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

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 relationship, until a saturation thickness where the yield stress is equal to the critical stress representing the strength of the interface barrier. In the lamellar polycrystal, a larger stress may be required for the dislocations to reach the grain boundary than to defeat the grain boundary, giving rise to a yield stress independent of the grain size and sensitive only to the lamellar spacing. When relatively few lamellae are present in the grains, the yield stress increases with increasing grain size, opposite to the Hall—Petch relation. This research, and the physical insights revealed thereby, are relevant to the understanding of the mechanical strength of multilayer structures as well as the fully lamellar grains present in some TiAl-based alloys.