AZ系镁合金PLC效应实验和机理研究
|
摘要
为了从宏观规律和微观机理深入研究探讨镁合金的PLC效应，以便进一步丰富和完善镁合金的塑性变形理论，为镁合金的塑性加工实践提供理论参考,本文选用航空航天及工业领域常用的AZ系挤压镁合金为研究对象，系统地对镁合金在系列温度和应变速率下进行了拉伸试验和微观组织结构观察，研究了镁合金在塑性变形过程中发生PLC效应的条件、内在规律和微观机理，建立了包含PLC效应发生机制的粘塑性本构模型，并对其进行了数值模拟。主要工作总结如下。
系统地对AZ31、AZ61和AZ91三种镁合金在较宽的温度区间和应变速率范围内进行了系列的拉伸试验，结果表明，AZ31没有观察到PLC效应；AZ61在中温区间发生了并不明显的PLC效应；而AZ91镁合金在一定的应变速率(ε=1.11×10~(-4)s~(-1)~1.67×10~(-3)s~(-1))和一定温区（T=248~423K）内发生了PLC效应。进一步系统地研究了固溶态AZ91镁合金产生PLC效应的条件及影响因素，发现产生锯齿屈服的临界应变量ε c随形变温度升高而减小，而随着应变速率增加而增大。锯齿屈服所表现的锯齿波类型呈“A”型或“A+B”混合型，与应变速率高低有关。此外，还显示了具有DSA的典型宏观特征，即出现锯齿屈服、屈服应力平台、应变速率敏感系数为负值、异常的加工硬化速率及其“蓝脆”现象。
采用McCormick模型中锯齿波的临界应变量ε c、应变速率ε和变形温度T之间的关系，计算得出固溶态AZ91镁合金产生PLC效应的溶质原子扩散激活能为140.7634kJ/mol。该值与Al原子在Mg基体中的扩散激活能非常接近，经综合分析，提出了该合金所产生PLC效应的微观机制主要是Al溶质原子以“空位扩散”的方式偏聚在位错周围形成Cottrell气团进而钉扎位错的结果。
进一步系统地研究了溶质原子浓度变化及第二相(β-Mg17Al12)析出对AZ91镁合金PLC效应的影响。经定量及定性分析结果表明，Mg17Al12析出相含量及颗粒大小对AZ91镁合金的PLC温区范围、应力跌落幅度等产生很大影响。发现析出相粒子与位错的交互作用也是控制PLC效应的一种重要机制。进而通过热处理或等径角挤压工艺制备不同晶粒尺寸的AZ91镁合金，从溶质原子气团对可动位错钉扎的微观机理解释和探讨了晶粒尺寸对发生PLC效应的临界应变量、最大应力振幅和锯齿数的影响规律。
在前述实验研究的基础上，把粘塑性统一本构模型应用于阐述镁合金的PLC效应产生机制，引入溶质原子浓度与位错相互作用的定量关系，对Yaguchi提出的粘塑性本构模型进行改进，构建了适用于AZ系镁合金PLC效应的理论模型。并用多岛遗传算法（MIGA）和序列二次规划（SQP）方法相结合的优化策略对材料参数进行了优化识别，得出了AZ91镁合金5个温度下的材料参数，数值模拟的曲线与实验结果吻合得很好。
Portevin-Le Chatelier(PLC) effect, a plastic instability in metals and alloysduring plastic deformation under at certain range of temperatures, affectedsignificantly the mechanical properties of materials. To investigate the PLC effectoccurred in AZ magnesium alloy can help not only to understand better themacro-process and micro-mechanism of plasticity, but also to utilize better to extendcapacity of magnesium alloy.
A series of tensile tests of AZ pressed magnesium alloys, which have beenwidely used in the aerospace and industry, were systematically carried out underdifferent temperature and strain rate ranges, by an Instron1185testing machine. Somemicroscopic analysis methods were used to survey microstructure evolution duringdeformation and to investigate micro-mechanism when PLC effect occurred. Thevisco-plastic constitutive relation was modeled to describe PLC effect inmathematical simulation and parametric recognition based on universal model wasadvanced.
The PLC effects in three AZ magnesium alloys, AZ31, AZ61and AZ91, weresystematically investigated under different temperature and strain rate ranges. Theresults show that no PLC effects are found in AZ31magnesium alloy, but someserrations characteristics appear in AZ61magnesium alloy under testing conditions.However, PLC effects occur in AZ91magnesium alloy treated by solid solutiontreatment, in which are subjected to plastic deformation at a set range of strain rates（ε=1.11×10~(-4)s~(-1)~1.67×10~(-3)s~(-1)）and a certain range of temperatures(T=248~423K).Here, the critical plastic strain εc, which is the strain for the onset of serrations,decreases with the increasing of deformation temperatures, while it increases with theincreasing of strain rate. Especially, the related serrated types are defined as A andA+B type, which is correlated to different strain rates. Moreover, the five typicalcharacteristics of DSA are found, including the serrated flow(PLC effect), a yielding stress platform independent of temperature, negative strain-rate sensitivity and theabnormal variation of work-hardening rate, and “Blue Brittleness”, and so on.
The interaction betweem the diffusion solute atoms and the mobile dislocationshas been widely accepted as micro-mechanism of PLC effect. The diffusing activationenergy of solute atoms during serrations occurring was calculated according to therelationships of the critical plastic strain εc, strain rate ε and temperature T byMcCormick theory. The result shows that the diffusing activation energy of soluteatoms during the PLC effect occurring in AZ91magnesium alloy is140.7634kJ/mol,which is highly correspondence with the diffusing activation energy of Al soluteatoms in Mg matrix. Therefore, the micro-mechanism of PLC effect in AZ91magnesium alloy is believed that the Al atoms in solid solution gather arounddislocations to form Cottrell solute atmospheres by vacant diffusion and then pin themoving dislocations, so it needs to increase applied forces to make pinningdislocation moving forward and finally results in PLC effect when repeated thisprocess.
Furthermore, the effects of the content of precipitates on the PLC effect of theAZ91magnesium alloy were systematically investigated, by means of differentheat-treatments such as annealing, solid solution and aging to get different precipitatesand microstructure of the AZ91magnesium alloy. According to the quantitative andqualitative analysis, the result reveals that the mass or concentration of Al soluteatoms dissolved into magnesium matrix are the major factor for the DSA occurring inthe AZ91magnesium alloy. It has been proved that there is a great effect on serratedyielding characteristic after different heat treatments such as temperature and timesabout annealing, solid solution treatment and aging, etc. Especially, the effects ofsecond-phase precipitation（β-Mg17Al12）on PLC effect of theAZ91magnesium alloyrepresent that the tensile curves do not appear serrated yielding when the content ofprecipitates is more than1.0wt.%. Also, it is not only to make the strain rate ranges ofPLC narrowing, but also to reduce the temperature ranges when the second-phaseprecipitation occurs. Moreover, compared with its solid solution state, the serratedyielding characteristic is not obvious and the stress drop is smaller in the tensilecurves. According to the present study and other viewpoint in the literatures, a newmicro-mechanism of controlling PLC effect has been developed, which demonstratesthe influences of second-phase precipitation on PLC through the interaction betweenthe precipitates and the mobile dislocations. What is worth mentioning, it is indispensable to theoretically enrich the mechanism of serrated yielding while takinginto account the interaction between the precipitates and the mobile dislocations. Also,different serrated yielding characteristics appear to vary with the grain size.Investigations on PLC effect of AZ91magnesium alloys with different grain sizeswhich have been obtained by heat-treatments or by equal channel angularpressing(ECAP), show that the critical plastic strain εcdecreases with the reducing oftheir sizes while the stress drop increases in the tensile curves. It seems very obviouschange when the grain size is in range from micro-scale to nano-scale.
Finally, a new visco-plastic constitutive relation and model for the PLC effect ofAZ magnesium alloy, quantitatively considering the interaction between the soluteatoms and the mobile dislocations, is constructed and developed by modifyingYaguchi model to express accurately the micro-mechanism of PLC effect in numericalmethods. Based on the experimental investigations in the present, the parameteridentification of the constitutive model is further developed in multi-object strategywith the multi-island genetic algorithm(MIGA) and the series quadratic programming(SQP). Also, the results of numerical simulation are well matched with the ones ofexperiments.
系统地对AZ31、AZ61和AZ91三种镁合金在较宽的温度区间和应变速率范围内进行了系列的拉伸试验，结果表明，AZ31没有观察到PLC效应；AZ61在中温区间发生了并不明显的PLC效应；而AZ91镁合金在一定的应变速率(ε=1.11×10~(-4)s~(-1)~1.67×10~(-3)s~(-1))和一定温区（T=248~423K）内发生了PLC效应。进一步系统地研究了固溶态AZ91镁合金产生PLC效应的条件及影响因素，发现产生锯齿屈服的临界应变量ε c随形变温度升高而减小，而随着应变速率增加而增大。锯齿屈服所表现的锯齿波类型呈“A”型或“A+B”混合型，与应变速率高低有关。此外，还显示了具有DSA的典型宏观特征，即出现锯齿屈服、屈服应力平台、应变速率敏感系数为负值、异常的加工硬化速率及其“蓝脆”现象。
采用McCormick模型中锯齿波的临界应变量ε c、应变速率ε和变形温度T之间的关系，计算得出固溶态AZ91镁合金产生PLC效应的溶质原子扩散激活能为140.7634kJ/mol。该值与Al原子在Mg基体中的扩散激活能非常接近，经综合分析，提出了该合金所产生PLC效应的微观机制主要是Al溶质原子以“空位扩散”的方式偏聚在位错周围形成Cottrell气团进而钉扎位错的结果。
进一步系统地研究了溶质原子浓度变化及第二相(β-Mg17Al12)析出对AZ91镁合金PLC效应的影响。经定量及定性分析结果表明，Mg17Al12析出相含量及颗粒大小对AZ91镁合金的PLC温区范围、应力跌落幅度等产生很大影响。发现析出相粒子与位错的交互作用也是控制PLC效应的一种重要机制。进而通过热处理或等径角挤压工艺制备不同晶粒尺寸的AZ91镁合金，从溶质原子气团对可动位错钉扎的微观机理解释和探讨了晶粒尺寸对发生PLC效应的临界应变量、最大应力振幅和锯齿数的影响规律。
在前述实验研究的基础上，把粘塑性统一本构模型应用于阐述镁合金的PLC效应产生机制，引入溶质原子浓度与位错相互作用的定量关系，对Yaguchi提出的粘塑性本构模型进行改进，构建了适用于AZ系镁合金PLC效应的理论模型。并用多岛遗传算法（MIGA）和序列二次规划（SQP）方法相结合的优化策略对材料参数进行了优化识别，得出了AZ91镁合金5个温度下的材料参数，数值模拟的曲线与实验结果吻合得很好。
Portevin-Le Chatelier(PLC) effect, a plastic instability in metals and alloysduring plastic deformation under at certain range of temperatures, affectedsignificantly the mechanical properties of materials. To investigate the PLC effectoccurred in AZ magnesium alloy can help not only to understand better themacro-process and micro-mechanism of plasticity, but also to utilize better to extendcapacity of magnesium alloy.
A series of tensile tests of AZ pressed magnesium alloys, which have beenwidely used in the aerospace and industry, were systematically carried out underdifferent temperature and strain rate ranges, by an Instron1185testing machine. Somemicroscopic analysis methods were used to survey microstructure evolution duringdeformation and to investigate micro-mechanism when PLC effect occurred. Thevisco-plastic constitutive relation was modeled to describe PLC effect inmathematical simulation and parametric recognition based on universal model wasadvanced.
The PLC effects in three AZ magnesium alloys, AZ31, AZ61and AZ91, weresystematically investigated under different temperature and strain rate ranges. Theresults show that no PLC effects are found in AZ31magnesium alloy, but someserrations characteristics appear in AZ61magnesium alloy under testing conditions.However, PLC effects occur in AZ91magnesium alloy treated by solid solutiontreatment, in which are subjected to plastic deformation at a set range of strain rates（ε=1.11×10~(-4)s~(-1)~1.67×10~(-3)s~(-1)）and a certain range of temperatures(T=248~423K).Here, the critical plastic strain εc, which is the strain for the onset of serrations,decreases with the increasing of deformation temperatures, while it increases with theincreasing of strain rate. Especially, the related serrated types are defined as A andA+B type, which is correlated to different strain rates. Moreover, the five typicalcharacteristics of DSA are found, including the serrated flow(PLC effect), a yielding stress platform independent of temperature, negative strain-rate sensitivity and theabnormal variation of work-hardening rate, and “Blue Brittleness”, and so on.
The interaction betweem the diffusion solute atoms and the mobile dislocationshas been widely accepted as micro-mechanism of PLC effect. The diffusing activationenergy of solute atoms during serrations occurring was calculated according to therelationships of the critical plastic strain εc, strain rate ε and temperature T byMcCormick theory. The result shows that the diffusing activation energy of soluteatoms during the PLC effect occurring in AZ91magnesium alloy is140.7634kJ/mol,which is highly correspondence with the diffusing activation energy of Al soluteatoms in Mg matrix. Therefore, the micro-mechanism of PLC effect in AZ91magnesium alloy is believed that the Al atoms in solid solution gather arounddislocations to form Cottrell solute atmospheres by vacant diffusion and then pin themoving dislocations, so it needs to increase applied forces to make pinningdislocation moving forward and finally results in PLC effect when repeated thisprocess.
Furthermore, the effects of the content of precipitates on the PLC effect of theAZ91magnesium alloy were systematically investigated, by means of differentheat-treatments such as annealing, solid solution and aging to get different precipitatesand microstructure of the AZ91magnesium alloy. According to the quantitative andqualitative analysis, the result reveals that the mass or concentration of Al soluteatoms dissolved into magnesium matrix are the major factor for the DSA occurring inthe AZ91magnesium alloy. It has been proved that there is a great effect on serratedyielding characteristic after different heat treatments such as temperature and timesabout annealing, solid solution treatment and aging, etc. Especially, the effects ofsecond-phase precipitation（β-Mg17Al12）on PLC effect of theAZ91magnesium alloyrepresent that the tensile curves do not appear serrated yielding when the content ofprecipitates is more than1.0wt.%. Also, it is not only to make the strain rate ranges ofPLC narrowing, but also to reduce the temperature ranges when the second-phaseprecipitation occurs. Moreover, compared with its solid solution state, the serratedyielding characteristic is not obvious and the stress drop is smaller in the tensilecurves. According to the present study and other viewpoint in the literatures, a newmicro-mechanism of controlling PLC effect has been developed, which demonstratesthe influences of second-phase precipitation on PLC through the interaction betweenthe precipitates and the mobile dislocations. What is worth mentioning, it is indispensable to theoretically enrich the mechanism of serrated yielding while takinginto account the interaction between the precipitates and the mobile dislocations. Also,different serrated yielding characteristics appear to vary with the grain size.Investigations on PLC effect of AZ91magnesium alloys with different grain sizeswhich have been obtained by heat-treatments or by equal channel angularpressing(ECAP), show that the critical plastic strain εcdecreases with the reducing oftheir sizes while the stress drop increases in the tensile curves. It seems very obviouschange when the grain size is in range from micro-scale to nano-scale.
Finally, a new visco-plastic constitutive relation and model for the PLC effect ofAZ magnesium alloy, quantitatively considering the interaction between the soluteatoms and the mobile dislocations, is constructed and developed by modifyingYaguchi model to express accurately the micro-mechanism of PLC effect in numericalmethods. Based on the experimental investigations in the present, the parameteridentification of the constitutive model is further developed in multi-object strategywith the multi-island genetic algorithm(MIGA) and the series quadratic programming(SQP). Also, the results of numerical simulation are well matched with the ones ofexperiments.
引文
[1] G. A. Malygin. Dynamic interaction of impurity atmospheres with moving dislocations duringserrated flow[J]. physica status solidi (a).1973,15:51–60.
[2] D. W. Moon. Considerations on the present state of lüders band studies[J]. Materials Scienceand Engineering.1971,8:235-243.
[3]钱匡武,李效琦,萧林钢等.金属和合金中的动态应变时效现象[J]．福州大学学报，2001,29(6):8-23.
[4] A.H. Cottrell. A note on the Portevin-Le Chatelier effect[J].Philosphical Magazine,1953,44(335):829-832.
[5] C. Wang, Y.B. Xu, E.H. Han. Serrated flow and abnormal strain rate sensitivity of amagnesium–lithium alloy[J]. Materials Letters,2006,60:2941–2944.
[6] S. Rajashekhar, K. Subodh, J.R. Hans,et al. Effect of specimen condition,oriention and alloycomposition on PLC band parameters[J]. Materials Science and Engineering A,2004,382:203-208.
[7] B. H. Tian. Ageing effect on serrated flow in Al-Mg alloys[J]. Materials Science andEngineering A,2003,349:272-278.
[8]钱匡武，李效琦，肖林钢.α黄铜晶体尺寸对锯齿屈服的影响[J].材料科学进展，1990，4（5）：420-424.
[9] A. P. Masson, Ann. Chem. Phys.，third series1841,3:451.
[10] J. F. Bell and A. Stein, The Incremental Loading Wave in the Prestressed Plastic Field.[J]. Journalde Mechanique,1962,1:395.
[11] O.W. Dillon. Experimental data on aluminium as a mechanically unstable solid[J]. Journal ofthe Mechanics and Physics of Solids.1963,11:289-304.
[12] Z.S. Kovacs, N.Q. Chinh and J. Lendvai, Orientation dependence of Portevin–Le Chatelier plasticinstabilities in depth-sensing microindentation [J]. Journal of Materials Research.，2001,16:1171.
[13] P.R. Cetlin, A.S. Gulec and R.E. Reed-Hill, Serrated Flow in Al6061Alloy [J]. Metall.Trans.，1973,4:513.
[14] K. Chihab, Y. Estrin, L. P. Kubin. The kinetics of the Portiven-Le Chatlier bands in an Al-5at%Mg alloy[J]. Scripta Metallurgica,1987,21:203-208.
[15] A. Ziegenbein, P. Hahner, H. Neuhauser. Correlation of temporal instabilities and spatiallocalization during Portiven-Le Chatelier deformation of Cu-10at%Al and Cu-15at%Al[J].Computational Materials Science,2000,19:27-34.
[16] S. Toyooka, X..L. Gong. Digital Speckle Pattern Interferometry for Observing the EntireProcess of Plastic Deformation of a Solid Object[J]. Japanese Journal of Applied Physics,1995,34:1666.
[17] Q.C. Zhang, S. Toyooka, Z.B. Meng, Suprapedi, In: Backlini G Y, Proc.of SPIE,Nondestructrue Evaluation of Aging Materials and Composites Ⅲ, Vol.3585, NewportBeach, CA, SPIE,1999:389.
[18]彭开萍.面心立方合金动态应变时效的研究：[博士论文].福州：福州大学材料科学与工程学院，2007.
[19] M. Wagenhofer, M. Erickson-Natishan, R.W. Armstrong. Influence of strain rate and grainsize on yield serrated flow in commercial Al-Mg alloy5086[J].Acta Metallurgica etMaterialia,1999,41:1177–1184.
[20] L.H. de Almeida, I.Le May, P.R.O. Emygdio. Mechanistic Modeling of Dynamic StrainAging in Austenitic Stainless Steels[J]. Material Characterization,1988,41:137–150.
[21]钱匡武，彭开萍，陈文哲.金属动态应变时效现象中的“锯齿屈服”[J].福建工程学院学报,2003,1(1):4-8.
[22] H.F. Jiang, Q.C. Zhang, X.D. Chen,et al. Three types of Portevin–Le Chatelier effects:Experiment and modelling [J]. Acta Materialia,2007,55:2219–2228.
[23] N. Ranc, D. Wagner. Experimental study by pyrometry of Portevin–Le Chatelier plastic instabilities-Type A to type B transition[J]. Materials Science and Engineering A,2008,474:188–196
[24] M.A. Soare, W.A. Curtin. Solute strengthening of both mobile and forest dislocations:Theorigin of dynamic strain aging in fcc metals[J]. Acta Materialia,2008,56:4046–4061.
[25]田宝辉，张永刚．铝-锂单晶体的反常流变行为和PLC效应[J].稀有金属材料与工程，1995,24(4):41-45.
[26]倪朝芳，钱匡武．动态应变时效强化奥氏体不锈钢[J]．理化检验(物理分册)，1987，23(5)：12-15.
[27]陈文哲，钱匡武．动态应变时效对奥氏体不锈钢静拉伸强度的影响[J]．金属科学与工艺，1989，8(3、4)：1-7．
[28]陈文哲，彭开萍，钱匡武．动态应变时效对不锈钢高温强度的影响[J]．机械工程学报，1992，28(2)：34-38．
[29]李效琦，陈文哲．动态应变时效对18-8型奥氏体不锈钢强度的影响[J]．福州大学学报(自然科学版)，1989，17(2)：30-34．
[30]陈文哲，钱匡武．动态应变时效对奥氏体不锈钢纯弯疲劳强度的影响[J]．金属学报，1989，25(2)：A132-136．
[31] Qian K W, Peng K P, Chen W Z. Influence of dynamic strain aging on the high temperaturestrength of18-8type austenitic stainless steel[A]. Proc of the6th international conference onmechanical behavior of materials (ICM-6)[C]. Kyoto, Japan,1991.4:601-606.
[32]彭开萍，陈文哲，钱匡武．动态应变时效对18-8型奥氏体不锈钢低周疲劳行为的影响[J]．金属学报，1993，29(6)：A283-288．
[33] Qian K W, Chen W Z, Peng K P. Effects of dynamic strain aging on high temperature fatigueproperties of austenitic stainless steel[A]. Proc of the6th international conference on creep&fatigue[C]. London,1996.203-210.
[34] A. Korbel, J. Zasadzinski, Z. Slieklucka. A new approach to the portevin-Le chatelier effect[J].Acta Metall,1976,24:919-923.
[35] L.P. Kubin, Y. Estrin. The Portevin-Le Chatelier effect in deformation with constant stressrate[J]. Acta Metallurgica et Materialia.1985:397-407.
[36] L.P. Kubin, Y. Estrin. Evolution of dislocation densities and the critical conditions for thePortevin-Le Chatelier effect[J]. Acta Metallurgica et Materialia.38(1990)697.
[37] G Ananthakrishna, D Sahoo. A model based on nonlinear oscillations to explain jumps oncreep curves[J]. J. Phys. D: Appl. Phys.1981,14:2081.
[38] D Sahoo and G Ananthakrishna A phenomenological dislocation transformation model forthe mobile fraction in simple systems[J]. J. Phys. D: Appl. Phys.1982,15:1439.
[39] M. Zaiser, M. Glazov, L. A. Lalli and O. Richmond. On the relations between strain andstrain-rate softening phenomena in some metallic materials: a computational study [J].Computational Materials Science.1999,15:35-49.
[40] C. Fressengeas, A.J. Beaudoin, M. Lebyodkin, et al. Dynamic strain aging: A coupleddislocation-Solute dynamic model[J]. Materials Science and Engineering A.2005,400-401:226-230.
[41] P.G. McCormick. A model for the Portevin–Le Chatelier effect in substitutional alloys[J].Acta Metallurgica et Materialia,1972,20:351–354.
[42] P.G. McCormick. Theory of flow localisation due to dynamic strain ageing[J]. ActaMetallurgica et Materialia,1988,36(12):3061-3067.
[43] P.G. McCormick, C.P. Ling. Numerical modelling of the Portevin-Le Chatelier effect[J].Acta Metallurgica et Materialia,1995,43(5):1969-1977.
[44] A. Van den Beukel. Theory of the effect of dynamic strain ageing on mechanical properties[J].Physica Status Solidi (a),1975,30:197–206.
[45]萧林钢,李效琦,钱匡武.置换合金中出现锯齿屈服现象的临界条件的模型[J].中国科学(A辑),1990，4：423．
[46] S.D. Mesarovic, J. Mech. Dynamic strain aging and plastic instabilities[J]. Phys. Solids,1995,43:671.
[47] P. Hahner, A. Ziegenbein, E. Rizzi and H. Neuhauser, Spatiotemporal analysis of Portevin–Le Chatelier deformation bands: Theory, simulation, and experiment [J]. Phys. Rev. B,2002,65:109-134.
[48] K.W. Qian, R.E. Reed-Hill. A model for determining the internal stress based on zero entropyof activation[J]. Scripta Metall,1982,16:807-810.
[49] K.W.Qian, R.E. Reed-Hill. A model for the flow stress and strain rate sensitivity of asubstitutional alloy Cu-3.1%atSn[J]. Acta Metallurgica et Materialia,1983,31:87-94.
[50] J. Z. Chen, Q.C. Zhang, Z.Y. Jiang, et al. A macroscopic model for the Portevin-Le Chateliereffect [J]. Mater. Sci. Tech.2004,20:535.
[51]黎文献.镁及镁合金[M].长沙：中南大学出版社，2005.
[52] J.W. Christian, S. Mahajan. Deformation twinning[J]. Progress in Matial Scince,1995,39:1-6.
[53] ASM International. Magnesium and Magnesium Alloy[M].O.H:Metal Park,1999.
[54] A. Staroselsky, L. Aband. A contitutive model for hcp material deforming by slip andtwinning:application to magenesium alloy AZ31B[J].Internation Journal of plasticity,2003,19:1843-1850.
[55] S.L. Couling.Yield Points in a dilute magnesium-thorium alloy[J]. Acta Metallurgic,1959,7:133-134.
[56] M.C. Chaturvedi, D.J. Lloyd.Onset of serrated yielding in Mg-10Ag alloy[J]. PhilosophyMagazine，1974,30:1199-1207.
[57] S.M. Zhu, J.F. Nie.Serrated flow and tensile properties of a Mg-Y-Nd alloy[J].ScripaMaterialia,2004，50:51-55.
[58] C. Corby, C.H. Caceres, P. Lukac. Serrated flow in magnesium alloy AZ91[J]. Mater. Sci.Eng. A,2004,387-389:22-24.
[59] V. Gartnerova, Z. Trojanova, A. Jager, et al.Deformation behaviour of Mg-0.7wt%Ndalloy[J]. Journal of alloys and Compounds,2004,378:180-183.
[60]王聪，徐永波，韩恩厚.LA41镁合金的PLC效应及其解释[J].金属学报，2006，42(2):191-194.
[61]智莹，王鑫，吴崴等.挤压变形Mg-Mn-Zn-Y合金的疲劳行为研究[J].汽车工艺与材料，2007，1：26-28.
[62]李锋，吴崴，陈立佳等.热处理对挤压变形AM50镁合金疲劳行为的影响[J].沈阳工业大学学报，2007,29(3):263-266.
[63]陈立佳，茆亮，张思倩等.热挤压AZ81镁合金的拉伸变形行为[J].沈阳工业大学学报，2008,30(4):419-423.
[64]张思倩.挤压变形AZ81镁合金的动态应变时效行为[硕士论文].辽宁：沈阳工业大学，2007.
[65] A K. Miller Ph.D. dissertation, Stanford University,1975.
[66] A.K. Miller. A constitutive model for monotonic, cyclic, and creep deformation: Parts I-Equations development and analytical procedures[J]. ASMEof Eng.Mat.and Tech,1976,98:97-105.
[67] A.K. Miller. An inelastic constitutive model for monotonic, cyclic, and creep deformation:Parts II-Applycation to304stainless steel [J]. ASME of Eng.Mat.andTech,1976,98:106-113.
[68] A.K. Miller. Modelling of Cyclic Plasticity With Unified Constitutive Equations:Improvements in Simulating Normal and Anomalous Bauschinger Effects. ASME of Eng[J].Mat.andTeeh. Vol.1021980.4:215-222.
[69] T.C. Lowe, A. K. Miller. Improved Constitutive Equations for Modeling Strain Softening一Part II: Predictions for Aluminum. ASME of Eng. Mat. and Tech.1984,106:343-347.
[70] T.C. Lowe, A. K. Miller. Improved Constitutive Equations for Modeling Strain Softening一Part II: Predictions for Aluminum. ASME of Eng. Mat. and Tech.1984,106:337-342.
[71] T.C. Lowe, A.K. Miller, Modeling internal Stresses in the nonelastic deformation ofmetals[J]. ASME of Eng. Mat. and Tech.1986,108:365-373.
[72] A. K. Miller Edited, Unified Constitutive Equations for Creep and Plasticity, ElsevierApplied Science Publishers Ltd,1987.
[73] K.P. Walker. Research and development program for non-lineal structural modeling withadvanced time-temperature dependent constructive relationships，Report NASA-cR-165533,1981.
[74] A. Chulya, K.P. Walker. A new uniformly valid asymptotic integration algorithm for elasto-plastic-creep and unified viscoplastic theories including continuum damage. Report NASAICOMI-89-22,1989.12.
[75] J.L. Chaboche, G.Rouselier. On the Plastic and Viscoplastic Constitutive Equations Part I:Rules Developed with Internal Variable Concept[J]. Trans. ASME, Nonlinear Mechanics1983,14:183-203.
[76] J.L. Chaboche, F.Rouselier. On the Plastic and Viscoplastic Constitutive Equations Part II:Application of Internal Variable Concept to the316Stainless Steel[J]. Trans. ASME,Nonlinear Mechanics.1983.14:183-203.
[77] J.L. Chaboche, D. Nouaihas. Constitutive modeling of ratchetting effect-Part I: Experimentalfacts and properties of the classical models[J]. ASME of Eng. Mat. and Tech.1989,111:384-392.
[78] J.L. Chaboche,D. Nouaihas. Constitutive modeling of ratchetting effect-Part II: Possibilitiesof some additional kinematic rules[J]. ASME of Eng. Mat. and Tech.1989,111:409-416.
[79] J. Lin, Y. Liu, A set of unified constitutive equations for modellingmicrostructure evolutionin hot deformation[J]. Journal of Materials Processing Technology,2003,143–144:281–285.
[80] J. Lin, J. B.Yang. GA-based multiple objective optimisation for determining viscoplasticconstitutive equations for superplastic alloys[J]. International Journal of Plasticity,1999,15:1181-1196.
[81] M. Yaguchi, Y. Takahashi. Unified Inelastic Constitutive Model for Modified9Cr-1MoSteel Incorporating Dynamic Strain Aging Effect[J]. JSME International Journal(A),1999,42:1-10.
[82] M. Yaguchi, Y. Takahashi. A viscoplastic constitutive model incorporating dynamic strainaging e.ect during cyclic deformation conditions[J]. International Journal of Plasticity,2000,16:241-262.
[83] T. Mayama, K. Sasaki, H. Ishikawa. A constitutive model of cyclic viscoplasticityconsidering changes in subsequent viscoplastic deformation due to the evolution ofdislocation structures[J]. International Journal of Plasticity,2007,23:915–930.
[84]王健,肖宏,张志国.流变应力逆分析确定静态再结晶动力学模型[J]．金属学报，2008，44(7)：837-842．
[85]赵社戍，匡震邦．热粘塑性体的积分一微分型本构关系[J]．固体力学学报，1987,16:48-55.
[86] M.H. Feng, L.Y. Ma, H.X. Lu. A new elastic-viscoplastic unified constitutive model forcyclic, creep, monotonic deformation[J]. Proceeding of International Symposium onStrength Theory: Application Development&Prospects for21th Century1998:889-897.
[87]曲杰．考虑动态再结晶的粘塑性本构模型的参数识别．[博士论文].北京：清华大学工程力学系，2004.4.
[88] Kubin L P, Chihab K. The rate dependence of the Portevin-Le Chatelier effect. Actametall.,1988,36(10):2707-2718.
[89] Kumar S, McShane H B. Serrated yielding in Al-Li alloys[J]. Scripta Metall. et Mater.,1993,28(9):1149-1154.
[90] Wang C, Xu Y B, Han E H. Serrated flow and abnormal strain rate sensitivity of amagnesium-lithium alloy[J]. Materials Letters,2006,60:2941-2944.
[91]彭开萍，陈文哲，钱匡武．H68黄铜动态应变时效后的组织与性能[J]．金属热处理，2006，31（2）：53-56.
[92] Hahner H, Hampel A. Observation of Luders bands in single crystals. Scripta Metallurgica etMaterialia,1993,29:1151-1157.
[93] Kovacs Zs. Localized deformation bands in Portevin Le-Chatelier plastic instabilities at aconstant stress rate. Materials Science and Engineering A: Preperties, Microstructure andProcessing,2000,279(1-2):179-184.
[94]彭开萍，陈文哲，钱匡武.3004铝合金动态应变时效的微观机理[J].材料热处理学报，2005,26(6):61-66.
[95] Hahner P. On the physics of the Portevin-Le Chatelier effect part1:the statistics of dynamicstrain aging. Materials Science and Engineering,1996,A207:208-215.
[96] Reed-Hill R E，Kaufman M J. On evaluating the flow stress in Niobium of commercial purity.Acta metal. Mater.,1995,43(5):1731-1739.
[97]中国机械工程学会热处理专业学会.热处理手册.第二版.第一卷.北京：机械工业出版社，1991.
[98] M A Michael, B. Hugh. ASM Specialty Handbook-Magnesium Alloys.Ohio:ASMinternational,Materials Park,1999.
[99] A. Galiyev, R. Kaibyshev, G. Gottetein. Correlation of plastic deformation and dynamicrecrystallization in magnesium alloy ZK60[J]. Acta mater.2001,49:1199-1207.
[100]张娅，马春江，卢晨．变形镁合金的塑性变形机制与动态再结晶[J]．轻合金加工技术，2003,31:35-39.
[101] R. Kaibyshev, O. Sitdikov. On the role of twinning in dynamic recrystallization[J]. FizikaMetallov i Metallovedenie,2000,89(4):7077.
[102]余琨，黎文献，王日初.镁合金塑性变形机制[J]．中国有色金属学报，2005,7：1081-1086.
[103]刘楚明,刘子娟,朱秀荣等.镁及镁合金动态再结晶研究进展[J]．中国有色金属学报，2006,16：1-11.
[104]黄孝瑛，侯耀永，李理编著.电子衍衬分析原理与图谱[M].山东：山东科学技术出版社，2000.5.
[105] P. Hahner.On the critical conditions of the portevin-le Chateller effect[J].Acta mater.2000，48(9):3695-3707.
[106] P. Penning, Mathematics of the portevin-le chatelier effect [J]. Acta Metallurgica.1972,20:1169-1175.
[107] S.H. van den Brink, A. van den Beukel, P.G. McCormick. Strain rate sensitivity and theportevin-le chatelier effect in Au–Cu alloys[J].Phys. Status Solidi A,1975,30:469-477.
[108] M. S. Bharathi, M. Leryodkin, G. Anthakrshna, et al. The hidden order behind jerkyflow[J]. Acta Materialia,2002,50:2813–2824.
[109] R C. Picu. A mechanism for the negative strain-rate sesitivity of dilute solidsolutions[J].Acta Materialia,2004,52:3447-3458.
[110] D. H. Kang, D. W. Kim, S. Kin, et al. Relationship between stretch formability andwork-hardening capacity of twin-roll cast Mg alloys at room temperature[J]. ScriptaMaterialia,2009,61:768–771.
[111] B. Wielke. Dislocation dynamics during rate changes [J]. Acta Metall,1978,26:103-107.
[112] A. Chatterjee, A. Sarkar, P. Barat, et al. Character of the deformation bands in the (A+B)regime of the Portevin-Le Chatelier effect in Al–2.5%Mg alloy[J]. Materials Science andEngineering A,2009,508:156-160.
[113] M. S. Bharathi, M. Leryodkin, G. Anthakrshna, et al. The hidden order behind jerky flow[J].Acta Materialia,2002,50:2813–2824.
[114] S. Spigarelli. Creep of a thixaformed and heat treated AZ91Mg-Al-Zn[J]. Scripta mater，2000，42：397-402.
[115] M. Suzuki, T. Kimura, J. Koike, et al. Strengthening effect of Zn in heat resistantMg–Y–Zn solid solution alloys[J]. Scripta Materialia,2003,48:997-1002.
[116]张俊善编著.材料强度学[M].哈尔滨：哈尔滨工业大学出版社，2004.
[117] R Onodera, T Ishibashi, M Koga,etal. Relation between the Portevin-Le Chatelier effect andthe solid solubility in some binary alloys[J]. Acta Metall.,1983,31:535-540.
[118] S. Zhang, P. G. McCormick,and Y. Estrin. The morphology of Portevin–Le Chatelier bands:finite element simulation for Al–Mg–Si [J]. Acta Materialia.2001,49:1087-1094.
[119]江慧丰. Al合金中塑性失稳现象的实验和机理研究.[博士论文].合肥：中国科技大学力学和机械工程系。
[120] Kumar S, Pink E. Effect of δ′precipitates on serrated flow[J]. Scripta Metall. et Mater.,1995,32(5):749-753.
[121] Pink E, Krol J. Precipitation and serrated flow in AlZn10[J]. Acta metall. Mater,1994,43(6):2351-2357.
[122] Brechet Y, Estrin Y. On the influence of precipitation on the Portevin-Le Chatelier effect[J].Acta Metall.Mater.,1995,43(3):955-963.
[123] Kumar S, McShane H B. Serrated yielding in Al-Li alloys[J]. Scripta Metall. et Mater.,1993,28(9):1149-1154.
[124] Nalawade S A, Sundararaman M, Kishorea R，et al. The influence of aging on the serratedyielding phenomena in a nickel-base superalloy[J]. Scripta Materialia,2008,59:991–994.
[125] Polmear I J.Magnesium alloys and application[J].Materials Science and Technology，1994，(l):1-16.
[126] D. Thevenet, M. Mliha-Touati, A. Zeghloul. The effect of precipitation on the Portevin-LeChatelier effect in an Al–Zn–Mg–Cu alloy[J]. Materials Science and Engineering A.1999,266:175–182
[127] Erwin Pink, Subodh Kumar, Baohui Tian. Serrated flow of aluminium alloys influenced byprecipitates[J]. Materials Science and Engineering A.2000,280:17–24.
[128] S.A. Nalawade, M. Sundararaman, R. Kishore. The influence of aging on the serratedyielding phenomena in a nickel-base superalloy[J]. Scripta Materialia.2008,59:991–994.
[129]匡震邦编著非线性连续介质力学[M].上海：上海交通大学出版社，2002.1.
[130] Z.B. Kuang. Integral constitutive equations of elastic-plastic materials[J]. Acta MechanicSolida Sinica.1990,3:245.
[131] B.D. Coleman, M.E. Gurtin. Thermodynamics with internal state variables[J]. J. ChemicalPhy.1967,47:597.
[132] J.R. Rice. Inelastic constitutive relations for solids: An internal-variable theory and itsapplication to metal plasticity[J]. Journal of the Mechanics and Physics of Solids,1971,19:433.
[133] J.L. Chaboche. Cyclic viscoplastic constitutive equations, Part I: A thermodyamicallyconsistent formulation[J]. Journal of Applied Mechanics (Transactions of the ASME)1993,60:813
[134] T. Oyamada, K. Kaneko. Influence of prestraining and deformation rate on viscoplasticityand strain aging of metal materials (2ndReport, The Case of Stress Relaxation of SCM435Steel under Uniaxial Loading),(in Japanese),Trans Jpn. Soc. Mech. Eng., Vol.59, No.567A(1993), p.2612-2617.
[135] C. N. Ahlquist, W.D. Nix. Technique for Measuring Mean Internal Stress During HighTemperature Creep[J]. Scripta Met,1969,3:679-681.
[136] A.H. Cottrell, B. A. Bilby. Dislocation Theory of Yielding and Strain Ageing of Iron [J].Proceedings of the Physical Society. Section A.1949,62:49.
[137] R. L. Fleischer. Substitutional solution hardening[J]. Acta Metallurgica.1963,11:203-209.
[138] A. Kalk, C. Schwindk. On the superposition of the effects of dynamic strain ageing and avarying mobile dislocation density-strain rate change experiments on Cu-Mn single crystals.Scripta Metallurgica et Materialia.1995,33:369-375.
[139]黄光远，刘小军编著.数学物理反问题[M].济南:山东科学技术出版社，1993.
[140]林锉云，董加礼编著.多目标优化的方法与理论[M].长春:吉林教育出版社，1992
[141] GP Steven, Q Li, YM Xie. Multicriteria optimization that minimizes maximum stress andmaximizes stiffness[J]. Computers and Structures.2002,80:2433-2488.
[142] R. Kumar, P. K. Singh, P. P. Chakrabarti. Multiobjective EA Approach for Improved Qualityof Solutions for Spanning Tree Problem[J]. Computer science.2005,3410:811-825.
[2] D. W. Moon. Considerations on the present state of lüders band studies[J]. Materials Scienceand Engineering.1971,8:235-243.
[3]钱匡武,李效琦,萧林钢等.金属和合金中的动态应变时效现象[J]．福州大学学报，2001,29(6):8-23.
[4] A.H. Cottrell. A note on the Portevin-Le Chatelier effect[J].Philosphical Magazine,1953,44(335):829-832.
[5] C. Wang, Y.B. Xu, E.H. Han. Serrated flow and abnormal strain rate sensitivity of amagnesium–lithium alloy[J]. Materials Letters,2006,60:2941–2944.
[6] S. Rajashekhar, K. Subodh, J.R. Hans,et al. Effect of specimen condition,oriention and alloycomposition on PLC band parameters[J]. Materials Science and Engineering A,2004,382:203-208.
[7] B. H. Tian. Ageing effect on serrated flow in Al-Mg alloys[J]. Materials Science andEngineering A,2003,349:272-278.
[8]钱匡武，李效琦，肖林钢.α黄铜晶体尺寸对锯齿屈服的影响[J].材料科学进展，1990，4（5）：420-424.
[9] A. P. Masson, Ann. Chem. Phys.，third series1841,3:451.
[10] J. F. Bell and A. Stein, The Incremental Loading Wave in the Prestressed Plastic Field.[J]. Journalde Mechanique,1962,1:395.
[11] O.W. Dillon. Experimental data on aluminium as a mechanically unstable solid[J]. Journal ofthe Mechanics and Physics of Solids.1963,11:289-304.
[12] Z.S. Kovacs, N.Q. Chinh and J. Lendvai, Orientation dependence of Portevin–Le Chatelier plasticinstabilities in depth-sensing microindentation [J]. Journal of Materials Research.，2001,16:1171.
[13] P.R. Cetlin, A.S. Gulec and R.E. Reed-Hill, Serrated Flow in Al6061Alloy [J]. Metall.Trans.，1973,4:513.
[14] K. Chihab, Y. Estrin, L. P. Kubin. The kinetics of the Portiven-Le Chatlier bands in an Al-5at%Mg alloy[J]. Scripta Metallurgica,1987,21:203-208.
[15] A. Ziegenbein, P. Hahner, H. Neuhauser. Correlation of temporal instabilities and spatiallocalization during Portiven-Le Chatelier deformation of Cu-10at%Al and Cu-15at%Al[J].Computational Materials Science,2000,19:27-34.
[16] S. Toyooka, X..L. Gong. Digital Speckle Pattern Interferometry for Observing the EntireProcess of Plastic Deformation of a Solid Object[J]. Japanese Journal of Applied Physics,1995,34:1666.
[17] Q.C. Zhang, S. Toyooka, Z.B. Meng, Suprapedi, In: Backlini G Y, Proc.of SPIE,Nondestructrue Evaluation of Aging Materials and Composites Ⅲ, Vol.3585, NewportBeach, CA, SPIE,1999:389.
[18]彭开萍.面心立方合金动态应变时效的研究：[博士论文].福州：福州大学材料科学与工程学院，2007.
[19] M. Wagenhofer, M. Erickson-Natishan, R.W. Armstrong. Influence of strain rate and grainsize on yield serrated flow in commercial Al-Mg alloy5086[J].Acta Metallurgica etMaterialia,1999,41:1177–1184.
[20] L.H. de Almeida, I.Le May, P.R.O. Emygdio. Mechanistic Modeling of Dynamic StrainAging in Austenitic Stainless Steels[J]. Material Characterization,1988,41:137–150.
[21]钱匡武，彭开萍，陈文哲.金属动态应变时效现象中的“锯齿屈服”[J].福建工程学院学报,2003,1(1):4-8.
[22] H.F. Jiang, Q.C. Zhang, X.D. Chen,et al. Three types of Portevin–Le Chatelier effects:Experiment and modelling [J]. Acta Materialia,2007,55:2219–2228.
[23] N. Ranc, D. Wagner. Experimental study by pyrometry of Portevin–Le Chatelier plastic instabilities-Type A to type B transition[J]. Materials Science and Engineering A,2008,474:188–196
[24] M.A. Soare, W.A. Curtin. Solute strengthening of both mobile and forest dislocations:Theorigin of dynamic strain aging in fcc metals[J]. Acta Materialia,2008,56:4046–4061.
[25]田宝辉，张永刚．铝-锂单晶体的反常流变行为和PLC效应[J].稀有金属材料与工程，1995,24(4):41-45.
[26]倪朝芳，钱匡武．动态应变时效强化奥氏体不锈钢[J]．理化检验(物理分册)，1987，23(5)：12-15.
[27]陈文哲，钱匡武．动态应变时效对奥氏体不锈钢静拉伸强度的影响[J]．金属科学与工艺，1989，8(3、4)：1-7．
[28]陈文哲，彭开萍，钱匡武．动态应变时效对不锈钢高温强度的影响[J]．机械工程学报，1992，28(2)：34-38．
[29]李效琦，陈文哲．动态应变时效对18-8型奥氏体不锈钢强度的影响[J]．福州大学学报(自然科学版)，1989，17(2)：30-34．
[30]陈文哲，钱匡武．动态应变时效对奥氏体不锈钢纯弯疲劳强度的影响[J]．金属学报，1989，25(2)：A132-136．
[31] Qian K W, Peng K P, Chen W Z. Influence of dynamic strain aging on the high temperaturestrength of18-8type austenitic stainless steel[A]. Proc of the6th international conference onmechanical behavior of materials (ICM-6)[C]. Kyoto, Japan,1991.4:601-606.
[32]彭开萍，陈文哲，钱匡武．动态应变时效对18-8型奥氏体不锈钢低周疲劳行为的影响[J]．金属学报，1993，29(6)：A283-288．
[33] Qian K W, Chen W Z, Peng K P. Effects of dynamic strain aging on high temperature fatigueproperties of austenitic stainless steel[A]. Proc of the6th international conference on creep&fatigue[C]. London,1996.203-210.
[34] A. Korbel, J. Zasadzinski, Z. Slieklucka. A new approach to the portevin-Le chatelier effect[J].Acta Metall,1976,24:919-923.
[35] L.P. Kubin, Y. Estrin. The Portevin-Le Chatelier effect in deformation with constant stressrate[J]. Acta Metallurgica et Materialia.1985:397-407.
[36] L.P. Kubin, Y. Estrin. Evolution of dislocation densities and the critical conditions for thePortevin-Le Chatelier effect[J]. Acta Metallurgica et Materialia.38(1990)697.
[37] G Ananthakrishna, D Sahoo. A model based on nonlinear oscillations to explain jumps oncreep curves[J]. J. Phys. D: Appl. Phys.1981,14:2081.
[38] D Sahoo and G Ananthakrishna A phenomenological dislocation transformation model forthe mobile fraction in simple systems[J]. J. Phys. D: Appl. Phys.1982,15:1439.
[39] M. Zaiser, M. Glazov, L. A. Lalli and O. Richmond. On the relations between strain andstrain-rate softening phenomena in some metallic materials: a computational study [J].Computational Materials Science.1999,15:35-49.
[40] C. Fressengeas, A.J. Beaudoin, M. Lebyodkin, et al. Dynamic strain aging: A coupleddislocation-Solute dynamic model[J]. Materials Science and Engineering A.2005,400-401:226-230.
[41] P.G. McCormick. A model for the Portevin–Le Chatelier effect in substitutional alloys[J].Acta Metallurgica et Materialia,1972,20:351–354.
[42] P.G. McCormick. Theory of flow localisation due to dynamic strain ageing[J]. ActaMetallurgica et Materialia,1988,36(12):3061-3067.
[43] P.G. McCormick, C.P. Ling. Numerical modelling of the Portevin-Le Chatelier effect[J].Acta Metallurgica et Materialia,1995,43(5):1969-1977.
[44] A. Van den Beukel. Theory of the effect of dynamic strain ageing on mechanical properties[J].Physica Status Solidi (a),1975,30:197–206.
[45]萧林钢,李效琦,钱匡武.置换合金中出现锯齿屈服现象的临界条件的模型[J].中国科学(A辑),1990，4：423．
[46] S.D. Mesarovic, J. Mech. Dynamic strain aging and plastic instabilities[J]. Phys. Solids,1995,43:671.
[47] P. Hahner, A. Ziegenbein, E. Rizzi and H. Neuhauser, Spatiotemporal analysis of Portevin–Le Chatelier deformation bands: Theory, simulation, and experiment [J]. Phys. Rev. B,2002,65:109-134.
[48] K.W. Qian, R.E. Reed-Hill. A model for determining the internal stress based on zero entropyof activation[J]. Scripta Metall,1982,16:807-810.
[49] K.W.Qian, R.E. Reed-Hill. A model for the flow stress and strain rate sensitivity of asubstitutional alloy Cu-3.1%atSn[J]. Acta Metallurgica et Materialia,1983,31:87-94.
[50] J. Z. Chen, Q.C. Zhang, Z.Y. Jiang, et al. A macroscopic model for the Portevin-Le Chateliereffect [J]. Mater. Sci. Tech.2004,20:535.
[51]黎文献.镁及镁合金[M].长沙：中南大学出版社，2005.
[52] J.W. Christian, S. Mahajan. Deformation twinning[J]. Progress in Matial Scince,1995,39:1-6.
[53] ASM International. Magnesium and Magnesium Alloy[M].O.H:Metal Park,1999.
[54] A. Staroselsky, L. Aband. A contitutive model for hcp material deforming by slip andtwinning:application to magenesium alloy AZ31B[J].Internation Journal of plasticity,2003,19:1843-1850.
[55] S.L. Couling.Yield Points in a dilute magnesium-thorium alloy[J]. Acta Metallurgic,1959,7:133-134.
[56] M.C. Chaturvedi, D.J. Lloyd.Onset of serrated yielding in Mg-10Ag alloy[J]. PhilosophyMagazine，1974,30:1199-1207.
[57] S.M. Zhu, J.F. Nie.Serrated flow and tensile properties of a Mg-Y-Nd alloy[J].ScripaMaterialia,2004，50:51-55.
[58] C. Corby, C.H. Caceres, P. Lukac. Serrated flow in magnesium alloy AZ91[J]. Mater. Sci.Eng. A,2004,387-389:22-24.
[59] V. Gartnerova, Z. Trojanova, A. Jager, et al.Deformation behaviour of Mg-0.7wt%Ndalloy[J]. Journal of alloys and Compounds,2004,378:180-183.
[60]王聪，徐永波，韩恩厚.LA41镁合金的PLC效应及其解释[J].金属学报，2006，42(2):191-194.
[61]智莹，王鑫，吴崴等.挤压变形Mg-Mn-Zn-Y合金的疲劳行为研究[J].汽车工艺与材料，2007，1：26-28.
[62]李锋，吴崴，陈立佳等.热处理对挤压变形AM50镁合金疲劳行为的影响[J].沈阳工业大学学报，2007,29(3):263-266.
[63]陈立佳，茆亮，张思倩等.热挤压AZ81镁合金的拉伸变形行为[J].沈阳工业大学学报，2008,30(4):419-423.
[64]张思倩.挤压变形AZ81镁合金的动态应变时效行为[硕士论文].辽宁：沈阳工业大学，2007.
[65] A K. Miller Ph.D. dissertation, Stanford University,1975.
[66] A.K. Miller. A constitutive model for monotonic, cyclic, and creep deformation: Parts I-Equations development and analytical procedures[J]. ASMEof Eng.Mat.and Tech,1976,98:97-105.
[67] A.K. Miller. An inelastic constitutive model for monotonic, cyclic, and creep deformation:Parts II-Applycation to304stainless steel [J]. ASME of Eng.Mat.andTech,1976,98:106-113.
[68] A.K. Miller. Modelling of Cyclic Plasticity With Unified Constitutive Equations:Improvements in Simulating Normal and Anomalous Bauschinger Effects. ASME of Eng[J].Mat.andTeeh. Vol.1021980.4:215-222.
[69] T.C. Lowe, A. K. Miller. Improved Constitutive Equations for Modeling Strain Softening一Part II: Predictions for Aluminum. ASME of Eng. Mat. and Tech.1984,106:343-347.
[70] T.C. Lowe, A. K. Miller. Improved Constitutive Equations for Modeling Strain Softening一Part II: Predictions for Aluminum. ASME of Eng. Mat. and Tech.1984,106:337-342.
[71] T.C. Lowe, A.K. Miller, Modeling internal Stresses in the nonelastic deformation ofmetals[J]. ASME of Eng. Mat. and Tech.1986,108:365-373.
[72] A. K. Miller Edited, Unified Constitutive Equations for Creep and Plasticity, ElsevierApplied Science Publishers Ltd,1987.
[73] K.P. Walker. Research and development program for non-lineal structural modeling withadvanced time-temperature dependent constructive relationships，Report NASA-cR-165533,1981.
[74] A. Chulya, K.P. Walker. A new uniformly valid asymptotic integration algorithm for elasto-plastic-creep and unified viscoplastic theories including continuum damage. Report NASAICOMI-89-22,1989.12.
[75] J.L. Chaboche, G.Rouselier. On the Plastic and Viscoplastic Constitutive Equations Part I:Rules Developed with Internal Variable Concept[J]. Trans. ASME, Nonlinear Mechanics1983,14:183-203.
[76] J.L. Chaboche, F.Rouselier. On the Plastic and Viscoplastic Constitutive Equations Part II:Application of Internal Variable Concept to the316Stainless Steel[J]. Trans. ASME,Nonlinear Mechanics.1983.14:183-203.
[77] J.L. Chaboche, D. Nouaihas. Constitutive modeling of ratchetting effect-Part I: Experimentalfacts and properties of the classical models[J]. ASME of Eng. Mat. and Tech.1989,111:384-392.
[78] J.L. Chaboche,D. Nouaihas. Constitutive modeling of ratchetting effect-Part II: Possibilitiesof some additional kinematic rules[J]. ASME of Eng. Mat. and Tech.1989,111:409-416.
[79] J. Lin, Y. Liu, A set of unified constitutive equations for modellingmicrostructure evolutionin hot deformation[J]. Journal of Materials Processing Technology,2003,143–144:281–285.
[80] J. Lin, J. B.Yang. GA-based multiple objective optimisation for determining viscoplasticconstitutive equations for superplastic alloys[J]. International Journal of Plasticity,1999,15:1181-1196.
[81] M. Yaguchi, Y. Takahashi. Unified Inelastic Constitutive Model for Modified9Cr-1MoSteel Incorporating Dynamic Strain Aging Effect[J]. JSME International Journal(A),1999,42:1-10.
[82] M. Yaguchi, Y. Takahashi. A viscoplastic constitutive model incorporating dynamic strainaging e.ect during cyclic deformation conditions[J]. International Journal of Plasticity,2000,16:241-262.
[83] T. Mayama, K. Sasaki, H. Ishikawa. A constitutive model of cyclic viscoplasticityconsidering changes in subsequent viscoplastic deformation due to the evolution ofdislocation structures[J]. International Journal of Plasticity,2007,23:915–930.
[84]王健,肖宏,张志国.流变应力逆分析确定静态再结晶动力学模型[J]．金属学报，2008，44(7)：837-842．
[85]赵社戍，匡震邦．热粘塑性体的积分一微分型本构关系[J]．固体力学学报，1987,16:48-55.
[86] M.H. Feng, L.Y. Ma, H.X. Lu. A new elastic-viscoplastic unified constitutive model forcyclic, creep, monotonic deformation[J]. Proceeding of International Symposium onStrength Theory: Application Development&Prospects for21th Century1998:889-897.
[87]曲杰．考虑动态再结晶的粘塑性本构模型的参数识别．[博士论文].北京：清华大学工程力学系，2004.4.
[88] Kubin L P, Chihab K. The rate dependence of the Portevin-Le Chatelier effect. Actametall.,1988,36(10):2707-2718.
[89] Kumar S, McShane H B. Serrated yielding in Al-Li alloys[J]. Scripta Metall. et Mater.,1993,28(9):1149-1154.
[90] Wang C, Xu Y B, Han E H. Serrated flow and abnormal strain rate sensitivity of amagnesium-lithium alloy[J]. Materials Letters,2006,60:2941-2944.
[91]彭开萍，陈文哲，钱匡武．H68黄铜动态应变时效后的组织与性能[J]．金属热处理，2006，31（2）：53-56.
[92] Hahner H, Hampel A. Observation of Luders bands in single crystals. Scripta Metallurgica etMaterialia,1993,29:1151-1157.
[93] Kovacs Zs. Localized deformation bands in Portevin Le-Chatelier plastic instabilities at aconstant stress rate. Materials Science and Engineering A: Preperties, Microstructure andProcessing,2000,279(1-2):179-184.
[94]彭开萍，陈文哲，钱匡武.3004铝合金动态应变时效的微观机理[J].材料热处理学报，2005,26(6):61-66.
[95] Hahner P. On the physics of the Portevin-Le Chatelier effect part1:the statistics of dynamicstrain aging. Materials Science and Engineering,1996,A207:208-215.
[96] Reed-Hill R E，Kaufman M J. On evaluating the flow stress in Niobium of commercial purity.Acta metal. Mater.,1995,43(5):1731-1739.
[97]中国机械工程学会热处理专业学会.热处理手册.第二版.第一卷.北京：机械工业出版社，1991.
[98] M A Michael, B. Hugh. ASM Specialty Handbook-Magnesium Alloys.Ohio:ASMinternational,Materials Park,1999.
[99] A. Galiyev, R. Kaibyshev, G. Gottetein. Correlation of plastic deformation and dynamicrecrystallization in magnesium alloy ZK60[J]. Acta mater.2001,49:1199-1207.
[100]张娅，马春江，卢晨．变形镁合金的塑性变形机制与动态再结晶[J]．轻合金加工技术，2003,31:35-39.
[101] R. Kaibyshev, O. Sitdikov. On the role of twinning in dynamic recrystallization[J]. FizikaMetallov i Metallovedenie,2000,89(4):7077.
[102]余琨，黎文献，王日初.镁合金塑性变形机制[J]．中国有色金属学报，2005,7：1081-1086.
[103]刘楚明,刘子娟,朱秀荣等.镁及镁合金动态再结晶研究进展[J]．中国有色金属学报，2006,16：1-11.
[104]黄孝瑛，侯耀永，李理编著.电子衍衬分析原理与图谱[M].山东：山东科学技术出版社，2000.5.
[105] P. Hahner.On the critical conditions of the portevin-le Chateller effect[J].Acta mater.2000，48(9):3695-3707.
[106] P. Penning, Mathematics of the portevin-le chatelier effect [J]. Acta Metallurgica.1972,20:1169-1175.
[107] S.H. van den Brink, A. van den Beukel, P.G. McCormick. Strain rate sensitivity and theportevin-le chatelier effect in Au–Cu alloys[J].Phys. Status Solidi A,1975,30:469-477.
[108] M. S. Bharathi, M. Leryodkin, G. Anthakrshna, et al. The hidden order behind jerkyflow[J]. Acta Materialia,2002,50:2813–2824.
[109] R C. Picu. A mechanism for the negative strain-rate sesitivity of dilute solidsolutions[J].Acta Materialia,2004,52:3447-3458.
[110] D. H. Kang, D. W. Kim, S. Kin, et al. Relationship between stretch formability andwork-hardening capacity of twin-roll cast Mg alloys at room temperature[J]. ScriptaMaterialia,2009,61:768–771.
[111] B. Wielke. Dislocation dynamics during rate changes [J]. Acta Metall,1978,26:103-107.
[112] A. Chatterjee, A. Sarkar, P. Barat, et al. Character of the deformation bands in the (A+B)regime of the Portevin-Le Chatelier effect in Al–2.5%Mg alloy[J]. Materials Science andEngineering A,2009,508:156-160.
[113] M. S. Bharathi, M. Leryodkin, G. Anthakrshna, et al. The hidden order behind jerky flow[J].Acta Materialia,2002,50:2813–2824.
[114] S. Spigarelli. Creep of a thixaformed and heat treated AZ91Mg-Al-Zn[J]. Scripta mater，2000，42：397-402.
[115] M. Suzuki, T. Kimura, J. Koike, et al. Strengthening effect of Zn in heat resistantMg–Y–Zn solid solution alloys[J]. Scripta Materialia,2003,48:997-1002.
[116]张俊善编著.材料强度学[M].哈尔滨：哈尔滨工业大学出版社，2004.
[117] R Onodera, T Ishibashi, M Koga,etal. Relation between the Portevin-Le Chatelier effect andthe solid solubility in some binary alloys[J]. Acta Metall.,1983,31:535-540.
[118] S. Zhang, P. G. McCormick,and Y. Estrin. The morphology of Portevin–Le Chatelier bands:finite element simulation for Al–Mg–Si [J]. Acta Materialia.2001,49:1087-1094.
[119]江慧丰. Al合金中塑性失稳现象的实验和机理研究.[博士论文].合肥：中国科技大学力学和机械工程系。
[120] Kumar S, Pink E. Effect of δ′precipitates on serrated flow[J]. Scripta Metall. et Mater.,1995,32(5):749-753.
[121] Pink E, Krol J. Precipitation and serrated flow in AlZn10[J]. Acta metall. Mater,1994,43(6):2351-2357.
[122] Brechet Y, Estrin Y. On the influence of precipitation on the Portevin-Le Chatelier effect[J].Acta Metall.Mater.,1995,43(3):955-963.
[123] Kumar S, McShane H B. Serrated yielding in Al-Li alloys[J]. Scripta Metall. et Mater.,1993,28(9):1149-1154.
[124] Nalawade S A, Sundararaman M, Kishorea R，et al. The influence of aging on the serratedyielding phenomena in a nickel-base superalloy[J]. Scripta Materialia,2008,59:991–994.
[125] Polmear I J.Magnesium alloys and application[J].Materials Science and Technology，1994，(l):1-16.
[126] D. Thevenet, M. Mliha-Touati, A. Zeghloul. The effect of precipitation on the Portevin-LeChatelier effect in an Al–Zn–Mg–Cu alloy[J]. Materials Science and Engineering A.1999,266:175–182
[127] Erwin Pink, Subodh Kumar, Baohui Tian. Serrated flow of aluminium alloys influenced byprecipitates[J]. Materials Science and Engineering A.2000,280:17–24.
[128] S.A. Nalawade, M. Sundararaman, R. Kishore. The influence of aging on the serratedyielding phenomena in a nickel-base superalloy[J]. Scripta Materialia.2008,59:991–994.
[129]匡震邦编著非线性连续介质力学[M].上海：上海交通大学出版社，2002.1.
[130] Z.B. Kuang. Integral constitutive equations of elastic-plastic materials[J]. Acta MechanicSolida Sinica.1990,3:245.
[131] B.D. Coleman, M.E. Gurtin. Thermodynamics with internal state variables[J]. J. ChemicalPhy.1967,47:597.
[132] J.R. Rice. Inelastic constitutive relations for solids: An internal-variable theory and itsapplication to metal plasticity[J]. Journal of the Mechanics and Physics of Solids,1971,19:433.
[133] J.L. Chaboche. Cyclic viscoplastic constitutive equations, Part I: A thermodyamicallyconsistent formulation[J]. Journal of Applied Mechanics (Transactions of the ASME)1993,60:813
[134] T. Oyamada, K. Kaneko. Influence of prestraining and deformation rate on viscoplasticityand strain aging of metal materials (2ndReport, The Case of Stress Relaxation of SCM435Steel under Uniaxial Loading),(in Japanese),Trans Jpn. Soc. Mech. Eng., Vol.59, No.567A(1993), p.2612-2617.
[135] C. N. Ahlquist, W.D. Nix. Technique for Measuring Mean Internal Stress During HighTemperature Creep[J]. Scripta Met,1969,3:679-681.
[136] A.H. Cottrell, B. A. Bilby. Dislocation Theory of Yielding and Strain Ageing of Iron [J].Proceedings of the Physical Society. Section A.1949,62:49.
[137] R. L. Fleischer. Substitutional solution hardening[J]. Acta Metallurgica.1963,11:203-209.
[138] A. Kalk, C. Schwindk. On the superposition of the effects of dynamic strain ageing and avarying mobile dislocation density-strain rate change experiments on Cu-Mn single crystals.Scripta Metallurgica et Materialia.1995,33:369-375.
[139]黄光远，刘小军编著.数学物理反问题[M].济南:山东科学技术出版社，1993.
[140]林锉云，董加礼编著.多目标优化的方法与理论[M].长春:吉林教育出版社，1992
[141] GP Steven, Q Li, YM Xie. Multicriteria optimization that minimizes maximum stress andmaximizes stiffness[J]. Computers and Structures.2002,80:2433-2488.
[142] R. Kumar, P. K. Singh, P. P. Chakrabarti. Multiobjective EA Approach for Improved Qualityof Solutions for Spanning Tree Problem[J]. Computer science.2005,3410:811-825.
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |