  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 approximate analytical solutions 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 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.
