6
[98]Bassani J L. Incompatibility and a simple gradient theory of plasticity [J]. Journal of the Mechanics and Physics of Solids,2001,49:1983-1996
[99]Zhang Ke-Shi, Shi Yan-Ke, Zhang Jing, Effect of Grain Size on Strain Hardening and Micro Failure of Metals, proceedings of the Fourteenth International Symposium on Plasticity,2008,316-318
[100]Taylor G I, The mechanism of plastic deformation of crystals [J]:Part Ⅰ- theoretical. Proceedings of the Royal Society of London A,1934,145:362-387
[101]Capolungo L, Cherkaoui M, Qu J. On the elastic-viscoplastic behavior of nanocrystalline materials [J]. International Journal of Plasticity,2007,23:561-591
[102]Pande C S, Rath B B, Imam M A. Effect of annealing twins on Hall-Petch relation in polycrystalline materials [J]. Materials Science and Engineering A,2004,367:171-175
[103]Pande C S, Imam M A, Rath B B. Study of annealing twina in FCC metals and alloys. Metallurgical and materials transaction A [J]:Physical Metallurgy and Materials Science,1990,21:2891-2896
[104]Sauzay M, Brillet H, Monnet I, et al. Cyclically induced softening due to low-angle boundary annihilation in a martensitic steel [J]. Materials science and engineering A:Structural Materials Properties Microstructure and Processing,2005,400-401,241-244
[105]Hibbit, Karlsson & Sorenson, ABAQUS Reference Manuals, V6.5,2005
[106]张克实.多晶体变形、应力的不均匀性及宏观响应[J].力学学报,2004,36(6)：714-723
[107]Stefan W, Andress F, Hernz R O, et al. Automatic finite element meshing of planar voronoi tessellations [J]. Engineering Fracture Mechanics,2002,69:945-958
[108]Torsten L, Carsten K. Polycrystal models for the analysis of intergranular crack growth in metallic materials [J]. Engineering Fracture Mechanics,2009,76:2332-2343
[109]Barbe F, Quey R. A numerical modeling of 3D polycrystal-to-polycrystal diffusive phase transformations involving crystal plasticity [J]. International Journal of Plasticity,2010, (xxx): xxx-xxx
[110]Liu Y, Kangeyama Y, Murakami S. Creep fracture modeling by use of continuum damage variable based on voronoi simulation of grain boundary cavity [J]. International Journal of Mechanical Sciences,1998,40(2-3):147-158
[111]Quey R, Dawson P R, Barbe F. Large-scale 3D random polycrystals for the finite element method: Generation, meshing and remeshing [J]. Computer Methods in Applied Mechanics and Engineering, 2011,200(17-20),1729-1745
[112]Rashid K, Abu A R. Interfacial gradient plasticity governs scale-dependent yield strength and strain hardening rates in micro/nano structured metals [J]. International Journal of Plasticity,2008,24: 1277-1306
[113]Armstrong P J, Frederick C O.1966. A mathematical representation of the multiaxial Bauschinger effect. Report RD/B/N731, CEGB, Central Electricity Board, Berkeley, UK
[114]郭运强.循环载荷作用下镍基高温合金的微观塑性和后继破坏分析[D].西安：西北工业大学,2008
[115]Gerard C, Guyen F N, Osipov, et al. Comparison of experimental results and finite element simulation of strain localization scheme under cyclic loading [J]. Computational Materials Science, 2009,46:755-760
[116]Rashid K, Al-Rub Abu. Modeling the interfacial effect on the yield strength and flow stress of thin metal films on substrates [J]. Mechanics Research Communications,2008,35:65-72
[117]许凌波.多道次等径道弯曲挤压纯铜的循环硬化与软化研究[D].南宁：广西大学,2010
[118]Asaro R J, Needleman A. Texture development and strain hardening in rate dependent polycrystals [J]. Acta Metallurgica,1985,33:923-953
[119]Coffin L F. A study of the effects of cyclic thermal stresses on a ductile metal [J]. Transactions of the American Society of Mechanical Engineers,1954,76:931-950
[120]Manson S S. Behaviour of materials under condition of thermal stress. NACA TN-2933,1954
[121]Zhang jing, Zhang Keshi, Shi Yanke, et al. Analysis on force of pressure head during ECAP based on simulation [J]. Advanced Materials Science and Technology,2011,181-182:299-304
[2]白以龙,汪海英,柯孚久,等.从“哥伦比亚”号悲剧看多尺度力学问题[J].力学与实践,2005,27(3)：1-6
[3]杨卫.微纳米尺度的力学行为[J].世界科技研究与发展,2001,26(4)：2-6
[4]白以龙,汪海英,夏蒙棼,等.固体的统计细观力学—连接多个耦合的时空尺度[J].力学进展,2006,36(2)：286-305
[5]王亚勇.概论汶川地震后我国建筑抗震设计标准的修订[J].土木工程学报,2009,42(5)：1-12
[6]黄克智,黄永刚.固体本构关系[M].北京：清华大学出版社,1999,1-36,150-156
[7]程素玲,杨根仓,樊建锋,等.Ca,Y对AZ91镁合金显微组织和力学性能的影响[J].稀有金属材料与工程,2006,35(9)：1400-1403
[8]王卓琳,林峰,顾祥林.基于离散单元法的混凝土细观力学模型研究进展[J].结构工程师,2007,23(5)：79-85
[9]Reihanian M, Ebrahimi R, Moshksar M M, et al. Microstructure quantification and correlation with flow stress of ultrafine grained commercially pure Al fabricated by equal channel angular pressing [J]. Materials Characterization,2008,59(9):1312-1323
[10]马怀发,陈厚群,黎保琨.细观结构不均匀性对混凝土动弯拉强度的影响[J].水利学报,2005,36(7)：846-852
[11]黄修山，尹小涛,陈厚群,等.不同粒组骨料对混凝土力学性质的影响[J].武汉理工大学学报,2010,32(19)：50-54
[12]杨卫.宏微观断裂力学[M].北京：国防工业出版社,1995,1-11
[13]戚力,董立峰,程华,等.高压条件下Pd-Ni合金熔体非晶形成过程及微观结构演化的分子动力学研究[J].金属学报,2008,44(2)：233-236
[14]Lugo N, Llorca N, Cabrera J M, et al. Microstructures and mechanical properties of pure copper deformed severely by equal-channel angular pressing and high pressure torsion [J]. Materials Science and Engineering A,2008,477(25):366-371
[15]Zhilyaev A P, Gimazov A A, Raab G I, et al. Using high-pressure torsion for the cold-consolidation of copper chips produced by machining [J]. Materials Science and Engineering,2008,486:123-126
[16]Segal V M. Materials processing by simple shear [J]. Materials Science and Engineering,1995, A197:157-164
[17]王自强,段祝平.塑性细观力学[M].科学出版社,北京,1995,28-31,90-91
[18]Hall E O. The deformation and ageing of mild steel:Ⅲ. Discussion of results [J]. Proceedings of the Physical Society,1951, B64:747-753
[19]Petch N J. The cleavage strength of polycrystals [J]. Journal of the Iron and Steel Institute,1953,174: 25-28
[20]Segal V M. Equal channel angular extrusion:from macromechanics to structure formation [J]. Material Science and Engineering,1999, A271:322-333
[21]Valiev R Z, Alexandrov I V. Nanostructured materials from severe plastic deformation [J]. Nanostructured Materials,1999,12:35-40
[22]Nishida Y, Arima H, Kim J C et al. Rotary-die equal-channel angular pressing of an Al-7 mass% Si-0.35 mass% Mg alloy [J]. Scripta Materialia,2001,45:261-266
[23]郝南海,王全聪.等径侧向挤压变形均匀程度的有限元分析[J].中国有色金属学报,2001,11(S2)：230-233
[24]Raab G I. Plastic flow at equal channel angular processing in parallel channels [J]. Materials Science and Engineering A,2005,410-411:230-233
[25]Lee J C, Seok H K, Suh J Y. Microstructural evolutions of the Al strip prepared by cold rolling and continuous equal channel angular pressing [J]. Acta Materialia,2002,50:4005-4019
[26]Lapovok R, Tomus D, Muddle B C. Low-temperature compaction of Ti-6Al-4V powder using equal channel angular extrusion with back pressure [J]. Materials Science and Engineering A,2008, 490(25):171-180
[27]Segal V M. Equal channel angular extrusion of flat products [J]. Materials Science and Engineering A,2008,476:178-185
[28]刘祖岩,梁国宪,王尔德,等.平面纯剪切大变形应变分析[J].塑性工程学报,1997,4(1)：42-46
[29]郝南海,刘祖岩.平面纯剪切大变形等效应变分析[J].塑性工程学报,2000,7(1)：4-5
[30]Iwahashi Y, Wang J, Horita Z. Principle of equal channel angular pressing for the processing of ultrafine-grained materials [J]. Scripta Mater,1996,35(2):143-146
[31]Segal V M, Hartwig K T, Goforth R E. In situ composites processed by simple shear [J]. Materials Science and Engineering A,1997,224:107-115
[32]Beyerlein I J, Tome C N. Modeling compression reloads in copper pre-strained by equal channel angular extrusion [J]. Materials Science and Engineering Technology,2005,26 (10):541-545
[33]Kim H S, Ryu W S, Janecek M, et al. Effect of equal channel angular pressing on microstructure and mechanical properties of if steel [J]. Advanced Engineering Materials,2005,7(1-2):43-46
[34]El-Danaf E A. Mechanical properties and microstructure evolution of 1050 aluminum severely deformed by ECAP to 16 passes [J]. Material Science and Engineering A,2008,487 (25):189-200
[35]Garcia-Infanta J M, Zhilyaev A P, Cepeda-Jimenez C M, et al. Effect of the deformation path on the ductility of a hypoeutectic Al-Si casting alloy subjected to equal-channel angular pressing by routes A, Ba, Bc and C [J]. Scripta Materialia.2008,58:138-141
[36]Purcek G, Saray O, Karaman I, et al. Effect of severe plastic deformation on tensile properties and impact toughness of two-phase Zn-40Al alloy [J]. Materials Science and Engineering A,2008, 490(25):403-410
[37]Hamu G B, Eliezer D, Wagner L. The relation between severe plastic deformation microstructure and corrosion behavior of AZ31 magnesium alloy [J]. Journal of Alloys and Compounds,2009, 468(22):222-229
[38]Chinh N Q, Gubicza J, Czeppe T, et al. Developing a strategy for the processing of age-hardenable alloys by ECAP at room temperature [J]. Materials Science and Engineering A,2009,516:248-252
[39]Chun Y B, Ahn S H, Shin D H, et al. Combined effects of grain size and recrystallization on the tensile properties of cryorolled pure vanadium [J]. Materials Science and Engineering A,2009,508: 253-258
[40]李永霞,张永刚,陈吕麒.等截面通道角形挤压对高纯铝微观组织及力学性能的影响[J].航空材料学报,2001,21(3)：33-38
[41]郑立静.北京航空航天大学博士后研究工作报告,2004
[42]郑立静,李树索,李焕喜,等.7050铝合金等通道转角挤压过程中显微结构和力学性能演化的小角X射线散射研究[J].物理学报,2005,54(4)：1665-1670
[43]王锦程,田景来,张忠明,等.等通道转角挤压对L2工业纯铝力学性能的影响[J].热加工工艺,2004,(8)：1-2
[44]王素梅,孙康宁,毕见强,等.等径角挤压法制备亚微米2A12铝合金块体材料[J].机械工程材料,2006,30(1)：42-45
[45]Fang Daran, Zhang Peng, Duan Qiqiang, et al. Fatigue behavior of Al-Cu alloy subjected to different numbers of ECAP passes [J]. Advanced Engineering Materials,2007,9(10):860-866
[46]Wang Xi-shu, Jin Li, Li Ying, et al. Effect of equal channel angular extrusion process on deformation behaviors of Mg-3Al-Zn alloy [J]. Materials Letters,2008,62:1856-1858
[47]Luis Perez C J, Gonzalez P, Garces Y. Equal channel angular extrusion in a commercial Al-Mn alloy [J]. Journal of Materials Processing Technology,2003,143-144:506-511
[48]Kim H S, Seo M H, Hong S I. Finite element analysis of equal channel angular pressing of strain rate sensitive metals [J]. Journal of Materials Processing Technology,2002,130-131:497-503
[49]Yang Y L, Lee S. Finite element analysis of strain condition after equal channel angular extrusion [J]. Journal of Materials Processing Technology,2003,140:583-587
[50]Li S Y, Bourke M A M, Beyerlein I J, et al. Finite element analysis of the plastic deformation zone and working load in equal channel angular extrusion [J]. Materials Science and Engineering A,2004, 382:217-236
[51]Yoon S C, Quang P, Hong S I, et al. Die design for homogeneous plastic deformation during equal channel angular pressing [J]. Journal of Materials Processing Technology,2007,187-188:46-50
[52]Chaboche J L, Jung O. Application of a kinematic hardening viscoplasticity model with thresholds to the residual stress relaxation [J]. International Journal of Plasticity,1998,13(10):785-807
[53]Chaboche J L. A review of some plasticity and viscoplasticity constitutive theories [J]. International Journal of Plasticity,2008,24:1642-1693
[54]Ohno N. Constitutive modeling of cyclic plasticity with emphasis on ratcheting. International Journal of Mechanical Sciences,1998,40(2-3):251-261
[55]Nakane K, Ohno N, Tsuda M, et al. Thermal ratcheting of solder-bonded elastic and elastoplastic layers [J]. International Journal of Plasticity,2008,24:1819-1836
[56]Kuroda M. Interpretation of the behavior of metals under large plastic shear deformation: comparison of macroscopic predictions to physically based predictions [J]. International Journal of Plasticity,1999,15:1217-1236
[57]冯露,张克实,张光.Hill屈服准则与晶体塑性模型对FCC单晶材料塑性各向异性描述能力的比较[J].计算力学学报,2003,20(5)：535-540
[58]Singh S B, Ray S. Modeling the anisotropy and creep in orthotropic aluminum-silicon carbide composite rotating disc [J]. Mechanics of Materials,2002,34:363-372
[59]Taylor G I, Elam C F. The distortion of an aluminum crystal during a tension test [J]. Proceedings of the Royal Society of London A,1923,102:643-667
[60]王亚男,陈树江,董希淳.位错理论及其应用[M].北京：冶金工业出版社,2007,1-2
[61]Taylor G L. Plastic strain in metals [J]. Journal Institute of Metals,1938,62:307-324
[62]Hill R. Generalized constitutive relations for incremental deformation of metals crystals by multi-slip [J]. Journal of the Mechanics and Physics of Solids,1966,14:95-102
[63]Hill R, Rice J R. Constitutive analysis of elastic-plastic crystals at arbitrary strain [J]. Journal of the Mechanics and Physics of Solids,1972,20:401-413
[64]Asaro R J, Rice J R. Strain localization in ductile single crystals [J]. Journal of the Mechanics and Physics of Solids,1977,25:309-338
[65]Pierces D, Asaro R J, Needleman A. A Material rate dependence and localized deformation in crystalline solids [J]. Acta Metallurgica,1983,31:1951-1976
[66]Hutchinson J M. Bounds and self-consistent estimates for creep of polycrystalline materials [J]. Proceedings of the Royal Society of London A:Mathematical Physical and Engineering Sciences, 1976,348:101-127
[67]Kalidindi S R. Incorporation of deformation twinning in crystal plasticity models [J]. Journal of the Mechanics and Physics of Solids,1998,46(2):267-290
[68]Kalidindi S R. Modeling anisotropic strain hardening and deformation textures in low stacking fault energy FCC metals [J]. International Journal of Plasticity,2001,17:837-860
[69]Kalidindi S R, Duvvru H K, Knezevic M. Spectral calibration of crystal plasticity models [J]. Acta Materialia,2006,54:1795-1804
[70]Cailletaud G. Micromechanical approach to inelastic behaviour of metal [J]. International Journal of Plasticity,1992,8(1):55-73
[71]Cailletaud G, Forest S, Jeulin D, et al. Some elements of microstructural mechanics [J]. Computational Materials Science,2003,27:351-374.
[72]张克实,张光,冯露.单晶体塑性滑移有限变形下的应力计算[J].力学学报,2002,34(4)：636-644
[73]Zhang K S, Wu M S, Feng R. Simulation of microplasticity-induced deformation in uniaxially strained ceramics by 3-D Voronoi polycrystal modeling [J]. International Journal of Plasticity,2005, 21(5):801-834
[74]Li S Y. Orientation stability in equal channel angular extrusion. Part Ⅰ:Face-centered cubic and body-centered cubic materials [J]. Acta Materialia,2008,56:1018-1030
[75]Li S Y. Orientation stability in equal channel angular extrusion. Part Ⅱ:Hexagonal close-packed materials [J]. Acta Materialia,2008,56:1031-1043
[76]Cailletaud G, Sai K. A polycrystalline model for the description of ratcheting:Effect of intergranular and intragranular hardening [J]. Materials Science and Engineering A,2008,480:24-39
[77]Chen Y P, Lee W B, Nakamachi E. Cystallographic homogenization finite element method and its application on simulation of evolution of plastic deformation induced texture [J]. Acta Mechanica Solida Sinica,2010,23(1):36-48
[78]Cheong K S, Busso E P, Arsenlis A. A study of microstructural length scale effects on the behaviour of FCC polycrystals using strain gradient concepts [J]. International Journal of Plasticity,2005,21: 1797-1714
[79]Starink M J, Wang S C. A model for the yield strength of overaged AL-Zn-Mg-Cu alloys [J]. Acta Materialia,2003,51:5153-5150
[80]Starink M J, Deschamps A, Wang S C. The strength of friction stir welded and friction stir processed aluminium alloys [J]. Scripta Materialia,2008,58:377-382
[81]耿小亮.晶粒尺度的金属微成形过程：试验与模拟研究[D].西安：西北工业大学,2008
[82]张光,张克实,冯露.硬化模型对多晶织构预测的影响[J].机械科学与技术,2004,23(8)：988-994
[83]冯露.晶体连续滑移理论的本构研究：计算方法和数值分析[D].西安：西北工业大学,2002
[84]Feng L, Zhang K S, Zhang G, et al. Anisotropic damage model under continuum slip crystal plasticity theory for single crystals [J]. International Journal of Solids and Structures,39(20): 5279-5293 OCT 2002
[85]Zhang M, McDowell D L, Neu R W. Microstructure sensitivity of fretting fatigue based on computational crystal plasticity [J]. Tribology International,2009,42:1286-1296
[86]Janssen P J M, Keijser T H, Geers M G D. An experimental assessment of grain size effects in the uniaxial straining if thin Al sheet with a few grains across the thickness [J]. Materials Science and Engineering A,2006,419:238-248
[87]Valiev R Z, Langdon T G. Principles of equal-channel angular pressing as a processing tool for grain refinement [J]. Progress in Materials Science,2006,51:881-981
[88]Segal V M. Engineering and commercialization of equal channel angular extrusion [J]. Materials Science and Engineering A,2004,386:269-276
[89]Yoon S C, Seo M H, Krishnaiah A, et al. Finite element analysis of rotary-die equal channel angular pressing [J]. Materials Science and Engineering A,2008,490:289-292
[90]张忠明,王锦程,唐文亭,等.等通道转角挤压工艺的研究现状[J].铸造技术,2004,25(1)：10-12
[91]Zhang Jing, Zhang Ke-shi, Wu Hwai-Chung, et al. Experimental and numerical investigation on pure aluminum by ECAP [J]. Transactions of Nonferrous Metals Society of China,2009,19(5):1303-131
[92]毛卫民,任学平,张建勋,等.金属材料成形与加工[M].北京：清华大学出版社,2008,86-88
[93]李文翔.ECAP制器的不同晶粒尺寸的纯铜可性质研究[D].南宁：广西大学,2009
[94]Koiter W T. Stress-strain relations uniqueness and variational theorems for elastic-plastic materials with a singular yield surface [J]. Quarterly of Applied Mathematics,1953,11:350-54
[95]Asaro R J. Crystal plasticity [J]. Journal of Applied Mechanics,1983,50:921-934
[96]Bassani J L, Wu T Y. Latent hardening in single crystals II:Analytical characterization and predictions [J]. Proceedings of the Royal Society of London A,1991,435:21-41
[97]Lee E H. Elastic-plastic deformation at finite strains [J]. Journal of Applied Mechanics Transactions of the ASME,1969,36:1-6
[98]Bassani J L. Incompatibility and a simple gradient theory of plasticity [J]. Journal of the Mechanics and Physics of Solids,2001,49:1983-1996
[99]Zhang Ke-Shi, Shi Yan-Ke, Zhang Jing, Effect of Grain Size on Strain Hardening and Micro Failure of Metals, proceedings of the Fourteenth International Symposium on Plasticity,2008,316-318
[100]Taylor G I, The mechanism of plastic deformation of crystals [J]:Part Ⅰ- theoretical. Proceedings of the Royal Society of London A,1934,145:362-387
[101]Capolungo L, Cherkaoui M, Qu J. On the elastic-viscoplastic behavior of nanocrystalline materials [J]. International Journal of Plasticity,2007,23:561-591
[102]Pande C S, Rath B B, Imam M A. Effect of annealing twins on Hall-Petch relation in polycrystalline materials [J]. Materials Science and Engineering A,2004,367:171-175
[103]Pande C S, Imam M A, Rath B B. Study of annealing twina in FCC metals and alloys. Metallurgical and materials transaction A [J]:Physical Metallurgy and Materials Science,1990,21:2891-2896
[104]Sauzay M, Brillet H, Monnet I, et al. Cyclically induced softening due to low-angle boundary annihilation in a martensitic steel [J]. Materials science and engineering A:Structural Materials Properties Microstructure and Processing,2005,400-401,241-244
[105]Hibbit, Karlsson & Sorenson, ABAQUS Reference Manuals, V6.5,2005
[106]张克实.多晶体变形、应力的不均匀性及宏观响应[J].力学学报,2004,36(6)：714-723
[107]Stefan W, Andress F, Hernz R O, et al. Automatic finite element meshing of planar voronoi tessellations [J]. Engineering Fracture Mechanics,2002,69:945-958
[108]Torsten L, Carsten K. Polycrystal models for the analysis of intergranular crack growth in metallic materials [J]. Engineering Fracture Mechanics,2009,76:2332-2343
[109]Barbe F, Quey R. A numerical modeling of 3D polycrystal-to-polycrystal diffusive phase transformations involving crystal plasticity [J]. International Journal of Plasticity,2010, (xxx): xxx-xxx
[110]Liu Y, Kangeyama Y, Murakami S. Creep fracture modeling by use of continuum damage variable based on voronoi simulation of grain boundary cavity [J]. International Journal of Mechanical Sciences,1998,40(2-3):147-158
[111]Quey R, Dawson P R, Barbe F. Large-scale 3D random polycrystals for the finite element method: Generation, meshing and remeshing [J]. Computer Methods in Applied Mechanics and Engineering, 2011,200(17-20),1729-1745
[112]Rashid K, Abu A R. Interfacial gradient plasticity governs scale-dependent yield strength and strain hardening rates in micro/nano structured metals [J]. International Journal of Plasticity,2008,24: 1277-1306
[113]Armstrong P J, Frederick C O.1966. A mathematical representation of the multiaxial Bauschinger effect. Report RD/B/N731, CEGB, Central Electricity Board, Berkeley, UK
[114]郭运强.循环载荷作用下镍基高温合金的微观塑性和后继破坏分析[D].西安：西北工业大学,2008
[115]Gerard C, Guyen F N, Osipov, et al. Comparison of experimental results and finite element simulation of strain localization scheme under cyclic loading [J]. Computational Materials Science, 2009,46:755-760
[116]Rashid K, Al-Rub Abu. Modeling the interfacial effect on the yield strength and flow stress of thin metal films on substrates [J]. Mechanics Research Communications,2008,35:65-72
[117]许凌波.多道次等径道弯曲挤压纯铜的循环硬化与软化研究[D].南宁：广西大学,2010
[118]Asaro R J, Needleman A. Texture development and strain hardening in rate dependent polycrystals [J]. Acta Metallurgica,1985,33:923-953
[119]Coffin L F. A study of the effects of cyclic thermal stresses on a ductile metal [J]. Transactions of the American Society of Mechanical Engineers,1954,76:931-950
[120]Manson S S. Behaviour of materials under condition of thermal stress. NACA TN-2933,1954
[121]Zhang jing, Zhang Keshi, Shi Yanke, et al. Analysis on force of pressure head during ECAP based on simulation [J]. Advanced Materials Science and Technology,2011,181-182:299-304