On the cavity-growth-model-based prediction of the stress dependence of time to creep fracture

Abstract

Abstract A model describing intergranular cavity growth and cavity shape evolution during its growth is applied to the numerical study of the growth of cavities by coupled diffusion and power-law creep, and to predict the stress dependence of time to creep fracture. It is shown that at stresses at which the power-law creep represents an important component of the growth the predicted time to fracture is inversely proportional to the third power of stress independent of the values of the ratio of surface diffusion to grain boundary diffusion conductance, while the minimum creep rate varies with approximately the fifth power of stress. Even if the cavity nucleation process is taken into account, assuming that the nucleation rate is proportional to the power-law creep rate, the predicted time to fracture is not inversely proportional to the creep rate, i.e. to the fifth power of stress. This contradicts the commonly observed proportionality of the product of time to fracture and minimum creep rate to the creep strain to fracture (modified Monkman-Grant (M-G) relationship). The analysis made suggests that the experimentally observed validity of the modified M-G relationship is always associated with the constrained cavity growth which cannot proceed unless accomodated by power-law creep.