Effective medium theory of elastic and thermoelastic properties of fiber composites

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Effective medium theory of elastic and thermoelastic properties of fiber composites


Author: Chen, Lai-tak
Title: Effective medium theory of elastic and thermoelastic properties of fiber composites
Degree: M.Phil.
Year: 1998
Subject: Fibrous composites
Composite materials
Hong Kong Polytechnic University -- Dissertations
Department: Dept. of Applied Physics
Pages: iv, 136 p. : ill. ; 30 cm
Language: English
InnoPac Record: http://library.polyu.edu.hk/record=b1442195
URI: http://theses.lib.polyu.edu.hk/handle/200/2232
Abstract: Fiber composite materials are investigated for many years and a wealth of theories and equations for the elastic and thermoelastic properties of composites have been accumulated.. The existing equations show good agreement with experimental data in the regime of low fiber volume concentration, but normally show much larger discrepancy at the high fiber volume concentration. We are proposing a new method to study the composite properties at high fiber volume concentration regime. Our work is based on a recent effective medium theory (EMT). Numerical calculation has been adopted to determine the elastic and thermoelastic properties of unidirectional fiber composites with anisotropic constituents and of composites with short randomly oriented fibers. Moreover, the coupled partial differential equations of EMT relating the five elastic moduli of the unidirectional fiber composites, which are based on the Hashin bounds, are solved analytically. In our project, we also use other equations, such as those of Chamis and Hashin, for the purpose of comparing with EMT results. The Chamis equations are for unidirectional composites with anisotropic fibers but isotropic matrix, while the Hashin bounds are good for composites with anisotropic constituents. For the EMT calculations of the thermoelastic properties of unidirectional composites with anisotropic constituents, we base on the Hashin bounds for calculating elastic properties and then use the equations of thermal expansion coefficients derived by Rosen and Hashin. Results computed by other equations, e.g. the equations by Chamis, Chamberlain, and Rojstaczer et al. are used for comparison. For short randomly oriented fiber composites, the Tandon and Weng equations are adopted for the EMT calculation. Results are compared with the Tandon and Weng equations, and also with the Halpin-Tsai equations for aligned fibers followed by randomizing through averaging. Measured values of some actual systems are reported in the literature are used to illustrate the ability of EMT on the determination of elastic and thermoelastic properties. They are the composite systems of polyethylene fibers in polyethylene matrix, liquid crystalline polymer fibers in polycarbonate matrix, graphite fibers in epoxy matrix and Kevlar fibers in epoxy matrix. For short fiber composites, we use systems of steel fibers in concrete cement, glass fibers in polyester matrix, whisker SiC fibers in Al2O3 and Si3N4 matrix as well as SiO2 spheres, Al2O3 fibers and Si3N4 fibers in Kerimid 601 matrix (K601). Furthermore, the difference in the predicted values of the effective elastic moduli of typical randomly oriented glass fiber/ epoxy composites between the EMT and Tandon and Weng equations have been investigated. The EMT results have quite good agreement with the experimental values in the predictions of elastic moduli and thermal expansion coefficients of unidirectional fiber composites. Also the EMT results have excellent agreement with measured values for composites with spherical fillers especially at high volume concentration. Moreover, in the prediction for elastic moduli of three dimensional randomly oriented short fiber composites, the EMT results are close to the experimental data and good results are obtained in the prediction of thermal expansion coefficient. In addition, we have demonstrated th edifference at the high concentration regime between the EMT and the Tandon and Weng calculations in the prediction of elastic moduli of a three dimensional randomly oriented glass fiber/ epoxy composite as a function of fiber aspect ratio from 0.0001 to 10000. In conclusion, this work shows that the EMT is able to give adequate predictions of the fiber composite properties investigated.

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