An Elastic-Plastic Analysis of Finite Plates with Side Notches

Abstract

The determination of the elastic-plastic stresses and strains ahead a sharp notch should be required in the study of the criteria on the initiation and propagation of fracture. Some kinds of modifications of elastic solutions on stress distribution around a notch have been used in the field of fracture mechanics to assess the behaviour of brittle and fatigue failures because of the difficulty of elastic-plastic analysis.Elastic-plastic analysis of stresses and strains ahead a notch is usually investigated with using deformation theory of plasticity, which could not be considered as the exact representation of the physical phenomena. Recent development of high speed digital computer, however, has made it possible to solve numerically elastic-plastic problems with the flow theory of plasticity.In the present paper non-linear system of equations is derived based on flow theory for linearly strain hardening square thin plates with side notches, which are slit shaped and 90°-V shaped notches. The load was increased in increments, and for each increment of load non-linear partial differential equations were solved numerically by using finite difference and iterative methods. The distributions of stresses and strains all over the plates and their changes were studied in this way.The distributions of strains calculated numerically were compared with the values of strain in experiment, and as the result it is concluded that the solution of numerical analysis approximates closely the stresses and strains in the finite plate with sharp side notches.