Time to failure of hierarchical load-transfer models of fracture

The time to failure, $T$, of dynamical models of fracture for a hierarchical load-transfer geometry is studied. Using a probabilistic strategy and juxtaposing hierarchical structures of height $n$, we devise an exact method to compute $T$, for structures of height $n+1$. Bounding $T$, for large $n$, we are able to deduce that the time to failure tends to a non-zero value when $n$ tends to infinity. This numerical conclusion is deduced for both power law and exponential breakdown rules.