Low volume-fraction microstructures in martensites and crystal plasticity

TL;DR

This paper analyzes microstructure formation in materials science, focusing on phase diagrams and the emergence of a new intermediate phase in martensites and crystal plasticity at low volume fractions.

Contribution

It introduces a novel phase characterized by partial branching, expanding understanding of microstructure patterns in shape-memory alloys and crystal deformation.

Findings

Determines energy scaling laws for microstructures.

Identifies a new intermediate phase with partial branching.

Characterizes the phase diagram at small volume fractions.

Abstract

We study microstructure formation in two nonconvex singularly-perturbed variational problems from materials science, one modeling austenite-martensite interfaces in shape-memory alloys, the other one slip structures in the plastic deformation of crystals. For both functionals we determine the scaling of the optimal energy in terms of the parameters of the problem, leading to a characterization of the mesoscopic phase diagram. Our results identify the presence of a new phase, which is intermediate between the classical laminar microstructures and branching patterns. The new phase, characterized by partial branching, appears for both problems in the limit of small volume fraction, that is, if one of the variants (or of the slip systems) dominates the picture and the volume fraction of the other one is small.