Defect-induced incompatibility of elastic strains: dislocations within the Landau theory of martensitic phase transformations

TL;DR

This paper investigates how dislocations induce elastic strain incompatibility in martensitic materials, affecting microstructure evolution through long-range interactions and stress fields, using a Landau theory framework.

Contribution

It introduces a self-consistent model linking dislocation density and elastic order parameter evolution, incorporating incompatibility effects into the Landau energy functional.

Findings

Dislocations cause elastic strain incompatibility proportional to Nye tensor gradients.

Incompatibility leads to additional long-range energy contributions and stress fields.

Dislocation effects influence microstructure, such as twinned domain walls in Fe-Pd alloys.

Abstract

In dislocation-free martensites the components of the elastic strain tensor are constrained by the Saint-Venant compatibility condition which guarantees continuity of the body during external loading. However, in dislocated materials the plastic part of the distortion tensor introduces a displacement mismatch that is removed by elastic relaxation. The elastic strains are then no longer compatible in the sense of the Saint-Venant law and the ensuing incompatibility tensor is shown to be proportional to the gradients of the Nye dislocation density tensor. We demonstrate that the presence of this incompatibility gives rise to an additional long-range contribution in the inhomogeneous part of the Landau energy functional and to the corresponding stress fields. Competition amongst the local and long-range interactions results in frustration in the evolving order parameter (elastic) texture. We show how the Peach-Koehler forces and stress fields for any distribution of dislocations in arbitrarily anisotropic media can be calculated and employed in a Fokker-Planck dynamics for the dislocation density. This approach represents a self-consistent scheme that yields the evolutions of both the order parameter field and the continuous dislocation density. We illustrate our method by studying the effects of dislocations on microstructure, particularly twinned domain walls, in an Fe-Pd alloy undergoing a martensitic transformation.