Strain localization in the diffuse neck in sheet metal

The onset of diffuse instability in sheet metals is associated with initially small, but grad-ually increasing, changes in the strain rate,e, and in the ratio of the minor to the major principal strains,p = e2/e1in the plane of the sheet. The hardening and softening contri-butions from such changes have been considered to obtain a condition for partial flow sta-biliity in the neck. The effect of the change ine on the uniaxial stress was determined from measurements of e changes in the neck and from the strain rate sensitivity of the materials. Similar evaluation of the change in the axial stress due to a change in p was made by means of an approximate analysis. The combination of these effects, along with the basic strain hardening of the materials, is used to explain the slowness or the rapid-ity of the process of necking in several materials, exhibiting different normal anisotropy, strain hardening and strain rate hardening behaviors. These results can also be used to explain the size of a diffuse neck and the strain distribution within it. Correlation has also been obtained between necking extensions to failure and the forming limits.