Interaction of Martensitic Microstructures in Adjacent Grains

It is often observed that martensitic microstructures in adjacent polycrystal grains are related. For example, micrographs of Arlt (J Mat Sci 22:2655–2666, 1990) [1] (one reproduced in (Bhattacharya, Microstructure of martensite, 2003) [10, p 225]) exhibit propagation of layered structures across grain boundaries in the cubic-to-tetragonal phase transformation in \( {\text{BaTiO}}_{3} \). 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.