Analytical study of a hollow sphere made of plastic porous material and subjected to hydrostatic tension-application to some problems in ductile fracture of metals

A solution to the problem stated in the title is given by treating the porous matrix as a homogeneous material obeying the Gurson-Tvergaard model. As a first application, it is shown that the flow stress under hydrostatic loading of a material containing two populations of voids with very different sizes is almost the same as that of a material with only one population of voids and the same total porosity. As a second application, a self-consistent method is used to derive a value for the parameter introduced by Tvergaard in the original Gurson model to account for the interactions between cavities. Other models are also considered and shown to fail to satisfy the self-consistency requirement, whatever the value chosen for the parameter characterizing interactions between voids.