The single-filament-composite test: a new statistical theory for estimating the interfacial shear strength and Weibull parameters for fiber strength

Abstract

For over two decades the single-filament-composite (SFC) test has been an important tool in the study of the failure of fibrous composites. The SFC test itself involves a single brittle fiber embedded along the center-line of a matrix specimen of both large cross-sectional area and strain to failure. With increasing strain, the fiber fractures progressively, breaking into an increasing number of shorter and shorter fragments. Surrounding each break a shielded or exclusion zone develops within which no further breaks typically occur. At some strain level ‘saturation’ occurs abruptly as the shielded zones finally occupy the whole fiber, thus leaving a final distribution of fiber fragments end-to-end. Two uses for the SFC test have emerged: one has been to estimate the interfacial shear stress, τ, in the exclusion zone, sometimes called the interfacial shear strength and usually idealized as a constant over this zone. The other has been to estimate the fiber strength distribution and in particular the Weibull shape and scale parameters, ρ and σl, for fiber strength appropriate to some characteristic ‘gage’ length, l, such as the mean fragmentation length. In the past, theoretical bases for these estimates have handled the statistics of shielding in ways that have led to quite large biases. The purpose of the present paper is to use some recent theoretical advances to develop more sophisticated estimation procedures for τ and the Weibull fiber strength parameters ‘in situ’, and thus to eliminate various errors in previous methods. Straightforward computer programs (written in release 3 of Maple), which calculate the various quantities in the paper, will be provided by the first or second author on request.