title: A theoretical investigation of orientation relationships and transformation strains in steels.
abstract: The identification of orientation relationships (ORs) plays a crucial role in the understanding of solid phase transformations. In steels, the most common models of ORs are the ones by Nishiyama-Wassermann (NW) and Kurdjumov-Sachs (KS). The defining feature of these and other OR models is the matching of directions and planes in the parent face-centred cubic γ phase to ones in the product body-centred cubic/tetragonal α/α' phase. In this article a novel method that identifies transformation strains with ORs is introduced and used to develop a new strain-based approach to phase-transformation models in steels. Using this approach, it is shown that the transformation strains that leave a close-packed plane in the γ phase and a close-packed direction within that plane unrotated are precisely those giving rise to the NW and KS ORs when a cubic product phase is considered. Further, it is outlined how, by choosing different pairs of unrotated planes and directions, other common ORs such as the ones by Pitsch and Greninger-Troiano can be derived. One of the advantages of our approach is that it leads to a natural generalization of the NW, KS and other ORs for different ratios of tetragonality r of the product body-centred tetragonal α' phase. These generalized ORs predict a sharpening of the transformation textures with increasing tetragonality and are thus in qualitative agreement with experiments on steels with varying alloy concentration.
authors.affiliation: Department of Mathematics, University of Sussex, Pevensey 2 Building, Brighton, England.
authors.forename: K
authors.initials: K
authors.lastname: Koumatos
authors.affiliation: Department of Civil Engineering, Davis Hall, University of California Berkeley, Berkeley, USA.
authors.forename: A
authors.initials: A
authors.lastname: Muehlemann
keywords: Bain; Greninger–Troiano; Kurdjumov–Sachs; Nishiyama–Wassermann; Pitsch; f.c.c. to b.c.c. transformations; f.c.c. to b.c.t. transformations; inverse Greninger–Troiano; orientation relationships; ratio of tetragonality; steel; transformation strains