The failure distribution in percolation models of breakdown

Abstract

The probability of finding a largest defect cluster of size n in a percolation network is calculated analytically using a new distribution function scaling equation. From this result and the stress (voltage) enhancement at the tip of the most critical defect in the network, the probability of failure in percolation models of breakdown is calculated. For defect fractions less than the percolation point, this distribution is found to be of the form exponential of an exponential. Numerical simulations on the two-dimensional random fuse network confirm the new distribution function and convincingly distinguish between it and the Weibull (1951) form most often used in the fitting of breakdown data.