Grain boundaries; plasticity; polycrystalline; slip; Taylor theory
This work was supported primarily by the MRSEC Program of the National Science Foundation under DMR-0079996. Most studies in crystal plasticity are based upon Taylor's original 1938 work. Within Taylor's framework the dependence of yield strength on microstructure, beyond lattice orientation, is carried within the critical resolved shear stress for slip. Thus, as the grain size decreases, the critical resolved shear stress is required to increase. This increase in critical resolved shear stress is applied, uniformly across the entire interior of the slipping grains according to the basic assumption of the model (uniform plastic strain or strain rate). It is well known that slip patterns are not uniform over the grain interior. (If they were there would be negligible development of geometrically necessary dislocation content in the grain interior.) It is known, from the evidence of transmission electron microscopy, that certain microscopic conditions must exist near grain boundaries and triple junctions within polycrystalline materials, leading to differences in the patterns of dislocation slip near the boundaries, as compared with the grain interior. The purpose of this paper is to introduce a framework in which these microscopic conditions can be incorporated within the classical Taylor model. It will be shown how these considerations lead to a grain-size and grain-boundary-character dependence in the initial yield stress. The results are expressed in the Fourier space of microstructures.