Characterization of anisotropie elastic constants of silicon-carbide participate reinforced aluminum metal matrix compos
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I.
INTRODUCTION
THE mechanical properties of composite materials are strongly influenced by the properties of their constituent materials, as well as by the geometry of the reinforcement. The geometry of the reinforcement may be described by the shape, size, and orientation distribution. Since the shape determines the interfacial area, it plays an important role in determining the extent of the interaction between the reinforcement and the matrix. The orientation of the reinforcement affects the anisotropy of the composite system. In certain cases, the manufacturing process [e.g., extrusion of short-fiber metal matrix composites (MMCs)] may induce a preferred orientation of the reinforcement and hence cause anisotropy as reported in Part I, a companion article. ~ When a new composite system is being developed, modeling provides the possibility of tailoring the unique properties from those of constituent phases and other microstructural variables, so that a composite with the desired material properties can be fabricated. A number of analytical models have been developed to predict the elastic behavior of short-fiber reinforced composites. Among those models, the one based on the average field theory by Mori-Tanaka t21 and the equivalent inclusion principle of Eshelby t3j has been widely employed for composites containing a finite volume fraction of ellipsoidal fibers. The use of the Mori-Tanaka method usually involved the explicit calculation of eigenstrain (transformation strain) or the average matrix HYUNJO JEONG, formerly with the Department of Aerospace Engineering and Engineering Mechanics, Iowa State University, is Senior Research Engineer, Agency for Defense Development, DaeJon, Korea, DAVID K. HSU, Senior Physicist, is with the Center for Nondestructive Evaluation, Iowa State University, Ames, IA 50011. ROBERT E. SHANNON, Senior Engineer, is with the Materials Reliability Department, Westinghouse Science & Technology Center, Pittsburgh, PA 15235. PETER K. LIAW, formerly with Westinghouse Science & Technology Center, is Professor, Department of Materials Science and Engineering, University of Tennessee, Knoxville, TN 37996-2200. Manuscript submitted April 9, 1993. METALLURGICALAND MATERIALSTRANSACTIONS A
strain in certain loading directions to obtain the overall engineering constants, t4-9] As outlined by Hill, ~176 the effective elastic constants can also be evaluated in terms of concentration factors that relate the average strain (stress) in the inclusion to the uniform strain (stress) imposed at the boundary. BenvenisteIH] applied the Mori-Tanaka approximation to the computation of the concentration factors and found a simple, closed tensor expression for the effective moduli. Within the framework of Benveniste's approach, Ferrari and Johnson tt21 introduced a harmonic method to treat the probability density function of oriented fibers. In this article, a theoretical model is developed for predicting the anisotropic elastic constants of two-phase composites reinforced with preferentially oriented part
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