Numerical modelling of creep crack propagation resulting from grain-boundary void growth.

A variational principle, and a corresponding finite-element procedure, have been developed to predict steady-state, creep crack growth rates. The cracks are assumed to propagate in a creeping material by the growth, and coalescence of micro-voids on the grain boundary, in the damage zone, ahead of the crack tip. Three mechanisms of void growth have been considered: grain-boundary diffusion, surface diffusion and power-law creep. The power-law creeping material surrounding the crack tip and damage zone has been modelled using well-established finite element methods for incompressible material; and the stiffness of the damage zone elements added to the overall stiffness matrix, to obtain a complete solution. Both stationary cracks, and by an extension of the procedure, growing cracks have been analysed. Only mode-1 type loading has been considered. Loads were applied on a circular boundary around the crack tip in accordance with the appropriate HRR field, with an amplitude given by the C* path-independent integral. Results of steady-state crack propagation rates arising from void growth by grain- boundary diffusion have been compared with published results from analytical models. These comparisons indicate that the developed technique works well, and is efficient in terms of computer resources. The transition between constrained and unconstrained void growth is particularly well defined. For the other two void growth mechanisms results are presented in a similarformat to grain-boundary diffusion, and comparisons made where possible. The relationships between crack velocity and the variables C* and damage-zone size have been established for the three void-growth processes. The methodology and numerical procedures developed have been shown to be viable, and capable of further development. This might include the consideration of more complex void-growth models, or the inclusion of the procedure within an existing finite element code.