The effect of disorder on the fracture nucleation process (original) (raw)
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Disorder enhances the effects of thermal noise in the fiber bundle model
Europhysics Letters (epl), 2001
The statistical properties of failure are studied in a fiber bundle model with thermal noise. We show that the macroscopic failure is produced by a thermal activation of microcracks. Most importantly, the effective temperature of the system is amplified by the spatial disorder (heterogeneity) of the fiber bundle. These results give new insight to the study of thermally activated cracks and they can be useful in the study of electrical networks.
Crack localization and the interplay between stress enhancement and thermal noise
Physica A: Statistical Mechanics and its Applications, 2021
We study the competition between thermal fluctuations and stress enhancement in the failure process of a disordered system by using a local load sharing fiber bundle model. The thermal noise is introduced by defining a failure probability that constitutes the temperature and elastic energy of the fibers. We observe that at a finite temperature and low disorder strength, the failure process, which nucleate in the absence of any thermal fluctuation, becomes spatially uncorrelated when the applied stress is sufficiently low. The dynamics of the model in this limit lies closely to the universality class of ordinary percolation. When applied stress is increased beyond a threshold value, localized fractures appear in the system that grow with time. We identify the boundary between the localized and random failure process in the space of temperature and applied stress, and find that the threshold of stress corresponding to the onset of localized crack growth increases with the increase of temperature.
A thermodynamical fibre bundle model for the fracture of disordered materials
Journal of Statistical Mechanics: Theory and Experiment, 2007
We investigate a disordered version of a thermodynamic fiber bundle model proposed by Selinger, Wang, Gelbart, and Ben-Shaul a few years ago. For simple forms of disorder, the model is analytically tractable and displays some new features. At either constant stress or constant strain, there is a non monotonic increase of the fraction of broken fibers as a function of temperature.
Failure time in the fiber-bundle model with thermal noise and disorder
Physical Review E, 2002
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.
Material failure time and the fiber bundle model with thermal noise
1999
The statistical properties of failure are studied in a fiber bundle model with thermal noise. We find that in agreement with recent experiments the macroscopic failure is produced by a thermal activation of microcracks. Most importantly the effective temperature of the system is amplified by the spatial disorder (heterogeneity) of the fiber bundle.
Continuous damage fiber bundle model for strongly disordered materials
Physical Review E, 2008
We present an extension of the continuous damage fiber bundle model to describe the gradual degradation of highly heterogeneous materials under an increasing external load. Breaking of a fiber in the model is preceded by a sequence of partial failure events occurring at random threshold values. In order to capture the subsequent propagation and arrest of cracks, furthermore, the disorder of the number of degradation steps of material constituents, the failure thresholds of single fibers are sorted into ascending order and their total number is a Poissonian distributed random variable over the fibers. Analytical and numerical calculations showed that the failure process of the system is governed by extreme value statistics, which has a substantial effect on the macroscopic constitutive behaviour and on the microscopic bursting activity as well.
Size Scaling and Bursting Activity in Thermally Activated Breakdown of Fiber Bundles
Physical Review Letters, 2008
We study subcritical fracture driven by thermally activated damage accumulation in the framework of fiber bundle models. We show that in the presence of stress inhomogeneities, thermally activated cracking results in an anomalous size effect; i.e., the average lifetime ht f i decreases as a power law of the system size ht f i $ L Àz , where the exponent z depends on the external load and on the temperature T in the form z $ fð=T 3=2 Þ. We propose a modified form of the Arrhenius law which provides a comprehensive description of thermally activated breakdown. Thermal fluctuations trigger bursts of breakings which have a power law size distribution.
The Effect of Disorder on Crackling Noise in Fracture Phenomena
Progress of Theoretical Physics Supplement, 2010
We study the effect of disorder on crackling noise accompanying the fracture of heterogeneous materials. Two different types of system are considered: we analyze the three-point bending of a bar shaped specimen where the boundary and loading conditions ensure that crackling occurs during the propagation of a single crack; then we study a bundle of fibers where noise emerges as a consequence of spatially uncorrelated stick-slip rearrangements. We show that bursts characterizing the jerky propagation of a crack have a power law size distribution with an exponent which does not depend on the amount of disorder. Our calculations revealed that varying the amount of disorder in a stick-slip system, a phase-transition occurs: at high disorder stick-slip rearrangements occur in small bursts, while at low disorder macroscopic avalanches snap the system. Our investigations demonstrate that the relevance of disorder on crackling noise is strongly influenced by the presence or absence of stress concentrations in the system.
Thermally induced creep rupture of fiber bundles
Subcritical fracture driven by thermally activated crack nucleation is studied in the framework of a fiber bundle model. Based on analytic calculations and computer simulations, we show that, in the presence of stress inhomogeneity thermally activated cracking results in an anomalous size effect, i.e., the average lifetime of the system decreases as a power-law of the system size. We propose a modified Arrhenius law which provides a comprehensive description of the load, temperature, and size dependence of the lifetime of the system. On the microscopic level, thermal fluctuations trigger bursts of breaking events which proved to have a power-law size distribution. The waiting times between consecutive bursts are also power-law distributed with an exponent switching between 1 and 2 as the load and temperature are varied. Analyzing the structural entropy and the location of consecutive bursts, we show that, in the presence of stress concentration, the acceleration of the rupture process close to failure is the consequence of damage localization.
Journal of Engineering Mechanics, 2001
This paper considers a model of crack propagation taking place at the interface between a rigid support and an elastic plate. The interface is modeled using a fiber bundle model (i.e., describing a damage behavior using a discrete set of elastic brittle elements having a random strength). This paper studies the fluctuations of the force required to propagate the crack along the interface. The statistics of avalanches, defined as a series of elements that are broken simultaneously under a load that decreases with the crack advance, are studied numerically and analytically. Local fiber breakage kinetics is related to a correlation length, which sets the size of a fracture process zone.