SELF-CONSISTENT ANALYSIS OF WAVES IN A POLYCRYSTALLINE MEDIUM

A simple method, of self-consistent type, which was developed recently for a matrix-inclusion composite, is placed in a form suitable for ap plication to composites in which no clearly-defined matrix phase exist s, as in a polycrystal. Information on grain size and shape is incorpo rated through the solution of relevant single scattering problems; app roximate account of multiple scattering is taken through ''self-consis tent'' choice of a background, ''effective'', medium. Finding the prop erties to assign to the effective medium is facilitated by the adoptio n of simple approximate solutions of the single scattering problems; w hen the scatterers can be modelled as spheres, this approximation beco mes exact in the static limit. Application of the method is illustrate d through a study of plane waves in equiaxed polycrystals comprising g rains of cubic symmetry with all orientations equally likely, modelled as spheres with a specified distribution of radii.