Some applications of Burzyński yield condition in metal plasticity

The classical J2 plasticity theory is widely used to describe the plastic response of metallic materials. However, this theory does not provide satisfactory predictions for materials which exhibit pressure-sensitive yielding or plastic dilatancy. Another difficulty is the difference between the values of yield stresses in tension and compression for isotropic materials, the so-called strength differential effect (SD), leading to the asymmetry of the elastic range. The Burzyński yield condition, proposed in 1928, can be used to overcome some of these problems. In this paper an implicit integration of the elasto-plastic constitutive equations for the paraboloid case of Burzyński’s yield condition is formulated. Also, the tangent operator consistent with the integration algorithm was developed and is presented. The proposed model was implemented in a commercial Finite Element code and different kinds of tests reported in the literature were simulated. The comparison between the numerical and experimental results shows that the plasticity theory with the paraboloid case of Burzyński’s yield condition describes adequately the strength differential effect, which is present in many kinds of materials significant for recent applications.