Strength of metallic multilayers at all length scales from analytic theory of discrete dislocation pileups

Metallic multilayers can 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 suggests that dislocation pileup theory can be used to predict the strength of multilayers from fundamental and microscopic material parameters. At large length scales, the behavior of multilayers can be described by a scaling law. At small length scales, the effect of discrete dislocations becomes important, and large deviation from the scaling law occurs. A complete analytic model should apply at all length scales and properly account for this dislocation discreteness effect. Such a model is proposed here. The layer thickness of multilayers are divided into four length-scale regimes, and simple analytic formulas are given for both the regime length scales and multilayer strength in each regime. The model is applied to Cu/Ni multilayers and the predicted strength is compared to experimental data. Furthermore, the predicted polycrystalline multilayer deformation map is presented.