Experimental Solution of Elastic-Plastic Plane-Stress Problems

Abstract

The paper presents an experimental method for the solution of the plane state of stress of an elastic-plastic, isotropic solid that obeys the Mises yield condition and the associated flow rule. The stress-strain law is an incremental type law, determined by the Prandtl-Reuss stress-strain relations. The method consists in determining the difference of principal strains in the plane of stress by using birefringent coatings cemented on the surface of the tested solid. A determination of relative retardation using polarized light at normal incidence, complemented by a determination in two oblique incidences at 45 deg along with the tracing of isoclinics, procures enough data for obtaining the principal strains all over the field. The calculation of the elastic and plastic components of strains is obtained in a step-by-step process of loading. It is assumed that during each step the Cartesian components of stress and strain remain constant. The stress increments and the stresses can be found thereafter by using the Prandtl-Reuss stress-strain relations and used for the evaluation of the components of strains and their increments in the next step. The method can be used with any material having any arbitrary stress-strain curve, provided that convenient formulas are established relating the stress and strain components and their increments at each point of the loading path. The method is applied to an example of contained plastic flow in a notched tensile bar of an elastic, perfectly plastic material under conditions of plane stress.