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

Shape memory alloys change crystal structure during cooling and heating, producing martensite variants that must fit together at interfaces. Compatibility at these interfaces is important for reducing hysteresis and improving cycling performance. The abstract describes how the phenomenological theory of martensite crystallography (PTMC) uses cofactor conditions to identify “supercompatibility,” which supports low-hysteresis, high-cyclability alloys. It also notes that an alternative approach, correspondence theory (CT), has recently replaced some continuum-mechanics tools with crystallographic tools like metric tensors and symmetry groups. Here, the authors report that CT can be used not only to determine transformation twins that ensure martensite/martensite compatibility, but also to determine conditions for austenite/martensite compatibility and austenite/martensite/martensite (A/M/M) supercompatibility.