Application of the double-shear theory of martensite crystallography to the β → α′ transformation in an U(Ga) alloy (original) (raw)

1990, Metallurgical Transactions A

The phenomenological double-shear theory of martensite crystallography has been applied to the/3 ~ a' martensitic transformation in the U-1.6 at. pct Ga alloy. A correspondence matrix for the/3 ~ a' transformation was derived from the experimentally determined/3/a' orientation relationship, and the double lattice invariant shear was considered as a combination of the principal slip (010) [100L with one of the minor slips in the a-uranium structure. The theoretical predictions of the habit plane are in good agreement with the experimental observations. I. INTRODUCTION SINCE the first formulation of the phenomenological theory of martensite crystallography based on the concept of an invariant plane strain (IPS), IL21 many investigations have been carried out in an attempt to evaluate the applicability of the theory to various martensitic transformations. In the early theories, the total shape deformation associated with the phase transformation was resolved into a rotation, a pure strain, and a single lattice invariant shear. The single-shear approach proved to be successful in accounting for the crystallographic characteristics of many martensitic transformations; however, the theoretical predictions, in some cases, were not in good agreement with available experimental observations. [31 This stimulated further theoretical work, and a martensite crystallography theory with a double lattice invariant shear was developed. [4.5,6] Although most of the studies focused on application of theories to the martensitic reactions in steels, it was pointed out [71 that the y ~ a' and the/3 ~ a' martensitic transformations in uranium alloys also provide a good opportunity for testing the crystallographic theories of martensite. The first detailed experimental investigation of the martensite in U-5 at. pct Mo alloy was performed by May, ls~ who proposed the correspondence matrix for the y-* a' transformation. Such correspondence, as well as the elements of lattice invariant shear and the lattice parameters of the parent and product, determines the data required to apply the IPS theories. Later, Crocker and Ross [7] discussed May's correspondence, comparing it with that adopted by Christian. [91 They attempted to account for the habit plane in the 3' ~ a' transformation in U-5 at. pct Mo alloy by using for the computation different possible twinning planes and directions as the elements of lattice invariant shear. However, basing their work on the assumption that only one shear system was operative, they failed to obtain a real solution. Speer and Edmonds I~~ have proposed another lattice correspondence for the 3' ~ a' transformation. In their D.