Analysis of shear localization in viscoplastic solids with pressure-sensitive structural transformations

Localization, in the form of adiabatic shear, is analyzed in viscoplastic solids that may undergo structural transformation driven by pressure, shear stress, temperature, and magnetic field. As pertinent to polycrystalline metals, transformations may include solid–solid phase transitions, twinning, and dynamic recrystallization. A finite-strain constitutive framework for isotropic metals is used to solve a boundary value problem involving simple shearing with superposed hydrostatic pressure and constant external magnetic field. Three-dimensional theory is reduced to a formulation simple enough to facilitate analysis without advanced numerical methods, yet sophisticated enough to maintain the salient physics. Ranges of constitutive parameters (e.g., strain hardening, strain-rate sensitivity, thermal softening, and strain-driven structure transformation limits influenced by pressure and magnetic field) are obtained for which localization to infinite shear strain is possible. Motivated by experimental and theoretical studies suggesting a non-negligible role of shear on phase transformations in iron (Fe), the model is used to understand influences of pressure and phase transitions on applied strains for which localization should occur in pure Fe and a high-strength steel. Results show, among other trends for the two materials, that shear localization in conjunction with phase transformation is promoted when the transformed phase is softer than the parent phase. Localization that would occur in the isolated parent phase can be mitigated if strain hardening or thermal softening tendencies of the transformed phase are sufficiently increased or reduced, respectively.