1,160 research outputs found
Time dependent fracture under unloading in a fiber bundle model
We investigate the fracture of heterogeneous materials occurring under
unloading from an initial load. Based on a fiber bundle model of time dependent
fracture, we show that depending on the unloading rate the system has two
phases: for rapid unloading the system suffers only partial failure and it has
an infinite lifetime, while at slow unloading macroscopic failure occurs in a
finite time. The transition between the two phases proved to be analogous to
continuous phase transitions. Computer simulations revealed that during
unloading the fracture proceeds in bursts of local breakings triggered by
slowly accumulating damage. In both phases the time evolution starts with a
relaxation of the bursting activity characterized by a universal power law
decay of the burst rate. In the phase of finite lifetime the initial slowdown
is followed by an acceleration towards macroscopic failure where the increasing
rate of bursts obeys the (inverse) Omori law of earthquakes. We pointed out a
strong correlation between the time where the event rate reaches a minimum
value and of the lifetime of the system which allows for forecasting of the
imminent catastrophic failure.Comment: 10 pages, 10 figures, revte
Damage process of a fiber bundle with a strain gradient
We study the damage process of fiber bundles in a wedge-shape geometry which
ensures a constant strain gradient. To obtain the wedge geometry we consider
the three-point bending of a bar, which is modelled as two rigid blocks glued
together by a thin elastic interface. The interface is discretized by parallel
fibers with random failure thresholds, which get elongated when the bar is
bent. Analyzing the progressive damage of the system we show that the strain
gradient results in a rich spectrum of novel behavior of fiber bundles. We find
that for weak disorder an interface crack is formed as a continuous region of
failed fibers. Ahead the crack a process zone develops which proved to shrink
with increasing deformation making the crack tip sharper as the crack advances.
For strong disorder, failure of the system occurs as a spatially random
sequence of breakings. Damage of the fiber bundle proceeds in bursts whose size
distribution shows a power law behavior with a crossover from an exponent 2.5
to 2.0 as the disorder is weakened. The size of the largest burst increases as
a power law of the strength of disorder with an exponent 2/3 and saturates for
strongly disordered bundles.Comment: 8 pages, 7 figures, accepted by PR
Local load sharing fiber bundles with a lower cutoff of strength disorder
We study the failure properties of fiber bundles with a finite lower cutoff
of the strength disorder varying the range of interaction between the limiting
cases of completely global and completely local load sharing. Computer
simulations revealed that at any range of load redistribution there exists a
critical cutoff strength where the macroscopic response of the bundle becomes
perfectly brittle, i.e. linearly elastic behavior is obtained up to global
failure, which occurs catastrophically after the breaking of a small number of
fibers. As an extension of recent mean field studies [Phys. Rev. Lett. 95,
125501 (2005)], we demonstrate that approaching the critical cutoff, the size
distribution of bursts of breaking fibers shows a crossover to a universal
power law form with an exponent 3/2 independent of the range of interaction.Comment: 4 pages, 4 figure
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