Crack Bridging in Polymer Nanocomposites

Abstract

Carbon nanotube reinforced composites offer enhancements in fracture properties since the reinforcing nanotubes provide a bridging mechanism to resist crack growth. In this paper, a study of crack bridging by nanotubes in a nanotube-reinforced polymer composite is presented. The process of crack bridging is idealized as normal pullout of the participating nanotubes from the polymer matrix. The resistance to crack growth due to bridging is taken as the aggregate of the resistance offered by all the nanotubes, ignoring any interaction among the nanotubes themselves. The pullout of a single nanotube from the polymer matrix is modeled as an axisymmetric, nearly one-dimensional problem. This is done by assuming that fracture along the nanotube–polymer interface is dominated by shear openings, and that the nanotube behaves as a rigid body. When the polymer is a linear elastic material, the force–displacement relation for pullout is obtained as a function of dimensionless variables representing the interfacial fracture energy and the pullout length scale. Applying the correspondence principle, the elastic results are extended to the case where the polymer is a linear viscoelastic material with a single relaxation time. The force–displacement relation is then a function of the viscoelastic properties of the polymer and the pullout velocity as well. Using these results, the apparent enhancement in the fracture energy of the composite is obtained. This provides a guideline to design these composites for desired fracture properties in terms of the interfacial strength of the nanotube–polymer interface and the volume fraction of the nanotubes. Results of numerical simulations of nanotube pullout are compared to the predictions of the analytical model.