Shear Transformation Zone (STZ) plasticity analysis of constrained shear

Abstract The response in constrained shear of materials characterized by discrete Shear Transformation Zone (STZ) plasticity is investigated. A plane strain strip of finite thickness is analyzed within a small deformation framework and with the STZs modeled as Eshelby inclusions in an isotropic elastic solid. The strip is unbounded and consists of periodic unit cells in the shear direction. Within each unit cell, potential STZ sites are randomly distributed with a specified density and with randomly distributed critical values of shear strain energy density for STZ activation. For both a narrow and a broad distribution of values of critical shear strain energy density, the maximum shear stress is essentially independent of cell geometry but the post-maximum stress–strain response can vary with the geometry and size of the unit cell. The distribution of critical values of STZ shear strain energy density plays a key role in determining the post-maximum stress–strain response, with the post stress maximum shear stress dropping sharply for a narrow distribution of values of critical shear strain energy density and more gradually for a broader distribution of values of critical shear strain energy density. The deformation mode involves bands of enhanced shear strain that are nearly uniformly spaced for a narrow distribution of values of critical shear strain energy density, while for a broad distribution of values of critical shear strain energy density, the band spacing is more irregular. Within the bands the Mises effective stress magnitude can exceed the theoretical strength estimate E ∕ 10 .