Modeling of branched needle microstructures at the edge of a martensite laminate

We present models of the microstructure of martensite that occurs when twinned layers of martensite meet a pure variant. This microstructure often occurs below the A(s) temperature, with loading that favors the passage from one pure variant of martensite to another. This microstructure gives a mechanism for variant rearrangement. In this microstructure, the layers are observed to pinch down to sharply pointed needles. If the laminate is sufficiently long, branching of the needles is observed. In materials with a reasonably large transformation strain, the needles exhibit a characteristic bent shape; the bending is in the opposite sense as might be expected from the overall shear. Our analytical and numerical results imply that this microstructure forms as a result of energy minimization in the transition layer between the martensite laminate and the pure variant. The bending of the needles plays a key role in lowering the energy of this transition layer.