Statistical treatment of fiber strength

Fignre 10.3 Tensile and failure strain of Kevlar 49 aramid fiber as a function of gage length (after Zweben, 1977). 

We can regard a fiber as consisting of a chain of links. We assume that fiber failure occurs when the weakest link fails. This is called the weakest-link assumption. It turns out that such a weak-link material is well described by the statistical distribution known as the Weibull distribution (Weibull, 1939,1951). We first describe the general Weibull treatment for brittle materials and then describe its application for fibers. 

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