Bridged crack models for the toughness of composites reinforced with curved nanotubes

In this work, the effect of nanotube curvature on nanocomposite toughness is studied by considering a matrix crack bridged by curved nanotubes. The bridging nanotubes undergo a pull-out process as the crack opening displacement increases. An approximate analytical form for the pull-out force versus displacement relationship for a single curved fiber is derived here based on the numerical pull-out model of Chen et al. (2009b). This new analytical description accounts for the sequential elastic, debonding, and sliding response of the interface. When incorporated into a crack bridging model it becomes possible to predict the crack bridging stress and nanocomposite toughness as a function of nanotube curvature, nanotube strength, and interfacial friction resistance. Model predictions indicate that increases in nanotube curvature increase the peak bridging stress, but also decrease the average pull-out lengths. The overall effect can be a reduction in toughness as nanotube curvature increases depending on chosen parameters including interfacial friction properties, nanotube and matrix modulus, and even crack opening.