Second-order estimates for the effective behaviour of viscoplastic polycrystalline materials

This paper is concerned with the application of the "second-order" nonlinea r homogenisation procedure (Ponte Castaneda, J. Mech. Phys. Solids 44 (6) ( 1996) 827) to generate estimates of the self-consistent type for the effect ive behaviour of fcc and hep viscoplastic polycrystals. The method has the distinctive property that it leads to estimates that are exact to second-or der in the heterogeneity contrast, and which are expected to be more accura te, particularly when compared to rigorous bounds, than those resulting fro m earlier homogenisation schemes such as the Hill "incremental" method or i ts "total" formulation (Hutchinson) for pure power-law viscous materials. S pecial attention is paid to large grain anisotropy leading to corresponding ly large heterogeneity contrast, and to highly nonlinear behaviour. Compari sons are also carried out with estimates derived from other more recent hom ogenisation schemes such as the "tangent" and "affine" methods. The results , illustrated for zirconium- and ice-type polycrystals, show that the secon d-order procedure offers the potential for significantly improved results, at least relative to the Hill incremental formulation. (C) 2001 Elsevier Sc ience Ltd. All rights reserved.