Martensite crystallography—The role of the shape strain

Abstract

The most significant characteristic of a martensitic transformation is the macroscopic change in shape of the region transformed—the shape strain. This results in a strain energy that opposes the transformation. The strain energy associated with a martensitic transformation can be calculated using the Eshelby equations for the strain energy of an oblate spheroid. The first aspect of the shape strain discussed in the paper is the reduction in the strain energy that results from the imposition of an appropriate applied stress—the familiar phenomenon of stress-induced martensitic transformation. An improved model for transformation toughening, which is based on using knowledge of the shape strain to calculate the characteristics of a stress-induced transformation, is described. The shape strain also dominates the crystallographic theories of the martensite transformation via the invariant plane strain concept that forms the basis of the very successful phenomenological theory of martensitic transformations (PTMT) developed just over half a century ago. This occurs when the transformed ellipsoid is infinitely thin (thickness to radius ratio t/ R = 0) and effectively ignores the surface energy of the interface. The paper explores the consequences of allowing the t/ R ratio to become finite and including a surface energy term. The analysis shows how this may be able to account for some of the characteristics of ferrous martensite that have, up to now, eluded explanation using the PTMT.