Axisymmetric stress field near a circular cut in a solid with stress state dependent plastic properties

The paper analyzes the properties of the constitutive relations of the theory of plasticity for a continuum, which plastic properties depend on the type of stress state. The plasticity condition presented in the corresponding generalized form is used, where the parameter of the type of stress state is introduced, which is the ratio of the hydrostatic stress component to the equivalent von Mises stress, named in the literature the stress triaxiality. For a particular type of plasticity condition, an analytical solution of the problem for a solid with a circular hole under plane strain is obtained. The stress distributions corresponding to the obtained solution are compared with the ones for a solid whose plastic properties are invariant to the stress state using the Huber – Mises plasticity condition. The influence of the degree of sensitivity of materials properties to the type of stress state on the stress distributions in plastic areas are studied.