An investigation was made of the relationship between the yield stress, and 2 length parameters which characterized a fully lamellar polycrystalline microstructure. These were the grain size, and the lamellar thickness. The study was carried out within the framework of the dislocation pile-up model that was used to explain the Hall-Petch relationship between yield stress and grain-size. Deformation in the multi-layer structure was assumed to proceed via propagating dislocations which formed a succession of mutually interacting pile-ups. These were blocked by the lamellar interfaces and finally piled up against the grain boundaries. Numerical calculations showed that the propagation of multiple pile-ups, through successive layers, required progressive increases in the applied stress. Macroscopic yielding occurred when the dislocation pile-up had crossed a large number of layers. In the case of so-called multi-layer single crystals, the yield stress increased with decreasing lamellar size (according to the Hall-Petch relationship) up to a saturation thickness; where the yield stress was equal to the critical stress that represented the strength of the interface barrier. In lamellar polycrystals, a larger stress could be required for the dislocations to reach the grain boundary than to overcome the grain boundary. This then gave rise to a yield stress that was independent of the grain size and was sensitive only to the lamellar spacing. When relatively few lamellae were present in the grains, the yield stress increased with increasing grain size; contrary to the Hall-Petch relationship.

An Extended Dislocation Pile-Up Model for the Yield Strength of Lamellar Microstructures Y.Q.Sun: Philosophical Magazine A, 1998, 77[4], 1107-26