Analytical Shear-Band Process Zone Model Incorporating Nonlinear Viscous Effects and Initial Defects Available to Purchase

Experimental, theoretical, and numerical studies of adiabatic shear in ductile metals suggest initial defects such as pores or material imperfections increase shear-band susceptibility. Conversely, viscous effects manifesting macroscopically as strain-rate sensitivity inhibit localization. The analytical shear-band process zone model by Grady, in turn based on a rigid-plastic solution for stress release by Mott, is advanced to account for these phenomena. The material contains an average defect measure (e.g., porosity) and a concentrated defect measure at a location where shear banding is most likely to initiate after an instability threshold. Shearing resistance and certain physical properties are reduced commensurately with local defect concentration. Non-Newtonian viscosity increases dissipative resistance. Viscous dissipation, if strong enough, prevents an infinitesimal-width shear band even in a nonconductor. Here, a pseudo-quadratic viscosity widens the band similar to heat conduction and akin to quadratic shock viscosity often used to resolve widths of planar shock waves. The model captures simulation data showing reduced localization strain with increasing maximum initial pore size in additively manufactured titanium and HY-100 steel. Predictions for shear-band width, local strain, and temperature are more accurate versus data than prior analytical modeling.