杨竞等：耦合孪生晶体塑性模型硬化参数的灵敏度分析 ·1083· 是详细给出了硬化参数确定步骤，即先根据屈服极限 hardening behavior in V-5Cr-5Ti alloy.Chin J Appl Mech, 确定初始滑移阻力s:,再根据应变硬化率拐点和阶段 2012,44(2):334 A分别确定8和孪生硬化指数b,最后对整个应变硬化 (余勇，潘晓霞，谢若泽，等.孪生诱发塑性对V5C5Ti合 率曲线微调确定饱和参数S 金应变硬化行为的影响.力学学报，2012,44(2)：334) 01] Li H W,Yang H,Sun Z C.A robust integration algorithm for (2)初始滑移阻力s8与屈服极限呈线性关系。孪 implementing rate dependent crystal plasticity into explicit finite 生硬化指数b增大使得孪生硬化阶段A减弱.孪生阻 element method.Int J Plast,2008,24(2)267 力与滑移阻力比值8增大，孪生增长率降低，且硬化率 [12]Zheng H L,Yang H,Li H W.Crystal plasticity finite element 拐点后移，直至8=1.2时拐点消失 modeling for uniaxial compression of commercially pure titanium. (3)获得了Fe-22Mn0.6C型孪生诱导塑性钢耦 JPlast Eng,2013,20(1):95 (郑华雷，杨合，李宏伟.纯钛压缩变形下的品体塑性有限 合孪生晶体塑性模型硬化参数的取值范围，其中s。为 元分析.塑性工程学报，2013,20(1)：95) 80~160MPa之间，b为0~3之间，8为1~1.3之间. 03] Bouaziz O,Allain S,Scott C P,et al.High manganese austenit- ic twinning induced plasticity steels:a review of the microstruc- 参考文献 ture properties relationships.Curr Opin Solid State Mater Sci, 2011,15(4):141 1]Zhang K S,Zhang G.Feng L Stress calculation of single crystal [14]Sarma G,Zacharia T.Integration algorithm for modeling the elastoviscoplastic response of polycrystalline materials.J Mech under finite slip plastic deformation.Acta Mech Sin,2002,34 (4):636 Phys Solid,1999,47(6):1219 [15]Wang W H.Study on Plastie Deformation Beharior Induced by (张克实，张光，冯露.单品体塑性滑移有限变形下的应力计 算.力学学报，2002,34(4)：636) Slipping and Ticinning for TWIP Steel [Dissertation].Beijing: Li D Y,Zhang S R.Peng Y H,et al.Finite element simulation University of Science and Technology Beijing,2012 (王伟华.TWP钢滑移和孪生耦合的塑性变形行为[学位论 of sheet metal stamping with polycrystalline plasticity.Chin 文].北京：北京科技大学，2012) Mech Eng,2008,44(1):190 06 (李大永，张少蓉，彭颖红，等.板材冲压成形的品体塑性有 Gebhardt T,Music D,Kossmann D,et al.Elastic properties of 限元模拟.机械工程学报，2008,44(1)：190) fce Fe-Mn-X (X=Al,Si)alloys studied by theory and experi- B3]Pi H C.Han JT,Zhang C G,et al.Simulation of the rolling tex- ment.Acta Mater,2011,59(8):3145 ture of pure Al using crystal plasticity finite element method.J [17]Sun C Y,Guo X R,Huang J,et al.Modelling of plastic deform- Univ Sci Technol Beijing,2007,29(9):920 ation on coupling twinning of single crystal TWIP steel.Acta Met- (皮华春，韩静涛，章传国，等.面心纯铝轧制织构的晶体塑 all Sin,2015,51(3):357 性有限元模拟.北京科技大学学报，2007,29(9)：920) (孙朝阳，郭样如，黄杰，等.耦合李生的TWP钢单品品体 4]Kalidindi S R.Modeling anisotropic strain hardening and deforma- 塑性变形行为模拟研究.金属学报，2015,51(3)：357) tion textures in low stacking fault energy fec metals.Int Plast, [18]Renard K,Jacques P J.On the relationship between work hard- 2001,17(6):837 ening and twinning rate in TWIP steels.Mater Sci Eng A,2012, [5]Barbier D.Favier V,Bolle B.Modeling the deformation textures 542:8 [19]Bouaziz O,Allain S,Scott C.Effect of grain and twin bounda- and microstructural evolutions of a Fe-Mn-C TWIP steel during ries on the hardening mechanisms of twinning-induced plasticity tensile and shear testing.Mater Sci Eng A,2012,540:212 [6]Dancette S,Delannay L,Renard K,et al.Crystal plasticity mod- steels.Scripta Mater,2008,58(6):484 [20] eling of texture development and hardening in TWIP steels.Acta Sun C Y,Huang J,Guo N,et al.A physical constitutive model Matr,2012,60(5):2135 for Fe-22Mn-0.6C TWIP steel based on dislocation density.Ac- [Wang N,Lei L P,Fang G,et al.Deformation analysis of magne- ta Metall Sin,2014,50(9)1115 sium alloy based on crystal plasticity theory.Chin Rare Met, (孙朝阳，黄杰，郭宁，等.基于位错密度的Fe一22Mn0.6C型 2008,32(6):766 TWP钢物理本构模型研究.金属学报，2014,50(9)：1115) (王娜，雷丽萍，方刚，等.镁合金变形的晶体塑性有限元分 221]Barbier D,Gey N,Allain S,et al.Analysis of the tensile behav- 析.稀有金属，2008,32(6)：766) ior of a TWIP steel based on the texture and microstructure evolu- [8]Salem AA,Kalidindi S R,Semiatin S L.Strain hardening due to tions.Mater Sci Eng A,2009,500(1-2)196 deformation twinning in a-titanium:constitutive relations and crys- [22] Grassel O,Kriiger L,Frommeyer G,et al.High strength Fe- tal-plasticity modeling.Acta Mater,2005,53(12):3495 Mn-(Al,Si)TRIP/TWIP steels development-properties-appli- 9]Wu X P,Kalidindi S R,Necker C,et al.Prediction of crystallo- cation.1 nt J Plast,2000,16(10-l1):1391 graphic texture evolution and anisotropic stress-strain curves during 23]Koyama M,SawaguchiT,Lee T,et al.Work hardening associ- large plastic strains in high purity aitanium using a Taylor-type ated with s-martensitic transformation,deformation twinning crystal plasticity model.Acta Mater,2007,55(2):423 and dynamic strain aging in Fe-17Mn-0.6C and Fe-17Mn- [10]Yu Y,Pan XX,Xie RZ,et al.Study on TWIP effect on strain 0.8C TWIP steels.Mater Sci Eng A,2011,528(24)7310杨 竞等: 耦合孪生晶体塑性模型硬化参数的灵敏度分析 是详细给出了硬化参数确定步骤，即先根据屈服极限 确定初始滑移阻力 s α 0，再根据应变硬化率拐点和阶段 A 分别确定 δ 和孪生硬化指数 b，最后对整个应变硬化 率曲线微调确定饱和参数 Spr ． ( 2) 初始滑移阻力 s α 0 与屈服极限呈线性关系． 孪 生硬化指数 b 增大使得孪生硬化阶段 A 减弱． 孪生阻 力与滑移阻力比值 δ 增大，孪生增长率降低，且硬化率 拐点后移，直至 δ = 1. 2 时拐点消失． ( 3) 获得了 Fe--22Mn--0. 6C 型孪生诱导塑性钢耦 合孪生晶体塑性模型硬化参数的取值范围，其中 s α 0 为 80 ～ 160 MPa 之间，b 为 0 ～ 3 之间，δ 为 1 ～ 1. 3 之间． 参 考 文 献 ［1］ Zhang K S，Zhang G，Feng L． Stress calculation of single crystal under finite slip plastic deformation． Acta Mech Sin，2002，34 ( 4) : 636 ( 张克实，张光，冯露． 单晶体塑性滑移有限变形下的应力计 算． 力学学报，2002，34( 4) : 636) ［2］ Li D Y，Zhang S Ｒ，Peng Y H，et al． Finite element simulation of sheet metal stamping with polycrystalline plasticity． Chin J Mech Eng，2008，44( 1) : 190 ( 李大永，张少睿，彭颖红，等． 板材冲压成形的晶体塑性有 限元模拟． 机械工程学报，2008，44( 1) : 190) ［3］ Pi H C，Han J T，Zhang C G，et al． Simulation of the rolling tex￾ture of pure Al using crystal plasticity finite element method． J Univ Sci Technol Beijing，2007，29( 9) : 920 ( 皮华春，韩静涛，章传国，等． 面心纯铝轧制织构的晶体塑 性有限元模拟． 北京科技大学学报，2007，29( 9) : 920) ［4］ Kalidindi S Ｒ． Modeling anisotropic strain hardening and deforma￾tion textures in low stacking fault energy fcc metals． Int J Plast， 2001，17( 6) : 837 ［5］ Barbier D，Favier V，Bolle B． Modeling the deformation textures and microstructural evolutions of a Fe--Mn--C TWIP steel during tensile and shear testing． Mater Sci Eng A，2012，540: 212 ［6］ Dancette S，Delannay L，Ｒenard K，et al． Crystal plasticity mod￾eling of texture development and hardening in TWIP steels． Acta Mater，2012，60( 5) : 2135 ［7］ Wang N，Lei L P，Fang G，et al． Deformation analysis of magne￾sium alloy based on crystal plasticity theory． Chin J Ｒare Met， 2008，32( 6) : 766 ( 王娜，雷丽萍，方刚，等． 镁合金变形的晶体塑性有限元分 析． 稀有金属，2008，32( 6) : 766) ［8］ Salem A A，Kalidindi S Ｒ，Semiatin S L． Strain hardening due to deformation twinning in α-titanium: constitutive relations and crys￾tal-plasticity modeling． Acta Mater，2005，53( 12) : 3495 ［9］ Wu X P，Kalidindi S Ｒ，Necker C，et al． Prediction of crystallo￾graphic texture evolution and anisotropic stress-strain curves during large plastic strains in high purity α-titanium using a Taylor-type crystal plasticity model． Acta Mater，2007，55( 2) : 423 ［10］ Yu Y，Pan X X，Xie Ｒ Z，et al． Study on TWIP effect on strain hardening behavior in V--5Cr--5Ti alloy． Chin J Appl Mech， 2012，44( 2) : 334 ( 余勇，潘晓霞，谢若泽，等． 孪生诱发塑性对 V--5Cr--5Ti 合 金应变硬化行为的影响． 力学学报，2012，44( 2) : 334) ［11］ Li H W，Yang H，Sun Z C． A robust integration algorithm for implementing rate dependent crystal plasticity into explicit finite element method． Int J Plast，2008，24( 2) : 267 ［12］ Zheng H L，Yang H，Li H W． Crystal plasticity finite element modeling for uniaxial compression of commercially pure titanium． J Plast Eng，2013，20( 1) : 95 ( 郑华雷，杨合，李宏伟． 纯钛压缩变形下的晶体塑性有限 元分析． 塑性工程学报，2013，20( 1) : 95) ［13］ Bouaziz O，Allain S，Scott C P，et al． High manganese austenit￾ic twinning induced plasticity steels: a review of the microstruc￾ture properties relationships． Curr Opin Solid State Mater Sci， 2011，15( 4) : 141 ［14］ Sarma G，Zacharia T． Integration algorithm for modeling the elasto-viscoplastic response of polycrystalline materials． J Mech Phys Solids，1999，47( 6) : 1219 ［15］ Wang W H． Study on Plastic Deformation Behavior Induced by Slipping and Twinning for TWIP Steel ［Dissertation］． Beijing: University of Science and Technology Beijing，2012 ( 王伟华． TWIP 钢滑移和孪生耦合的塑性变形行为［学位论 文］． 北京: 北京科技大学，2012) ［16］ Gebhardt T，Music D，Kossmann D，et al． Elastic properties of fcc Fe--Mn--X ( X = Al，Si) alloys studied by theory and experi￾ment． Acta Mater，2011，59( 8) : 3145 ［17］ Sun C Y，Guo X Ｒ，Huang J，et al． Modelling of plastic deform￾ation on coupling twinning of single crystal TWIP steel． Acta Met￾all Sin，2015，51( 3) : 357 ( 孙朝阳，郭祥如，黄杰，等． 耦合孪生的 TWIP 钢单晶晶体 塑性变形行为模拟研究． 金属学报，2015，51( 3) : 357) ［18］ Ｒenard K，Jacques P J． On the relationship between work hard￾ening and twinning rate in TWIP steels． Mater Sci Eng A，2012， 542: 8 ［19］ Bouaziz O，Allain S，Scott C． Effect of grain and twin bounda￾ries on the hardening mechanisms of twinning-induced plasticity steels． Scripta Mater，2008，58( 6) : 484 ［20］ Sun C Y，Huang J，Guo N，et al． A physical constitutive model for Fe--22Mn--0. 6C TWIP steel based on dislocation density． Ac￾ta Metall Sin，2014，50( 9) : 1115 ( 孙朝阳，黄杰，郭宁，等． 基于位错密度的 Fe--22Mn--0. 6C 型 TWIP 钢物理本构模型研究． 金属学报，2014，50( 9) : 1115) ［21］ Barbier D，Gey N，Allain S，et al． Analysis of the tensile behav￾ior of a TWIP steel based on the texture and microstructure evolu￾tions． Mater Sci Eng A，2009，500( 1 － 2) : 196 ［22］ Grssel O，Krüger L，Frommeyer G，et al． High strength Fe-- Mn--( Al，Si) TＲIP /TWIP steels development--properties--appli￾cation． Int J Plast，2000，16( 10--11) : 1391 ［23］ Koyama M，Sawaguchi T，Lee T，et al． Work hardening associ￾ated with ε － martensitic transformation，deformation twinning and dynamic strain aging in Fe--17Mn--0. 6C and Fe--17Mn-- 0. 8C TWIP steels． Mater Sci Eng A，2011，528( 24) : 7310 · 3801 ·