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TECHNICAL PAPERS

Four Phase Model: A New Formulation to Predict the Effective Elastic Moduli of Composites

[+] Author and Article Information
El H. Barhdadi1

Laboratoire de Physique et Mécanique des Matériaux, Ecole Nationale d’Ingénieurs de Metz, Ile du Saulcy, 57045 Metz, Francee.barhdadi@enim.fr

P. Lipinski

Laboratoire de Physique et Mécanique des Matériaux, Ecole Nationale d’Ingénieurs de Metz, Ile du Saulcy, 57045 Metz, France

M. Cherkaoui

School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0405

1

Corresponding author.

J. Eng. Mater. Technol 129(2), 313-320 (Nov 24, 2006) (8 pages) doi:10.1115/1.2712472 History: Received March 23, 2006; Revised November 24, 2006

We consider a linearly elastic composite medium, which consists of a homogeneous matrix containing coated spherical inclusions. The composite is modeled by a four phase pattern consisting of inclusion, interphase, matrix layer, and equivalent homogeneous medium. The overall elastic moduli are obtained using a micromechanical approach based on the Green function techniques and the interfacial operators. The four phase model assumes that all constituents are elastic and perfectly bonded. The model is used to derive the effective elastic properties of representative volume element using classical averaging schemes assuming the isotropy of constituent. Finally, effect of the thickness and stiffness of interphase on the global behavior of real composite materials are examined. Comparisons with experimental results show a good agreement.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 3

Effect of the interphase thickness on the effective properties: (a) effective shear moduli and (b) effective bulk moduli

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Figure 4

Effect of the interphase stiffness on the effective properties: (a) effective shear moduli and (b) effective bulk moduli

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Figure 5

Micrographic of syntactic foams. Subscript A indicates the unwanted voids.

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Figure 6

Effective Young’s modulus of syntactic foams composite plotted against the volume fractions of hollow spheres

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Figure 7

Young’s modulus of glass beads reinforcement epoxy matrix composite plotted against the volume fractions of glass beads

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Figure 8

Normalized effective Young’s modulus of mortar plotted against the sand grains surface area

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Figure 1

Assemblage of composite sphere of present work

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Figure 2

Four phase model

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