An analysis of Gurson model with parameters dependent on triaxiality based on unitary cells

Abstract

The Gurson model is widely used in the continuum-mechanics framework to analyse the ductile fracture process promoted by the nucleation, growth, and coalescence of voids. Further works improved the original Gurson model by introducing two parameters, q1 and q2, to adjust model predictions to the numerical results of a periodic array of cylindrical and spherical voids in hardening materials. This modified model is known as the Gurson–Tvergaard (GT) model. Commonly, these parameters are considered constants or dependent only on the material-hardening properties. However, there is evidence that these parameters also depend on the triaxiality of the stress field, as well as on initial porosity. In this work, a consistent fully implicit integration of the constitutive equations of the GT model, considering the q-parameters dependent on the triaxiality and the initial porosity of the stress field, is presented, and the corresponding consistent tangent operator is proposed. The model is validated by comparing the stress–strain behaviour, as well as the evolution of void volume fraction, of a voided cell and the equivalent cell of GT material with dependent parameters. The cases considered correspond to variable triaxiality stress fields, present in non-proportional loading conditions.