TENSILE-STRENGTH OF FIBER-REINFORCED COMPOSITES - I - MODEL AND EFFECTS OF LOCAL FIBER GEOMETRY

Predictions of the ultimate tensile strength of 3-dimensional fiber-re inforced composites as a function of the fiber statistical strength di stribution and fiber geometry (square vs. hexagonal packing) are prese nted for materials in which the load transfer from broken to unbroken fibers is very localized. The predictions are obtained using a previou sly-developed simulation model adapted here for hexagonal fiber arrays . The model includes (1) the Hedgepeth and Van Dyke load transfer mode l to determine in-plane load transfer and (2) fiber slip in the longit udinal direction via a shear-lag model. Results show that, although th e load transfer does depend on fiber geometry, the average composite t ensile strength and the statistical distribution of strengths do not d epend strongly on the fiber geometry. The size scaling of strength is then also shown to be nearly-independent of local fiber geometry. Thes e results are physically reasonable since the critical clusters of fib er damage causing failure are observed to be larger than 15-20 fibers, so that the detailed local geometry at smaller length scales is not c rucial to failure. Hence, analytic models developed previously for squ are fiber arrangements can be used with reasonable accuracy independen t of fiber arrangements. Applications of the model to polymer matrix c omposites are discussed in a companion paper (Part II).