The Modified Gurson Model Accounting For The Void Size Effect

The nucleation, growth and coalescence of microvoids resulting from the cracking or debonding of second phase particles is the dominant ductile failure mechanism of metallic materials. Mounting experimental investigations and numerical studies have shown that materials display strong size effects when the characteristic length scale asscocated with non-uniform plastic deformation is on the order of microns. Among them the porous ductile materials show void size dependence of void growth. The micron-and submicron-sized voids tend to grow slower than large voids under the same stress (rate) level. Both the Rice-Tracey model and the Gurson Model cannot account for the phenomena since the classical plasticity theories possess no intrinsic material length. In this paper, Gurson's model is extended in order to account for the void size effect.In this paper, the whole theory starts from the Taylor dislocation model, accounting for the void size effect. The extended Σ_eqv (equivalent stress) versus Σ_m(mean stress) yield curve is obtained, in which the void size effect comes into play through the ratio E_kk^pl/a, where l is the intrinsic material length on the order of microns, E_kk^p is the first invariant of plastic strain tensor, and a the void radius. Using asymptotic analysis and numerical optimization, approximative yield equations are obtained for the extended Gurson model, accounting for the void size effect. From the results of computation, we can see obvious effect of the plastic strain gradient in microscopic cell. Assuming f is relatively small, our consideration of the plastic strain gradient in cell is mainly limited to the axisymmetric volumetric strain, i.e., attention is concentrated on the gradient of the strain which changes the volume of the cell, while the gradient of the deviatoric strain which changes the cell's shape is neglected for the former is predominating. This is in conformity with Rice-Tracey model in that the volumetric deformation predominates.The Gurson-Tvergaard constitutive equations with void size effect are extended assuming the plastic strain rate tensor orthogonal to the yield curve. The constitutive equations are formulated for porous solid with cylindrical orspherical voids. Some simple applications of the constitutive equations are presented.Besides the approach of approximate yield curve with fitting constants, an alternative approach is proposed making direct use of the yield curves expressed in parametric form. The constitutive equations accounting for size effect are formulated and results of simple applications agree well with result using approximate yield curves.A simple model is proposed to study the effect of void-size and porosity on the strength and ductility against flow localization of porous plastic material with linear hardening matrix, based on the extended Gurson model.