A phase-field model is developed in this paper based on the similarity between mechanical fracture and dielectric breakdown. Electrical treeing is associated with the dielectric breakdown in solid dielectrics by the application of high voltages. Instead of explicitly tracing the propagation of conductive channel, this model initializes a continuous phase field to characterize the extent of damage. So far, limited research has been conducted for simulating the effect of nanofiller dispersion on electrical treeing. No study has modeled the effect of uniform and nonuniform dispersion of nanofillers with varying filler concentration on treeing. Since electrical treeing tends to decrease the breakdown strength of solid dielectrics therefore, nanofillers are widely used to distract the tree from a straight channel to distribute its energy in multiple paths. Diverting a straight treeing channel into multiple paths reduces the chances of its propagation from live to dead-end hence, improving the breakdown strength. The physical and chemical nature of nanofillers has a crucial impact on increasing the resistance to treeing. In this paper, phase-field model is developed and used to simulate electrical treeing in polyethylene for varying concentrations of alumina nanofiller using COMSOL Multiphysics. Tree inception time, tree-growth patterns, and corresponding changes in dielectric strength is studied for both dispersions. Electrical treeing under different concentrations of alumina nanofillers with uniform and nonuniform dispersion is investigated in polyethylene as a base material. It is observed that fillers with uniform dispersion increases the resistance to treeing and tree inception time. Highest resistance to treeing is observed by adding 1% nanoalumina uniformly in raw polyethylene. Moreover, in uniform dispersion the tree deflects into multiple branches earlier than nonuniform dispersion impeding the damage speed as well.
