Interaction of martensitic microstructures in adjacent grains

TL;DR

This paper investigates how martensitic microstructures in neighboring grains of polycrystals are related, focusing on compatibility conditions at grain boundaries within a nonlinear elasticity framework.

Contribution

It generalizes the Hadamard jump condition to analyze microstructure compatibility across grain boundaries in a nonlinear elasticity model for bicrystals.

Findings

Propagation of layered structures across grain boundaries observed in models.

Compatibility conditions depend on grain orientation and interface geometry.

Theoretical framework explains microstructure relationships in martensitic transformations.

Abstract

It is often observed that martensitic microstructures in adjacent polycrystal grains are related. For example, micrographs of Arlt exhibit propagation of layered structures across grain boundaries in the cubic-to-tetragonal phase transformation in $\rm BaTiO_3$. Such observations are related to requirements of compatibility of the deformation at the grain boundary. Using a generalization of the Hadamard jump condition, this is explored in the nonlinear elasticity model of martensitic transformations for the case of a bicrystal with suitably oriented columnar geometry, in which the microstructure in both grains is assumed to involve just two martensitic variants, with a planar or non-planar interface between the grains.