A Burr type X chain-of-links model for carbon fibers

A model for application to carbon fibrous composites is proposed based on the Burr type X (BurrX) distribution first proposed by Burr (Burr, I.W. (1942). Annals of Mathematical Statistics, 13: 215-222) with an included parameter to account for fiber length. The model is further generalized similar to the generalization of the Weibull proposed by Padgett et al. (Padgett, W.J., Durham, S.D. and Mason, A.M. (1995). Journal of Composite Materials, 29: 1873-1884). Maximum likelihood estimation is briefly discussed, and the model is applied to the single-filament data of Bader and Priest (Bader, M.G. and Priest, A.M. (1982). In: Hayashi, T., Kawata, K. and Umekawa, S. (eds), Progress in Science and Engineering of Composites, pp. 1129-1136. ICCM-IV, Tokyo).