Analysis of Plastic Flow Through Inclined Planes in Plane Strain

Abstract

A wide strip of thickness t0 is pulled or extruded through inclined planes converging with semiangle α and exit gap tf . While passing through the die, the thickness of the strip changes from t0 to tf , its length increases, but no change occurs in its width. A kinematically admissible velocity field is assumed to describe the flow. The expected distorted grid pattern is studied. Strain and strain rate fields are analyzed. Effective strain and effective strain rate distributions and their averages are defined. The same velocity field is utilized to obtain an upper-bound solution for the drawing and extrusion forces. Maximum reductions possible are predicted and the optimal included angle between the planes, required to minimize the forces, is evaluated. Formation and prevention of a dead zone are indicated. The analytical results are compared with other solutions and with published experimental data, where the independent variables are: Thicknesses t0 and tf , semiangle of the die α, friction (m), and flow stress of the material.