Influence of dislocations on the spatial variation of microstructure in martensites

TL;DR

This paper develops a mean-field mesoscopic model incorporating dislocation effects into the Landau free energy framework, revealing how dislocations influence microstructure evolution and phase transformations in martensitic materials.

Contribution

It introduces a novel field-theoretical approach that integrates dislocation-induced incompatibilities into microstructure modeling, bridging atomistic and macroscopic scales.

Findings

Dislocations affect microstructure evolution and phase transformation temperatures.

Long-range anisotropic interactions between dislocations are naturally included.

Heterogeneous nucleation of phases is caused by dislocation-induced distortions.

Abstract

The continuum theory of dislocations, as developed predominantly by Kr\"oner and Kosevich, views each dislocation as a source of incompatibility of strains. We show that this concept can be employed efficiently in the Landau free energy functional to develop a mean-field mesoscopic model of materials with dislocations. The order parameters that represent the distortion of the parent phase (often of cubic symmetry) are written in terms of elastic strains which are themselves coupled by incompatibility constraints. Since the "strength" of the incompatibility depends on the local density of dislocations, the presence of dislocations affects the evolution of the microstructure and vice versa. An advantage of this formulation is that long range anisotropic interactions between dislocations appear naturally in the formulation of the free energy. Owing to the distortion of the crystal structure around dislocations, their presence in multiphase materials causes heterogeneous nucleation of the product phase and thus also shifts of the transformation temperature. This novel field-theoretical approach is very convenient as it allows to bridge the gap in studying the behavior of materials at the length and time scales that are not attainable by atomistic or macroscopic models.