A half-space Peierls-Nabarro model was developed in order to evaluate dislocation mobility on a material surface. The free-surface size-effect upon the mobility of an edge dislocation in thin films was investigated by using the model. The thickness of the thin layer between the dislocation and the free surface significantly influenced the mobility of the dislocation. The Peierls stress of the edge dislocation in a thin film could be expressed as a function of the thickness of the film. A closed-form solution was obtained for the scaling factor, defined as the ratio of the modified Peierls stress to the conventional one in bulk materials. This allowed for a characterization of the size (depth) effect upon the Peierls stress of the edge dislocation in the half-space. Depending upon the core-size of the dislocation, the Peierls stress of a surface edge dislocation was some 5 to 25% less than that found in bulk materials.

The Size Effect of Thin Films on the Peierls Stress of Edge Dislocations. C.L.Lee, S.Li: Mathematics and Mechanics of Solids, 2008, 13[3-4], 316-35