The crystallography of the (225) F-transformation in steels

Abstract

The set of all strains compatible with a given habit plane is calculated for an arbitrary transformation and resolved into component strains. The assumptions made are those common to all current theories of the crystallographic relationships in martensite transformations together with the assumption that the shape strain distorts the habit plane isotropically, if at all. The theory is specifically applied to those transformations in steel with a habit plane in the neighbourhood of (225) F. Some exact numerical results are given and these are co-ordinated by their relation to the results for a crude but remarkably effective approximation. It is shown that both the directions and the magnitudes of the shape strain and the plane of the complementary shear vary very rapidly with the orientation relationship. By comparison of these results with a preliminary result of a measurement of the direction and magnitude of the shape strain, the proposal that the complementary strain is a simple shear on a, low index plane and in a low index direction is shown to be untenable if the habit plane is distorted isotropically. The experimental results are not yet adequate to exclude the hypothesis that the shear direction is generated from [1−10] F and the shear plane irrational. It is pointed out that the complementary shear could have rational elements if the habit plane were distorted anisotropically.