On Using a Dual Bound Approach to Characterize the Yield Behaviour of Porous Ductile Materials Containing Void Clusters

Two constitutive models for porous ductile materials are employed together to predict the yield behaviour of ductile materials containing void clusters. In this dual bound approach, the upper and lower bound constitutive models of Gurson (1977) and Sun and Wang (1989) are each evaluated in order to obtain upper and lower estimates for the material behaviour. By combining these two solutions, a predictive band can be created to capture the experimental variation in the yielding behaviour. Although these constitutive models have been derived with the assumption of a periodic void distribution, real materials contain void clusters that can significantly alter the onset of yielding and fracture. Therefore it is of great interest to determine if using dual constitutive models can produce an acceptable first-order approximation of the yielding behaviour in these materials. In the present work, the upper and lower bound yield loci are superimposed over numerical data available in the literature for the yielding of materials containing void clusters. It is shown that the dual bound approach is able to capture the material behaviour over a wide range of practically encountered stress triaxialities.