Electrical treeing: A phase-field model

Electrical treeing is a commonly observed phenomenon associated with dielectric breakdown in solid dielectrics. In this work, a phase-field model is developed to study the initiation and propagation of electrical trees in two different geometries: a parallel capacitor and a cylindrical capacitor. The model utilizes a continuous field of damage variable to distinguish the localized damaged regions from the undamaged bulk material. Factors that affect electrical tree morphology, including discharge speed and damage mobility, are studied. Electrical treeing tends to exhibit a fractal shape with more branches at a relatively high discharge speed relative to the rate of damage. Furthermore, the effect of fillers on electrical treeing is also studied. Numerical results suggest that fillers of lower permittivity, higher breakdown energy or lower damage mobility will promote fractal treeing and thus resist catastrophic breakdown.