To Describe the Deformation from DO ₃ Austenite to 18R Martensite in Shape Memory Alloys using Group Theory

Abstract

Martensitic transformation is a first-order diffusionless phase transformation from high-temperature austenite phase to low-temperature martensite phase. In Shape Memory Alloys (SMAs), the lattice structure of austenite has higher order of symmetry than that of martensite. As such, more than one martensite variants may be induced from one austenite. Martensite variants are identical crystal lattice but orient along different directions with regard to austenite. The relationship among these lattice structures is essential for understanding better the mechanism behind the surprising shape memory phenomenon, and furthermore, for modeling the sophisticated thermo-mechanical behavior under various loading conditions. So far significant progress has been made both theoretically (Wechsler et al., 1953, Saburi and Nenno, 1981, Ball and James, 1987, Bhattacharya, 1992, Pitteri and Zanzotto, 1998, Hane, 1999) and experimentally (Saburi et al., 1976, 1980, Saburi and Wayman, 1979, Zhang et al., 1999a, 1999b). It was found that self-accommodation plays an important role in shape recovery. However, a systematic description of lattice relationship and the corresponding deformation are still missing. The purpose of this paper is to present an explicit formula for DO ₃ to 18R martensitc transformation by group theory. This method has been successfully used in the estimation of the deformation energy in martensitic transformation (Zhu et al., 2001). Sections 2 and 3 present the mathematical expression of habit plane variants and the orientation relationship among martensite variants, respectively. Section 4 describes the self-accommodation group.