Crack arrest by residual bonding in resistor and spring networks

A propagating crack in a resistor (spring) network may stop because of residual resistance (residual or ligamentary bonding) behind the crack tip. In breakdown networks containing random flaws, this leads to failure by microcracking rather than by the growth of a dominant crack. Numerical simulations of two-dimensional random resistor networks indicate that the transition between these two regimes occurs near $R\sim 35$ for $p=0.75\mathrm{}$, where $R$ is the ratio of the residual resistance to the original resistance.