A breakdown from the dislocation-pile-up-based Hall-Petch model was typically observed in metallic multi-layers when the layer thickness (one half of the bilayer period) was of the order of a few tens of nm. The multi-layer strength, however, continued to increase with decreasing layer thickness to a few nm. A model based on the glide of single dislocations was developed in order to interpret the increasing strength of multi-layered metals with decreasing layer thickness when the Hall-Petch model was no longer applicable. The model was built on the hypothesis that plastic flow was initially confined to one layer and occurred by the motion of single so-called hair-pin dislocation loops that deposit misfit-type dislocations at the interface and transfer load to the other, elastically deforming layer. The composite yield occurred when slip was eventually transmitted across the interface, overcoming an additional resistance from the interface dislocation arrays. In a lower-bound estimate, the stress for the initial glide of 'hairpin' dislocation loops, confined to one layer, was similar to the classical Orowan stress. In the upper-bound estimate, the interaction of the glide loop with the existing misfit dislocation arrays at the interface was also considered in deriving the Orowan stress. The effect of in-plane residual stresses in the layers on the Orowan stress calculation was also considered. The
model predictions compared favourably with experimentally measured strengths on Cu-based multi-layers. When the layer thickness was decreased to a couple of nm, the strength reaches a plateau and, in some cases, drops with decreasing layer thickness. The single-dislocation model developed here predicted strengthening with decreasing layer thickness and, therefore, did not explain the deformation behaviour in this regime. In the regime of several nm, the deformation behaviour could be explained by dislocation transmission across the interface followed by glide of loops that span several layer thicknesses.

Single-Dislocation Based Strengthening Mechanisms in Nanoscale Metallic Multilayers. A.Misra, J.P.Hirth, H.Kung: Philosophical Magazine A, 2002, 82[16], 2935-51