Theoretical prediction of tensile strength of fibers as a function of thickness of brittle zones on fiber surfaces

Abstract

A theoretical model of longitudinal strength of fibers as a function of the thickness of brittle zones on fiber surfaces was presented. Unifying parameters, corresponding to a formation of a notch due to a premature failure of the brittle zone, to an extension of the notch and to an interfacial debonding between the fiber and the brittle zone, were derived by modifying Weibull theory, fracture mechanics and shear lag analysis of Dow, respectively. A framework for interpreting the interrelation between the magnitudes of these unifying parameters and the failure mode of the fiber/brittle zone composites was carried out. It was shown that, if the thickness of the brittle zone is thicker than a critical value and if the interfacial bonding is stronger than a critical value, the fiber strength is reduced. Some examples of combinations of these unifying parameters given as a function of the thickness of the brittle zone were presented and the failure mode of the fiber/brittle zone composite was described schematically also as a function of the thickness of the zone.