Diffusive Crack Growth at a Bimaterial Interface

Abstract

The high temperature microcrack growth behavior along a planar interface between two elastic dissimilar media is investigated with an aim at estimating service life of advanced ceramic composites under creep-rupture conditions. The crack is assumed to grow along the interface normal to a remote applied tensile stress via a coupled surface and grain-boundary diffusion under steady-state creep conditions. The crack-tip conditions were first derived from the asymmetric tip morphology developed by surface self-diffusion. The governing integro-differential equation containing the unknown tensile stress distribution along the interface ahead of the moving crack tip was derived and it was found that a new length parameter exists as a scaling factor for the interface for which the solution becomes identical to that of the single-phase media when plotted on the nondimensional physical plane. In contrast to the elastic stress solution which shows singularity at the tip and oscillatory character away from the tip, the creep stresses have a peak value away from the tip due to a wedging effect and interfacial sliding eliminates stress oscillation resulting in a decoupling between mode I and mode II stress fields. This stress solution ties the far-field loading parameter to the crack-tip conditions in terms of the unknown crack velocity to give a specific V-K functional relationship. It was shown that a stress exponent of 12 in the conventional power-law crack growth emerges at higher applied stress levels. An analysis on energy balance shows that the energy release during crack growth amounts to the J-integral which derives mostly from work done by “wedging,” not from strain energy loss. A constraint on interfacial diffusivities of the two species was found and its implications on possible microstructural developments were discussed.