Adiabatic Shear Localization and Phase Transformations in Ferrous Metals: Limit Analysis and Approximate Analytical Solutions

Author(s):

John D. Clayton

Abstract:

Adiabatic shear banding is analyzed in viscoplastic solids that may undergo structural transformations driven by pressure, shear stress, temperature, and magnetic field. Transformations can 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. Ranges of constitutive parameters are obtained for which localization to infinite shear strain is possible. The model is used to understand influences of pressure and phase transitions on applied strains for which localization should occur in pure iron (Fe) and a high-strength steel. Results show, among other trends for these 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 the strain hardening or thermal softening tendencies of the transformed phase are sufficiently increased or reduced, respectively. An appendix reports new calculations on effects of magnetic field for transformation thresholds in a heat-treated alloy tested at the DEVCOM Army Research Laboratory. Uniaxial strain and simple shear are considered. A previously overlooked constraint on transformation kinetics is explained.