Plane Strain Solutions for Highly Undermatched Specimens in Bending

Abstract

This chapter concerns with highly undermatched welded plates with no crack subject to pure bending. Two different kinematically admissible velocity fields are adopted. One of the fields results from an exact analytic solution for deformation of a plastic wedge between two rotating plates. The other kinematically admissible velocity field is obtained using simple assumptions and the known asymptotic singular behaviour of the real velocity field near velocity discontinuity surfaces given in Eq. (1.9). Since plane strain deformation is assumed, integration in the thickness direction is replaced with the multiplier 2B where 2B is the thickness of the plate. For the same reason, the term “velocity discontinuity surface” is replaced with the term “velocity discontinuity curve (or line)”. The latter refers to curves (lines) in the plane of flow. Base material is supposed to be rigid. The solutions given below have been proposed by Alexandrov and Kocak (2007) and Alexandrov (2008). Reviews of other solutions, including plates with cracks and three-point bending, have been presented in Kim and Schwalbe (2001a–c).