Optimizing strength and toughness of nanofiber-reinforced CMCs

Nanofibers used in current ceramic matrix composites (CMCs) are usually wavy and of finite length. Here, a shear-lag model for predicting the tensile strength and work of fracture of a composite containing a “single matrix crack”, as a function of all the material parameters including constant plus Coulomb interfacial friction, is presented for a CMC containing wavy, finite-length nanofibers having a statistical distribution of strengths. Literature results are recovered for straight infinite fibers, with strength and toughness depending on a characteristic strength σc and a characteristic length δc. For nanofibers of finite length L, radius of curvature R, and with Coulomb friction coefficient μ, the strength and toughness are found to depend only on σc, δc, and two new dimensionless parameters μδc/R and L/δc. Parametric results for a typical carbon nanotube CMC show an optimal region of morphology (L and R) that maximizes composite strength and toughness, exceeding the properties of composites with straight (R=∞) and/or long (L=∞) reinforcements. Therefore, while factors such as the nanofiber strength distribution and the nanofiber–matrix interface sliding resistance may not be easily controlled, the tuning, via processing, of purely geometrical properties of the nanofibers (L and R) alone can aid in maximizing composite properties. These results have important application in hybrid CMCs such as “fuzzy fiber” CMCs, where micron-scale fibers are covered with a forest of nanofibers such that the nanofiber array can bridge longitudinal cracks and thus improve delamination resistance.