Campus Units

Aerospace Engineering, Materials Science and Engineering, Mechanical Engineering, Ames Laboratory

Document Type

Article

Publication Version

Published Version

Publication Date

10-2015

Journal or Book Title

Physical Review B

Volume

92

Issue

14

First Page

144106

DOI

10.1103/PhysRevB.92.144106

Abstract

The main focus of this paper is to introduce, in a thermodynamically consistent manner, an anisotropic interface energy into a phase field theory for phase transformations. Here we use a small strain formulation for simplicity, but we retain some geometric nonlinearities, which are necessary for introducing correct interface stresses. Previous theories have assumed the free energy density (i.e., gradient energy) is an anisotropic function of the gradient of the order parameters in the current (deformed) state, which yields a nonsymmetric Cauchy stress tensor. This violates two fundamental principles: the angular momentum equation and the principle of material objectivity. Here, it is justified that for a noncontradictory theory the gradient energy must be an isotropic function of the gradient of the order parameters in the current state, which also depends anisotropically on the direction of the gradient of the order parameters in the reference state. A complete system of thermodynamically consistent equations is presented. We find that the main contribution to the Ginzburg-Landau equation resulting from small strains arises from the anisotropy of the interface energy, which was neglected before. The explicit expression for the free energy is justified. An analytical solution for the nonequilibrium interface and critical nucleus has been found and a parametric study is performed for orientation dependence of the interface energy and width as well as the distribution of interface stresses.

Comments

This article is published as Levitas, Valery I., and James A. Warren. "Thermodynamically consistent phase field theory of phase transformations with anisotropic interface energies and stresses." Physical Review B 92, no. 14 (2015): 144106. doi:10.1103/PhysRevB.92.144106. Posted with permission.

Copyright Owner

American Physical Society

Language

en

File Format

application/pdf

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