Ductile fracture in sheets under transverse strain gradients

The fully plastic fracture of a metal sheet subjected to a small transverse gradient of tensile strain near a reinforcement is modeled as mode I fracture under transverse plane strain (TPS). Necking and fracture were analyzed by assuming that they were set by prior uniform strains and then necking displacements. Equations for the spreading of TPS necking and fracture were thus derived for a sheet with strain gradient. Experiments on tapered specimens confirmed the expected fracture displacements within 12 percent, but Moiré studies suggest the agreement may be fortuitous. In any event, in-plane transverse displacements and normal strains in the crack growth direction, as well as shear strains, were negligible. This should simplify any future numerical analysis.