Multiple scattering theoretical and computer simulated dynamic model approaches to effective elastic properties of randomly disordered composites

Abstract

In the present investigation we have generalized the result obtained in the preceding paper [J. Appl. Phys. 59, 2368 (1985)] to treat composites containing crystallites of different crystal symmetries and arbitrary values of the elastic constants. This result has been used to discuss the existing theories intended to solve the same problem. An interesting finding of this analysis is that the present approach provides a single framework to discuss all the previous results which are particular cases of the general formulas derived here. Earlier all these cases were treated separately employing different approaches. Next we apply our results to six different binary composites and we find that our predictions compare quite favorably with experiment. For comparison we also calculate the same quantities by simulating the composite on a computer by the dynamic method originally developed by [T. R. Middya, A. N. Basu, and S. Sengupta [J. Appl. Phys. 57, 1844 (1985)] to discuss monocomponent polycrystal elastic properties. The two sets of results agree with each other for small differences in elastic properties of the components of a composite. But for larger differences, they diverge. Since the two approaches are based on widely different assumptions and the overall agreement of the effective-medium theory is distinctly superior, it appears that the existing experiments are consistent with the assumptions of the multiple scattering theory.