A three-dimensional sharp phase front -based theory and application to shape memory alloy wires and thin films

This dissertation presents a complete theoretical framework for a three-dimensional (3D) sharp phase front-based model for phase transformations in shape memory alloys. The phases of austenite and martensite are taken to be separated by a phase front, and the phase transformation is taken to occur when the phase front moves. The usual balance laws (for conservation of mass, linear momentum and energy) are written for the bulk phases and the interface. Equality of the chemical potential at the interface leads to a generalized formulation of the Clausius-Clapeyron equation, which then gives the condition for the evolution of the interface during phase transformation. The theoretical framework is general enough to incorporate any Helmholtz free energy function. Specific results are then given in the context of the quasistatic, small strain approximation and a trilinear Helmholtz free energy function.

The developed theoretical framework was used to model the phase transformations in SMA thin wires (1D) and thin films (2D). In both studies the predictions of the theory were calculated and compared with available experimental data. The obtained results demonstrate the ability of the suggested theory to adequately model different types of phase transformations in SMA (pseudoelasticity, shape memory effect and reorientation). The simulations were performed by applying two separate numerical algorithms, developed for solving 1D and 2D problems of phase transformations in SMA. A moving boundary finite element method (MBFEM)-based numerical approach was proposed to solve one-dimensional (1D) thermomechanical problem. The Newton-Raphson method and recursive iterations, respectively, are used to address the non-linearity and coupling in the system of equations. In two dimensions, the 2D finite element-based method implements a front tracking, which is realized by mesh update at each time step. Nonoscillatory interpolation (SuperBee) was used to transfer data between the “old” and the “new” mesh.