Phase-field theory of adiabatic shear

A geometrically nonlinear framework is constructed for modeling material failure by adiabatic shear. Mechanisms encompassed include nonlinear thermoelasticity pertinent for high-pressure and high-temperature states, dynamic plasticity from combined actions of dislocation glide and twinning, initial and evolving porosity, rotational dynamic recrystallization (DRX), and localized material degradation from softening and ductile fracture. An order parameter of phase-field type accounts for softening mechanisms at a microstructure length scale too small to be resolved in structural mechanics applications. Phase-field regularization sets the finite width of a shear band or ductile crack, analogous to application of phase-field theory for regularizing sharp cracks in brittle fracture. The framework depicts the reduction in resistance to shear banding with (initial) defects or pores, and DRX, in a physically motivated scheme different from prior theory. Model calculations reproduce experimental observations on shear localization and fracture in steel and titanium, the latter with and without initial pores and DRX, under dynamic shear-dominant loading. Further results predict decreased shear stability from void growth under tensile pressure. Compressive pressure increases flow strength, leading to higher temperature and earlier localization in some cases, but later localization in others due to suppressed thermoelastic expansion. Higher loading rates can increase stability due to rate dependence of flow stress, transient phase-field kinetics, and possible inertial effects.