A 3-D model for void evolution in viscous materials under large compressive deformation

The paper presents a study on the evolution of dilute ellipsoidal voids in power-law viscous materials under triaxial loading condition. Firstly, referring to the work of Eshelby (1957), a semi-analytical expression is deduced to evaluate the deformation of ellipsoidal void in linear viscous material. Then, for the non-linear viscous materials, the concept of mesoscopic representative volume element (RVE) is applied to study the voids deformation under different stress states, and a rigid visco-plastic finite element (FE) procedure is applied to solve the RVE model. For the condition of stress triaxiality ranging from −1 to +1, it is found that the voids deformation behaves similarly in both linear and non-linear viscous materials. Due to this fact, the framework of the expression of void deformation in linear viscous material is inferred to describe the void evolution in non-linear viscous materials, while the parameters of the expression are re-evaluated for the specific materials. The results show that the void shapes and loading conditions take important roles in the void evolution. Therefore, for an ellipsoidal void, the void radius strain rate is expressed as a function of the void shape index, the macroscopic stress and strain-rate. Meanwhile, the void volume strain rate is obtained as a function of the void radius strain rate. This void evolution model is integrated into FE code and applied to study the void closure problem in the metal forming process. The FE simulation provides the evolution of macroscopic stress, strain and strain-rate, and then the model is used to calculate the changes of void shape and volume in each step of the deformation history. It can be found that the results predicted by this model agree well with the analytical solution, experiment measurements and numerical simulations with embedded void shapes, which demonstrates that this method can be appropriately used to predict the void evolution during the large compressive deformation process.