A new dynamic void Growth Model

Abstract

This work develops a new void growth model which is capable of describing the deformation and fracture of ductile materials under dynamic loading conditions. A representative volume element (RVE) which consists of a spheroidal void and a confocal spheroidal cell has been studied. A power law visco-plastic matrix material was assumed in the study in order to include the strain rate sensitivity effect. The formulations of Gåråjeu's model were used as basis for mathematical derivation. Particular attention is paid to inertia effect. In the new constitutive equations the inertia effect is represented by an individual term in the mesoscopic stress expression compared with the Gåråjeu's model. And this term is a function of the current void shape, void size, mesoscopic strain rate and matrix material density.

A parametric study of the new model has been carried out by calculating the constitutive equations using FORTRAN code. Inertia effect and strain rate sensitivity have been evaluated numerically. The results of the new model have been shown to agree with the existing models very well. The relationships between inertia and parameters such as void shape, void size, strain rate, matrix material properties and void volume fraction were explained in details. It has been found that the strain rate effect dominates the void growth process at the early stage, and the effect decreases as the time elapses.

FEM model analysis has been carried out to evaluate the new void growth model by ABAQUS. A special velocity boundary condition has been used in the FEM simulations to get the identical strain rate boundary condition as in the analytical calculations. It has been shown that the agreement of the present model with the FEM models is quite satisfactory on a wide range of strain rate, except the void shape which can not be predicted accurately. It has been found that the inertia effect is very small under the strain rate from quasi static up to several thousand 1/s.