Electrical tree modelling in dielectric polymers using a phase-field regularized cohesive zone model

Electrical treeing is a leading cause of the eventual breakdown of dielectric polymers under high voltages. This paper presents a simulation scheme developed based on the phase-field regularized cohesive zone model (PF-CZM) for electrical tree modelling. By using the electrical analog of the crack propagation, the localized breakdown is modelled by the evolution of surface energy, and the electrical treeing is driven by the competition between the surface energy and the stored energy following the laws of thermodynamics. The microscopic Weibull distribution of the dielectric breakdown strength is the key factor resulting in the fractal structures of the electrical tree. The model developed is mesh independent and length-scale insensitive when the mesh size is no greater than 2.5μm. The validity of the model was confirmed through experiments, which strengthens its credibility. Three types of composites are designed and compared. The results indicate that the epoxy resin enhanced with 5 vol% silica and 1 vol% graphene sheet have a 3.5% longer dielectric breakdown time and a 29.2% higher thermal conductivity than the pure epoxy resin. Overall, the model provides a valuable tool for understanding the physics of electrical treeing and designing new dielectric materials with high withstand voltages.