Analysis of fragmentation in the single filament composite: Roles of fiber strength distributions and exclusion zone models

Abstract

Exact equations are derived governing the evolution of fragments in a long fiber loaded according to the “single filament composite test.” These equations are derived with no a priori assumptions regarding the distribution for fiber strength except that the distribution of fiber flaws along the length follows a compound Poisson process in terms of flaw strength. Furthermore, the interface model and the fiber stress profile in the exclusion zone around a fiber break can be arbitrary as long as the exclusion zone is well defined. Explicit and exact closed-form solutions of the governing equations are obtained under these general conditions including random initial breaks before load is applied, which have exponentially distributed spacings of a given normalized rate a along the fiber. We demonstrate this method by finding the exact closed-form solution for a bilinear stress interface model proposed earlier.