Diffusional relaxation of the dislocation-inclusion repulsion

While previous analyses of the elastic interaction between dislocations and inclusions predict repulsion when the shear modulus of the inclusion exceeds that of the matrix, experimental observations in oxide-dispersion-strengthened alloys show that dislocations are able to reach the surface of the stiffer oxide particles. We attempt to rectify this apparent contradiction by analysing the effects of diffusion, in the vicinity of the inclusion, on the elastic interactions. The problem is divided into two parts, depending on whether the dislocation loads the inclusion predominantly in shear or hydrostatically. We show that in each case the dislocation-particle separation decays exponentially with time, the time constant being proportional to the ratio of the inclusion volume and the inclusion-matrix interfacial diffusivity for shear loading, and proportional to the ratio of the square of the inclusion radius and the bulk diffusivity for hydrostatic loading. A comparison of the time required for diffusional relaxation with that required for a dislocation to climb over an inclusion shows that relaxation dominates for most conditions likely to be encountered during high-temperature creep. When the dislocation-inclusion separation is of the order of a dislocation core diameter, the dislocation core relaxes into the inclusion-matrix interface, thereby pinning the dislocation. To unpin the dislocation, a stress of order the Orowan stress must be applied. It is suggested that the unpinning of the dislocation from the inclusion gives rise to the threshold stress for creep in dispersion-strengthened alloy systems.