Dynamic Thermo-Mechanical Phase-Field Models for Martensitic Transformations in Shape Memory Alloys

Shape memory alloys (SMAs) exhibit complex microstructures and non-linear hysteretic behaviors that arise from a strong interaction between mechanical and thermal phenomena. It is imperative to couple the thermal physics and the mechanical dynamics to study the influence of such coupling on the mechanical properties of SMA systems, including nanostructures. However, the majority of phase-field models in the literature related to SMAs account for structural physics only. With the aim to incorporate thermal physics, in this thesis, first the 2D and 3D dynamic fully coupled thermo-mechanical phase-field models are developed based on the strain-based order parameters. The developed models are highly nonlinear, strongly hysteretic with fourth-order spatial differential terms, which impose several computational challenges. Secondly, to overcome these computational challenges, a numerical formulation based on the isogeometric analysis is developed for a straightforward solution to the fourth-order differential equations using continuously differentiable non-uniform rational B-splines (NURBS).;Several numerical examples of microstructure evolution in SMA systems, in particular nanostructures of different geometries, under temperature and stress induced loadings illustrated the flexibility, accuracy and robustness of the developed numerical formulation. The numerical simulations revealed a significant impact of the temperature dynamics on mechanical properties of SMAs. The developed models successfully captured experimentally observed mechanical and thermal hysteresis phenomena, local non-uniform phase transformations and corresponding non-uniform temperature and deformations distributions. The predicted microstructure evolution is in qualitative agreement with the results reported in the literature.;The material properties of austenite and martensite phases are different, as observed experimentally during phase transformations. However, the majority of macroscale non-isothermal phase-field models in the literature related to SMAs account only for uniform material properties of different phases. Therefore, the new 1D and 3D macroscale non-isothermal phase-field models incorporating the phase dependent properties are developed in this thesis for a better description of hysteresis phenomena in SMAs. Specifically, the non-linear thermo-mechanical phase dependent material properties are incorporated via the compliance variable as a function of local scalar phase order parameter and stress state. The simplicity of the proposed 1D and 3D non-isothermal phase-field models allowed efficient numerical implementations.