Symmetry and microstructure in martensites

Abstract

The shape memory effect and superelastic behaviour occur by the nucleation and growth of microstructure during a thermoelastic martensitic transformation. A constrained geometrically nonlinear theory is used to construct the twinned martensite, austenite-martensite, wedge, triangle, and diamond microstructures. The latter three microstructures are special microstructures, and they are of interest because they provide a mechanism through which the specimen can easily undergo the transformation. In this paper, it is shown that all of the twinning elements can be determined for any given transition, and that the twins are related by a symmetry transformation. Additionally, it is shown that there exists a symmetry amongst solutions to the habit plane equation with different variants, and this symmetry is exploited to show that the special microstructures are possible only for materials with special lattice parameters. This symmetry amongst the solutions provides a method by which all possible microstructures can be enumerated. A specific example of the calculations is given for the cubic to tetragonal transition.