Limiting Mechanisms of Mode I Interlaminar Toughening of Composites Reinforced with Aligned Carbon Nanotubes

Analytical models are presented for the Mode I interlaminar fracture of laminated composites reinforced with aligned carbon nanotubes (CNTs). The models are based on the crack-closure technique for fiber bridging, where the aligned CNTs enhance toughness mechanistically through either pullout (frictional sliding) from the matrix or sword-in-sheath sliding. The models are independent of the scale of reinforcement and demonstrate significant enhanced toughening for nanoscale reinforcement (CNTs) as opposed to typical mm-scale reinforcements (stitches and Z-pins). Complete analytical expressions for crack-growth resistance (G(R)(Delta a)) are obtained including normalized closed-form expressions for steady-state toughness for any scale of z-direction fiber reinforcement. The model is verified by comparison to previous experimental results for Z-pins and also aligned CNTs, and is used to define regimes where the competing mechanisms of toughening are operative. CNT strength is a key parameter limiting toughness enhancement in the frictional pullout mechanism.