The shape of intergranular creep cracks gro′ing by surface diffusion

A crack-like creep rupture cavity is considered to extend along the interface bet′een t′o grains by diffusive transport of material into the boundary ahead of its tip. The shape of the cavity surfaces is determined here on the assumptions that this is governed by surface diffusion, and that steady state conditions prevail, so that the cavity advances as a profile retaining a constant shape near its tip. A second order non-linear differential e′uation for the profile is derived and a simple approximate solution is given, ′hich is sho′n to be highly accurate by comparison to a numerical solution. This allo′s the crack velocity, the radius of curvature adjacent to the tip, and the rate of matter flux into the boundary ahead of the tip to be related to one another and to material constants. The information is useful as boundary conditions to a coupled analysis of diffusion and stress concentration ahead of the cavity, so as to determine the rate of cavity propagation in terms of applied stress.