Stochastic simulation of water treeing in heterogeneous media using a field enhancement equation

Water treeing simulation using a field enhancement equation is performed in this study. Tree shape and growth time are stochastically governed by growth probability directly proportional to the enhanced local stress when it is greater than tree inception strength. Trees grow only if a growth criterion (a dimensionless treeing number ⩾1) is met. The heterogeneous media are composed of one of four heterogeneous inclusions randomly distributed in a homogeneous matrix. A tree can grow into type I and II, toward but not into type III, and always around type IV inclusions. The treeing number is less than 1 for type II but not for type I. Of course, it is irrelevant to type III and IV. The effects of the presence of each inclusion type at various percentages and sizes on tree shape and growth time are studied. Some of the simulated tree shapes are close to those observed in our laboratory studies. In general, the order from long to short growth time is from type III, II, I, to IV. The physical implication for each inclusion type is also given