Deformation of Hierarchically Twinned Martensite

Shape-memory alloys deform via the reorganization of a hierarchically twinned microstructure. Twin boundaries themselves present obstacles for twin boundary motion. In spite of a high density of obstacles, twinning stresses of Ni–Mn–Ga Heusler alloys are very low. Neither atomistic nor dislocation-based models account for such low yield stresses. Twinning mechanisms are studied here on a mesoscopic length scale making use of the disclination theory. In a first approach, a strictly periodic twin pattern containing periodic disclination walls with optimally screened stress fields is considered. Strict periodicity implies that the twin microstructure reorganizes homogeneously. In a second approach, a discontinuity of the fraction of secondary twins is introduced and modeled as a disclination dipole. The stress required for nucleation of this discontinuity is larger than the stress required for homogeneous reorganization. However, once the dipole is formed, it can move under a much smaller stress in agreement with experimental findings.