Why do the solutions of the habit plane of lath martensite converge? —An application of decomposition of the transformation displacement field

Abstract

The decomposition of the total displacement field is an alternative approach to the separation of a transformation strain. The analytical relationship between the vector elements in the decomposed displacement field is clearer than the one implied in the double shear version of the PTMC. According to this relationship, we conclude that the habit plane depends only on the orientation relationship for all lattice invariant shear systems suggested by Kelly [3]. Based on the reciprocal principle of vector elements in the shear fields and the construction of the p-unit cell we have analyzed the effect of rotation of a pair of faces of the p-unit cell, p 2′, on other vector elements and the total displacement field. We have demonstrated that the condition that the transformation displacement associated with [1 1−1] bcc is parallel to [−1 1 1] bcc (i.e., TAd 2 //- Ad 3) is the key reason for the convergence of the habit plane; in this condition rotations of p 2′ do not affect the total displacement field. For a selected set of shear planes p 3′, the above condition is satisfied only for a particular orientation relationship. For this orientation relationship, the solutions of the habit plane appear to converge while other elements can still be variable. The present analytical conclusions are completely consistent with the numerical results reported by Kelly [3].