Creep rupture and creep crack growth by grain boundary cavitation have been concerns of practical interest for several decades. Existing models for the diffusive growth of cavities on grain boundaries are usually based on the assumptions of periodic cavity spacing and simultaneous cavity nucleation. However, creep cavities nucleate continually during the creep process at random grain boundary sites, and it is appropriate to investigate non-periodic, and stochastic models for diffusive creep rupture.
The present study shows an analysis of diffusional cavity growth when cavities are continually nucleating at random grain boundary sites. For the creep rupture analysis, the method treats a 2-D version of the real 3-D problem. Based on the analysis by Yu and Chung[1,2] when cavities of varying size are randomly distributed on the bicrystal interface, rupture times are numerically calculated by using the 2-D cavity nucleation rates which are deduced from 3-D cavity nucleation data in such a way that the average inter-cavity spacings of the two cases are always equal. Predicted rupture times show agreements with experimental data within a factor of 3 for all the materials studied under various stress and temperatureranges, and manifest stronger stress dependence than expected from the models which do not take cavity nucleation into account. The most revealing facts from the analysis are that cavity nucleation is the most important factor determining the rupture time and that differences in cavit growth mode really do not matter.
When a macroscopic crack is embedded in polycrystalline solids, the extension of the crack at creeping temperature is usually described by specific load parameters such as $C^*$ or K, which depends on the stress field around the crack tip. Under these stresses, grain boundary cavities develope ahead of the crack tip, and the crack extends when the damage ahead of the crack tip reaches a critical value.
In the present study of crack extension, ...