Thermodynamic model for electrical tree propagation kinetics in combined electrical and mechanical stresses

In this paper we develop a kinetic model for the growth of electrical tree structures in solid polymeric insulation that allows for combined electrical and mechanical stresses. We present an energy balance analysis during the tree growth process and show the total tree extension driving force is not a material constant due to the existence of a damage process zone around the tree tip and the dissipated heat and the trapped energy remaining in the damage process zone. We derive both the tree growth rate equation and life formula of tree propagation to breakdown, based on the specific tree growth mechanism and the fractal nature of tree structures. We perform electrical tree growth tests in epoxy resin samples with and without mechanical residual stresses, and present results which show that the proposed model can give predicted tree propagation times to failure in good agreeement with the experimental data of the tree growth subjected to a combined electrical and mechanical stress.