Full three dimensional cavitation instabilities using a non-quadratic anisotropic yield function

Full three dimensional cell models containing a small cavity are used to study the effect of plastic anisotropy on cavitation instabilities. Predictions for the Barlat-91 model (Int. J. Plast. 7, 693-712, 1991), with a non-quadratic anisotropic yield function, are compared with previous results for the classical anisotropic Hill-48 quadratic yield function (Proc. Royal Soc. Lond. A193, 281-297, 1948). The critical stress, at which the stored elastic energy will drive the cavity growth, is strongly affected by the anisotropy as compared to isotropic plasticity, but does not show much difference between the two models of anisotropy. While a cavity tends to remain nearly spherical during a cavitation instability in isotropic plasticity, the cavity shapes in an anisotropic material develop towards near-spheroidal elongated shapes, which differ for different values of the coefficients defining the anisotropy. The shapes found for the Barlat-91 model, with a non-quadratic anisotropic yield function, differ noticeably from the shapes found for the quadratic Hill-48 yield function. Computations are included for a high value of the exponent in the Barlat-91 model, where this model represents a Tresca-like yield surface with rounded corners.