ABSTRACT
CHAPTER 14
POLYCRYSTALLINE MODELS
The approximate models of the polycrystalline plastic response are discussed
in this chapter. The objective is to correlate the polycrystalline to single
crystal behavior and to derive the constitutive relation for a polycrystalline
aggregate in terms of the known constitutive relations for single crystals and
known (or assumed) distribution of crystalline grains within the aggregate.
The classical model of Taylor (1938a,b) and the analysis by Bishop and
Hill (1951a,b) are rst presented. Determination of the polycrystalline axial
stress-strain curve and the polycrystalline yield surface is considered. The
main theme of the chapter is the self-consistent method, introduced in the
polycrystalline plasticity by Kroner (1961), and Budiansky and Wu (1962).
Hill's (1965a) formulation and generalization of the method is followed in
the presentation. The self-consistent calculations of elastic and elastoplastic
moduli, the development of the crystallographic texture, and the eects of
the grain-size on the aggregate response are then discussed.
