Substantiation of Experimentally Observed Self-Accommodation Complexes of Martensite Crystals in Alloys with Shape Memory Effects

Abstract

This paper presents an algorithm for analyzing the possibility of the formation of self-accommodation complexes of martensite crystals in alloys with shape memory effects with consideration for twinning and minimization of the strain averaged over a corresponding set of domains. It has been shown that complete self-accommodation is possible only in the complexes that simultaneously contain all the orientation relationship variants. The calculation performed for the case of rhombohedral martensite (four possible orientation relationship variants) has demonstrated that there is no average shape strain in the four domains. The thus-formed four-domain complex incorporates all the possible variants of the orientation relationship and, for this reason is a self-accommodation complex. Such complexes have been repeatedly observed in titanium nickelide alloys. The analysis of monoclinic 18R-martensite shows that complete self-accommodation can be attained only in the complex of 12 different domains. The experimentally observed four-domain complexes in the Cu—Al—Ni and Cu—Al—Mn alloys can be explained by partial self-accommodation, which takes the exposure of a martensite crystal on the outer surface of a crystal into account.