Microstructures in thermoelastic martensites

This thesis studies microstructures in crystalline solids which undergo thermoelastic martensitic transformations. Such structural transformations are displacive, reversible, and occur between a high temperature, high symmetry parent phase called austenite and a low temperature, low symmetry product phase called martensite. There are multiple symmetry related configurations of the martensite and these are called variants. Microstructures are geometric arrangements of the phases, and they provide mechanisms by which the transformation takes place. The transformation can be induced by either a change in temperature or application of stress giving rise to the shape memory effect and superelastic behavior, respectively.; The tool used to construct microstructures is a geometrically nonlinear theory of martensite. This theory views microstructure to result from energy minimization and strain compatibility. The microstructures considered are; twinned martensite, parallelogram, austenite-martensite, wedge, triangle, and diamond. The first two involve only martensite variants, while the remainder involve both phases. Furthermore, the wedge, triangle, and diamond (the special microstructures) are of interest because they provide a mechanism that allows the transformation to begin.; Specifically, for the twinned martensite microstructures, the twin shears and twin planes along with the corresponding twinning elements are found, and it is shown that there are twins related by a symmetry transformation. Parallelogram microstructures seen in twin crossings are also constructed with four variants. Additionally, austenite-martensite microstructures are studied with both a single variant of martensite and twinned martensite coexisting with austenite. A symmetry exists amongst various austenite-martensite microstructures with different variants, and this symmetry is exploited to show that the special microstructures are possible only with specific lattice parameters. Further, the symmetry provides a method by which all possible realizations of a given microstructure can be enumerated and organized. All of these microstructures are constructed for the cubic to trigonal, the cubic to tetragonal, and a cubic to orthorhombic transitions in general, and for a cubic to monoclinic transition in a Ti-Ni shape memory alloy in particular. Comparisons between theoretical predictions and experimental observations are also given. Lastly, microstructures are constructed and compared to those observed in specimens of a Cu-Al-Ni shape memory alloy under tension.