Slip-Line Solutions for Plain-Strain Indentation of Sandwich Metal Strips Between Flat Dies

Abstract

The method of slip-lines has been used historically to solve two-dimensional problems of plane-strain plasticity in homogeneous metals. The application of the theory to obtain solutions for sandwich metals consisting of a hard core and softer clad is described here. The behavior of stress components, strain rate components, and velocity discontinuities at the interface between the two metals is examined. Some slip-line solutions for incipient plastic flow due to indentation of a sandwich strip with flat dies are presented. Three modes of deformation are considered: full penetration of the plastic zone with lateral motion of the rigid overhangs, bulging with clad flow only, and bulging with flow of clad and core. The numerical construction of the slip-line fields and hodagraphs is described and some results given. The differences between these results and the results of using homogeneous theory with an average yield strength are shown to be significant for strips of intermediate clad fraction. In addition, the results show that bulging, rather than full penetration of the plastic zone, is the expected mode of deformtion for a wide range of the strip parameters.