A simplified analysis of the effect of microstructure gradient on the stress relief of aluminum plates and extrusions

Many bulk forms of metal products are quenched after heat treatment in order to preserve material characteristics. Rapid quenching results in large thermal stress gradients that lead to high levels of residual stress. For products such as plates and extrusions, stretching by a few percent can reduce these stresses, but the stresses are not completely relieved. This report presents a simplified analytical model of the stress relief process illustrating the effects of through-thickness property gradients on residual stress after stretching. The basic conclusion is that for plates with uniform yield surface shapes through the thickness, the through-thickness residual stress range after stress relief is equal to the strength range in the direction of stretch. In extrusions, the bow after stress relief is proportional to this strength range. Cases are also considered in which the yield surface shapes range from isotropic to anisotropic through the thickness. Plastic anisotropy can perturb the effect of strength range on residual stress.