Probabilistic aspects of the strength of fiber-dominated short-fiber composites I: Aligned fibers

The strength of a short-fiber composite may be postulated in terms of the number of fibers bridging a critical damage zone or gap before fracture. On the assumption that the fibers are long enough for the fracture mode to be fiber dominated, the entire strength distribution for the composite is derived from first principles for an aligned-fiber system, both including and excluding the inherent variability of the fiber strength. All results exclude the effect of any load transfer length, which is assumed to be relatively small compared with the fiber length. The average strength of the composite is seen to increase with increasing fiber length, while the coefficient of variation (COV) decreases. The addition of fiber strength variability is seen to reduce the average composite strength as well as to increase its COV by introducing a number of lower strength fibers. As the fiber strength variability decreases, the results for the variable fiber strength approach those for a constant fiber strength. A lower volume fraction composite is predicted to have a higher COV for strength. The strength calculation is shown to be robust with respect to the exact specimen volume chosen.