Plasticity and ductile fracture damage: Study of void growth in metals

Abstract

The kinetics of internal deterioration by void growth around a spherical inclusion is studied as coupled with inelastic deformation. The void growth is described by the rate of a second-order damage tensor φ, whose definition supposes an appropriate averaging process over a statistically significant representative volume (the “unit cell”). The correlation between the damage tensor rate and the plastic deformation rate is established on the basis of results from auxiliary solutions of model boundary value problems for cavity growth in an infinite body. These results are properly adapted to the finite cell case. The damage tensor definition and the hypothesis on the microscopic pointwise displacement field within the cell constitute the basis of a method proposed for setting up the damage evolution equation quantifying the void growth process. The method has the advantage of being flexible enough so that the more refined approximations for a microscale displacement field can be adjusted to increase the accuracy of void growth description. Nevertheless, even starting from the simple Rice-Tracey-like microscopic velocity approximation, by applying the present method one can arrive at the tensorial damage kinetics relation which expresses the important features of the phenomena under consideration in a quantified manner. Thus, the relations obtained in this paper have the general form ·φ = ·φ(·E (p), φ, k ) and indicate the following effects: 1. (i) The damage rate as coupled with the macroscopic plastic strain rate Ė (p) depends on the actual damage state (φ); 2. (ii) it is affected by an initial inclusion size and spacing (viz. the presence of a scale factor k in the kinetics equations); 3. (iii) there is no coaxiality between strain rate and damage-rate tensors in the general case. Some exemplary situations are presented; relevant examples are developed.