The Influence of Random Filament Packing on the Elastic Properties of Composite Materials.

by Donald Frederick Adams, Stephen W. Tsai

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A new method of micromechanical analysis of composite materials (such as boron- or glass-fiber-reinforced aluminum or epoxy) that takes account of the randomness of arrangement of the reinforcing filaments. Previous analyses assumed a regular geometric array, in which case a physically unrealistic square array showed surprising agreement with experimental data. Since available computers cannot handle a completely random arrangement, a basic pattern was generated by random-number techniques and was then reflected to obtain symmetry; this unit was assumed to repeat iteself throughout the material. Solutions for the modulus of elasticity were obtained for a 10-by-10 random array, for each of 20 random geometries using constituent stiffness ratios corresponding to boron/aluminum, glass/epoxy, and boron/epoxy composites, for filament volume contents of 39, 55, and 70 percent. The assumed symmetry permitted the use of standard boundary/value solution methods. When the assumed filament packing array is randomized, the more physically realistic "hexagonal random array" is in better agreement with the data than the "square random array." Since the latter results in much higher local stress concentrations, use of the square array model could lead to unduly conservative analyses. 48 pp. Refs. (MW)

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