Mathematics of Crystallographic Texture in Martensitic and Related Transformations

This paper is an introduction to the mathematical estimation of the crystallographic texture and microstructure resulting from the displacive transformation of austenite in steels, under the influence of an externally applied system of stresses. It begins with an introduction to the problem, a description of the phenomenological theory of martensite crystallography, and the application of this theory along with a variant selection criterion to determine the texture due to solid-state, displacive transformation. It is demonstrated that there remain difficulties which make a complete closure between theory and experiment unlikely. Progress is needed in relating the chemical and mechanical driving forces for phase transformation to the evolution of overall volume fractions of different crystallographic variants.