[SY-K2] Avalanche precursors and fracture strength in the limit of high disorder
Most of the materials have an inherent disorder which appears at different length scales in the form of dislocations, flaws, microcracks, grain boundaries, or internal frictional interfaces. Under mechanical load, this quenched disorder plays a decisive role in the emerging fracture process: Increasing the extension of samples a size effect emerges, i.e. the ultimate strength of disordered materials is a decreasing function of their size. On the microscale the fracture process is composed of a large number of crack nucleation - propagation - arrest steps which generate a sequence of precursory cracking avalanches. This crackling noise is of ultimate importance to forecast natural catastrophes such as landslides and earthquakes, and the catastrophic failure of engineering constructions.
We investigate how the amount of microscale disorder affects the emerging fracture process focusing on the size scaling of the ultimate fracture strength and on the time series of avalanche precursors. We consider a fiber bundle model where the strength of fibers is described by a power law distribution. Tuning the amount of disorder by varying the power law exponent and the upper cutoff of fibers' strength, in the mean field limit an astonishing size effect is revealed: For small system sizes the bundle strength increases with the number of fibers and the usual decreasing size effect is only restored beyond a characteristic size. We show that the extreme order statistics of the micro-scale disorder is responsible for this peculiar behavior, which can be exploited for materials' design.
In the limit of very high disorder the avalanche activity does not show any acceleration so that no signatures of the imminent catastrophic failure can be identified. Limiting the disorder to a finite range an acceleration period emerges with precursors, however, the predictability of the catastrophic event depends on the details of the tail of the disorder distribution.
[1] V. Kádár, Zs. Danku, and F. Kun, Physical Review E 96, 033001 (2017).
[2] Zs. Danku and F. Kun, J. Stat. Mech.: Theor. Exp. 2016, 073211 (2016).
We investigate how the amount of microscale disorder affects the emerging fracture process focusing on the size scaling of the ultimate fracture strength and on the time series of avalanche precursors. We consider a fiber bundle model where the strength of fibers is described by a power law distribution. Tuning the amount of disorder by varying the power law exponent and the upper cutoff of fibers' strength, in the mean field limit an astonishing size effect is revealed: For small system sizes the bundle strength increases with the number of fibers and the usual decreasing size effect is only restored beyond a characteristic size. We show that the extreme order statistics of the micro-scale disorder is responsible for this peculiar behavior, which can be exploited for materials' design.
In the limit of very high disorder the avalanche activity does not show any acceleration so that no signatures of the imminent catastrophic failure can be identified. Limiting the disorder to a finite range an acceleration period emerges with precursors, however, the predictability of the catastrophic event depends on the details of the tail of the disorder distribution.
[1] V. Kádár, Zs. Danku, and F. Kun, Physical Review E 96, 033001 (2017).
[2] Zs. Danku and F. Kun, J. Stat. Mech.: Theor. Exp. 2016, 073211 (2016).