A viscoelastic-viscoplastic constitutive model for nanoparticle-reinforced epoxy composites: Particle, temperature, and strain rate effects

Abstract

The mechanical behavior of nanoparticle-reinforced epoxy (NP/epoxy) exhibits highly nonlinear characteristics accompanied by particle, temperature, and strain rate effects, which are of great significance in the study of composites. This study presents a viscoelastic-viscoplastic (VE-VP) constitutive model applied to rigid silica and soft rubber nanoparticle reinforced epoxies (SNP/epoxy and RNP/epoxy), which are subjected to a wide strain rates and temperatures. The proposed constitutive model is based on the decomposition of the Helmholtz free energy into equilibrium and non-equilibrium parts. The equilibrium part employs the hyperelastic strain energy density function to capture the rubbery state property. The non-equilibrium part is decomposed into viscoelastic strain energy density functions and viscoplastic dissipation potential to capture the glassy state behavior. Temperature- and particle- dependent models were introduced into the proposed VE-VP model. To validate the effectiveness of the VE-VP model, the uniaxial compressive responses of the SNP/epoxy and RNP/epoxy were systematically tested. The results demonstrate that the VE-VP constitutive model can capture the nonlinear compressive behaviors of SNP/epoxy and RNP/epoxy over a strain-rate range of 10 − 2 s − 1 to 10 3 s − 1 and a temperature range of − 80 ℃ to 80 ℃ . Finally, the analysis of the model parameters indicates that the strain softening and hardening are strongly affected by the temperature and strain rate. • Two typical nanoparticles (rigid silica and soft rubber) are utilized to reinforced epoxy. • A viscoelastic-viscoplastic constitutive model for nanoparticles reinforced epoxy incorporating the particle, temperature and strain rate effects is proposed. • The compressive behaviors over wide range of temperature and strain rate are experimentally investigated and well predicted by proposed model. • The activation energy and hyperelastic coefficient in proposed model are strongly affected by temperature and strain rate.