Extended weakest link distribution family and analysis of fiber strength dependence on length

An extension of the weakest link distribution family (WLDF) developed in Paramonov and Andersons [Paramonov Yu, Andersons J. A new model family for the strength distribution of fibers in relation to their length. Mech Compos Mater 2006;42(2):179–92; Paramonov Yu, Andersons J. A family of weakest link models for fibers strength distribution. Composite A 2007;38:1227–1233] and its application to the carbon fiber material strength data processing are presented in this paper. As in Paramonov and Andersons (2006, 2007) we consider the specimen as a chain of n elements (links). The fracture process is modeled as follows: in the first stage an initiation of defects (before loading or during loading) and in the second stage a specimen fracture take place. As it is distinct from our previous publications, the strength of items without defects is taken into account; two types of defects (independent on load (“technological”) and dependent on load) and two types of the influence of defect number on the specimen strength are considered. It is shown that for carbon fiber material some models from WLDF and linear law (LW) traditional Weibull model provide some better prediction of strength–length dependence than power law Weibull model which sometimes provides better fitting of experimental data.