Compatibilities and supercompatibility conditions in shape memory alloys determined from correspondence, metrics and symmetries

Abstract

The phenomenological theory of martensite crystallography (PTMC) developed in the 1950s explains the main crystallographic and microstructural features of martensite in shape memory alloys, such as the habit planes of bi-variant laminate martensite product, and the transformation twins between the variants. It also permits to determine the austenite and martensite lattice parameters that allow supercompatibility, which has driven important research and development of new shape memory alloys with low hysteresis and high cyclability. Supercompatibility takes the form of three mathematical equations called cofactor conditions. The calculations are in great part based mathematical tools from continuum mechanics (polar decompositions and stretch tensors). They were recently replaced by pure crystallographic tools (metric tensors, group of symmetries and correspondence) in an alternative approach called correspondence theory (CT). The CT allows for the direct calculation of the transformation twins and their generic and non-generic characteristics. These twins ensure the compatibility at martensite/martensite (M/M) junction planes. Here, we show that the CT can also be used to determine the conditions of austenite/martensite (A/M) compatibility, and A/M/M supercompatibility.