An orthotropic ductile damage model for visco-plastic materials

Numerical modelling of bulk forming processes has to identify the conditions that may result in unsatisfactory products. In ductile materials, damage may occur with the micro void nucleation at the site of second phase particles and inclusions in the plastic or viscoplastic matrix and then with the micro void growth. In this work an isotropic ductile damage model is extended to load cases with successive tensile and compressive steps and with pure deviatoric stress state. The constitutive equations satisfy the Clausius-Duhem inequality for negative or positive voids volume fraction rate. The constitutive parameters are identified with the Rice and Tracey model modified for a sphere initially filled with a soft or a hard inclusion. Axisymmetric geometries are considered for remote strain fields without distortion. A plane cell and a 3D unit cell are analysed numerically for the deviatoric strain state and various combined deviatoric and volumetric deformations.