A new approach to the determination of equivalent inhomogeneity for spherical particles and the spring layer model of their interphases with the matrix material is developed. To validate this approach the effective properties of random composites containing spherical inhomogeneities surrounded by an interphase material of constant thickness are evaluated. The properties of equivalent inhomogeneity, incorporating only properties of the original inhomogeneity and its interphase, are determined employing a new approach based on the exact Lurie's solution for spheres. This constitutes the central aspect of the proposed approach being in contrast with some existing definitions of equivalent inhomogeneity whose properties dependent also on the properties of the matrix. With the equivalent inhomogeneity specified as proposed here, the effective properties of the material with interphases can be found using any method applicable to analysis of the materials with perfect interfaces (i.e., without interphases) and any properties of the matrix. In this work, the method of conditional moments is employed to this end. The choice of that method is motivated by the method's solid formal foundations, its potential applicability to inhomogeneities other than spheres and to anisotropic materials. The resulting effective properties of materials with randomly distributed spherical particles are presented in the closed-form and are in excellent agreement with values reported in technical literature, which are based on both formally exact and approximate methods.
Bibliographical noteFunding Information:
LN and HS gratefully acknowledge the financial support by the German Research Foundation (DFG) via Project NA1203/1-1 . SB gratefully acknowledges financial support by the German Research Foundation (DFG) via SFB 986 “M3 (project B6).
© 2016 The Authors.
Copyright 2016 Elsevier B.V., All rights reserved.
- Effective properties
- Random composites
- Spherical equivalent inhomogeneity
- Spring layer model