The phenomenological theory of composite martensite part I—The { hhl} habit in steels

Abstract

Recently Lieberman and Bullough reported the development of a theory of martensite which appears to account satisfactorily for the ‘225’ habit in steels, a transformation which has frustrated analysis by the Wechsler-Lieberman-Read and Bowles-Mackenzie phenomenological theories and the equivalent Bullough-Bilby surface dislocation treatment. These theories, which have been so remarkably successful in describing the ‘259’ habit in steels as well as transformations in several nonferrous systems, have been conspiciously unable to account for this ‘225’ type habit even when modified by different systems of invariant plane strain or isotropic—or even anisotropic—distortion in the interface. The new theory incorporates the physical ideas deduced from the observations that martensite plates exhibiting this type of habit are composite, i.e. they consist of twinned and untwinned regions. In this paper the concepts of composite martensite formation are first discussed briefly and then a phenomenological formulation of the theory is developed and applied to a steel for which a { hhl} A habit has been reported. A considerable simplification of the physics and mathematical analysis of composite martensite is effected by a different factorization of the transformation distortion than that of the original L-B theory. Analysis by both the graphical method employed by Lieberman suitably modified to include the additional operations implicit in the model of composite martensite and by computer program are delineated. The discrepancey between the predicted plane of zero average distortion and the experimentally determined habit plane is less than 1° and the calculations of the other crystallographic features are also in general agreement with experiment. When the plates are completely twinned, the general L-B theory, a limiting case of which is considered here, reduces to the original W-L-R treatment for martensite exhibiting the ‘259’ habit and hence, includes it also as a limiting case.