Dependence of fracture stress upon diameter in strong polymeric fibers

The axial and radial dimensions of a fiber are known to be key factors with respect to the mechanical stress necessary to promote failure, this being known as the size effect. Usually different methods are used to quantify the two types of size effects: Linear elastic fracture mechanics (lefm) and related schemes provide the theoretical basis for the effect of diameter variability upon strength whereas statistical theories, generally based upon the Weibull probability distribution combined with the weakest-link theorem, describe length effects. Here we show that simple modifications of the classical Poisson/Weibull form yield a new failure probability function which provides a more adequate explanation for diameter effects on strength in polydiacetylene fibers, and also resolves in a satisfactory way a current problematic issue inherent to the Weibull/weakest-link model. A maximum likelihood estimation procedure is presented for the evaluation of the most appropriate parameters of the proposed failure probability function.