A Diffusive Crack-Growth Model for Creep Fracture

Abstract

A grain-boundary creep-crack-growth model is presented based on the assumptions that a crack propagates along the grain boundary by a coupled process of surface and grain-boundary self-diffusion, the adjoining grains on either side of the boundary behave elastically, and steady state conditions prevail. Under the action of the applied stress, atoms on the crack surfaces are driven by surface diffusion toward the crack tip, from where they are deposited nonuniformly by grain-boundary diffusion along the grain interface so that the grain boundary opens up hi a wedge shape ahead of the advancing tip which, hi turn, produces a misfit residual stress field. The total grain-boundary normal stresses which are the sum of this misfit stress field and that due to applied stress as well as the boundary opening displacements due to materials deposition are solved from a singular integrodifferential equation to give the following equation relating K to v: where K is the applied mode I crack-tip stress intensity factor,Kmin=1.69 kg is the minimum K below which no crack growth is predicted, KG being the critical K based on the Griffith theory; ν is the fixed crack-tip velocity, and νmin is the minimum v for which K=Kmia. In terms of the conventional expression of ν∝Kn, the present model predicts the values of n varying from 12 to infinity. A comparison with a set of creep crack-growth data on Si-Al-O-N at 1400°C shows good agreement between theory and experiment. A detailed analysis of the energy balance for the present model is also presented which indicates that / or (1–ν2)K2/E is indeed the correct energy release rate during the crack growth, as is true in the theory of elastic fracture mechanics. However, the major portion of the energy released in the diffusion processes comes from work done by the normal stress in opening up the grain boundary to accommodate the diffused material rather than from strain energy released by the adjoining grains.