A theory of diffusion controlled intergranular creep crack growth

A theory of intergranular creep crack growth in brittle materials has been developed. The mechanism of crack propagation is removal of atoms from the crack tip by stress induced grain boundary diffusion and their deposition at the grain boundary. The width of the crack is assumed to be constant during crack propagation. Any possible plastic deformation at the crack tip has been neglected. The stress relaxation ahead of the crack tip which arises due to the non-uniform deposition of material onto the grain boundary is calculated and the diffusion process governed by this relaxed stress studied. Thus the theory is analogous to those developed previously for the growth of r-type voids in grain boundaries. Both the steady state and the transient were considered. It was found that the rate of crack growth at any moment was determined by the nominal stress intensity factor K. A minimum stress intensity, K_min' exists below which no crack growth can take place. Conversely there is a maximum limiting rate of crack growth determined by the maximum surface diffusion rate. For K > K_min the steady state is always reached quickly and the length of the transient period t_tr is proportional to K⁻⁶. For K > K_min the rate of crack growth is proportional to K⁴. A comparison with experimental measurements on brittle ½Cr-½Mo-¼V steels show good agreement between the theory and experiment.