Numerical Simulation of Twin-Twin Interaction in Magnetic Shape-Memory Alloys

Twin boundary motion is the mechanism that drives the plastic deformation in magnetic shape memory alloys (MSMAs), and is largely dependent on the twin microstructure of the MSMA. The twin microstructure is established during the martensitic transformation, and can be influenced through thermo-magneto-mechanical training. For self-accommodated and ineffectively trained martensite, twin thickness and magnetic-field-induced strain (MFIS) are very small. For effectively trained crystals, a single crystallographic domain may comprise the entire sample and MFIS reaches the theoretical limit. In this paper, a numerical simulation is presented describing the twin microstructures and twin boundary motion of self-accommodated martensite using disclinations and disconnections (twinning dislocations). Disclinations are line defects such as dislocations, however with a rotational displacement field. A quadrupole solution was chosen to approximate the defect structure where two quadrupoles represent an elementary twin double layer unit. In the simulation, the twin boundary was inclined to the twinning plane which required the introduction of twinning disconnections, which are line defects with a stress field similar to dislocations. The shear stress - shear strain properties of self-accommodated martensite were analyzed numerically for different initial configurations of the twin boundary (i.e. for different initial positions of the disconnections). The shear stress - shear strain curve was found to be sensitive to the initial configuration of disconnections. If the disconnections are very close to boundaries of hierarchically higher twins – such as is the case for self-accommodated martensite, there is a threshold stress for twin-boundary motion. If the disconnections are spread out along the twin boundary, twinning occurs at much lower stress.