Finite element analysis of phase transformation dynamics in shape memory alloys with a consistent Landau-Ginzburg free energy model
Mahapatra, D.R. and Melnik, R.V.N.
Mechanics of Advanced Materials and Structures, 13 (6), 443-455, 2006
The Landau theory of phase transition has been successfully applied to solve a number of important problems in the dynamics of martensitic phase transformations in alloys. On the other hand, although a precise mathematical description of the microstructures is known within the framework of Cauchy-Born hypothesis, its discrete version is not well elucidated in the literature, especially for multivariant transformations in three-dimensional samples. A major reason for such a situation lies with computational difficulties connected with quasi-convexity of the associated minimization problem. In this paper we develop a Landau-Ginzburg free energy model for dynamic problems of phase transformations and show a possible link of the developed framework with the continuum description of phase transformations. We demonstrate how the precise description of compatible microstructures in the phase-field model can be used in computational finite element models. The developed framework is sufficiently general to be applied to different types of phase transforming alloys and under general thermo-mechanical loadings. We exemplify the developed technique and its finite element implementation on cubic to tetragonal transformations.