Z. Hashin Nathan Cummings Professor of Mechanics of Solids, Department of Solid Mechanics, Materials and Structures, Tel Aviv University, Tel Aviv, Israel Fellow AS ME Analysis of Composite Materials— A Survey The purpose of the present survey is to review the analysis of composite materials from the applied mechanics and engineering science point of view. The subjects under consideration will be analysis of the following properties of various kinds of composite materials: elasticity, thermal expansion, moisture swelling, viscoelasticity, conductivity (which includes, by mathematical analogy, dielectrics, magnetics, and diffusion) static strength, and fatigue failure. "Where order in variety we see And where, though all things differ, all agree' Alexander Pope 1 Introduction Composite materials consist of two or more different materials that form regions large enough to be regarded as continua and which are usually firmly bonded together at the interface. Many natural and artificial materials are of this nature, such as: reinforced rubber, filled polymers, mortar and concrete, alloys, porous and cracked media, aligned and chopped fiber composites, polycrystalline aggregates (metals), etc. Analytical determination of the properties of composite materials originates with some of the most illustrious names in science. J. C. Maxwell in 1873 and Lord Rayleigh in 1892 computed the effective conductivity of composites consisting of a matrix and certain distributions of spherical particles (see Part 6). Analysis of mechanical properties apparently originated with a famous paper by Albert Einstein in 1906 in which he computed the effective viscosity of a fluid con- taining a small amount of rigid spherical particles. Until about 1960, work was primarily concerned with macroscopically isotropic composites, in particular, matrix/particle composites and also polycrystalline aggregates. During this period the primary motivation was scientific. While the composite materials investigated were of technological importance, a technology of composite materials did not as yet exist. Such a technology began to emerge about 1960 with the advent of modern fiber com- posites consisting of very stiff and strong aligned fibers (glass, boron, carbon, graphite) in a polymeric matrix and later also in a light weight metal matrix. The engineering significance of reliable analysis of Contributed by the Applied Mechanics Division for publication in the JOURNAL OF APPLIED MECHANICS. Discussion on this paper should be addressed to the Editorial Department, ASME, United Engineering Center, 345 East 47th Street, New York, N.Y. 10017, and will be accepted until two months after final publication of the paper itself in the JOURNAL OF APPLIED MECHANICS. Manuscript received by ASME Applied Mechanics Division, February, 1983. properties is quite different for particulate composites and for fiber composites. For the former, such capability is desirable, while for the latter it is crucial. The reason is that the range of realizable properties and the ability to control the internal geometry are quite different in the two cases. For example: the effective Young's modulus of an isotropic composite consisting of matrix and very much stiffer and stronger spherical type particles will depend primarily on volume fractions and can be increased in practice only up to about four-five times the matrix modulus. The strength of such a composite is only of the order of the matrix strength and may even be lower. The effect of stiffening and strengthening increases if particles have elongated shapes but at the price of lowering the maximum attainable particle volume fraction. A unidirectional fiber composite is highly anisotropic and therefore has many more stiffness and strength parameters than a particulate composite. Stiffness and strength in the fiber direction are of fiber value order, and thus very high. Stiffnesses and strengths transverse to the fiber direction are of matrix order, similar to those of a particulate composite, and thus much lower. Carbon and graphite are themselves significantly anisotropic, their elastic properties being defined by five numbers instead of the usual two for an isotropic material. Furthermore, matrix properties may be strongly influenced by environmental changes such as heating, cooling, and moisture absorption. All of this creates an enormous variety of properties, of much wider range than for a particulate composite. The generally low values of stiffness and strength trans- versely to the fibers provide the motivation for laminate construction consisting of thin unidirectional layers with different reinforcement directions. The laminates are formed into laminated structures. The layer thicknesses, fiber directions, choice of fibers, and matrix are at the designers disposal and should, ideally, be chosen from the point of view of optimization of an important quantity such as weight or price. The design of such structures is an integrated process leading from constituents to structure in the sequence: Journal of Applied Mechanics SEPTEMBER 1983, Vol. 50/481 Copyright © 1983 by ASME Downloaded 18 Feb 2010 to 153.104.2.21. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm
Analysis of Composite Materials
May 20, 2023
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