Determination of principal stresses in an isotropic material under conditions of plane strain

Abstract

Starting from basic considerations, equations have been developed for the determination of principal stresses in an isotropic material, under the action of a twodimensional stress system. It has been shown that the slip lines, in the case of a plastic state of stress; and the shear stress pattern and the isoclinics in the case of an elastic state, together with the boundary conditions, provide enough data for solving any specific problems. An example has been given to show that the equations developed hold for theperfectly plastic state. But the authors are precluded from giving a numerical example for the general plastic condition, as the required experimental data are not available to them. In the case of a loading producing a completely elastic state of stress throughout the material a numerical example has been worked out, based on published experimental data, showing the actual application of the proposed equations. The method is, perhaps, not applicable in a case where plastic and elastic states of stress coexist.