M. Bornert et Pp. Castaneda, 2ND-ORDER ESTIMATES OF THE SELF-CONSISTENT TYPE FOR VISCOPLASTIC POLYCRYSTALS, Proceedings - Royal Society. Mathematical, physical and engineering sciences, 454(1979), 1998, pp. 3035-3045
Citations number
19
Categorie Soggetti
Multidisciplinary Sciences
Journal title
Proceedings - Royal Society. Mathematical, physical and engineering sciences
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.