Elastic interaction energy analysis during twin plane formation in the martensitic transformation process of α"-martensite in Ti-Nb-Al

To understand the twin selection mechanism that occurs in the initial stage of the martensitic transformation of shape memory alloys, the stress state during twin plane formation was numerically analyzed by micromechanics. The self-accommodation microstructure of α''-martensite of the Ti-23Nb-3Al (at%) shape memory alloy, in which the lattice parameter was adjusted to eliminate the formation of internal twinning due to lattice-invariant deformation, was adopted for analysis. The two lattice correspondence variants (CVi and CVj) formed a twin plane. CVi was assumed to be spheroid, and the elastic strain energy during twin plane formation was evaluated by analyzing the elastic interaction energy when CVj formed around CVi. There are three types of twins ({011}α" compound twin, {111}α" type I twin, and <211>α" type II twin) in the self-accommodation microstructure of α"-martensite. Regardless of the CVi geometry (i.e., aspect ratio (1 to 0.01) and minor axis orientation), the {111}α" type I twin exhibited minimum elastic interaction energy, indicating that minimum elastic strain energy was generated during this twin plane formation. This result is consistent with the experimental results, which showed the selective formation of {111}α" type I twins in the initial stage of martensitic transformation.