The average time for the onset of macroscopic fractures is analytically and
numerically investigated in the fiber-bundle model with quenched disorder and
thermal noise under a constant load. We find an implicit exact expression for
the failure time in the low-temperature limit that is accurately confirmed by
direct simulations. The effect of the disorder is to lower the energy barrier.Comment: 11 pages, 6 figures; accepted for publication in Phys. Rev.