A water treeing model

A new model for water treeing is introduced. It assumes that when the field-induced stress applied on nano cavities filled with a liquid is larger than the yield strength of the polymer, bonds will be broken and the nano cavity will expand. The growth of the water trees is enhanced by the fatigue induced by the alternating electric field. The diffusion of the liquid is also a parameter affecting the water tree length. A simple equation relating the water tree length with field, time, frequency, and the nature of the solution is presented. A very good agreement between theory and experiments for a wide variety of results obtained with low density polyethylene (LDPE) tested under various fields, frequencies and ionic solutions is observed. This model also predicts the growth of water trees under DC fields after very long times or after many polarity reversals. Some aspects of this model requiring further refinements or experimental data are also pointed out.