Analytical fracture toughness model for multiphase epoxy matrices modified by thermoplastic and carbon nanotube/thermoplastic

The introduction of a toughener is considered one of the most effective approaches to address the brittleness of epoxy resins. This paper introduces an analytical model for investigating the Mode-I fracture toughness of modified epoxy resins by including a phase-separating thermoplastic (TP) polymer, polyetherimide (PEI), and the combination of PEI and carbon nanotubes (CNTs). The fracture energy contributions from different toughening mechanisms, identified by the fractographical studies of the modified epoxy resins, were calculated, in which the energy contribution from TP deformation was obtained by molecular dynamics model simulation. The developed fracture toughness model showed satisfactory agreement with the experimental data. In the TP/epoxy binary system, the increase in TP content from 5 to 20 wt% resulted in a rise in the contribution of TP deformation (crack bridging) leading to a commensurate increase in fracture toughness from 33% to 70%. This transformation established TP deformation as the dominant mechanism for crack energy dissipation. In the CNT/TP/epoxy ternary system, from the model, the observed synergy in toughness was attributed to the improved dispersion of nanotubes. The developed analytical model may be used to formulate multiphase toughened resin matrices for optimal fracture toughness.