Metallic multi-layers could be used as ultra-high strength coatings. They exhibit a very strong Hall–Petch-like size-effect where the mechanical strength depends on the layer thickness. This trend suggested that dislocation pileup theory could be used to predict the strength of multi-layers from fundamental and microscopic material parameters. At large length scales, the behavior of multi-layers could be described by a scaling law. At small length scales, the effect of discrete dislocations became important, and large deviation from the scaling law occurred. A complete analytic model should apply at all length scales and properly account for this dislocation discreteness effect. Such a model was proposed here. The layer thickness of multi-layers were divided into four length-scale regimes, and simple analytic formulas were given for both the regime length scales and multilayer strength in each regime. The model was applied to Cu/Ni multi-layers and the predicted strength was compared to experimental data. Furthermore, the predicted polycrystalline multilayer deformation map was presented.

Strength of Metallic Multilayers at all Length Scales from Analytic Theory of Discrete Dislocation Pile-Ups. L.Fang, L.H.Friedman: Philosophical Magazine, 2005, 85[28], 3321-55