On the interaction of grain boundaries and triple junctions with a free surface

Grain boundaries interact with free surfaces in order to reduce their interface and strain energy. A finite tilt boundary is considered, which terminates at the free surface of a semi-infinite body and at a triple junction. The effect of the free surface on the distribution of edge dislocations in the finite boundary is studied. Triple junction and grain boundaries are modeled in terms of disclinations and dislocations. A non-vanishing net force acts on each boundary dislocation if they are equidistant. The equilibrium positions are obtained numerically. It turns out that independent of boundary length and misorientation, one third of all dislocations escape through the surface. The stress fields of the equilibrium dislocation configuration and of a disclination (power one third of the initial misorientation) are compared. The stress is concentrated at the surface and at the triple junction where it forms a singularity. The disclination approach overestimates the stress at the junction and near the surface. The strength of the stress singularity decreases if relaxation across the triple junction occurs. Implications of these results to material properties such as corrosion resistance and fracture strength are discussed.