Numerical simulation of creep fracture with internal time-dependent hyperelastic-Kelvin cohesive bonds

Abstract

The macro brittle creep is closely related to the fracturing process on the micro scale. The virtual internal bond (VIB) is a microstructure-based continuum modeling method. It considers a solid as a bond network on the micro scale. The macro constitutive relation is directly derived from the micro bond potential, which intrinsically contains the micro fracture mechanisms. In this study, the VIB is firstly extended for modeling viscoelasticity, and then it is applied to creep fracture simulation. To reflect the time-dependence property of creep, a viscous bond is introduced to join a time-dependent hyperelastic bond in parallel to constitute a hybrid hyperelastic-Kelvin bond. Based on the hybrid bond potential, the macro viscohyperelastic constitutive relation is derived. The corresponding relationship between the micro bond parameters and the macro material constants is theoretically calibrated. Through this model, the typical three-stage feature of the brittle creep is well reproduced and the creep fracture is effectively simulated. The simulation results suggest that the fast and unstable fracture growth leads to the tertiary stage of creep. The viscosity mainly affects the deformation rate in the primary and tertiary stage of creep. The constitutive relation of the VIB stems from the 1D micro bond; thus, the rheology model derived from the cluster of rheological elements (e.g., spring, dashpot) is easily incorporated into the VIB framework, avoiding the 1D-to-3D generalization of the rheology law. For both the micro viscosity and fracture mechanisms that are incorporated into the macro constitutive relation, the present VIB can simulate complex creep fractures without a separate fracture criterion. It has great potential to simulate fracture propagation in a more extensive viscohyperelastic material.