Effective Elastic Moduli of Spherical Particle Reinforced Composites Containing Imperfect Interfaces

• Published in: International journal of damage mechanics Vol. 21; no. 1; pp. 97 - 127
• Main Authors: Yanase, K., Ju, J. W.
• Format: Journal Article
• Language: English
• Published: London, England SAGE Publications 01-01-2012
• Subjects: Computational efficiency; Homogenizing; Inclusions; Mathematical analysis; Modulus of elasticity; Particle-matrix interfaces; Particulate composites; Tensors; homogenization; effective medium theories; modified Eshelby tensor; imperfect interface; particle reinforced composite; micromechanics; interfacial damage
• ISSN: 1056-7895; 1530-7921
• DOI: 10.1177/1056789510397076

The effective elastic moduli of composite materials are investigated in the presence of imperfect interfaces between the inclusions and the matrix. The primary focus is on the spherical particle reinforced composites. By admitting the displacement jumps at the particle–matrix interface, the modified Eshelby inclusion problem is studied anew. To derive the modified Eshelby tensor, three approximate methods are presented and compared by emphasizing the existence of a unique solution and computational efficiency. Subsequently, the effective elastic stiffness tensor of the composite is formulated based on the proposed micromechanical framework and homogenization. Specifically, by incorporating imperfect interface, the modified versions of the Mori–Tanaka method, the self-consistent method, and the differential scheme are presented. By comparing these three methods, the effects of interfacial sliding and separation on the degradation (damage) of the effective elastic moduli of composites are analyzed and assessed. Finally, a critical aspect of the presented formulations is specifically addressed.