The Effective Properties of Composite Materials With Constant Reinforcement Density by the Linear Mori-Tanaka Method

[+] Author and Article Information
J. R. Zuiker

Wright Laboratory/Materials Directorate, WL/MLLN, Wright-Patterson AFB, OH 45433-7817

G. J. Dvorak

Department of Mechanical Engineering, Aeronautical Engineering and Mechanics, Rensselaer Polytechnic Institute, Troy, NY 12180-3590

J. Eng. Mater. Technol 116(3), 428-437 (Jul 01, 1994) (10 pages) doi:10.1115/1.2904309 History: Received September 30, 1993; Revised January 10, 1994; Online April 29, 2008


In its original form, the Mori-Tanaka method estimates constant overall properties of statistically homogeneous composite materials subjected to uniform overall stresses, strain or temperature changes, from averages of local fields in the phases. To permit applications involving large overall stress and/or temperature gradients, and functionally graded materials with a variable reinforcement density, the method has been extended to linearly variable overall and local fields by Zuiker and Dvorak (Composites Engineering, Vol. 4, 19–35, 1994 ) as a first step toward application of the method to statistically inhomogeneous materials with variable reinforcement density. Here, the effective properties are examined in detail. Non-zero components of the stiffness matrix are shown to satisfy invariance requirements and to vary with reinforcement volume fraction and size of the representative volume. It is shown that the linear and constant field approaches provide different estimates of overall properties for small representative volumes, but nearly identical estimates for large volumes.

Copyright © 1994 by The American Society of Mechanical Engineers
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