非局部摩擦及应变梯度理论在超塑性成形中的应用研究
|
摘要
在金属超塑性成形加工力学中,接触面上逐点采用的库仑摩擦定律是局部性质的,即接触面上摩擦域内某质点的摩擦效应只与该点的状态有关。然而,实际上金属表面往往是粗糙的,接触界面是粗糙面之间的接触,某一点的摩擦效应不仅与该点的状态直接相关,还与该点有限大小邻域内的其它点的状态有关,这是一种非局部摩擦效应。因此,在细观尺度上有必要用非局部摩擦模型替代库仑摩擦模型来考虑接触界面上微凸结构所引起的非局部摩擦效应,其中Oden等提出的非局部摩擦模型得到了广泛应用。另外,为了解释微米和亚微米量级实验中发现的尺度效应,以及解决工业领域在该尺度下遇到的日益增多的问题,人们建立了各种非局部本构模型,其中M(u｜¨)hlhaus和Aifantis提出的一种梯度依赖非局部本构模型,可能是此类模型中形式最简单的一个,在这个模型中,M(u｜¨)hlhaus和Aifantis将一个系数引入流动应力方程中,同时考虑等效塑性应变的二阶梯度,而保留经典塑性理论的其它特征不变,该理论自提出后,得到了广泛应用。本文的主要工作就是利用Oden等提出的非局部摩擦模型以及M(u｜¨)hlhaus和Aifantis提出的一种梯度依赖非局部本构模型研究了如下五个具体问题:
本论文的主要内容有:
采用非局部摩擦模型代替库仑摩擦模型研究了圆板超塑性锻压工艺,得出了两种摩擦模型下压力差的计算公式,并分析了不同工况条件下非局部摩擦模型与库仑摩擦模型对接触面上压力分布影响的差异。
将Oden等提出的非局部摩擦模型应用于锥形模圆柱体超塑性拉拔或挤压中,并利用摄动方法求出了其近似解。
将Oden等提出的非局部摩擦模型应用于楔形模宽条料超塑性拉拔或挤压中,并利用摄动方法求出了其近似解。
基于应变梯度塑性理论,求得了内压作用下厚壁圆筒和球壳的极限荷载的分析解,经典塑性解是当前解的特例。
基于应变梯度塑性理论,分析了自由胀形工艺中的尺度效应现象,并与有关实验结果进行比较。
以上研究结果表明,采用非局部摩擦模型代替局部的库仑摩擦模型对超塑性成形加工过程的摩擦行为进行分析,虽然增加了问题的复杂性,但有助于我们更加深入地认识金属超塑性成形加工过程中的摩擦机理,有益于探索非局部摩擦模型的应用价值、拓展非局部摩擦模型的应用范围,同时,将应变梯度理论引入塑性成形分析中,为细微成形加工技术的应用与发展奠定良好的理论基础,为塑性加工工艺和塑性加工技术的改进与创新提供广阔的前景。
In mental superplastic forming processing, the Coulomb friction model applied on each point of the contact surface is local, which means the friction stress at one point in a certain range of contact surface is only affected by normal stress at the same point. However, real metal surfaces are not smooth, and the contact surface is actually contacts between rough surfaces. In this case, the friction stress of a certain point is not only related to the normal stress of this point, but is affected by the other points' normal stress in a neighborhood of the point. This is called the nonlocal friction effect. Therefore, it is necessary to use nonlocal friction model as a replacement of Coulomb's friction model to analyse the nonlocal friction effect caused by the asperity structure on the contact surface on micro-level. The nonlocal friction model proposed by Oden et al. has been widely used. In addition, all kinds of nonlocal constitutive theories have been established to explain the size effect and to solve the industrial problems at the micron and submicron scales. The simplest version of nonlocal constitutive theories may be suggested by Mühlhaus and Aifantis. The theory introduces the second-order gradients of the effective plastic strain into the constitutive equation for the flow stress, while leaving all other features of classical plasticity unaltered. This theory has been widely used. The major work of this dissertation is to investigate a series of problems with the above mentioned theory.
The main content of the research paper is:
The nonlocal friction model is applied as a replacement of Coulomb's friction model to study the distribution of pressure on the contact surface in the superplastic forging process of disks. A formula to caculate the pressure in the forging process with nonlocal friction model is obtained. What's more, the differences between the influences on the distribution of pressure on the contact surface caused by nonlocal friction model and Coulomb's friction model under different conditions is also studied.
The nonlocal friction model proposed by Oden et al. is adopted in the analysis of superplastic drawing or extrusion process of cylindrical body through a cone-shaped die. Perturbation theory is used to get approximate solution.
The nonlocal friction model proposed by Oden et al. is adopted in the analysis of superplastic drawing or extrusion process of wide strip through a tapered die. Perturbation theory is used to get approximate solution.
Plastic limit load of viscoplastic thick-walled cylinder and spherical shell subjected to internal pressure is investigated using the strain gradient plasticity theory.
The size effects of free bulging process are investigated using the strain gradient theory and the theoretical results are compared with the available experimental data.
All the research findings show that although using nonlocal friction model in replacement of Coulomb's friction model to analyse the friction in the superplastic forming process has made the problem more complex, the findings of the analysis is more accurate and true. The application of nonlocal friction model is helpful for us to gain a deeper understanding of the friction mechanism in the metal superplastic forming process. It is helpful for us to explore the value of the nonlocal friction model and extending the application range of it. In addition, the strain gradient theory is adopted to explain the size effect of superplastic free bulging. It can serve as good theoretical bases for the application and development of the minor forming and processing technology. It can provide a promising future for the improvement and innovation of plastic processing technology.
本论文的主要内容有:
采用非局部摩擦模型代替库仑摩擦模型研究了圆板超塑性锻压工艺,得出了两种摩擦模型下压力差的计算公式,并分析了不同工况条件下非局部摩擦模型与库仑摩擦模型对接触面上压力分布影响的差异。
将Oden等提出的非局部摩擦模型应用于锥形模圆柱体超塑性拉拔或挤压中,并利用摄动方法求出了其近似解。
将Oden等提出的非局部摩擦模型应用于楔形模宽条料超塑性拉拔或挤压中,并利用摄动方法求出了其近似解。
基于应变梯度塑性理论,求得了内压作用下厚壁圆筒和球壳的极限荷载的分析解,经典塑性解是当前解的特例。
基于应变梯度塑性理论,分析了自由胀形工艺中的尺度效应现象,并与有关实验结果进行比较。
以上研究结果表明,采用非局部摩擦模型代替局部的库仑摩擦模型对超塑性成形加工过程的摩擦行为进行分析,虽然增加了问题的复杂性,但有助于我们更加深入地认识金属超塑性成形加工过程中的摩擦机理,有益于探索非局部摩擦模型的应用价值、拓展非局部摩擦模型的应用范围,同时,将应变梯度理论引入塑性成形分析中,为细微成形加工技术的应用与发展奠定良好的理论基础,为塑性加工工艺和塑性加工技术的改进与创新提供广阔的前景。
In mental superplastic forming processing, the Coulomb friction model applied on each point of the contact surface is local, which means the friction stress at one point in a certain range of contact surface is only affected by normal stress at the same point. However, real metal surfaces are not smooth, and the contact surface is actually contacts between rough surfaces. In this case, the friction stress of a certain point is not only related to the normal stress of this point, but is affected by the other points' normal stress in a neighborhood of the point. This is called the nonlocal friction effect. Therefore, it is necessary to use nonlocal friction model as a replacement of Coulomb's friction model to analyse the nonlocal friction effect caused by the asperity structure on the contact surface on micro-level. The nonlocal friction model proposed by Oden et al. has been widely used. In addition, all kinds of nonlocal constitutive theories have been established to explain the size effect and to solve the industrial problems at the micron and submicron scales. The simplest version of nonlocal constitutive theories may be suggested by Mühlhaus and Aifantis. The theory introduces the second-order gradients of the effective plastic strain into the constitutive equation for the flow stress, while leaving all other features of classical plasticity unaltered. This theory has been widely used. The major work of this dissertation is to investigate a series of problems with the above mentioned theory.
The main content of the research paper is:
The nonlocal friction model is applied as a replacement of Coulomb's friction model to study the distribution of pressure on the contact surface in the superplastic forging process of disks. A formula to caculate the pressure in the forging process with nonlocal friction model is obtained. What's more, the differences between the influences on the distribution of pressure on the contact surface caused by nonlocal friction model and Coulomb's friction model under different conditions is also studied.
The nonlocal friction model proposed by Oden et al. is adopted in the analysis of superplastic drawing or extrusion process of cylindrical body through a cone-shaped die. Perturbation theory is used to get approximate solution.
The nonlocal friction model proposed by Oden et al. is adopted in the analysis of superplastic drawing or extrusion process of wide strip through a tapered die. Perturbation theory is used to get approximate solution.
Plastic limit load of viscoplastic thick-walled cylinder and spherical shell subjected to internal pressure is investigated using the strain gradient plasticity theory.
The size effects of free bulging process are investigated using the strain gradient theory and the theoretical results are compared with the available experimental data.
All the research findings show that although using nonlocal friction model in replacement of Coulomb's friction model to analyse the friction in the superplastic forming process has made the problem more complex, the findings of the analysis is more accurate and true. The application of nonlocal friction model is helpful for us to gain a deeper understanding of the friction mechanism in the metal superplastic forming process. It is helpful for us to explore the value of the nonlocal friction model and extending the application range of it. In addition, the strain gradient theory is adopted to explain the size effect of superplastic free bulging. It can serve as good theoretical bases for the application and development of the minor forming and processing technology. It can provide a promising future for the improvement and innovation of plastic processing technology.
引文
[1]温诗铸,黄平主编.摩擦学原理[M].北京:清华大学出版社,2002.
[2]王祖唐,关廷栋,肖景容等主编.金属塑性成型理论[M].北京:机械工业出版社,1989.
[3]朱谨,阮雪榆.板料变形中两种摩擦模型的比较[J].上海交通大学学报,1995,29(2):72-78.
[4]C.C.Chen.Et al.Rigid plastic finite element analysis of ring compression.Applications of numerical method to forming processes[J].ASME.AMD.1978,28(2):163-169.
[5]黄毅坚,李国基.金属成型过程刚塑性有限元分析中的摩擦问题[J].模具技术,1986,6(2):10-15.
[6]肖宏,申光宪,木原谆二,相泽龙彦.三维弹塑性接触边界元法对摩擦的处理[J].工程力学,1997,14(4):83-88.
[7]S.L.WANG and K.P.RAO,AN UPPER-BOUND ANALYSIS OF FRICTION IN METAL FORMING[J].Jnt.J.Mech.Sci.1997,39(2):201-209.
[8]姚齐水,王桥医.基于包装铝箔轧制过程的一种较精确的摩擦模型[J].包装食品机械,2002,20(3):6-8.
[9]A.C.Eringen.et al.On nonlocal elasticity[J].Int.J.Engng Sci.1972,10:233-248.
[10]A.C.Eringen et al.Theories of nonlocal plasticity[J].Int.J.Engng Sci.1983,21:741-751.
[11]扶名福,丁成辉,吴洪飞.非局部塑性内时本构理论[J].南昌大学学报,1998,2(3):1-10.
[12]A.C.Eringen.et al.A lubrication theory for fluids with microstructure[J].Int.J.Engng.Sci.33(1995):2297-2308.
[13]Duvaut,G.LOI DE FROTTEMENT NON LOCALE[J].Journal de Mecanique Theorique et Appliquee Jun23-28 1980 p 73-78 0750-7240.
[14]Oden J T.Pire E B.Nonlocal and nonlinear friction laws and variational principles for contact problems in elasticity[J].J of Appl Mech ASME,1983,50:67-76.
[15]Pires,E.B.;Trabucho,L.Steady sliding problem with nonlocal friction[J].International Journal of Engineering Science v 28 n 7 1990 p 631-641 0020-7225.
[16]Mahrenholtz,O.,Appeltauer,J.,Bontcheva,N.;Brzozowski,M..Nonlocal friction-application to rolling with spread[J].Zeitschrift fuer Angewandte Mathematik und Mechanik,ZAMM,Applied Mathematics and Mechanics 76 Suppl 4 1996 p 603.
[17]Mahrenholtz O.,N.Bontcheva,R.Iankov,M.Datcheva.Investigation of the infuence of surface roughness on metal forming,processes[J].Mechanics Research Communications,Vol.27,No.4,393-402,2000.
[18]Mahrenholtz O.,N.Bontcheva,R.Iankov,M.Datcheva,Influence of asperitieson friction during metal forming processes[J],Proc.ECCM'99,Munich,31 August- 3 Sept.1999.
[19]Mahrenholtz O.,N.Bontcheva,Application of the non-linear non-local friction law to metal forming processes[J],In:Umformung 2000 Plus,Ed.M.Geiger,Meisenbach-Verlag Bamberg,1999,207-214.
[20]Mahrenholtz O.,N.Bontcheva,R.Iankov,Nonlocal friction during metal forming processes [J],ZAMM,2001,81,Suppl.2,353-354.
[21]扶名福,郭良.圆柱体镦粗非局部摩擦问题及近似求解[J].固体力学的现代进展(杨桂通教授七十寿辰贺文集).徐秉业,张善元主编.北京:万国学术出版社,2000.
[22]扶名福,郭良.采用非局部摩擦定律处理平面镦粗问题及其近似解[J].塑性工程学报,2001,8(1):59-61.
[23]扶名福,郭良.通过圆弧模具库仑摩擦下的平面拉拔数值滑移线场求解[J].塑性工程学报,2001,8(4):67-71.
[24]扶名福,郭良,陈桂尧.非局部摩擦在塑性加工中的应用[J].力学季刊,2001,22(1):112-116.
[25]郭良,扶名福.楔形模宽条料拉拔非局部摩擦问题及近似求解[J].南昌大学学报(工科版),2001,23(1):1-4.
[26]罗海宝,扶名福.非局部摩擦在变薄翻边成形工序中的应用[J].塑性工程学报,2003,100(6):26-29.
[27]罗海宝,扶名福.采用非局部摩擦模型处理半圆形砧拔长问题时的近似解[J].南昌大学学报(理科版),2003,27(专辑):88-91.
[28]罗海宝,扶名福.平辊轧制非局部摩擦问题及近似求解[J].南昌大学学报(工科版),2003,25(4):1-4.
[29]罗小艳,刘伟平.重力坝坝基面的非局部摩擦分析[J].南昌大学学报(工科版),2004.26(4):59-62.
[30]刘伟平,扶名福,曾宪坤,彭强生.深长摩擦桩的非局部摩擦分析[J].地质与勘探.2005.41(4):103-105.
[31]蔡改贫,翁海珊,姜志宏.振动拉拔的非局部摩擦问题的近似求解及表面效应初探术[J].机械工程学报.2006.42(8):190-194.
[32]Cosserat E,Cosserat F.Theories des Corps Deformables[J].Paris:Herman et fils,1909.
[33]杨璐,朱浮声,沈新普.弹塑性损伤模型在应变局部化分析中的应用[J].力学与实践.2006,28(2):9-15.
[34]Bazant ZP,Cedolin L.Stability of Structures:Elastic,Inelastic,Fracture and Damage Theories[J].New York:Oxford University Press,1991.
[35]Bazant ZP,Jirasek Milan.Nonloeal integral formulations of plasticity and damage:survey of progress.Journal of Engineering Mechanies[J],ASCE,2002,128:1119-1149,
[36]黄克智,黄永刚.固体本构关系[M].北京:清华大学出版社,1999.
[37]Fleck NA,Hutchinson JW.A formulation of strain gradient plasticity[J].J Mech Phys Solids,2001,49:2245-2271.
[38]Borst R de,Pamin Jerzy,Marc G,et al.On coupled gradient-dependent plasticity and damage theories with a view to localization analysis[J].Eur J Mech A/Solids,1999,18:939-962.
[39]Giessen EV de.Plastic flow in a composite:a comparison of nonlocal continuum and discrete dislocation prediction[J].Int J Solids and Structures,2001,38:833-853.
[40]Bazant ZP,Pijaudier-Cabot.Nonlocal continuum damage,localization instability and convergence[J].ASME J Appl Mech,1988,55:287-293.
[41]Lena S,Ristinmaa M.FE-formulation of a nonlocal plasticity theory[J].Comp Meth Appl Mech Engng,1996,136:127-144.
[42]Eringen E,Mcdowell DL,Talreja R.Gradient concepts for evolution of damage.Mech Mater[J],1987,31:831-860.
[43]陈少华,王自强.应变梯度理论进展[J].力学进展.2003,33(2):207-216.
[44]Fleck N A,Hutchinson J W.A phcnomenological theory for strain gradient effects in plasticity[J].J Mech Phys Solids.1993,41:1825-1857.
[45]Fleck N A,Hutchinson J W.Strain gradient plasticity.In:Hutchinson W,Wu T Y,eds.Applied Mechanics[J].New York:Academic Press,1997,33:295-361.
[46]Shu J Y,Fleck N A.Strain gradient crystal plasticity:size-dependent deformation of bicrystals[J].J Mech Phys Solids,1999,7:297-324.
[47]Nix W D,Gao H.Indentation size effects in crystalline materials:a law for strain gradient plasticity[J].J Mech Phys Solids,1998,46:411-425.
[48]Gao H,Huang Y,Nix W D,Hutchinson J W.Mechanism-based strain gradient plasticity-Ⅰ.theory[J].J Mech Phys Solids,1999,47:1239-1263.
[49]Aifantis E C.On the microstructural origin of certain inelastic models[J].Trans ASME J Eng Mater Technol,1984,106:326-330.
[50]Aifantis E C.The physics of plastic deformation.Int J Plasticity[j],1987,3:211-248.
[51]M(u|¨)hlhaus H B,Aifantis E C.The influence of microstructure-induced gradients on the localization of deformation in viscoplastic materials[J].Acta Mech,1991,89:217-231.
[52]Acharya A,Bassani J L.On non-local flow theories that preserve the classical structure of incremental boundary value problems.In:Micromechanics of Plasticity and Damage of Multiphase Materials IUTAM Symposium[J],Paris,19995-08-29-09-01.
[53]Chen S H,Wang T C.A new hardening law for strain gradient plasticity[J].Acta Materialia,2000,48:3997-4005.
[54]Chen S H,Wang T C.A new deformation theory for strain gradient effects[J].Int J Plasticity,2002,18(8):971-995.
[55]Chen S H,Wang T C.Strain gradient theory with couple stress for crystalline solids[J],European Journal of Mechanics A/Solids,2001,20:739-756.
[56]Gao H,Huang Y.Taylor-based nonlocal theory of plasticity[J].Int J Solids Struct,2001,38: 2615-2637.
[57]Wang G F,Feng X Q,Yu S W.Interface Problem with Strain Gradient Effects.见:徐秉业,张善元主编固体力学的现代进展.北京:万国学术出版社,2000,63-68.
[58]Fleck N A,Hutchinson J W.A phenomenological theory for strain gradient effects in plasticity[J].J Mech Phys Solids.1993,41:1825-1857.
[59]Fleck N A,Hutchinson J W.Strain gradient plasticity.In:Hutchinson W,Wu T Y,eds.Applied Mechanics[J].New York:Academic Press,1997,33:295-361.
[60]Berley M R,Hutchinson J W.The mechanics of size-dependent indentation[J].J Mech Phys Solids,1998,46(10):2049-2068.
[61]Wei Y.and Hutchinson J.W.Models of interface separation accompanied by plastic dissipation a multiple scales[J].Int.J.Fracture,1999,95:1-17
[62]Huang Y,Xue Z,Gao H,Nix W D,Xia Z C.A study of micro-indentation hardness tests by mechanism-based strain gradient plasticity[J].J Mater Res,2000,44:74-82.
[63]Wei Y,Hutchinson J W.Steady-state crack growth and work of fracture for solids characterized by strain gradient plasticity[J].J Mech Phys Solids,1997,45:1253-1273.
[64]Huang Y,Zhang L,Guo T F,Hwang K C.Near-tip fields for cracks in materials with strain -gradient effects[J].In:Willis J R,ed.Proceeding of IUTAM Symposium on Nonlinear analysis of fracture.Cambridge,England:Kluwer Academic Publishers,1995.231-242.
[65]Huang Y,Zhang L,Guo T F,Hwang K C.Mixed mode near-tip fields for cracks in materials with strain gradient effects[J].J Mech Phys Solids,1997,45:439-465.
[66]Huang Y,Chen J Y,Guo T F,Zhang L,Hwang K C.Analysis and numerical studies on mode Ⅰand mode Ⅱ fracture in elastic-plastic materials with strain gradient effects[J].Int J Fract,1999,100:1-27.
[67]Xia Z C,Hutchinson J W.Crack tip fields in strain gradient plasticity[J].J Mech Phys Solids,1996,44:1621-1648.
[68]Chen J Y,Huang Y,Hwang K C.Mode Ⅰ and mode Ⅱ plane sress near tip fields for cracks in materials with strain gradient effeets[J].Key Engineering Materials,1997,19:145-149.
[69]Chen S H,Wang T C.Mode Ⅰ crack tip field with strain gradient effects[j].Acta Mechanica Solida Sinica,2000,13(4):290-298.
[70]Chen S H,Wang T C.Mode I and mode Ⅱ crack tip asymptotic fields with strain gradient effeets[J].Acta Mechanica Solida Sinica,2000,13(4):290-298.
[71]Wei Y,Hutchinson J W.Steady-state crack growth and work of fracture for solids characterized by strain gradient plasticity[J].J Mech Phys Solids,1997,45:1253-1273.
[72]Chen J Y,Wei Y,Huang Y,Hutchinson J W,Hwang K C.The crack tip fields in strain gradient plasticity:the asymptotic and numerical analyses.Eng Fracture Mech,1999,64:2049-2068.
[73]Shi M X,Huang Y,Gao H,Hwang K C.Non-existenee of separable crack tip field in mechanism-based strain gradient plastieity[J].Int J Solids Struct,2000,37:5995-6010.
[74]Jiang H,Huang Y,Zhuang Z,Hwang K C.Fracture in mechanism-based strain gradient plasticity[J].J Mech Phys Solids,2001.49:979-993.
[75]Bao G,Hutchinson J W,McMeeking R M.Partiele reinforcement of ductile matrices against plastic flow and creep[J].Acta Metall Mater,1991,39:1871-1882.
[76]Corbin S F,Wilkinson D S.The influence of particle distribution on the mechanical response of a particulate metal-matrix composite[J].Acta Metall Mater,1994,42:1311-1318.
[77]Boland F,Colin C,Salmon C,et al.Tensile flow properties of Al-based matrix composites reinforced with a random planar network of continuous metallic fibers[J].Acta Mater,1998,46:6311-6323.
[78]Kamat S V,Rollett A D,Hirth J P.Plastic-deformation in Al-alloy matrix-alumina particulate composites[J].Scripta Metall Mater,1991,25:27-32.
[79]Kiser M T,Zok F W,Wilkinson D S.Plastic flow and fracture of a particulate metal matrix composites[J].Acta Mater,1996,44:3465-3476.
[80]Nan C W,Clarke D R.The influence of particle size and particle fracture on the elastic/plastic deformation of metal matrix composites[J].Acta Mater,1996,44:3801-3811.
[81]Maire E,Wilkinson D S,Embury D,et al.Role of damage on the flow and fracture of particulate reinforced alloys and metal matrix composites[J].Acta Mater,1997,45:5261-5274.
[82]Shu J Y,Barlow C Y.Strain gradient effects on microscopic strain field in a metal matrix composite[J].Int J Plasticity,2000,16:563-592.
[83]Bassani J L,Needleman A,Giessen E,Van Der.Plastic flow in a composite:a comparison of nonlocal continuum and discrete dislocation predictions[J].Int J Solids Struct,2001,38:833-853.
[84]Wei Y.Particulate size effects in the particle-reinforced metal- matrix composites.Acta Mechanica Sinica[J].2001,17(1):45-58.
[85]Xue Z,Huang Y,Li M.Particle size effect in metallic materials:a study by the theory of mechanism-based strain gradient plasticity[J].Acta Mater,2002,50:149-160.
[86]Eringen E,Mcdowell DL,Talreja R.Gradient concepts for evolution of damage[J].Mech Mater,1987,31:831-860.
[87]Aifantis EC.On the role of gradient in the localization of deformation and fracture[J].Int J Engng Sci,1992,30:1279-1299.
[88]Geiger M,Mebner A,Engel U.Produetion of microparts-size effects in bulk metal forming.similarity theory.Production Engineering,1997,4(1):55-58.
[89]Kocanda A,Pres T.The effect of miniaturization on the final geometry of the bent product.The English International Conference on Metal Forming,Rotterdam,2000.
[90]J.F.Miehel,P.Picart.Size effects on the constitutive behaviour for brass in sheet metal forming.Journal of Materials Processing Technology,2003,141:439-446.
[91]R.Kals,F.Vollertsen,M.Geiger.Scaling effects in sheet metal forming,in:Proceedings of the Fourth International Conference on Sheet Metal,vol.2,Enschede,1996,pp.65-75.
[92]Sasawat Mahabunphachai,Muammer Koc.Investigation of size effects on material behavior of thin sheet metals using hydraulic bulge testing at micro/meso-scales[J].2008,48:1014-1029.
[93]Messner A,Engel U,Kals R,Vollertsen.Size effect in the FE-simulation of micro-forming processes.Journal of Materials Processing Technology[J].1994,45(1-4):371-376.
[94]Ghobrial M L,Lee J Y,Altan A.Factors affecting the double cup extrusion test for Evaluation of friction in cold and warm forging.Annals of the CIRP[J].1993,42(1):347-351.
[95]Tan X,Bay N,Zhang W.On parameters affection metal flow and friction in the double-cup extrusion test.Annals of the CIRP,1997,46(1):311-314.
[96]J.F.Michel,P.Picart.Modelling the constitutive behaviour of thin metal sheet using strain gradient theory[J].Journal of Materials Processing Technology,2002,140:164-169.
[97]Jian Cao,Kornel F.Ehmann.Microforming:study of grain size and friction effects in the extrusion of micropins[J].International workshop on microfactory,Shanghai,china,Oct.2004
[98]Jian Cao,Neil Krishnan,Zhong Wang,et al.Microforming:experimental investigation of the extrusion process for micropins and its numerical simulation using RKEM.Transactions of the ASME[J].Journal of Manufacturing Science and Engineering,2004,126,642-652.
[99]Assempour A,Safikhani A R,Hashemi R.An Improved Strain Gradient Approach for Determination of Deformation Localization and Forming Limit Diagrams[J].Journal of Materials Processing Technology(2008),doi:10.1016/j.jmatprotec.2008.04.030.
[100]M.B Taylor,H.M.Zbib.Damage and size effect during superplastic deformation[J].International Journal of Plasticity,2002,18:415-442.
[101]Yan Xiao-qing,Luo Hai-bao,Fu Ming-fu,Jiang Wu-gui.Application of Nonlocal Friction in Several Kinds of Plastic Forming Problems[J].Applied Mathematics and Mechanics.2005.26(11):1420-1426.
[102]程三品.脆性断裂的非局部力学理论[J].力学学报.1992,24(3):229-234.
[103]程三品,袁文伯.Griffith裂纹的非局部弹性解析应力场[J].科学通报.1988,33(18):1430-1433.
[104]吴诗惇著.金属超塑性变形理论[M].北京:国防工业出版社,1997.
[105]A.H.奈弗著.摄动方法[M].王辅俊等译.上海:上海科技出版社,1984.
[106]Tang S.Mechanics of Superplasticity[M].New York:Robert E Krieger Publish Company,1979.
[107]Zhu H X,Karihaloo B L.Size-dependent bending of thin metallic films[J].International Journal of Plasticity.2008,24(6):991-1007.
[108]Tsagrakis I,Aifantis E C.strain gradient and wavelet interpretation of size effects in yield and strength[J].Mechanics of Materials.2003,35(8):733-745.
[109]Aifantis E C.Update on a class of gradient theories[J].Mechanics of Materials.2003,35(3):259-280.
[110]Lapovok R,Toth L S,Molinari A,Estrin Y.Strain localisation patterns under equal-channel angular pressing[J].Journal of the Mechanics and Physics of Solids.2009,57:122-136.
[111]Haghi M,Anand L.Analysis of strain-hardening viscoplastic thick-walled sphere and cylinder under external pressure[J].Internal Journal of Plasticity.1991,7(3):123-140.
[112]Leu S Y.Analytical and numerical investigation of strain-hardening viscoplastic thick-walled cylinders under internal pressure by using sequential limit analysis[J].Computer Methods in Applied Mechanics and Engineering.2007,196(25):2713-2722.
[113]Gao X L.An expanding cavity model incorporating strain-hardening and indentation size effects[J].Internal Journal of Solids and Structure.2006,43(21):6615-6629.
[114]Mahabunphachai S,Koc M.Investigation of size effects on material behavior of thin sheet metals using hydraulic bulge testing at micro/meso-scales[J].International Journal of Machine Tools & Manufacture.2008,48:1014-1029.
[115]宋玉泉,赵军.超塑性自由胀形的解析理论[J].吉林工业大学学报,1985,2(3):245-255.
[2]王祖唐,关廷栋,肖景容等主编.金属塑性成型理论[M].北京:机械工业出版社,1989.
[3]朱谨,阮雪榆.板料变形中两种摩擦模型的比较[J].上海交通大学学报,1995,29(2):72-78.
[4]C.C.Chen.Et al.Rigid plastic finite element analysis of ring compression.Applications of numerical method to forming processes[J].ASME.AMD.1978,28(2):163-169.
[5]黄毅坚,李国基.金属成型过程刚塑性有限元分析中的摩擦问题[J].模具技术,1986,6(2):10-15.
[6]肖宏,申光宪,木原谆二,相泽龙彦.三维弹塑性接触边界元法对摩擦的处理[J].工程力学,1997,14(4):83-88.
[7]S.L.WANG and K.P.RAO,AN UPPER-BOUND ANALYSIS OF FRICTION IN METAL FORMING[J].Jnt.J.Mech.Sci.1997,39(2):201-209.
[8]姚齐水,王桥医.基于包装铝箔轧制过程的一种较精确的摩擦模型[J].包装食品机械,2002,20(3):6-8.
[9]A.C.Eringen.et al.On nonlocal elasticity[J].Int.J.Engng Sci.1972,10:233-248.
[10]A.C.Eringen et al.Theories of nonlocal plasticity[J].Int.J.Engng Sci.1983,21:741-751.
[11]扶名福,丁成辉,吴洪飞.非局部塑性内时本构理论[J].南昌大学学报,1998,2(3):1-10.
[12]A.C.Eringen.et al.A lubrication theory for fluids with microstructure[J].Int.J.Engng.Sci.33(1995):2297-2308.
[13]Duvaut,G.LOI DE FROTTEMENT NON LOCALE[J].Journal de Mecanique Theorique et Appliquee Jun23-28 1980 p 73-78 0750-7240.
[14]Oden J T.Pire E B.Nonlocal and nonlinear friction laws and variational principles for contact problems in elasticity[J].J of Appl Mech ASME,1983,50:67-76.
[15]Pires,E.B.;Trabucho,L.Steady sliding problem with nonlocal friction[J].International Journal of Engineering Science v 28 n 7 1990 p 631-641 0020-7225.
[16]Mahrenholtz,O.,Appeltauer,J.,Bontcheva,N.;Brzozowski,M..Nonlocal friction-application to rolling with spread[J].Zeitschrift fuer Angewandte Mathematik und Mechanik,ZAMM,Applied Mathematics and Mechanics 76 Suppl 4 1996 p 603.
[17]Mahrenholtz O.,N.Bontcheva,R.Iankov,M.Datcheva.Investigation of the infuence of surface roughness on metal forming,processes[J].Mechanics Research Communications,Vol.27,No.4,393-402,2000.
[18]Mahrenholtz O.,N.Bontcheva,R.Iankov,M.Datcheva,Influence of asperitieson friction during metal forming processes[J],Proc.ECCM'99,Munich,31 August- 3 Sept.1999.
[19]Mahrenholtz O.,N.Bontcheva,Application of the non-linear non-local friction law to metal forming processes[J],In:Umformung 2000 Plus,Ed.M.Geiger,Meisenbach-Verlag Bamberg,1999,207-214.
[20]Mahrenholtz O.,N.Bontcheva,R.Iankov,Nonlocal friction during metal forming processes [J],ZAMM,2001,81,Suppl.2,353-354.
[21]扶名福,郭良.圆柱体镦粗非局部摩擦问题及近似求解[J].固体力学的现代进展(杨桂通教授七十寿辰贺文集).徐秉业,张善元主编.北京:万国学术出版社,2000.
[22]扶名福,郭良.采用非局部摩擦定律处理平面镦粗问题及其近似解[J].塑性工程学报,2001,8(1):59-61.
[23]扶名福,郭良.通过圆弧模具库仑摩擦下的平面拉拔数值滑移线场求解[J].塑性工程学报,2001,8(4):67-71.
[24]扶名福,郭良,陈桂尧.非局部摩擦在塑性加工中的应用[J].力学季刊,2001,22(1):112-116.
[25]郭良,扶名福.楔形模宽条料拉拔非局部摩擦问题及近似求解[J].南昌大学学报(工科版),2001,23(1):1-4.
[26]罗海宝,扶名福.非局部摩擦在变薄翻边成形工序中的应用[J].塑性工程学报,2003,100(6):26-29.
[27]罗海宝,扶名福.采用非局部摩擦模型处理半圆形砧拔长问题时的近似解[J].南昌大学学报(理科版),2003,27(专辑):88-91.
[28]罗海宝,扶名福.平辊轧制非局部摩擦问题及近似求解[J].南昌大学学报(工科版),2003,25(4):1-4.
[29]罗小艳,刘伟平.重力坝坝基面的非局部摩擦分析[J].南昌大学学报(工科版),2004.26(4):59-62.
[30]刘伟平,扶名福,曾宪坤,彭强生.深长摩擦桩的非局部摩擦分析[J].地质与勘探.2005.41(4):103-105.
[31]蔡改贫,翁海珊,姜志宏.振动拉拔的非局部摩擦问题的近似求解及表面效应初探术[J].机械工程学报.2006.42(8):190-194.
[32]Cosserat E,Cosserat F.Theories des Corps Deformables[J].Paris:Herman et fils,1909.
[33]杨璐,朱浮声,沈新普.弹塑性损伤模型在应变局部化分析中的应用[J].力学与实践.2006,28(2):9-15.
[34]Bazant ZP,Cedolin L.Stability of Structures:Elastic,Inelastic,Fracture and Damage Theories[J].New York:Oxford University Press,1991.
[35]Bazant ZP,Jirasek Milan.Nonloeal integral formulations of plasticity and damage:survey of progress.Journal of Engineering Mechanies[J],ASCE,2002,128:1119-1149,
[36]黄克智,黄永刚.固体本构关系[M].北京:清华大学出版社,1999.
[37]Fleck NA,Hutchinson JW.A formulation of strain gradient plasticity[J].J Mech Phys Solids,2001,49:2245-2271.
[38]Borst R de,Pamin Jerzy,Marc G,et al.On coupled gradient-dependent plasticity and damage theories with a view to localization analysis[J].Eur J Mech A/Solids,1999,18:939-962.
[39]Giessen EV de.Plastic flow in a composite:a comparison of nonlocal continuum and discrete dislocation prediction[J].Int J Solids and Structures,2001,38:833-853.
[40]Bazant ZP,Pijaudier-Cabot.Nonlocal continuum damage,localization instability and convergence[J].ASME J Appl Mech,1988,55:287-293.
[41]Lena S,Ristinmaa M.FE-formulation of a nonlocal plasticity theory[J].Comp Meth Appl Mech Engng,1996,136:127-144.
[42]Eringen E,Mcdowell DL,Talreja R.Gradient concepts for evolution of damage.Mech Mater[J],1987,31:831-860.
[43]陈少华,王自强.应变梯度理论进展[J].力学进展.2003,33(2):207-216.
[44]Fleck N A,Hutchinson J W.A phcnomenological theory for strain gradient effects in plasticity[J].J Mech Phys Solids.1993,41:1825-1857.
[45]Fleck N A,Hutchinson J W.Strain gradient plasticity.In:Hutchinson W,Wu T Y,eds.Applied Mechanics[J].New York:Academic Press,1997,33:295-361.
[46]Shu J Y,Fleck N A.Strain gradient crystal plasticity:size-dependent deformation of bicrystals[J].J Mech Phys Solids,1999,7:297-324.
[47]Nix W D,Gao H.Indentation size effects in crystalline materials:a law for strain gradient plasticity[J].J Mech Phys Solids,1998,46:411-425.
[48]Gao H,Huang Y,Nix W D,Hutchinson J W.Mechanism-based strain gradient plasticity-Ⅰ.theory[J].J Mech Phys Solids,1999,47:1239-1263.
[49]Aifantis E C.On the microstructural origin of certain inelastic models[J].Trans ASME J Eng Mater Technol,1984,106:326-330.
[50]Aifantis E C.The physics of plastic deformation.Int J Plasticity[j],1987,3:211-248.
[51]M(u|¨)hlhaus H B,Aifantis E C.The influence of microstructure-induced gradients on the localization of deformation in viscoplastic materials[J].Acta Mech,1991,89:217-231.
[52]Acharya A,Bassani J L.On non-local flow theories that preserve the classical structure of incremental boundary value problems.In:Micromechanics of Plasticity and Damage of Multiphase Materials IUTAM Symposium[J],Paris,19995-08-29-09-01.
[53]Chen S H,Wang T C.A new hardening law for strain gradient plasticity[J].Acta Materialia,2000,48:3997-4005.
[54]Chen S H,Wang T C.A new deformation theory for strain gradient effects[J].Int J Plasticity,2002,18(8):971-995.
[55]Chen S H,Wang T C.Strain gradient theory with couple stress for crystalline solids[J],European Journal of Mechanics A/Solids,2001,20:739-756.
[56]Gao H,Huang Y.Taylor-based nonlocal theory of plasticity[J].Int J Solids Struct,2001,38: 2615-2637.
[57]Wang G F,Feng X Q,Yu S W.Interface Problem with Strain Gradient Effects.见:徐秉业,张善元主编固体力学的现代进展.北京:万国学术出版社,2000,63-68.
[58]Fleck N A,Hutchinson J W.A phenomenological theory for strain gradient effects in plasticity[J].J Mech Phys Solids.1993,41:1825-1857.
[59]Fleck N A,Hutchinson J W.Strain gradient plasticity.In:Hutchinson W,Wu T Y,eds.Applied Mechanics[J].New York:Academic Press,1997,33:295-361.
[60]Berley M R,Hutchinson J W.The mechanics of size-dependent indentation[J].J Mech Phys Solids,1998,46(10):2049-2068.
[61]Wei Y.and Hutchinson J.W.Models of interface separation accompanied by plastic dissipation a multiple scales[J].Int.J.Fracture,1999,95:1-17
[62]Huang Y,Xue Z,Gao H,Nix W D,Xia Z C.A study of micro-indentation hardness tests by mechanism-based strain gradient plasticity[J].J Mater Res,2000,44:74-82.
[63]Wei Y,Hutchinson J W.Steady-state crack growth and work of fracture for solids characterized by strain gradient plasticity[J].J Mech Phys Solids,1997,45:1253-1273.
[64]Huang Y,Zhang L,Guo T F,Hwang K C.Near-tip fields for cracks in materials with strain -gradient effects[J].In:Willis J R,ed.Proceeding of IUTAM Symposium on Nonlinear analysis of fracture.Cambridge,England:Kluwer Academic Publishers,1995.231-242.
[65]Huang Y,Zhang L,Guo T F,Hwang K C.Mixed mode near-tip fields for cracks in materials with strain gradient effects[J].J Mech Phys Solids,1997,45:439-465.
[66]Huang Y,Chen J Y,Guo T F,Zhang L,Hwang K C.Analysis and numerical studies on mode Ⅰand mode Ⅱ fracture in elastic-plastic materials with strain gradient effects[J].Int J Fract,1999,100:1-27.
[67]Xia Z C,Hutchinson J W.Crack tip fields in strain gradient plasticity[J].J Mech Phys Solids,1996,44:1621-1648.
[68]Chen J Y,Huang Y,Hwang K C.Mode Ⅰ and mode Ⅱ plane sress near tip fields for cracks in materials with strain gradient effeets[J].Key Engineering Materials,1997,19:145-149.
[69]Chen S H,Wang T C.Mode Ⅰ crack tip field with strain gradient effects[j].Acta Mechanica Solida Sinica,2000,13(4):290-298.
[70]Chen S H,Wang T C.Mode I and mode Ⅱ crack tip asymptotic fields with strain gradient effeets[J].Acta Mechanica Solida Sinica,2000,13(4):290-298.
[71]Wei Y,Hutchinson J W.Steady-state crack growth and work of fracture for solids characterized by strain gradient plasticity[J].J Mech Phys Solids,1997,45:1253-1273.
[72]Chen J Y,Wei Y,Huang Y,Hutchinson J W,Hwang K C.The crack tip fields in strain gradient plasticity:the asymptotic and numerical analyses.Eng Fracture Mech,1999,64:2049-2068.
[73]Shi M X,Huang Y,Gao H,Hwang K C.Non-existenee of separable crack tip field in mechanism-based strain gradient plastieity[J].Int J Solids Struct,2000,37:5995-6010.
[74]Jiang H,Huang Y,Zhuang Z,Hwang K C.Fracture in mechanism-based strain gradient plasticity[J].J Mech Phys Solids,2001.49:979-993.
[75]Bao G,Hutchinson J W,McMeeking R M.Partiele reinforcement of ductile matrices against plastic flow and creep[J].Acta Metall Mater,1991,39:1871-1882.
[76]Corbin S F,Wilkinson D S.The influence of particle distribution on the mechanical response of a particulate metal-matrix composite[J].Acta Metall Mater,1994,42:1311-1318.
[77]Boland F,Colin C,Salmon C,et al.Tensile flow properties of Al-based matrix composites reinforced with a random planar network of continuous metallic fibers[J].Acta Mater,1998,46:6311-6323.
[78]Kamat S V,Rollett A D,Hirth J P.Plastic-deformation in Al-alloy matrix-alumina particulate composites[J].Scripta Metall Mater,1991,25:27-32.
[79]Kiser M T,Zok F W,Wilkinson D S.Plastic flow and fracture of a particulate metal matrix composites[J].Acta Mater,1996,44:3465-3476.
[80]Nan C W,Clarke D R.The influence of particle size and particle fracture on the elastic/plastic deformation of metal matrix composites[J].Acta Mater,1996,44:3801-3811.
[81]Maire E,Wilkinson D S,Embury D,et al.Role of damage on the flow and fracture of particulate reinforced alloys and metal matrix composites[J].Acta Mater,1997,45:5261-5274.
[82]Shu J Y,Barlow C Y.Strain gradient effects on microscopic strain field in a metal matrix composite[J].Int J Plasticity,2000,16:563-592.
[83]Bassani J L,Needleman A,Giessen E,Van Der.Plastic flow in a composite:a comparison of nonlocal continuum and discrete dislocation predictions[J].Int J Solids Struct,2001,38:833-853.
[84]Wei Y.Particulate size effects in the particle-reinforced metal- matrix composites.Acta Mechanica Sinica[J].2001,17(1):45-58.
[85]Xue Z,Huang Y,Li M.Particle size effect in metallic materials:a study by the theory of mechanism-based strain gradient plasticity[J].Acta Mater,2002,50:149-160.
[86]Eringen E,Mcdowell DL,Talreja R.Gradient concepts for evolution of damage[J].Mech Mater,1987,31:831-860.
[87]Aifantis EC.On the role of gradient in the localization of deformation and fracture[J].Int J Engng Sci,1992,30:1279-1299.
[88]Geiger M,Mebner A,Engel U.Produetion of microparts-size effects in bulk metal forming.similarity theory.Production Engineering,1997,4(1):55-58.
[89]Kocanda A,Pres T.The effect of miniaturization on the final geometry of the bent product.The English International Conference on Metal Forming,Rotterdam,2000.
[90]J.F.Miehel,P.Picart.Size effects on the constitutive behaviour for brass in sheet metal forming.Journal of Materials Processing Technology,2003,141:439-446.
[91]R.Kals,F.Vollertsen,M.Geiger.Scaling effects in sheet metal forming,in:Proceedings of the Fourth International Conference on Sheet Metal,vol.2,Enschede,1996,pp.65-75.
[92]Sasawat Mahabunphachai,Muammer Koc.Investigation of size effects on material behavior of thin sheet metals using hydraulic bulge testing at micro/meso-scales[J].2008,48:1014-1029.
[93]Messner A,Engel U,Kals R,Vollertsen.Size effect in the FE-simulation of micro-forming processes.Journal of Materials Processing Technology[J].1994,45(1-4):371-376.
[94]Ghobrial M L,Lee J Y,Altan A.Factors affecting the double cup extrusion test for Evaluation of friction in cold and warm forging.Annals of the CIRP[J].1993,42(1):347-351.
[95]Tan X,Bay N,Zhang W.On parameters affection metal flow and friction in the double-cup extrusion test.Annals of the CIRP,1997,46(1):311-314.
[96]J.F.Michel,P.Picart.Modelling the constitutive behaviour of thin metal sheet using strain gradient theory[J].Journal of Materials Processing Technology,2002,140:164-169.
[97]Jian Cao,Kornel F.Ehmann.Microforming:study of grain size and friction effects in the extrusion of micropins[J].International workshop on microfactory,Shanghai,china,Oct.2004
[98]Jian Cao,Neil Krishnan,Zhong Wang,et al.Microforming:experimental investigation of the extrusion process for micropins and its numerical simulation using RKEM.Transactions of the ASME[J].Journal of Manufacturing Science and Engineering,2004,126,642-652.
[99]Assempour A,Safikhani A R,Hashemi R.An Improved Strain Gradient Approach for Determination of Deformation Localization and Forming Limit Diagrams[J].Journal of Materials Processing Technology(2008),doi:10.1016/j.jmatprotec.2008.04.030.
[100]M.B Taylor,H.M.Zbib.Damage and size effect during superplastic deformation[J].International Journal of Plasticity,2002,18:415-442.
[101]Yan Xiao-qing,Luo Hai-bao,Fu Ming-fu,Jiang Wu-gui.Application of Nonlocal Friction in Several Kinds of Plastic Forming Problems[J].Applied Mathematics and Mechanics.2005.26(11):1420-1426.
[102]程三品.脆性断裂的非局部力学理论[J].力学学报.1992,24(3):229-234.
[103]程三品,袁文伯.Griffith裂纹的非局部弹性解析应力场[J].科学通报.1988,33(18):1430-1433.
[104]吴诗惇著.金属超塑性变形理论[M].北京:国防工业出版社,1997.
[105]A.H.奈弗著.摄动方法[M].王辅俊等译.上海:上海科技出版社,1984.
[106]Tang S.Mechanics of Superplasticity[M].New York:Robert E Krieger Publish Company,1979.
[107]Zhu H X,Karihaloo B L.Size-dependent bending of thin metallic films[J].International Journal of Plasticity.2008,24(6):991-1007.
[108]Tsagrakis I,Aifantis E C.strain gradient and wavelet interpretation of size effects in yield and strength[J].Mechanics of Materials.2003,35(8):733-745.
[109]Aifantis E C.Update on a class of gradient theories[J].Mechanics of Materials.2003,35(3):259-280.
[110]Lapovok R,Toth L S,Molinari A,Estrin Y.Strain localisation patterns under equal-channel angular pressing[J].Journal of the Mechanics and Physics of Solids.2009,57:122-136.
[111]Haghi M,Anand L.Analysis of strain-hardening viscoplastic thick-walled sphere and cylinder under external pressure[J].Internal Journal of Plasticity.1991,7(3):123-140.
[112]Leu S Y.Analytical and numerical investigation of strain-hardening viscoplastic thick-walled cylinders under internal pressure by using sequential limit analysis[J].Computer Methods in Applied Mechanics and Engineering.2007,196(25):2713-2722.
[113]Gao X L.An expanding cavity model incorporating strain-hardening and indentation size effects[J].Internal Journal of Solids and Structure.2006,43(21):6615-6629.
[114]Mahabunphachai S,Koc M.Investigation of size effects on material behavior of thin sheet metals using hydraulic bulge testing at micro/meso-scales[J].International Journal of Machine Tools & Manufacture.2008,48:1014-1029.
[115]宋玉泉,赵军.超塑性自由胀形的解析理论[J].吉林工业大学学报,1985,2(3):245-255.