Effects of strength difference and intermediate principal stress on plane strain elastic–plastic bending of a curved beam

Abstract

Based on the unified strength criterion, the plane strain elastic–plastic bending of a linear strain hardening curved beam is analyzed in this study. The solutions for the properties of plane strain bending of the curved beam are obtained, taking into account the strength difference effect and the intermediate principal stress effect. Those solutions based on different strength criteria, such as Tresca, von Mises, Mohr–Coulomb, TS and GTS, are the special cases (Tresca, Mohr–Coulomb, TS and GTS) or linear approximation (von Mises) of the present solutions. Besides, a series of solutions that can take account of the strength difference effect and the differing effect of intermediate principal stress can be obtained from it. Consequently, the present solutions are suitable for various kinds of engineering materials. The influences of strength difference and intermediate principal stress on the two critical bending moments, the two interface radii between the elastic and plastic regions, and the radial displacements and stresses of points at the symmetrical plane of the curved beam are discussed comprehensively. It can be concluded from the analyses that the strength difference effect and the intermediate principal stress effect on the properties of plane strain bending of the curved beam are considerable and cannot be ignored.