Multiscale modelling of nanoparticle toughening in epoxy: Effects of particle-matrix interface, particle size, and volume fraction

Toughening matrix materials by incorporating rigid nanoparticles has received significant interest for mitigating matrix microcracking in fibre-reinforced polymer-matrix composites, particularly at cryogenic temperatures. Despite recent experimental observations indicating the effectiveness of nanoparticle toughening, a notable gap remains in understanding the effects of nanoparticle size and volume fraction, and particle-matrix interfacial properties, on toughening efficacy. To address this gap, a multiscale model has been developed which employs a high-fidelity micromechanical model to quantify the deformation and energy dissipation caused by the rigid nanoparticles under a triaxial strain state determined from a macroscopic elastoplastic analysis. The interface between the nanoparticle and the matrix is characterized by a cohesive zone model (CZM), revealing a size-dependent phenomenon distinct to nanoparticles, sharply contrasting with micrometre-sized particles. Furthermore, the results reveal, for the first time, an optimum particle size that maximizes the toughening effect for a given particle-matrix combination. The existence of an optimum size is ascribed to the incomplete particle debonding from the matrix as the particle radius approaches the critical separation distance of the CZM. This revelation challenges the prevailing belief that, for a fixed volume fraction of nanoparticles, the enhancement in toughness rises as the particle size decreases as a result of the increase in total particle surface area. The implications for enhancing cryogenic performance are explored.