Metallic multi-layers exhibited a very pronounced size effect where the mechanical strength depended on the layer thickness. Traditionally the Hall–Petch relation was used to account for the size effect. However, rigorous application of dislocation pileup theory predicted significant deviation from the Hall–Petch relation due to elastic inhomogeneity, discreteness of dislocations and dislocation source operation. Elastic inhomogeneity led to anomalous scaling where the scaling exponent deviates from the ½ of the classical Hall–Petch relation. The discrete dislocation effect was properly accounted for by a piecewise approach that could be applied at all length scales. A key step in the formulation was made here: the dislocation source characteristics were taken into consideration. Thus, all 3 effects were accounted for. Analytic formulas linking yield stress to microscopic interface strength, dislocation source activation stress and other easily obtainable parameters (the Burgers vector, the elastic constants of constituent materials, crystal structure and layer thickness) were provided for all length scales. The model was then applied to Cu/Ni multi-layers and the predicted strength was compared with experimental data.

Analytic Treatment of Metallic Multilayer Strength at All Length Scales - Influence of Dislocation Sources. L.Fang, L.H.Friedman: Acta Materialia, 2007, 55[5], 1505-14