基于不可逆热力学的Ni-Ti合金动态本构模型及其有限元实现
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摘要
为了准确描述Ni-Ti形状记忆合金在高应变率下的动态压缩力学行为,基于不可逆热力学理论框架假定了两个内变量表征Ni-Ti合金应力诱发马氏体相变与塑性屈服的不可逆变形过程,分别推导了马氏体相变与塑性屈服演化规律的主控方程,构建了Ni-Ti合金的三维动态本构模型。根据材料单轴动态压缩实验的应力-应变曲线并采用最小二乘法对本构参数进行了优化识别,然后采用应力补偿更新算法,通过隐式用户子程序接口UMAT将动态本构模型嵌入ABAQUS有限元软件,实现了Ni-Ti合金在高应变率下动态压缩力学行为的数值模拟。通过比对发现,模拟结果与实验数据吻合良好,验证了动态本构模型与UMAT子程序的准确性。本工作为Ni-Ti合金在高速冲击、切削等极端条件下的工程应用奠定了基础。
In order to actually describe the mechanical behaviourof Ni-Ti shape memory alloys(SMAs) subjected to high strain rate, the master equations which based on irreversible thermodynamics theory is derived by assuming two internal variables to characterize stress-induced martensitic transformation evolution and plastic evolution. Thus a three-dimensional dynamic constitutive model is developed by summarizing master equations of phase transformation and plasticity in the loading process of Ni-Ti alloy. Adopting a stress compensation updating algorithm to update inelastic strain increment, the phenomenological-based constitutive model is embedded into ABAQUS finite element software through user subroutine UMAT with FORTRAN code. Numerical simulation of dynamic responses of Ni-Ti alloy under high strain rate is successfully implemented. The numerical simulation results are in good agreement with experimental data so that the proposed model validation is conducted. The results show that the proposed model not only can describe well the different deformation stage of Ni-Ti alloy but also the constitutive behavior subjected to different strain rates. And it provides the basis for the practical application of Ni-Ti alloy in the condition of impact and high speed cutting.
In order to actually describe the mechanical behaviourof Ni-Ti shape memory alloys(SMAs) subjected to high strain rate, the master equations which based on irreversible thermodynamics theory is derived by assuming two internal variables to characterize stress-induced martensitic transformation evolution and plastic evolution. Thus a three-dimensional dynamic constitutive model is developed by summarizing master equations of phase transformation and plasticity in the loading process of Ni-Ti alloy. Adopting a stress compensation updating algorithm to update inelastic strain increment, the phenomenological-based constitutive model is embedded into ABAQUS finite element software through user subroutine UMAT with FORTRAN code. Numerical simulation of dynamic responses of Ni-Ti alloy under high strain rate is successfully implemented. The numerical simulation results are in good agreement with experimental data so that the proposed model validation is conducted. The results show that the proposed model not only can describe well the different deformation stage of Ni-Ti alloy but also the constitutive behavior subjected to different strain rates. And it provides the basis for the practical application of Ni-Ti alloy in the condition of impact and high speed cutting.
引文
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2 Zheng Biyu,Shang Zejin,Wang Zhongmin.Mechanical Science and Technology of Aerospace Engineering,2008,27(9),1236(in Chinese).郑碧玉,商泽进,王忠民.机械科学与技术,2008,27(9),1236.
3 Lagoudas D C,Ravi-Chandar K,Sarh K,et al.Mechanics of Materials,2003,35(7),689.
4 Liu Jinxu,HuDandan,Zheng Xiuhua,et al.Rare Metal Materials and Engineering,2013,42(5),942(in Chinese).刘金旭,胡丹丹,郑秀华,等.稀有金属材料与工程,2013,42(5),942.
5 Tanaka K.Res Mechanica,1986,18,251.
6 Liang C,Rogers C A.Journal of Intelligent Material Systems and Structures,1990,1(2),207.
7 Brinson L C,Lammering R.International Journal of Solids and Structures,1993,30(23),3261.
8 Urbano M F,Auricchio F.Journal of Functional Biomaterials,2015,6(2),398.
9 Lagoudas D C,BoZ.International Journal of Engineering Science,1999,37(9),1141.
10 Lagoudas D C,Shu S G.International Journal of Mechanical Sciences,1999,41(6),595.
11 Auricchio F,Taylor R L.Computer Methods in Applied Mechanics and Engineering,1997,143(1),175.
12 Auricchio F,Taylor R L,Lubliner J. Computer Methods in Applied Mechanics and Engineering,1997,146(3),281.
13 Lubliner J,Auricchio F.International Journal of Solids and Structures,1996,33(7),991.
14 Peng X,Chen B,Chen X,et al.Acta Mechanica Solida Sinica,2012,25(3),285.
15 Saint-Sulpice L,Chirani S A,Calloch S.Mechanics of Materials,2009,41(1),12.
16 Hu Guijuan,Zhang Keshi,Huang Shihong.Journal of Guangxi University (Natural Science),2011,36(1),166 (in Chinese).胡桂娟,张克实,黄世鸿.广西大学学报(自然科学版),2011,36(1),166.
17 Chen Huayan,Chen Cheng,Zeng Xiangguo,et al.Journal of Sichuan University (Engineering Science),2016,48(2),219(in Chinese).陈华燕,陈成,曾祥国,等.四川大学学报(工程科学版),2016,48(2),219.