An embedded-layer (2-interface) approximation was applied to a 2-component multi-layered material. This was used to examine how the critical resolved shear stress for the slip transmission of a pile-up depended upon the layer thickness, the moduli of the components, the interface slip properties, source properties, and pile-up orientation. It was found that, at nm layer dimensions, small numbers of dislocations in the critical pile-up produced significant departures from continuum Hall-Petch behavior. The multi-layer geometry could enhance or suppress source operation so that a sharp transition, or even a peak in the critical transmission stress, could occur at a particular layer thickness. The multi-layer geometry also exhibited a large anisotropy that was related to the effective glide distance between layers.

Hall-Petch Relationships for Multi-Layered Materials. P.M.Anderson, C.Li: Nanostructured Materials, 1995, 5[3], 349-62