Void Growth due to Creep and Grain Boundary Diffusion at High Triaxialities

The growth of grain boundary voids at elevated temperatures by coupled creep and grain boundary diffusion is studied numerically using a cylindrical unit cell model. Emphasis is on the influence of the remote stress triaxiality, which is taken to cover the full range of axisymmetric stress states, from purely effective to purely hydrostatic states of stress. The motivation for extending previous results stems from the need for an accurate cavity growth model to analyse damage due to hydrogen attack, where the grain boundary voids are internally pressurized. Because of the wide range of stress states considered, numerical stability requires the use of two normalizations of the variational principle for the coupled void growth problem; one when the effective stress is dominant and the other when the mean stress is dominant. In the regime where deformation is primarily by creep, two distinct modes of deformation appear for each level of porosity; one for low triaxialities and one that takes over for sufficiently high triaxialities. Approximate models found in the literature for a dilute concentration of voids, or for finite concentrations, are explored to check their ability to represent the stress state dependence of the volumetric void growth rate. A novel approximate formula is derived for creep dominated growth and is shown to give good agreement with numerically computed void growth rates in the high triaxiality regime and for finite concentrations. A fairly abrupt transition between creep dominated void growth and diffusion dominated void growth is found when the stress triaxiality is very high, so that the interaction between creep and diffusion is then relatively unimportant. Finally, formulae are presented which give an approximate, yet fairly accurate, expression for the void volume growth rate due to coupled diffusional and creep growth over the full range of axisymmetric stress states.