Modeling magnetoelasticity and magnetoplasticity with disconnections and disclinations

The magneto-mechanical properties of magnetic shape-memory alloy single crystals depend strongly on the twin microstructure which is established during the martensitic transformation, and through thermo-magneto-mechanical training. For self-accommodated martensite, twin thickness and magnetic-field-induced strain are very small. For effectively trained crystals, a single twin may comprise the entire sample and magnetic-field-induced strain reaches the theoretical limit. Furthermore, the deformation of self-accommodated martensite is pseudo-elastic (magnetoelasticity) while the deformation of effectively trained crystals is plastic (magnetoplasticity). Twin microstructures of self-accommodated martensite were modeled using disclinations which are line defects such as dislocations, however with a rotational displacement field. The defect structure was approximated in a quadrupole solution where two quadrupoles represent an elementary twin double layer unit. The twin boundary was inclined to the twinning plane which required the introduction of twinning disconnections. 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 is sensitive to the initial configuration indicating that disconnection nucleation is controlling the magneto-mechanical properties of self-accommodated martensite.