Role of cracks in creep of brittle, polycrystalline, structural ceramics

Abstract

An analytical study was conducted of the effect of cracks on creep of polycrystalline, brittle structural ceramics. Two independent mechanisms of contribution of cracks were defined. The mechanism of elastic creep by crack growth represents the rate of increase in strain, with time, resulting from the time-dependent decrease in elastic moduli of the material, due ·to crack growth. The mechanism of crack-enhanced creep provides a measure of the increase in creep rate over that in an identical but crack-free material, due to the local stress field associated with the cracks and the resultant transfer of stress to the adjacent, crack-free material. Creep rates due to these mechanisms were quantified for simple crack geometries. It was shown that the contribution of cracks can result in an idealized 4-stage creep curve for a brittle, polycrystalline ceramic, in contrast to the conventional 3-stage creep curve for metals. The four stages consist of a primary or crack incubation period, a secondary sigmoidal region resulting from growth of microcracks along grain boundary facets, a tertiary or crack-enhanced stage associated with arrested microcracks, and a quarternary stage comprising crack linkage and coalescence. It was demonstrated that the formation and growth of cracks during creep can result in apparent power-law creep, positive grain size dependence of the creep rate, and grain size-dependent creep activation energy. It can also account for observations of decreasing creep rate with increasing time in constant load creep tests, anomalous stress relaxation behavior in structural ceramics, significantly higher creep rates in tension tests than in compression tests, and discrepancy between diffusion coefficients inferred from creep studies and measured in diffusivity experiments.

A simple model was presented for the effect of cracks on creep rate in bending, based on the time-rate of change of curvature of a bend specimen.

Analysis of the effect of cracks on creep was extended to a general state of multiaxial stress, through matrix formulation of stress, creep rate, and creep compliance tensors. Derivation of components of the creep compliance tensor from analogs in elasticity was demonstrated for crack-enhanced creep, for uniaxial and uniform triaxial tension, for simple crack geometries. It was demonstrated that materials containing cracks can exhibit a finite rate of creep under hydrostatic tension, in contrast to a corresponding creep rate of zero in crack-free materials.

Recommendations are made for analysis and interpretation of experimental creep data for structural ceramics.