A multiphase phase-field study of three-dimensional martensitic twinned microstructures at large strains
A multiphase phase-field study of three-dimensional martensitic twinned microstructures at large strains
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DOI：
10.1007/s00161-022-01177-6
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发表时间：
2022-06
影响因子：
2.6
通讯作者：
Anup Basak;V. Levitas
中科院分区：
文献类型：
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作者：
Anup Basak;V. Levitas
本文回顾了作者在Basak和Levitas(J Mech Phys Solid 113：162-196,2018)中建立的大应变下应力和温度诱导的多变量马氏体相变的纳米尺度多相相场模型，解决了有序参数的梯度能和耦合动力学方程的问题，并发展了一个热力学上一致的非矛盾模型。该模型考虑了序数参数来描述奥氏体和N马氏体的变种。其中一个序参数描述了奥氏体相变，其余的N阶参数描述了变种之间的相变，其求和被限制为1。在系统的自由能内使用非矛盾的梯度能来解释界面的能量。此外，还提出了有序参数的速率与热力学驱动力之间的动力学关系，从而得到了有序参数的一致耦合Ginzburg-Landau方程组。给出了孪晶内孪晶的近似一般解，并导出了立方到四方相变的显式解。发展了一种求解Ginzburg-Landau和弹性耦合方程的大应变有限元方法，并用它模拟了孪晶组织中的三维复杂孪晶。给出了晶体溶液与模拟结果的对比研究。
The nanoscale multiphase phase-field model for stress and temperature-induced multivariant martensitic transformation under large strains developed by the authors in Basak and Levitas (J Mech Phys Solids 113:162–196, 2018) is revisited, the issues related to the gradient energy and coupled kinetic equations for the order parameters are resolved, and a thermodynamically consistent non-contradictory model for the same purpose is developed in this paper. The model considersorder parameters to describe austenite andNmartensitic variants. One of the order parameters describes austenitemartensite transformations, and the remainingNorder parameters, whose summation is constrained to the unity, describe the transformations between the variants. A non-contradictory gradient energy is used within the free energy of the system to account for the energies of the interfaces. In addition, a kinetic relationship for the rate of the order parameters versus thermodynamic driving forces is suggested, which leads to a system of consistent coupled Ginzburg–Landau equations for the order parameters. An approximate general crystallographic solution for twins within twins is presented, and the explicit solution for the cubic to tetragonal transformations is derived. A large strain-based finite element method is developed for solving the coupled Ginzburg–Landau and elasticity equations, and it is used to simulate a 3D complex twins within twins microstructure. A comparative study between the crystallographic solution and the simulation results is presented.