An extended dislocation pile-up model for the yield strength of lamellar microstructures

Abstract

Abstract This paper investigates the relationship between the yield stress and the two length parameters specifying the fully lamellar polycrystalline microstructure, the grain size d GB and the lamellar thickness d LM. This is done in the framework of the dislocation pile-up model that has been used to explain the Hall—Petch relation between the yield stress and the grain-size. Deformation in the multilayer structure is assumed to proceed by dislocations propagating in the formation of a succession of mutually interacting pile-ups, blocked at the lamellar interfaces and piled up ultimately against the grain boundary. Numerical calculations of the model show that the propagation of the multiple pile-up through the successive layers requires progressive increases in the applied stress, and macroscopic yielding occurs after the dislocation pile-up has crossed a large number of layers. For the multilayer ‘single crystal’, the yield stress increases with decreasing lamellar size following the Hall—Petch relat...