Effect of nanofiller length and orientation distributions on Mode i fracture toughness of unidirectional fiber composites

Although several experiments demonstrate a statistical variability of length and orientation of nanofillers in composites, a limited number of analytical studies include these effects in the prediction of fracture energy, particularly in composites containing micro-sized continuous fibers together with nano-sized fillers such as carbon nanotubes. In this investigation, we model the Mode I interlaminar fracture toughness of unidirectional fiber composites containing carbon nanotubes with known length and orientation distributions. A micromechanical model, based on an analytical framework developed for "classical" short fiber composites, is presented to quantify the enhancement of fracture toughness due to either carbon nanotube pullout from the matrix or carbon nanotube fracture. The results show remarkable differences compared to the models that utilize a unique (average) carbon nanotube length value, especially with regard to maximum achievable energy enhancement, depending on mean length and on interfacial shear strength between carbon nanotubes and matrix. Some key characteristics of the carbon nanotube statistical length distribution are also analyzed along with the limit of mean carbon nanotube length between the two competing mechanisms of toughening. The analytical framework is also supported by Mode I fracture toughness experiments conducted on nanofilled S2-glass fiber/epoxy laminated composites. The inclusion of experimentally determined distributions of carbon nanotube lengths in the presented model led to good estimations of the effect of carbon nanotubes on the Mode I interlaminar fracture toughness. Comparable results were obtained for carbon nanofibers, as well.