A work-hardening elastic-plastic wedge

Abstract

The first complete solution to a plane problem of an infinite elastic-perfectly plastic wedge was given by Naghdi [1]. This closed-form solution pertained to the infinitesimal plane strain of an acute wedge under uniform pressure on one of its faces. The wedge material was incompressible and obeyed von Mises’ yield condition and the associated Prandtl-Reuss stress-strain relations. Subsequently, Bland and Naghdi [2] solved this same problem for a compressible elastic-perfectly plastic material obeying Tresca’s yield condition and its associated flow rule. Plane stress solutions to this same problem were given by Naghdi [3] and Kalnins [4]. Wedges of arbitrary opening angle acted on by general uniform surface tractions were treated by Murch and Naghdi [5]. The solutions for all of these plane wedge problems are made tractable by the fact that the components of stress and strain depend only on the angular coordinate in a system of plane polar coordinates. Thus, the elastic-plastic boundaries are radial lines. Furthermore, the uniform state of stress in the plastic zones is determined from the yield condition and the equations of equilibrium. With the stress field known, the displacement field is determined by integration of the constitutive equations and the strain-displacement relations.