On Stiffness and Strength of an Aligned Short-Fiber Reinforced Composite Containing Fiber-End Cracks Under Uniaxial Applied Stress

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Abstract
One of the experimental findings on short-fiber reinforced composite materials is that the fiber-ends act as a crack initiator. The effect of the fiber-end crack on the overall stiffness and the strength of the composite are investigated here. A particular emphasis is placed upon the weakening longitudinal Young’s modulus by the fiber-end crack which is assumed to be penny-shaped. The energy release rate of the penny-shaped crack at the fiber-end under a uniaxial applied stress is also calculated for a fracture criterion. It is assumed in our theoretical model that short-fibers are all aligned in the loading direction and the penny-shaped crack at the fiber-end extends in the direction perpendicular to the fiber axis. Our analytical technique is a combination of Eshelby’s equivalent inclusion method and Mori-Tanaka’s back stress analysis so that our results are valid even for large volume fraction of fibers.

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