A phase field model for the propagation of electrical tree in nanocomposites

Electrical treeing is a main cause of long term degradation of polymeric insulation and inorganic nanofillers have been added to improve the treeing resistance of polymers. In this work, a phase field model for the propagation of electrical tree in nanocomposites is presented, in which the damage status of insulation is described with a spatially and time dependent continuous variable. The evolution of damage phase is described with a modified Allen-Cahn equation, which is driven by the free energies originated from the phase separation, interface and electric field. The electric field distribution during growth of electrical tree is obtained by solving the iterative form of Poisson's equation with the spectral iterative perturbation method. Then the phase field model is applied to investigate the influence of nanofillers shape and distribution on propagation process of electrical tree. The results indicate that the phase field model can reproduce the dendritic shape of electrical tree, and the parallel nanosheet presents superior performance in hindering electrical tree than nanoparticle and random nanosheet.