Evaluation of mechanical properties of particulate composites with a combined self-consistent and Mori–Tanaka approach

Abstract

The effective elastic property of particulate composites is investigated with a combined self-consistent and Mori–Tanaka approach by simply introducing a parameter n. Suppose in a representative volume element (RVE) of a particulate composite there are sufficient and randomly distributed identical particle inclusions with total volume fraction c, these inclusions are separated into two groups, with volume fractions (1 − n −1) c and c/n over the RVE, respectively. We assume that the particle inclusions in the first group have already been embedded in the original matrix to form a fictitious matrix, and the RVE of the composite consists of the fictitious matrix and the particle inclusions in the second group. The property of the fictitious matrix is determined with the conventional self-consistent scheme, while the effective property of the composite is determined with the conventional Mori–Tanaka scheme. Analysis shows that, the conventional Mori–Tanaka scheme and self-consistent scheme can be obtained as the two special cases of the proposed approach as n=1 and n→∞, respectively. It is shown that the constitutive behavior of any inclusion (either in Group I or in Group II) in the composite is identical, indicating the consistency in the description of the constitutive behavior of the particle inclusions. The effective elastic property of some typical particulate composites is analyzed and compared with experimental results, demonstrating the validity of the proposed approach. An important and interesting finding from our investigations is that the introduced parameter n is not only an arbitrary one simply fitted from experimental data for a more accurate evaluation of the mechanical properties of composites, but also a bridge connecting the particle size to the macroscopic behaviors of composites. Based on this approach and a baseline experimental data of a composite with particle inclusions of a specified size, the mechanical properties of composites with the particle inclusions of different sizes can be estimated, which indicates the capability of the presented approach in the indirect description of the size-effect of particle inclusions.