Elastic-plastic strain and stress distribution in notched plates under plane stress

Abstract

An experimental solution is presented for the plane state of stress in an elastic-plastic isotropic solid obeying the Mises yield condition. The elastic and plastic strains were determined by using birefringent coatings cemented on the surface of the model. Normal incidence of circularly polarized light yielded the difference of principal strains at the model-coating interface. Linearly polarized light gave the directions of principal strains. The values of ϵ z-principal strains, normal to the surface of the plate, were determined from an analogy relating this strain to another potential field. The values of ϵ z-strains together with data from the birefringent coatings yielded enough information for the explieit analytic solution of the elastic-plastic plane stress problem. The stress-components were determined by means of the Prandtl-Reuss stress-strain relations in a step-by-step process of loading. It was assumed that stresses and strains remained constant during each step and they only changed when the next step started. This method may have a general applicability to any plane-stress restricted plasticity problem, provided that convenient formulae are established satisfying the yield condition of the material and the associated flow rule. The method was applied to the solution of a series of plane-stress problems of restricted plasticity. Thin flat plates containing symmetrical deep notches with circular roots subjected to a uniform tension were considered and their elastoplastic stress and strain distribution was evaluated. Four cases were solved for various flank angles between 0 and 120°, the minimum width of the plates remaining constant. The influence of the flank angle on the shape of the spreading plastic zones was determined and the critical loads for incipient plastic flow were evaluated.