基于变形特征值及特征状态参数的金属材料高温变形本构方程
High Temperature Deformation Constitutive Equation of Metal Materials Based on Deformation Eigenvalues and Characteristic State Parameters
摘 要
基于变形特征值（σss，σp，εp，εr）及特征状态参数（LM，Z，erf，MTS参数），建立了一个描述金属材料高温变形的本构方程，包括高温变形过程方程和特征参数方程，并通过商业纯铝、无氧铜、超低碳钢的高温压缩试验，对该本构方程的计算准确度进行了验证。结果表明：使用该本构方程计算得到的纯铝和超低碳钢的高温变形结果与试验结果吻合性较好，其峰值应力计算值与试验值的相对误差均小于10%，但无氧铜的却达到了15%，模拟计算精度略低；该本构方程可用于预测纯铝和超低碳钢在热加工变形条件下的流变应力。
高温变形
流变应力
纯铝
无氧铜
超低碳钢
constitutive equation
high temperature deformation
flow stress
pure aluminum
oxygen free copper
ultra-low carbon steel
Abstract
A constitutive equation for high temperature deformation of metal materials, including high temperature deformation process equation and characteristic parameter equation, was established based on the deformation eigenvalues (σss,σp,εp,εr) and characteristic state parameters (LM, Z, erf, MTS). By the high temperature compression test of commercial pure aluminum, oxygen free copper and ultra-low carbon steel, the calculation accuracy of the constitutive equation was verified. The results show that the high temperature deformation results of pure aluminum and ultra-low carbon steel calculated by the constitutive equation were in agreement with the test results. The relative error between the calculated values and the test values of the peak stress of pure aluminum and ultra-low carbon steel was less than 10%, while that of oxygen free copper was up to 15%, indicating that the calculation accuracy of oxygen free copper was slightly lower. The constitutive equation can be used to predict the flow stress of pure aluminum and ultra-low carbon steel under the condition of hot working deformation.
中图分类号 TG142.7 DOI 10.11973/jxgccl202002014
所属栏目 物理模拟与数值模拟
基金项目
收稿日期 2019/2/26
修改稿日期 2020/1/14
网络出版日期
作者单位点击查看
备注曹金荣(1966-),男,宁夏石嘴山人,教授级高级工程师,博士
引用该论文: CAO Jinrong. High Temperature Deformation Constitutive Equation of Metal Materials Based on Deformation Eigenvalues and Characteristic State Parameters[J]. Materials for mechancial engineering, 2020, 44(2): 73～78
曹金荣. 基于变形特征值及特征状态参数的金属材料高温变形本构方程[J]. 机械工程材料, 2020, 44(2): 73～78
共有人对该论文发表了看法，其中：
人认为该论文很差
人认为该论文较差
人认为该论文一般
人认为该论文较好
人认为该论文很好
参考文献
【1】VOCE E. The relationship between stress and strain for homogeneous deformation[J].Journal of the Institute of Metals, 1948, 74:537-540.
【2】MISAKA Y, YOSHIMOTO T. Formularization of mean resistance to deformation of plain carbon steels at elevated temperature[J].Journal of the Japan Society Technology Plasticity, 1967, 8(79):414-422.
【3】SAH J P,RICHARDSON G J,SELLARS C M.Recrystallization during hot deformation of nickel[J]. Journal of the Australian Institute, 1969, 14(4):292-297.
【4】JOHNSON G R,COOK W H.A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures[C]//Proceedings of the Seventh International Symposium on Ballistics, Hague, Nethedands:[s.n.], 1983.
【5】BERGSTRÖM Y. A dislocation model for the stress-strain behaviour of polycrystalline α-Fe with special emphasis on the variation of the densities of mobile and immobile dislocations[J].Materials Science and Engineering, 1970,5(4):193-200.
【6】ESTRIN Y, MECKING H.A unified phenomenological description of work hardening and creep based on one-parameter models[J].Acta Metallurgica,1984,32(1):57-70.
【7】ZERILLI F J,ARMSTRONG R W. Dislocation-mechanics-based constitutive relations for material dynamics calculations[J].Journal of Applied Physics, 1987,61(5):1816-1825.
【8】FOLLANSBEE P S,KOCKS U F.A constitutive description of the deformation of copper based on the use of the mechanical threshold stress as an internal state variable[J].Acta Metallurgica, 1988,36(1):81-93.
【9】PRESTON D L,TONKS D L,WALLACE D C.Model of plastic deformation for extreme loading conditions[J].Journal of Applied Physics, 2003,93(1):211-220.
【10】SELLARS C M, MCTEGART W J. On the mechanism of hot deformation[J].Acta Metallurgica,1966,14(9):1136-1138.
【11】LAASRAOUI A,JONAS J J. Prediction of steel flow stresses at high temperatures and strain rates[J].Metallurgical Transactions A, 1991,22(7):1545-1558.
【12】CABRERA J M,AL OMAR A,PRADO J M,et al. Modeling the flow behavior of a medium carbon microalloyed steel under hot working conditions[J].Metallurgical and Materials Transactions A, 1997,28(11):2233-2244.
【13】CAO J R, LIU Z D,CHENG S C,et al. Constitutive equation models of hot-compressed T122 heat resistant steel[J]. Journal of Iron and Steel Research,International,2012,19(6):53-58.
【14】VILELA J J,BARBOSA R.Prediction of stress-strain curves of hot deformed IF austenite[J].ISIJ International, 2002,42(3):319-321.
【15】JONAS J J, QUELENNEC X, JIANG L, et al. The Avrami kinetics of dynamic recrystallization[J].Acta Materialia, 2009, 57(9):2748-2756.
【16】QUELENNEC X,JONAS J J.Simulation of austenite flow curves under industrial rolling conditions using a physical dynamic recrystallization model[J].ISIJ International, 2012,52(6):1145-1152.
【17】BAMMANN D J, CHIESA M L, JOHNSON G C. A state variable damage model for temperature and strain rate dependent materials[C]//Constitutive Laws:Theory, Experiments and Numerical Implementation. Mauna Lani, Hawaii:[s.n.], 1995.
【18】ROWN A A,BAMMANN D J.Validation of a model for static and dynamic recrystallization in metals[J].International Journal of Plasticity, 2012,32/33:17-35.
【19】BROWN S,KIM K,ANAND L.An internal variable constitutive model for hot working of metals[J].International Journal of Plasticity, 1989,5(2):95-130.
【20】PRASAD Y, RAO K P. Influence of oxygen on rate-controlling mechanisms in hot deformation of polycrystalline copper:Oxygen-free versus electrolytic grades[J]. Materials Letters,2004,58(14):2061-2066.
【21】PRASAD Y, RAO K P. Kinetics of high-temperature deformation of polycrystalline OFHC copper and the role of dislocation core diffusion[J]. Philosophical Magazine, 2004, 84(28):3039-3050.
【22】PRASAD Y, RAO K P. Kinetics and dynamics of hot deformation of OFHC copper in extended temperature and strain rate ranges[J]. Materials Research and Advanced Techniques,2005, 96(1):71-77.
【23】PUCHI-CABRERA E S, GUÉRIN J D, DUBAR M, et al. A novel approach for modeling the flow stress curves of austenite under transient deformation conditions[J]. Materials Science and Engineering:A, 2016, 673:660-670.
【2】MISAKA Y, YOSHIMOTO T. Formularization of mean resistance to deformation of plain carbon steels at elevated temperature[J].Journal of the Japan Society Technology Plasticity, 1967, 8(79):414-422.
【3】SAH J P,RICHARDSON G J,SELLARS C M.Recrystallization during hot deformation of nickel[J]. Journal of the Australian Institute, 1969, 14(4):292-297.
【4】JOHNSON G R,COOK W H.A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures[C]//Proceedings of the Seventh International Symposium on Ballistics, Hague, Nethedands:[s.n.], 1983.
【5】BERGSTRÖM Y. A dislocation model for the stress-strain behaviour of polycrystalline α-Fe with special emphasis on the variation of the densities of mobile and immobile dislocations[J].Materials Science and Engineering, 1970,5(4):193-200.
【6】ESTRIN Y, MECKING H.A unified phenomenological description of work hardening and creep based on one-parameter models[J].Acta Metallurgica,1984,32(1):57-70.
【7】ZERILLI F J,ARMSTRONG R W. Dislocation-mechanics-based constitutive relations for material dynamics calculations[J].Journal of Applied Physics, 1987,61(5):1816-1825.
【8】FOLLANSBEE P S,KOCKS U F.A constitutive description of the deformation of copper based on the use of the mechanical threshold stress as an internal state variable[J].Acta Metallurgica, 1988,36(1):81-93.
【9】PRESTON D L,TONKS D L,WALLACE D C.Model of plastic deformation for extreme loading conditions[J].Journal of Applied Physics, 2003,93(1):211-220.
【10】SELLARS C M, MCTEGART W J. On the mechanism of hot deformation[J].Acta Metallurgica,1966,14(9):1136-1138.
【11】LAASRAOUI A,JONAS J J. Prediction of steel flow stresses at high temperatures and strain rates[J].Metallurgical Transactions A, 1991,22(7):1545-1558.
【12】CABRERA J M,AL OMAR A,PRADO J M,et al. Modeling the flow behavior of a medium carbon microalloyed steel under hot working conditions[J].Metallurgical and Materials Transactions A, 1997,28(11):2233-2244.
【13】CAO J R, LIU Z D,CHENG S C,et al. Constitutive equation models of hot-compressed T122 heat resistant steel[J]. Journal of Iron and Steel Research,International,2012,19(6):53-58.
【14】VILELA J J,BARBOSA R.Prediction of stress-strain curves of hot deformed IF austenite[J].ISIJ International, 2002,42(3):319-321.
【15】JONAS J J, QUELENNEC X, JIANG L, et al. The Avrami kinetics of dynamic recrystallization[J].Acta Materialia, 2009, 57(9):2748-2756.
【16】QUELENNEC X,JONAS J J.Simulation of austenite flow curves under industrial rolling conditions using a physical dynamic recrystallization model[J].ISIJ International, 2012,52(6):1145-1152.
【17】BAMMANN D J, CHIESA M L, JOHNSON G C. A state variable damage model for temperature and strain rate dependent materials[C]//Constitutive Laws:Theory, Experiments and Numerical Implementation. Mauna Lani, Hawaii:[s.n.], 1995.
【18】ROWN A A,BAMMANN D J.Validation of a model for static and dynamic recrystallization in metals[J].International Journal of Plasticity, 2012,32/33:17-35.
【19】BROWN S,KIM K,ANAND L.An internal variable constitutive model for hot working of metals[J].International Journal of Plasticity, 1989,5(2):95-130.
【20】PRASAD Y, RAO K P. Influence of oxygen on rate-controlling mechanisms in hot deformation of polycrystalline copper:Oxygen-free versus electrolytic grades[J]. Materials Letters,2004,58(14):2061-2066.
【21】PRASAD Y, RAO K P. Kinetics of high-temperature deformation of polycrystalline OFHC copper and the role of dislocation core diffusion[J]. Philosophical Magazine, 2004, 84(28):3039-3050.
【22】PRASAD Y, RAO K P. Kinetics and dynamics of hot deformation of OFHC copper in extended temperature and strain rate ranges[J]. Materials Research and Advanced Techniques,2005, 96(1):71-77.
【23】PUCHI-CABRERA E S, GUÉRIN J D, DUBAR M, et al. A novel approach for modeling the flow stress curves of austenite under transient deformation conditions[J]. Materials Science and Engineering:A, 2016, 673:660-670.
相关信息
