Time-dependent fracture under unloading in a fiber bundle model

We investigate the fracture of heterogeneous materials occurring under\nunloading from an initial load. Based on a fiber bundle model of time dependent\nfracture, we show that depending on the unloading rate the system has two\nphases: for rapid unloading the system suffers only partial failure and it has\nan infinite lifetime, while at slow unloading macroscopic failure occurs in a\nfinite time. The transition between the two phases proved to be analogous to\ncontinuous phase transitions. Computer simulations revealed that during\nunloading the fracture proceeds in bursts of local breakings triggered by\nslowly accumulating damage. In both phases the time evolution starts with a\nrelaxation of the bursting activity characterized by a universal power law\ndecay of the burst rate. In the phase of finite lifetime the initial slowdown\nis followed by an acceleration towards macroscopic failure where the increasing\nrate of bursts obeys the (inverse) Omori law of earthquakes. We pointed out a\nstrong correlation between the time where the event rate reaches a minimum\nvalue and of the lifetime of the system which allows for forecasting of the\nimminent catastrophic failure.\n