Figure 4 shows a comparison of (a) the correlated
bounds of Hashin and
Shtrikman (HSX) based on the random polycrystal microgeometry,
(b) the microstructure-based bounds (assuming disk inclusions) of
Beran (B), (c) the random polycrystal lower bounds of
Avellaneda *et al.* (1988) [ACLMX^{-}] laminated (hexagonal symmetry) grains. A self-consistent (CPAX) estimate
is based on the random polycrystal microstructure. A new estimator
(B^{G}) is based on the Beran bounds and uses a geometric mean
approximation in order to incorporate information contained in the
microstructure constants .

Figure 4

5/3/2005