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 σ is ${\mathrm{\sigma }}^{\mathrm{\eta }}$. For all η, it predicts the system-size scaling of the number of broken elements at breakdown found in simulations. The breakdown is shown to be percolationlike for η≤2 but is due to the dominance of one large growing crack, despite the absence of a failure threshold, for η>2. This transition in fracture behavior and in scaling at η>2 is found to be directly related to the dependence of crack tip stress enhancement on the square root of crack size.