Lurie solution for spherical particle and spring layer model of interphases: Its application in analysis of effective properties of composites. (May 2016)

• Record Type: Journal Article
• Authors: Nazarenko, Lidiia; Bargmann, Swantje; Stolarski, Henryk
• Is Part Of: Mechanics of materials. Volume 96(2016:May)
• Page Start: 39
• Page End: 52
• Publication Date: 2016-05
• Subjects: Spherical equivalent inhomogeneity -- Spring layer model -- Interphase -- Random composites -- Effective properties; Strength of materials -- Periodicals; Mechanics, Applied -- Periodicals; Résistance des matériaux -- Périodiques; Mécanique appliquée -- Périodiques; Mechanics, Applied; Strength of materials; Periodicals; Electronic journals; 620.11
• DOI: 10.1016/j.mechmat.2016.01.011
• Languages: English
• ISSNs: 0167-6636

Abstract

Highlights: Model based on the concept of equivalent inhomogeneity. Inhomogeneity/interphase system replaced by equivalent inhomogeneity. The interphase modeled as a layer of linear springs. Equivalent properties of original inhomogeneity and its interphase with the matrix. Closed-form formulas for overall properties of composites accounting for intephases. Abstract: 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.