Strain-hardening extrusion—I. Construction of slip-line fields from experimental flow patterns

Abstract

A possible method of solving problems in strain-hardening flows is by perturbation of known perfectly-plastic solutions. It is shown that vertex singularities, which are possessed by most such solutions, are not admissible in steady hardening flows. The structure of regular local solutions, both perfectly-plastic and strain-hardening, is investigated, and it is shown how vertex singularities can be replaced by regular local corner solutions. A scheme for constructing strain-hardening slip-line fields based on experimental flow patterns is described, which uses the maximum shear strain-rate directions calculated from the digitized and smoothed flow pattern to perturb local Hencky-Prandtl nets, which are then patched together in conformity with the topology of the solution to form a complete slip-line field. This method has been implemented in a computer program to construct slip-line fields from flow patterns for extrusion through wedge-shaped dies, and some fields computed by the program are presented.