Cavitation in elastic and elastic-plastic solids

Abstract

I n this study, we examine the phenomenon of cavitation under non-symmetric loading. We seek all points in (τ 1, τ 2, τ 3)-stress space, such that, when the local principal true stress components (τ 1, τ 2, τ 3) at a particle reach a point on that set, cavitation ensues. This set can be described by a surface (τ 1, τ 2, τ 3) = 0 in stress space, which we refer to as a cavitation surface, and corresponds to a cavitation criterion that arises naturally from the analysis. By considering a particular subclass of the set of all kinematically admissible deformation fields, we determine an approximate analytical expression for by using the principle of virtual work. We explicitly determine and discuss the cavitation surface for a neo-Hookean material. We then consider the special case of axisymmetric cavitation corresponding to a stress state (τ 1, τ 2, τ 3), and illustrate our results for a neo-Hookean material and for a piccewisc power-law clastic-plastic material of the deformation theory. If cavitation occurs before yielding, we find that a good approximate criterion for cavitation is that it occurs when the mean stress τ m = (τ 1 + 2τ 2)/3 reaches a critical value, even if τ 1 ≠ τ 2; however, if cavitation is preceded by yielding, we find that this is not a good approximation. The accuracy of our approximate analytical results is assessed by comparing them with finite element results and the results of other researchers. The utility of the cavitation surface is illustrated by applying the cavitation criterion = 0 to two experimental settings.