Finite element method for conserved phase field models: Solid state phase transformations.

摘要

Cahn-Hilliard type of phase field model coupled with elasticity equations is used to derive governing equations for the stress-mediated diffusion and solid state phase transformations. The partial differential equations governing diffusion and mechanical equilibrium are of different orders. A mixed-order finite element formulation is developed, with C0 interpolation functions for displacements, and C1 interpolation functions for the phase field variable---the concentration. Uniform quadratic convergence, expected for conforming elements, is achieved for both one and two dimensional systems.;The developed finite element model (FEM) is used to simulate the nucleation and growth of the intermediate phase in a thin film diffusion couple as one-dimensional (1D) problem and the results are compared with Johnson's finite difference model (FDM). Two-dimensional (2D) simulations are divided into two categories. In the first category, 2D model is applied to study phase transformations of single precipitates in solid state binary systems, and the effects of using complete and incomplete Hermite cubic elements on the transformation rate of systems with isotropic and anisotropic gradient energy coefficients are investigated. In the second category, 2D model is used to study the stability of multilayer thin film diffusion couples in solid state. Maps of transformations in multilayer systems are carried out considering the effects of thickness of layers, volume fraction of films, and compositional strain on the instability of the multilayer thin films. It is shown that at some cases phase transformations and intermediate phase nucleation and growth lead to the coarsening of the layers which can result in different mechanical and materials behaviors of the original designed multilayer.