Analysis of Shear Banding in Plane Strain Compression of a Bimetallic Thermally Softening Viscoplastic Body Containing an Elliptical Void

Abstract

We study plane strain thermomechanical deformations of a prismatic viscoplastic body of square cross-section and deformed at a nominal strain-rate of 5000 s−1. The body has two thin layers placed symmetrically about the horizontal centroidal axis and an elliptical void at the center. The major axis of the void coincides with the vertical centroidal axis and also with the direction of loading. The layer material differs from that of the body in only the value of the yield stress in a quasistatic simple compression test. The yield stress for the layer material is taken to be either one-fifth or five times that of the matrix material. The deformations are assumed to be symmetrical about the vertical and horizontal centroidal axes. It is found that in each case shear bands initiate from points on the traction free edges where the matrix/layer interfaces intersect them and propagate into the softer material. For the soft layer these bands initially merge into one and propagate horizontally. Subsequently, each of these bands bifurcates into two which propagate into the matrix material along the direction of the maximum shear stress. There is minimal interaction between these bands and those initiating from points slightly away from the void tips. These latter bands pass through the soft layer rather easily. When the layer material is harder than the matrix material, the material in the first quadrant is eventually divided into five subregions each of which is deforming virtually rigidly and the velocity suffers a sharp jump across the boundaries between these regions.