·556· 工程科学学报，第39卷，第4期 (3)试验与仿真结果对比，可以验证0.8mm厚 03] Chaboche J L,Jung O.Application of a kinematic hardening vis- AZ31B镁合金板料实际塑性变形过程中动态硬化占 coplasticity model with thresholds to the residual stress relaxa- tion.Int J Plast,1997,13(10)785 比大约在0.5~0.9.这种方法简单易行，可应用于其 他金属板料类零件回弹预测中 [14]Yoshida F,Uemori T.A model of large-strain cyclic plasticity describing the Bauschinger effect and workhardening stagnation. Int J Plast,2002,18(5):661 参考文献 [15]Chung K,Lee M G,Kim D,et al.Springack evaluation of au- tomotive sheets based on isotropic-kinematic hardening laws and [Liu Y.The Plastic Deformation Mechanism of Magnesium Alloy non-quadratic anisotropic yield functions Part I:theory and for- AZ31B [Dissertation].Beijing:University of Chinese Academy mulation.Int J Plast,2005,21(5):861 of Sciences,2015 [16]Feigenbaum H P,Dafalias Y F.Directional distortional harden- (刘垚.镁合金AZ31B塑性变形机理[学位论文].北京：中 ing at large plastic deformations.Int J Solids Struct,2014,51 国科学院大学，2015) (23):3904 2]Zhang H.Yan Y,Fan JF,et al.Improved mechanical properties [17]Pietryga M P,Vladimirov I N,Reese S.A finite deformation of AZ31 magnesium alloy plates by pre-olling followed by warm model for evolving flow anisotropy with distortional hardening in- compression.Mater Sci Eng A,2014,618:540 cluding experimental validation.Mech Mater,2012,44:163 B3]Li B,McClelland Z,Horstemeyer S J.et al.Time dependent [18]Borgqvist E,Lindstrom T,Tryding J,et al.Distortional harden- springback of a magnesium alloy.Mater Des,2015,66:575 ing plasticity model for paperboard.Int Solids Struct,2014,51 4]Yu H Y,Wang Y.A combined hardening model based on (13):2411 Chaboche theory and its application in the springback simulation. [19]Shi B D,Mosler J.On the macroscopic description of yield sur- J Mech Eng,2015,51(16):127 face evolution by means of distortional hardening models:appli- (余海燕，王友.一种基于Chaboche理论的混合硬化模型及 cation to magnesium.Int J Plast,2013,44:I 其在回弹仿真中的应用.机械工程学报，2015,51(16)： 0]Yue Z M.Ductile Damage Prediction in Sheet Metal Forming 127) Processes [Dissertation].Troyes:University of Technology of [5]Lee J Y,Lee M G,Barlat F,et al.Evaluation of constitutive Troyes,2014 models for springback prediction in U-draw/bending of DP and 221]Yue Z M,Badreddine H,Saanouni K,et al.On the distortion of TRIP steel sheets.AlP Conf Proc,2011,1383:571 yield surface under complex loading paths in sheet metal forming 6]Lee M G,Kim C,Pavlina E J,et al.Advances in sheet form- /IDDRG 2014 Conference.Paris,2014 ingmaterials modeling,numerical simulation,and press technol- 22] Francois M.A plasticity model with yield surface distortion for ogies.J Manuf Sci Eng,2011,133(6):061001 non proportional loading.Int J Plast,2001,17(5):703 Wagoner R H,Lim H,Lee MG.Advanced issues in springback. 23] Zang S L,Lee M G,Sun L,et al.Measurement of the Bausch- Int J Plast,2013,45:3 inger behavior of sheet metals by three-point bending springback [8]Li X C.Yang Y Y,Wang YZ,et al.Effect of hardening mode of test with pre-strained strips.Int J Plast,2014,59:84 material on springback-simulation accuracy of bending.Mater Sci 4]Shao R.Analysis of high-strength sheet metal springback influ- Technol,,2002,10(3):277 encing factors based on orthogonal experiment.Hot Work (李雪春，杨玉英，王永志，等。材料硬化模式对弯曲回弹模 Technol,2014,43(7):142 拟精度的影响.材料科学与工艺，2002,10(3)：277) (邵燃.基于正交试验的高强度板料回弹影响因素分析.热 ]Prager W.A new method of analyzing stresses and strains in work- 加工工艺，2014,43(7)：142) hardening plastic solids.J Appl Mech,1956,23:493 25] Shi Y P,Zhou Y R.ABAOUS Finite Element Analysis of Detailed [10]Ziegler H.A modification of Prager's hardening rule.0 Appl Examples Attached.Beijing:China Machine Press,2006 Math,1959,17(1):55 (石亦平，周玉蓉.ABAQUS有限元分析实例详解.北京：机 [11]Sabourin F,Morestin F,Brunet M.Effect on non-inear kine- 械工业出版社，2006) matic hardening on spring-back analysis //Numisheet 2002. 26]Gao L H,Xie D X,Chen X D.Analysis on error and measure- Coree du Sud,2002 ment uncertainty of the rebound method.Concrete,2011(7):27 [12]Chaboche J L.A review of some plasticity and viscoplasticity (高连海，谢德霞，陈旭东.浅析回弹法的误差及其不确定 constitutive theories.Int J Plast,2008,24(10):1642 度.混凝土，2011(7)：27)工程科学学报，第 39 卷，第 4 期 ( 3) 试验与仿真结果对比，可以验证 0. 8 mm 厚 AZ31B 镁合金板料实际塑性变形过程中动态硬化占 比大约在 0. 5 ～ 0. 9． 这种方法简单易行，可应用于其 他金属板料类零件回弹预测中． 参 考 文 献 ［1］ Liu Y． The Plastic Deformation Mechanism of Magnesium Alloy AZ31B ［Dissertation］． Beijing: University of Chinese Academy of Sciences，2015 ( 刘垚． 镁合金 AZ31B 塑性变形机理［学位论文］． 北京: 中 国科学院大学，2015) ［2］ Zhang H，Yan Y，Fan J F，et al． Improved mechanical properties of AZ31 magnesium alloy plates by pre-rolling followed by warm compression． Mater Sci Eng A，2014，618: 540 ［3］ Li B，McClelland Z，Horstemeyer S J，et al． Time dependent springback of a magnesium alloy． Mater Des，2015，66: 575 ［4］ Yu H Y，Wang Y． A combined hardening model based on Chaboche theory and its application in the springback simulation． J Mech Eng，2015，51( 16) : 127 ( 余海燕，王友． 一种基于 Chaboche 理论的混合硬化模型及 其在回弹 仿 真 中 的 应 用． 机 械 工 程 学 报，2015，51 ( 16 ) : 127) ［5］ Lee J Y，Lee M G，Barlat F，et al． Evaluation of constitutive models for springback prediction in U-draw / bending of DP and TＲIP steel sheets． AIP Conf Proc，2011，1383: 571 ［6］ Lee M G，Kim C，Pavlina E J，et al． Advances in sheet form￾ing—materials modeling，numerical simulation，and press technol￾ogies． J Manuf Sci Eng，2011，133( 6) : 061001 ［7］ Wagoner Ｒ H，Lim H，Lee M G． Advanced issues in springback． Int J Plast，2013，45: 3 ［8］ Li X C，Yang Y Y，Wang Y Z，et al． Effect of hardening mode of material on springback--simulation accuracy of bending． Mater Sci Technol，2002，10( 3) : 277 ( 李雪春，杨玉英，王永志，等． 材料硬化模式对弯曲回弹模 拟精度的影响． 材料科学与工艺，2002，10( 3) : 277) ［9］ Prager W． A new method of analyzing stresses and strains in work-- hardening plastic solids． J Appl Mech，1956，23: 493 ［10］ Ziegler H． A modification of Prager's hardening rule． Q Appl Math，1959，17( 1) : 55 ［11］ Sabourin F，Morestin F，Brunet M． Effect on non-linear kine￾matic hardening on spring-- back analysis / /Numisheet 2002． Corée du Sud，2002 ［12］ Chaboche J L． A review of some plasticity and viscoplasticity constitutive theories． Int J Plast，2008，24( 10) : 1642 ［13］ Chaboche J L，Jung O． Application of a kinematic hardening vis￾coplasticity model with thresholds to the residual stress relaxa￾tion． Int J Plast，1997，13( 10) : 785 ［14］ Yoshida F，Uemori T． A model of large--strain cyclic plasticity describing the Bauschinger effect and workhardening stagnation． Int J Plast，2002，18( 5) : 661 ［15］ Chung K，Lee M G，Kim D，et al． Spring-back evaluation of au￾tomotive sheets based on isotropic--kinematic hardening laws and non-quadratic anisotropic yield functions Part I: theory and for￾mulation． Int J Plast，2005，21( 5) : 861 ［16］ Feigenbaum H P，Dafalias Y F． Directional distortional harden￾ing at large plastic deformations． Int J Solids Struct，2014，51 ( 23) : 3904 ［17］ Pietryga M P，Vladimirov I N，Ｒeese S． A finite deformation model for evolving flow anisotropy with distortional hardening in￾cluding experimental validation． Mech Mater，2012，44: 163 ［18］ Borgqvist E，Lindstrm T，Tryding J，et al． Distortional harden￾ing plasticity model for paperboard． Int J Solids Struct，2014，51 ( 13) : 2411 ［19］ Shi B D，Mosler J． On the macroscopic description of yield sur￾face evolution by means of distortional hardening models: appli￾cation to magnesium． Int J Plast，2013，44: 1 ［20］ Yue Z M． Ductile Damage Prediction in Sheet Metal Forming Processes ［Dissertation］． Troyes: University of Technology of Troyes，2014 ［21］ Yue Z M，Badreddine H，Saanouni K，et al． On the distortion of yield surface under complex loading paths in sheet metal forming / / IDDＲG 2014 Conference． Paris，2014 ［22］ Franois M． A plasticity model with yield surface distortion for non proportional loading． Int J Plast，2001，17( 5) : 703 ［23］ Zang S L，Lee M G，Sun L，et al． Measurement of the Bausch￾inger behavior of sheet metals by three-point bending springback test with pre--strained strips． Int J Plast，2014，59: 84 ［24］ Shao Ｒ． Analysis of high--strength sheet metal springback influ￾encing factors based on orthogonal experiment． Hot Work Technol，2014，43( 7) : 142 ( 邵燃． 基于正交试验的高强度板料回弹影响因素分析． 热 加工工艺，2014，43( 7) : 142) ［25］ Shi Y P，Zhou Y Ｒ． ABAQUS Finite Element Analysis of Detailed Examples Attached． Beijing: China Machine Press，2006 ( 石亦平，周玉蓉． ABAQUS 有限元分析实例详解． 北京: 机 械工业出版社，2006) ［26］ Gao L H，Xie D X，Chen X D． Analysis on error and measure￾ment uncertainty of the rebound method． Concrete，2011( 7) : 27 ( 高连海，谢德霞，陈旭东． 浅析回弹法的误差及其不确定 度． 混凝土，2011( 7) : 27) · 655 ·