Phase-field modeling of fracture in viscoelastic–viscoplastic thermoset nanocomposites under cyclic and monolithic loading

Abstract

In this study, a finite deformation phase-field formulation is developed to investigate the effect of hygrothermal conditions on the viscoelastic–viscoplastic fracture behavior of epoxy nanocomposites under cyclic and monolithic loading. The formulation incorporates a definition of the Helmholtz free energy, which considers the effect of nanoparticles, moisture content, and temperature. The free energy is additively decomposed into a deviatoric equilibrium, a deviatoric non-equilibrium, and a volumetric contribution. The proposed derivation offers a realistic modeling of damage and viscoplasticity mechanisms in the nanocomposites by coupling the phase-field damage model and a viscoelastic–viscoplastic model. Numerical simulations are conducted to study the cyclic force–displacement response of both dry and saturated boehmite nanoparticle (BNP)/epoxy samples, considering BNP contents and temperature. Comparing numerical results with experimental data shows good agreement at various BNP contents. In addition, the predictive capability of the phase-field model is evaluated through simulations of notched nanocomposite plates subjected to monolithic tensile and shear loading.