Nucleation versus percolation: Scaling criterion for failure in disordered solids

One of the major factors governing the mode of failure in disordered solids is the effective range $R$, over which the stress field is modified following a local rupture event. In random fiber bundle model, considered as a prototype of disordered solids, we show that the failure mode is nucleation dominated in the large system size limit, as long as $R$ scales slower than $L^{\zeta}$, with $\zeta=2/3$. For a faster increase in $R$, the failure properties are dominated by the mean-field critical point, where the damages are uncorrelated in space. In that limit, the precursory avalanches of all sizes are obtained even in the large system size limit. We expect these results to be valid for systems with finite (normalizable) disorder.