AZ31镁合金板热成形中的屈服和损伤:本构实现与数值分析
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摘要
为了准确预测各向异性镁合金板的成形质量,将改进的GTN损伤模型与各向异性拉压不对称的CPB06屈服本构耦合,并考虑了屈服面形状随塑性应变累积的变化,得到了考虑本构参数随塑性应变演化的各向异性屈服CPB06-GTN损伤模型。基于该模型,在ABAQUS/Explict中编译得到了相应的VUMAT子程序,采用单个单元进行了单轴拉伸和压缩模拟,并通过与实验一致性对比验证了子程序的正确性。使用子程序不仅能够模拟镁合金的各向异性屈服及其不规则的硬化,同时也能够模拟镁合金的损伤破坏。此外,采用编写的子程序进行了热拉深成形的数值模拟,模拟预测与实验结果对比表明,采用各向异性损伤模型的计算结果能够准确预测镁合金的变形及其损伤破坏,模拟结果与实验数据吻合;采用合适的压边力和成形的温度条件及非等温成形方法能够提高镁合金的成形性。
In order to predict the forming quality of the anisotropic magnesium alloy sheet accurately,a modified GTN damage model that incorporates anisotropic/asymmetric CPB06 yield criterion and yield locus evolution with the accumulated plastic strain,the so-called CPB06-GTN anisotropy yielding model with parametric evolution is developed.The modified CPB06-GTN model is implemented into a VUMAT subroutine for ABAQUS/Explicit,and the subroutine is then tested using a single unit.The results show that the simulation predictions are in good agreement with the experimental results in uniaxial tension and compression.Using the VUMAT subroutine,not only anisotropic yielding and irregular hardening but also damage and fracture of magnesium alloys can be well predicted.In addition,the corresponding VUMAT subroutine is compiled to simulate the warm deep drawing process of magnesium alloy,and the simulation results are compared with the experimental data.The results show that the anisotropic yield CPB06-GTN damage model can well predict the deformation and fracture of the magnesium alloy.The formability of magnesium alloys can be improved by adopting the proper blank holder force and forming temperature as well as non isothermal warm forming method.
In order to predict the forming quality of the anisotropic magnesium alloy sheet accurately,a modified GTN damage model that incorporates anisotropic/asymmetric CPB06 yield criterion and yield locus evolution with the accumulated plastic strain,the so-called CPB06-GTN anisotropy yielding model with parametric evolution is developed.The modified CPB06-GTN model is implemented into a VUMAT subroutine for ABAQUS/Explicit,and the subroutine is then tested using a single unit.The results show that the simulation predictions are in good agreement with the experimental results in uniaxial tension and compression.Using the VUMAT subroutine,not only anisotropic yielding and irregular hardening but also damage and fracture of magnesium alloys can be well predicted.In addition,the corresponding VUMAT subroutine is compiled to simulate the warm deep drawing process of magnesium alloy,and the simulation results are compared with the experimental data.The results show that the anisotropic yield CPB06-GTN damage model can well predict the deformation and fracture of the magnesium alloy.The formability of magnesium alloys can be improved by adopting the proper blank holder force and forming temperature as well as non isothermal warm forming method.
引文
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[17]GURSON A L.Continuum theory of ductile rupture byvoid nucleation and growth:Part 1—Yield criteria and flow rules for porous ductile media[J].Journal of Engineering Materials and Technology,1977,99(1):2-15.
[18]NEEDLEMAN A,TVERGAARD V.An analysis of dynamic,ductile crack growth in a double edge cracked specimen[J].International Journal of Fracture,1991,49(1):41-67.
[19]KIM J,RYOU H,KIM D,et al.Constitutive law for AZ31B Mg alloy sheets and finite element simulation for three-point bending[J].International Journal of Mechanical Sciences,2008,50(10):1510-1518.
[20]STEWART J B,CAZACU O.Analytical yield criterion for an anisotropic material containing spherical voids and exhibiting tension-compression asymmetry[J].International Journal of Solids and Structures,2011,48(2):357-373.
[21]YOON J,CAZACU O,MISHRA R K.Constitutive modeling of AZ31sheet alloy with application to axial crushing[J].Materials Science and Engineering:A,2013,565:203-212.
[22]WANG R,CHEN Z,LI Y,et al.Failure analysis of AZ31magnesium alloy sheets based on the extended GTN damage model[J].International Journal of Minerals,Metallurgy,and Materials,2013,20(12):1198-1207.
[23]陈志英,董湘怀.各向异性GTN损伤模型及其在板料成形中的应用[J].上海交通大学学报,2008,42(9):1414-1419.CHEN Z Y,DONG X H.The Anisotropic GTN Damage model and its application in sheet metal forming[J].Journal of Shanghai Jiaotong University,2008,42(9):1414-1419(in Chinese).
[24]TARI D G,WORSWICK M J,WINKLER S.Experimental studies of deep drawing of AZ31B magnesium alloy sheet under various thermal conditions[J].Journal of Materials Processing Technolog,2013,213(8):1337-1347.
[25]LI W J,ZHAO G Q,MA X W,et al.Study on forming limit diagrams of AZ31Balloy sheet at different temperatures[J].Materials&Manufacturing Processes,2013,28(3):306-311.
[26]LEE S,HAM H J,KWON S Y,et al.Thermal conductivity of magnesium alloys in the temperature range from-125℃to 400℃[J].International Journal of Thermophysics,2013:34(12):2343-2350.
[2]唐荻,王丹,江海涛,等.异步轧制对AZ31镁合金组织及高温塑性的影响[J].塑性工程学报,2013,20(2):78-83.TANG D,WANG D,JIANG H T,et al.Effects of differential speed rolling process on microstructure and plastic deformation of magnesium alloy[J].Journal of Plasticity Engineering,2013,20(2):78-83(in Chinese).
[3]吴章斌,桂良进,范子杰.AZ31B镁合金挤压材料的力学性能与本构分析[J].中国有色金属学报,2015,25(2):293-300.WU Z B,GUI L J,FAN Z J.Mechanical properties and constitutive analysis of extruded AZ31B magnesium alloy[J].Chinese Journal of Nonferrous Metals,2015,25(2):293-300(in Chinese).
[4]钟敏,唐伟琴,李大永,等.AZ31B镁合金板材温热成形极限实验研究[J].塑性工程学报,2011,18(5):59-63.ZHONG M,TANG W Q,LI D Y,et al.Experiment research on forming limit diagram(FLD)of magnesium alloy sheet AZ31Bat warm condition[J].Journal of Plasticity Engineering,2011,18(5):59-63(in Chinese).
[5]何维均,张士宏,程明,等.宏观弹塑性本构模型的研究进展[J].塑性工程学报,2015,22(3):1-11.HE W J,ZHANG S H,CHENG M,et al.Review on the development of macroscopic elastic-plastic constitutive models[J].Journal of Plasticity Engineering,2015,22(3):1-11(in Chinese).
[6]HILL R.A theory of the yielding and plastic flow of anisotropic metals[C]∥Proceedings of the Royal Society of London Series A,Mathematical and Engineering Sciences.London:The Royal Society Publishing,1948,193(1033):281-297.
[7]BARLAT F,LEGE D J,BREM J C.A six-component yield function for anisotropic materials[J].International Journal of Plasticity,1991,7(7):693-712.
[8]BARLAT F,MAEDA Y,CHUNG K,et al.Yield function development for aluminum alloy sheets[J].Journal of the Mechanics and Physics of Solids,1997,45(11):1727-1763.
[9]BARLAT F,BREM J C,YOON J W,et al.Plane stress yield function for aluminum alloy sheets—Part 1:Theory[J].International Journal of Plasticity,2003,19(9):1297-1319.
[10]HOSFORD W F.Incorporating work hardening in yield loci calculations[C]∥Strength of Metals and Alloys.Aachen:Federal Republic of Germany,1979,775-780.
[11]CAZACU O,PLUNKETT B,BARLAT F.Orthotropic yield criterion for hexagonal closed packed metals[J].International Journal of Plasticity,2006,22(7):1171-1194.
[12]PLUNKETT B,CAZACU O,BARLAT F.Orthotropic yield criteria for description of the anisotropy in tension and compression of sheet metals[J].International Journal of Plasticity,2008,24(5):847-866.
[13]TARI D G,WORSWICK M J.Elevated temperature constitutive behavior and simulation of warm forming of AZ31B[J].Journal of Materials Processing Technology,2015,221:40-55.
[14]郎利辉,杨希英,刘康宁,等.一种韧性断裂准则中材料常数的计算模型及其应用[J].航空学报,2015,36(2):672-679.LANG L H,YANG X Y,LIU K N,et al.A calculating model of material constants in ductile fracture criterion and its applications[J].Acta Aeronautica et Astronautica Sinica,2015,36(2):672-679(in Chinese).
[15]TENG B G,YUAN S J,CHEN Z T,et al.Plastic damage of T-shape hydroforming[J].Transactions of Nonferrous Metals Society of China,2012,22(S2):s294-s301.
[16]王瑞泽,陈章华,臧勇.基于Gurson模型的镁合金板材温热冲压成形研究[J].北京科技大学学报,2014,36(4):459-466.WANG R Z,CHEN Z H,ZANG Y.Thermal stamping formability of magnesium alloy sheet based on the Gurson model[J].Journal of University of Science and Technology Beijing,2014,36(4):459-466(in Chinese).
[17]GURSON A L.Continuum theory of ductile rupture byvoid nucleation and growth:Part 1—Yield criteria and flow rules for porous ductile media[J].Journal of Engineering Materials and Technology,1977,99(1):2-15.
[18]NEEDLEMAN A,TVERGAARD V.An analysis of dynamic,ductile crack growth in a double edge cracked specimen[J].International Journal of Fracture,1991,49(1):41-67.
[19]KIM J,RYOU H,KIM D,et al.Constitutive law for AZ31B Mg alloy sheets and finite element simulation for three-point bending[J].International Journal of Mechanical Sciences,2008,50(10):1510-1518.
[20]STEWART J B,CAZACU O.Analytical yield criterion for an anisotropic material containing spherical voids and exhibiting tension-compression asymmetry[J].International Journal of Solids and Structures,2011,48(2):357-373.
[21]YOON J,CAZACU O,MISHRA R K.Constitutive modeling of AZ31sheet alloy with application to axial crushing[J].Materials Science and Engineering:A,2013,565:203-212.
[22]WANG R,CHEN Z,LI Y,et al.Failure analysis of AZ31magnesium alloy sheets based on the extended GTN damage model[J].International Journal of Minerals,Metallurgy,and Materials,2013,20(12):1198-1207.
[23]陈志英,董湘怀.各向异性GTN损伤模型及其在板料成形中的应用[J].上海交通大学学报,2008,42(9):1414-1419.CHEN Z Y,DONG X H.The Anisotropic GTN Damage model and its application in sheet metal forming[J].Journal of Shanghai Jiaotong University,2008,42(9):1414-1419(in Chinese).
[24]TARI D G,WORSWICK M J,WINKLER S.Experimental studies of deep drawing of AZ31B magnesium alloy sheet under various thermal conditions[J].Journal of Materials Processing Technolog,2013,213(8):1337-1347.
[25]LI W J,ZHAO G Q,MA X W,et al.Study on forming limit diagrams of AZ31Balloy sheet at different temperatures[J].Materials&Manufacturing Processes,2013,28(3):306-311.
[26]LEE S,HAM H J,KWON S Y,et al.Thermal conductivity of magnesium alloys in the temperature range from-125℃to 400℃[J].International Journal of Thermophysics,2013:34(12):2343-2350.