An Analysis for Plane Strain Plastic Deformation in Metal-Working Process

Abstract

The two-dimensional plane strain equation of large plastic flow, expressed in terms of the stream function gradients, is modified using complex variables. The resulting governing equation is solved analytically for a class of nonlinear materials whose stress-strain rate behavior can be expressed by σ̄ = cē̇m . A one-to-one correspondence between the plastic flow equation using the Levy-Mises constitutive relations and the Navier-Stokes equation of fluid flow with zero inertia term is established for constant λ̇. This correspondence allows the existing fluid dynamic solution to be used for the plasticity analysis. An analytical solution of plane strain extrusion of linear material through square-cornered die is presented to illustrate the procedure.