Analytic treatment of metallic multilayer strength at all length scales: Influence of dislocation sources

Metallic multilayers exhibit a very pronounced size effect where the mechanical strength depends on the layer thickness. Traditionally the Hall–Petch relation is used to account for the size effect. However, rigorous application of dislocation pileup theory predicts significant deviation from the Hall–Petch relation due to elastic inhomogeneity, discreteness of dislocations and dislocation source operation. Elastic inhomogeneity leads to anomalous scaling where the scaling exponent deviates from 1/2 of the classical Hall–Petch relation. The discrete dislocation effect is properly accounted for by a piecewise approach that can be applied at all length scales. In this article, a key step in the formulation is taken: the dislocation source characteristics are taken into consideration. Thus, all the three effects are 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) are provided for all length scales. The model is then applied to Cu/Ni multilayers and the predicted strength is compared with experimental data.