Martensitic phase transformations (PTs) play a very important part in material science, being responsible for formation of unique

microstructure, mechanical properties, and material phenomena in steels, shape memory alloys and ceramics. In particular, surface-induced PTs and pretransformations, surface energy, surface tension, interface, and scale effect at the nanoscale play essential roles in thermodynamics, kinetics, and nanostructures. In addition, various material phenomena are related to the interaction of martensitic PTs and plastic deformation due to twinning and dislocations and are of fundamental and technological importance. Examples are: heat and thermomechanical treatment of material to obtain desired structure and properties; pseudoelasticity, pseudoplasticity, shape memory effect; transformation-induced plasticity (TRIP); and synthesis of materials under high pressure with large plastic deformations, e.g., during ball milling; and PTs during friction, surface treatment, and projectile penetration. The two main approaches to study martensitic PTs are the sharp interface approach (SIA) and the phase field approach (FPA). In the SIA, the interface between two phases is considered as a single surface across which there is a jump in all thermomechanical properties. In contrast, in the FPA, the interface has a finite width across which properties smoothly vary from one phase to another. Each phase is shown by an order parameter which varies from 0, corresponding to austenite (A), to 1, corresponding to martensite (M).

The PFA is broadly used to study the martensitic PTs, however the current FP models cannot describe a lot of basic physics. In our work, we advanced the PFA to martensitic PTs in three important directions: the potential is developed that introduces the surface tension at interfaces; a mixed term in gradient energy is introduced to control the martensite-martensite interface energy independent of that for austenite-martensite; and a noncontradictory expression for variable surface energy is suggested. The problems of surface-induced pretransformation, barrierless multivariant nucleation, and the growth of an embryo in a nanosize sample are solved to elucidate the effect of the above contributions. Also, an in-detail study of

M-M interface width, energy, and surface tension, as well as the effect of finite element discretization on the width and the energy, and the formation of martensitic nanostructures in the trasnforming grain is presented. In addition, the external surface layer, as a new key parameter in surface-induced PTs, is introduced in PFA, and the effect of the width of this layer and internal stresses on surface-induced pretransformation and PTs is revealed.

In addition to study martensitic PTs using FPA, we used FPA to study dislocations evolution. The current PFA to dislocations, which is based on a formalism similar to the PFA for martensitic PTs, suffers from several main drawbacks. In our work, the PF theory to dislocations is conceptually advanced in the following directions: (a) Large strain formulation is developed. (b) A new local potential is developed to eliminate stress-dependence of the Burgers vector and to reproduce desired local stress-strain curve, as well as the desired, mesh-independent, dislocation height for any dislocation orientation. (c) A new gradient energy is defined to exclude localization of dislocation within height smaller than the prescribed height but does not produce artificial interface energy and dislocation widening.

After developing the most advanced PFA to PTs and dislocations, we developed a new PF theory to coupled evolution of PTs and dislocations and the following problems of the interaction of PTs and dislocations are studied: hysteretic behavior and propagation of A-M interface with incoherency dislocations for temperature-induced PT; evolution of phase and dislocation structures for stress-induced PT, and the growth and arrest of martensitic plate for temperature-induced PT.