A thermodynamically consistent multiphase phasefield approach for stress and temperatureinduced martensitic phase transformation at the nanoscale and under large strains is developed. A total of N independent order parameters are considered for materials with N variants, where one of the order parameters describes A ↔ M transformations and the remaining N − 1 independent order parameters describe the transformations between the variants. A noncontradictory gradient energy is used within the free energy of the system to account for the energies of the interfaces. In addition, a noncontradictory kinetic relationships for the rate of the order parameters versus thermodynamic driving forces is suggested. As a result, a system of consistent coupled GinzburgLandau equations for the order parameters are derived. The crystallographic solution for twins within twins is presented for the cubic to tetragonal transformations. A 3D complex twins within twins microstructure is simulated using the developed phasefield approach and a largestrainbased nonlinear finite element method. A comparative study between the crystallographic solution and the simulation result is presented.
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A multiphase phasefield study of threedimensional martensitic twinned microstructures at large strains
The nanoscale multiphase phasefield model for stress and temperatureinduced 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 noncontradictory model for the same purpose is developed in this paper. The model considers N+1 order parameters to describe austenite and N martensitic variants. One of the order parameters describes austenite↔martensite transformations, and the remaining N order parameters, whose summation is constrained to the unity, describe the transformations between the variants. A noncontradictory 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 strainbased 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.
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 NSFPAR ID:
 10404631
 Publisher / Repository:
 Springer Nature
 Date Published:
 Journal Name:
 Continuum Mechanics and Thermodynamics
 ISSN:
 09351175
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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