第11期 周靖等：耦合损伤的22MnB5热变形本构模型 ·1457· 密度作为微观内变量演化的“驱动力”，耦合了损伤 pled with dislocation density for hot deformation of 6111 演化方程，实现了对拉伸应力-应变曲线下降段的 aluminum alloy.J Univ Sic Technol Beijing,2013,35(10): 数学描述. 1333 (4④)利用遗传算法确定并优化本构模型中的材 (傅垒，王宝雨，林建国，等.耦合位错密度的6111铝合金 热变形本构模型.北京科技大学学报，2013,35(10)：1333) 料常数，所得材料常数确定的本构模型能够较好地 [8]Lin J G,Liu Y,Dean T A.Investigation of damage fea 预测22MB5高温拉伸变形下的流变应力，并能较 tures in hot metal forming//AIP Conference proceedings 好地描述材料损伤演化行为. Columbus,2004:185 [9]Lin J G,Dean T A.Modelling of microstructure evolu- 参考文献 tion in hot forming using unified constitutive equations.J Mater Process Technol,2005,167(2/3):354 [1]Karbasian H,Tekkaya A E.A review on hot stamping.J [10]Lin J,Liu Y.A set of unified constitutive equations for Mater Process Technol,2010,210(15):2103 modelling microstructure evolution in hot deformation.J [2]Kachanov L M.Time of the rupture process under creep Mater Process Technol,2003,143/144:281 conditions.Isv Akad Nauk SSR Otd Tekh Nauk,1958(8): [11]Mohamed M S,Foster A D,Lin J G,et al.Investiga- 26 tion of deformation and failure features in hot stamping [3 Lin J G,Liu Y,Dean TA.A review on damage mecha- of AA6082:experimentation and modelling.Int J Mach nisms,models and calibration methods under various de- Tool Manuf,2012.53(1):27 formation conditions.Int J Damage Mech,2005,14(4): [12]Lin J G,Cheong B H,Yao X.Universal multi-objective 299 function for optimising superplastic-damage constitutive [4]Bariani P F,Bruschi S,Ghiotti A.Advances in predicting equations.J Mater Process Technol,2002,125/126:199 damage evolution and fracture occurrence in metal form- [13]Li B,Lin J G,Yao X.A novel evolutionary algorithm for ing operations.J Manuf Process,2012,14(4):495 determining unified creep damage constitutive equations. [5]Li H P,Zhao G Q,He L F,et al.Research on the consti- Int J Mech Sci.2002.44(5):987 tutive relationship of hot stamping boron steel B1500HS [14 Li H Y.Nie J X.A method to evaluate the material param- at high temperature.J Mech Eng,2012,48(8):21 eters of viscoplastic damage uniform constitutive equa- (李辉平，赵国群，贺连芳，等.热冲压硼钢B1500HS高温 tions.J Aerosp Power,2003,18(3):388 本构方程的研究.机械工程学报，2012,48(8)：21) (李海燕，聂景旭.粘塑性损伤统一本构模型中材料常数的 [6 Cai J Q.Modelling of Phase Transformation in Hot 一种确定方法.航空动力学报，2003,18(3)：388) Stamping of Boron Steel [Dissertation].London:Impe-[15]Cao J.Lin J G.A study on formulation of objective func- rial College,2011 tions for determining material models.Int J Mech Sci, [7 Fu L,Wang B Y,Lin J G,et al.Constitutive model cou- 2008,50(2:193第 11 期 周 靖等：耦合损伤的 22MnB5 热变形本构模型 1457 ·· 密度作为微观内变量演化的 “驱动力”，耦合了损伤 演化方程，实现了对拉伸应力 - 应变曲线下降段的 数学描述. (4) 利用遗传算法确定并优化本构模型中的材 料常数，所得材料常数确定的本构模型能够较好地 预测 22MnB5 高温拉伸变形下的流变应力，并能较 好地描述材料损伤演化行为. 参 考 文 献 [1] Karbasian H, Tekkaya A E. A review on hot stamping. J Mater Process Technol, 2010, 210(15): 2103 [2] Kachanov L M. Time of the rupture process under creep conditions. Isv Akad Nauk SSR Otd Tekh Nauk, 1958(8): 26 [3] Lin J G, Liu Y, Dean T A. A review on damage mecha￾nisms, models and calibration methods under various de￾formation conditions. Int J Damage Mech, 2005, 14(4): 299 [4] Bariani P F, Bruschi S, Ghiotti A. Advances in predicting damage evolution and fracture occurrence in metal form￾ing operations. J Manuf Process, 2012, 14(4): 495 [5] Li H P, Zhao G Q, He L F, et al. Research on the consti￾tutive relationship of hot stamping boron steel B1500HS at high temperature. J Mech Eng, 2012, 48(8): 21 (李辉平, 赵国群, 贺连芳, 等. 热冲压硼钢 B1500HS 高温 本构方程的研究. 机械工程学报, 2012, 48(8): 21) [6] Cai J Q. Modelling of Phase Transformation in Hot Stamping of Boron Steel [Dissertation]. London: Impe￾rial College, 2011 [7] Fu L, Wang B Y, Lin J G, et al. Constitutive model cou￾pled with dislocation density for hot deformation of 6111 aluminum alloy. J Univ Sic Technol Beijing, 2013, 35(10): 1333 (傅垒, 王宝雨, 林建国, 等. 耦合位错密度的 6111 铝合金 热变形本构模型. 北京科技大学学报, 2013, 35(10): 1333) [8] Lin J G, Liu Y, Dean T A. Investigation of damage fea￾tures in hot metal forming // AIP Conference proceedings. Columbus, 2004: 185 [9] Lin J G, Dean T A. Modelling of microstructure evolu￾tion in hot forming using unified constitutive equations. J Mater Process Technol, 2005, 167(2/3): 354 [10] Lin J, Liu Y. A set of unified constitutive equations for modelling microstructure evolution in hot deformation. J Mater Process Technol, 2003, 143/144: 281 [11] Mohamed M S, Foster A D, Lin J G, et al. Investiga￾tion of deformation and failure features in hot stamping of AA6082: experimentation and modelling. Int J Mach Tool Manuf, 2012, 53(1): 27 [12] Lin J G, Cheong B H, Yao X. Universal multi-objective function for optimising superplastic-damage constitutive equations. J Mater Process Technol, 2002, 125/126: 199 [13] Li B, Lin J G, Yao X. A novel evolutionary algorithm for determining unified creep damage constitutive equations. Int J Mech Sci, 2002, 44(5): 987 [14] Li H Y, Nie J X. A method to evaluate the material param￾eters of viscoplastic damage uniform constitutive equa￾tions. J Aerosp Power, 2003, 18(3): 388 (李海燕, 聂景旭. 粘塑性损伤统一本构模型中材料常数的 一种确定方法. 航空动力学报, 2003, 18(3): 388) [15] Cao J, Lin J G. A study on formulation of objective func￾tions for determining material models. Int J Mech Sci, 2008, 50(2): 193