ANALYTIC MODEL FOR SCALING OF BREAKDOWN

A theory is presented for the time-dependent breakdown of a network of spring (fuse) elements where the probability of breaking an element under load-sigma is sigma-eta. For all eta, it predicts the system-size scaling of the number of broken elements at breakdown round in simulations. The breakdown is shown to be percolationlike for eta less-than-or-equal-to 2 but is due to the dominance of one large growing crack, despite the absence of a failure threshold, for eta > 2. This transition in fracture behavior and in scaling at eta > 2 is found to be directly related to the dependence of crack tip stress enhancement on the square root of crack size.