Localization in rate-dependent shearing deformation, with application to torsion testing

In discussions on the localization of plastic deformation in situations such as the formation of "ductile" shear zones, it is commonly conjectured that strain softening, as evidenced by a falling stress-strain curve at constant strain rate, is likely to lead to strain localization in simple shear. Yet observations in torsion tests at constant twist rate on calcite and olivine aggregates fail to show such an effect. This apparent discrepancy is resolved by going to a continuum mechanics analysis using the theory of Fressengeas and Molinari (J. Mech. Phys. Solids 1987, 35, 185-211) for material showing strain-rate dependence of the flow stress. Their treatment of simple shear shows that, in the absence of material changes, whether localization occurs or not can depend on the nature of the boundary conditions. Thus, when the boundary conditions are specified in terms of displacements, no localization is predicted in case of strain softening, in agreement with the torsion test observations. In contrast, if the boundary conditions are set in terms of forces, localization can be expected for a strain-softening material. This prediction needs experimental testing in torsion creep tests at constant torque.