Analysis of stress-induced phase transformations in elastoplastic materials with strain-softening behavior under plane shear

Possible two-phase piecewise-homogeneous deformations in elastoplastic materials with strain-softening behavior under plane shear are analyzed. Discontinuities of stress and deformation gradient across interfaces between phases are considered and continuity of traction and displacement across interfaces and the Maxwell relation is imposed. The governing equations are obtained. The analysis is reduced to finding a minimum value of the loading at which governing equations have a unique, real, physically acceptable solution. It is found that for a plate with constant thickness under plane shear two-phase piecewise-homogeneous deformations are possible, and the Maxwell stress, the stresses and strains in both phases, the jumps of stress and deformation gradient across interfaces and the inclination angle of the localized deformed band can all be determined. As an illustration, a NiTi alloy plate under plane shear is numerically analyzed. The inclination angle of the martensite band is predicted to be 90 , and this predicted value can be applied to explain why no locally deformed spiral martensite band was observed in experiments on thin-walled NiTi alloy tubes under torsion.