VARIATIONAL ESTIMATES FOR THE CREEP-BEHAVIOR OF POLYCRYSTALS

A variational procedure is developed for estimating the effective cons titutive behaviour of polycrystalline materials undergoing high-temper ature creep. The procedure is based on a new variational principle all owing the determination of the effective potential function of a given nonlinear polycrystal in terms of the corresponding potential for a l inear comparison polycrystal with an identical geometric arrangements of its constituent single-crystal grains. As such, it constitutes an e xtension, to locally anisotropic behaviour, of the variational procedu re developed by Ponte Castaneda (1991) for nonlinear heterogeneous med ia with locally isotropic behaviour. By way of an example, the procedu re is applied to the determination of bounds of the Hashin-Shtrikman t ype for the effective potentials of statistically isotropic nonlinear polycrystals. The bounds are computed for the special class of untextu red FCC polycrystals with isotropic pure power-law viscous behaviour, first considered by Hutchinson (1976), in the context of a calculation of the self-consistent type. The new bounds are found to be more rest rictive than the corresponding classical Taylor-Bishop-Hill bounds, an d also more restrictive, if only slightly so, than related bounds of t he Hashin-Shtrikman type by Dendievel et al. (1991). The new procedure has the advantage over the self-consistent procedure of Hutchinson (1 976) that it may be applied, without any essential complications, to a ggregates of crystals with slip systems exhibiting different creep rul es - with, for example, different power exponents - and to general loa ding conditions. However, the distinctive feature of the new variation al procedure is that it may be used in conjunction with other types of known bounds and estimates for linear polycrystals to generate corres ponding bounds and estimates for nonlinear polycrystals.