[SY-K2] Time dependent fracture under unloading in a fiber bundle model
Failure of materials can also occur due to unloading from a previously applied stress level. Excavation during underground engineering rapidly releases stress which can result in rock bursts. Similar conditions may also occur on much larger length and time scales at the emergence of earthquakes: crustal unloading due to near-surface mass redistribution (water, ice or quarried material) can affect the subsurface stress field altering seismic activity and being also responsible for rupture activation and induced earthquakes. Fracture processes under unloading present a high degree of complexity which makes it difficult to achieve a general understanding.
To consider this problem, we investigate the process of sub-critical fracture which occurs when unloading from an initial load. We use a fiber bundle model of time dependent deformation and rupture which captures the slow damaging of loaded fibers and their immediate breaking when the local load exceeds the fibers' fracture strength. We focus on the case when a constant sub-critical load gives rise to failure in a finite time so that unloading may prevent the final breakdown. We show that the system has two phases: at rapid unloading only partial failure occurs and the sample has an infinite lifetime, however, slow unloading results in global failure in a finite time. We demonstrate that the transition between the phases of finite and infinite lifetime occurs as a continuous phase transition.
The unloading process is accompanied by breaking bursts of fibers with a varying rate. We show by computer simulations that in the regime of finite lifetime the initial relaxation is followed by a short acceleration period of bursting activity towards failure which is described by the Omori law. Based on the pattern of the time varying burst rate we propose a method to forecast the impending failure under unloading.
To consider this problem, we investigate the process of sub-critical fracture which occurs when unloading from an initial load. We use a fiber bundle model of time dependent deformation and rupture which captures the slow damaging of loaded fibers and their immediate breaking when the local load exceeds the fibers' fracture strength. We focus on the case when a constant sub-critical load gives rise to failure in a finite time so that unloading may prevent the final breakdown. We show that the system has two phases: at rapid unloading only partial failure occurs and the sample has an infinite lifetime, however, slow unloading results in global failure in a finite time. We demonstrate that the transition between the phases of finite and infinite lifetime occurs as a continuous phase transition.
The unloading process is accompanied by breaking bursts of fibers with a varying rate. We show by computer simulations that in the regime of finite lifetime the initial relaxation is followed by a short acceleration period of bursting activity towards failure which is described by the Omori law. Based on the pattern of the time varying burst rate we propose a method to forecast the impending failure under unloading.