2ND-ORDER ESTIMATES OF THE SELF-CONSISTENT TYPE FOR VISCOPLASTIC POLYCRYSTALS

The 'second-order' homogenization procedure of Ponte Castaneda is used to propose new estimates of the self-consistent type for the effectiv e behaviour of viscoplastic polycrystals. This is accomplished by mean s of appropriately generated estimates of the self-consistent type for the relevant 'linear thermoelastic comparison composite', in the homo genization procedure. The resulting nonlinear self-consistent estimate s are the only estimates of their type to be exact to second order in the heterogeneity contrast, which, for polycrystals, is determined by the grain anisotropy. In addition, they satisfy the recent bounds of K ohn & Little for two-dimensional power-law polycrystals, which are kno wn to be significantly sharper than the Taylor bound at large grain an isotropy. These two features combined, suggest that the new self-consi stent estimates, obtained from the second-order procedure, may be the most accurate to date. Direct comparison with other self-consistent es timates, including the classical incremental and secant estimates, for the special case of power-law creep, appear to corroborate this obser vation.