·478 工程科学学报，第41卷，第4期 forming and its application.J Mech Eng,2010,46(14):68 ping steel.J Mater Eng,2016,44(5):15 (马宁，胡平，闫康康，等.高强度硼钢热成形技术研究及其 (张施琦，冯定，张跃，等.新型超高强度热冲压用钢的热变 应用.机械工程学报，2010,46(14)：68) 形行为及本构关系.材料工程，2016,44(5)：15) Merklein M,Lechler J.Investigation of the thermo-mechanical [13]Qi M J.Zhang X B,Song K X,et al.Deformation behavior and properties of hot stamping steels.J Mater Process Technol,2006, constitutive equation of 35MnB steel at high temperature.J Plast 177(13):452 Eng,2017,24(2):168 B3]Naderi M,Durrenberger L,Molinari A,et al.Constitutive rela- (齐敏杰，张学宾，宋克兴，等.35MB钢高温变形行为及本 tionships for 22MnB5 boron steel deformed isothermally at high 构方程.塑性工程学报，2017,24(2)：168) temperatures.Mater Sci Eng A,2008,478(12)130 [14]Li GC,Deng T,Lu R Z.Experimental research on hot deforma- 4]Ma N,Hu P,Wu W H,et al.Constitutive theory and experiment tion behavior of ultra strength steel and simulation analysis of the analysis of hot forming for high strength steel.Chin J Theor Appl constitutive 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and Arhenius-Type constitutive [0]Taylor T,Danks S,Fourlaris G.Dynamic tensile testing of ultra- models to predict high-emperature flow behavior of Ti6Al4V alloy high strength hot stamped martensitic steels.Steel Res Int,2017, in a+B phase.High Temp Mater Processes,2016,35(3):297 88(3):1600144 1]Wang Q L,Tang B T,Zheng W.A modified Norton-Hoff consti- [11]Gladman T.Grain refinement in multiple micro-alloyed steels. tutive model and experimental verification.China Mech Eng, HSLA Steels.Warrendale,1992:3 2015,26(14):1978 [12]Zhang S Q.Feng D.Zhang Y,et al.Hot deformation behavior (王巧玲，唐炳祷，郑伟.一种修正的Norton-Hof本构模型 and constitutive model of advanced ultra-high strength hot stam- 及实验验证.中国机械工程，2015,26(14)：1978)工程科学学报，第 41 卷，第 4 期 forming and its application． J Mech Eng，2010，46( 14) : 68 ( 马宁，胡平，闫康康，等． 高强度硼钢热成形技术研究及其 应用． 机械工程学报，2010，46( 14) : 68) ［2］ Merklein M，Lechler J． Investigation of the thermo-mechanical properties of hot stamping steels． J Mater Process Technol，2006， 177( 1-3) : 452 ［3］ Naderi M，Durrenberger L，Molinari A，et al． Constitutive rela￾tionships for 22MnB5 boron steel deformed isothermally at high temperatures． Mater Sci Eng A，2008，478( 1-2) : 130 ［4］ Ma N，Hu P，Wu W H，et al． Constitutive theory and experiment analysis of hot forming for high strength steel． Chin J Theor Appl Mech，2011，43( 2) : 346 ( 马宁，胡平，武文华，等． 高强度钢板热成形本构理论与实 验分析． 力学学报，2011，43( 2) : 346) ［5］ Murty S V S N，Sarkar A，Narayanan P Ｒ，et al． Development of processing maps and constitutive relationship for thermomechanical processing of aluminum alloy AA2219． J Mater Eng Perform， 2017，26( 5) : 2190 ［6］ Chu Y D，Li J S，Zhao F T，et al． Flow behavior and constitutive relationship for elevated temperature compressive deformation of a high Nb containing TiAl alloy with ( α2 + γ) microstructure． Ma￾ter Lett，2018，210: 58 ［7］ Shi B D，Peng Y，Yang C，et al． Loading path dependent distor￾tional hardening of Mg alloys: experimental investigation and con￾stitutive modeling． Int J Plast，2017，90: 76 ［8］ Li H P，He L F，Zhao G Q，et al． Constitutive relationships of hot stamping boron steel B1500HS based on the modified Arrhenius and Johnson-Cook model． Mater Sci Eng A，2013，580: 330 ［9］ Taylor T，Fourlaris G，Evans P，et al． New generation ultrahigh strength boron steel for automotive hot stamping technologies． Ma￾ter Sci Technol，2014，30( 7) : 818 ［10］ Taylor T，Danks S，Fourlaris G． Dynamic tensile testing of ultra￾high strength hot stamped martensitic steels． Steel Ｒes Int，2017， 88( 3) : 1600144 ［11］ Gladman T． Grain refinement in multiple micro- alloyed steels． HSLA Steels． Warrendale，1992: 3 ［12］ Zhang S Q，Feng D，Zhang Y，et al． Hot deformation behavior and constitutive model of advanced ultra-high strength hot stam￾ping steel． J Mater Eng，2016，44( 5) : 15 ( 张施琦，冯定，张跃，等． 新型超高强度热冲压用钢的热变 形行为及本构关系． 材料工程，2016，44( 5) : 15) ［13］ Qi M J，Zhang X B，Song K X，et al． Deformation behavior and constitutive equation of 35MnB steel at high temperature． J Plast Eng，2017，24( 2) : 168 ( 齐敏杰，张学宾，宋克兴，等． 35MnB 钢高温变形行为及本 构方程． 塑性工程学报，2017，24( 2) : 168) ［14］ Li G C，Deng T，Lu Ｒ Z． Experimental research on hot deforma￾tion behavior of ultra strength steel and simulation analysis of the constitutive relationship． Forg Stamp Technol，2016，41 ( 3 ) : 110 ( 李国城，邓涛，卢任之． 超高强度钢板热流变行为试验研 究及本构模型仿真分析． 锻压技术，2016，41( 3) : 110) ［15］ Johnson G Ｒ，Holmquist T J． Evaluation of cylinder-impact test data for constitutive model constants． J Appl Phys，1988，64 ( 8) : 3901 ［16］ Zhao Y H，Sun J，Li J F，et al． A comparative study on John￾son-Cook and modified Johnson-Cook constitutive material model to predict the dynamic behavior laser additive manufacturing FeCr alloy． J Alloys Compd，2017，723: 179 ［17］ Lin Y C，Chen X M． A combined Johnson-Cook and Zerilli-Arm￾strong model for hot compressed typical high-strength alloy steel． Comput Mater Sci，2010，49( 3) : 628 ［18］ Li Z Z，Wang B F，Zhao S T，et al． Dynamic deformation and failure of ultrafine-grained titanium． Acta Mater，2017，125: 210 ［19］ He S，Li C S，Huang Z Y，et al． A modified constitutive model based on Arrhenius-type equation to predict the flow behavior of Fe--36% Ni Invar alloy． J Mater Ｒes，2017，32( 20) : 3831 ［20］ Cai J，Wang K S，Han Y Y． A comparative study on Johnson Cook，modified Zerilli-Armstrong and Arrhenius-Type constitutive models to predict high-temperature flow behavior of Ti--6Al--4V alloy in α + β phase． High Temp Mater Processes，2016，35( 3) : 297 ［21］ Wang Q L，Tang B T，Zheng W． A modified Norton--Hoff consti￾tutive model and experimental verification． China Mech Eng， 2015，26( 14) : 1978 ( 王巧玲，唐炳涛，郑伟． 一种修正的 Norton--Hoff 本构模型 及实验验证． 中国机械工程，2015，26( 14) : 1978) · 874 ·