Longitudinal Shear Loading of a Unidirectional Composite

Abstract

The behavior of a unidirectional fiber-reinforced composite ma terial subjected to a shear loading in the direction of the filaments is of fundamental importance in the understanding of composite material behavior. The shear stiffness and strength values asso ciated with this type of loading can be considered as fundamental properties characterizing the material. The problem of a doubly periodic rectangular array of parallel elastic filaments of doubly symmetric but otherwise arbitrary shape contained in an elastic matrix material subjected to shear stress components in the directions of the filament axes has been formulated using a theory of elasticity analysis. A finite difference representation of the governing partial differential equations of equilibrium and stress-displacement equations has been utilized in obtaining a solution by a systematic over-relaxation procedure. Numerical results have been obtained for a variety of filament cross-sectional shapes, various filament-to-matrix shear modulus ratios (ranging from zero to infinity), and a range of filament spacings varying from filaments nearly in contact to extremely wide spacings in which interaction effects between filaments are essentially zero. Theoretical results have been compared with the limited experimental data presently available. The results obtained permit a detailed description of the micro mechanical behavior of a composite material subjected to longitudinal shear loading. A study of local stress distributions in the composite provides a means of predicting shear strength as well as stiffness as a function of the material properties of the constituents and their geometry. 1. S. W. Tsai, "Strength Characteristics of Composite Materials," NASA Contractor Report NASA CR-224, April 1965. 2. S. W. Tsai, D. F. Adams, and D. R. Doner, "Effect of Constituent Material Properties on the Strength of Fiber-Reinforced Composite Materials," Air Force Materials Laboratory Contractor Report AFML-TR-66-190, August 1966. 3. Z. Hashin and B. W. Rosen, "The Elastic Moduli of Fiber-reinforced Materials," J. Applied Mechanics, Vol. 31E (1964), p. 223. 4. C. H. Chen and Shun Cheng, "Mechanical Properties of Fiber-reinforced Com posites and of Perforated Solids," J. Composite Materials, Vol. 1 (1967), p. 30. 5. H. B. Wilson, Jr. and J. G. Goree, "Transverse Shear Loading in an Elastic Matrix Containing Two Elastic Circular Cylindrical Inclusions," Mathematical Studies of Composite Materials III, Rohm and Haas Company Report, Hunts ville, Alabama, June 1966.