Failure processes in elastic fiber bundles

Pradhan, Srutarshi; Hansen, Alex; Chakrabarti, Bikas K.

doi:10.1103/revmodphys.82.499

Cited by 331 publications

(443 citation statements)

References 177 publications

(222 reference statements)

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“…For the classical FBM (as described above) with forcecontrolled load, democratic load sharing, and without healing mechanisms, other authors have reported the following results (see reviews, e.g., [3,25]): The avalanche size S (number of broken fibers) is power-law distributed P (S) ≈ S b with b = 5/2 for all avalanches. If just the avalanches near failure are considered, the avalanche size is still power-law distributed but has a lower exponent with b = 3/2.…”

Section: Theoretical Considerations Of Fbm Model With Healingmentioning

confidence: 93%

“…Moreover, it has been shown that the b value does not depend on the type of fiber strength distribution [27]. For these reasons the change of the b value towards failure is considered to be a good precursor, and the divergence of the order parameter and fiber failure rate can be used to predict the time when the bundle fails (e.g., [3]). Potentially damaging bursts or avalanches can be measured from outside without influencing the failure process (e.g., by acoustic emissions) and therefore the FBM theoretical results can be applied in practice.…”

Section: Consequences For Failure Predictionmentioning

confidence: 99%

“…We used the Weibull distribution because it is commonly used for statistical fracture models. The failure behavior of the classical FBM is not influenced by the type of distribution and shape factor k [3,27]. The mean fiber strength is set to 1, adjusting the scale factor μ accordingly.…”

Section: Theoretical Considerations Of Fbm Model With Healingmentioning

confidence: 99%

“…For the classical FBM without healing the order parameter (difference in fraction of broken fibers at the critical load and a smaller load) converges to zero towards failure following a power law O ∼ (σ c − σ ) α with α = 1/2 [3]. Figure 10 The fiber failure rate was computed with a running window of size 1000.…”

Section: Order Parametermentioning

confidence: 99%

“…FBMs are often used to study material failure in the context of statistical physics and the analogy to phase transitions and critical phenomena. A variety of modifications of FBMs have been proposed to study the failure of different types of heterogeneous materials (e.g., [2,3]). …”

Section: Introductionmentioning

confidence: 99%

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Fiber-bundle model with time-dependent healing mechanisms to simulate progressive failure of snow

et al. 2018

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Snow is a heterogeneous material with strain-and/or load-rate-dependent strength. In particular, a transition from ductile-to-brittle failure behavior with increasing load rate is observed. The rate-dependent behavior can partly be explained with the existence of a unique healing mechanism in snow that stems from its high homologous temperature (temperature close to melting point). As soon as broken elements in the ice matrix get in contact, they start sintering and the structure may regain strength. Moreover, the ice matrix is subjected to viscous deformation, inducing a relaxation of local load concentrations and, therefore, further counteracting the damage process. Ideal tools for studying the failure process of heterogeneous materials are the fiber-bundle models (FBMs), which allow investigating the effects of basic microstructural characteristics on the general macroscopic failure behavior. We present an FBM with two concurrent time-dependent healing mechanisms: sintering of broken fibers and relaxation of load inhomogeneities. Sintering compensates damage by creating additional intact, load-supporting fibers which lead to an increase of the bundle strength. However, the character of the failure is not changed by sintering alone. With combined sintering and load relaxation, load is distributed from old stronger fibers to new fibers that carry fewer load. So as we additionally incorporated load redistribution to the FBM, the failure occurred suddenly without decrease of the order parameter-describing the amount of damage in the bundle-and without divergence of the fiber failure rate. Moreover, the b value, i.e., the power-law exponent of frequency-magnitude statistics of fibers breaking in load redistribution steps, at failure converged to b ≈ 2, a value higher than that of a classical FBM without healing (b = 3 2 ). These results indicate that healing, as the combined effect of sintering and load relaxation, changes the type of the phase transition at failure. This change of the phase transition is important for quantifying or predicting the failure (e.g., by monitoring acoustic emissions) of snow or other materials for which healing plays an important role.

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Section: Theoretical Considerations Of Fbm Model With Healingmentioning

confidence: 93%

Section: Consequences For Failure Predictionmentioning

confidence: 99%

Section: Theoretical Considerations Of Fbm Model With Healingmentioning

confidence: 99%

Section: Order Parametermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Fiber-bundle model with time-dependent healing mechanisms to simulate progressive failure of snow

et al. 2018

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Shear‐induced force fluctuations and acoustic emissions in granular material

Michlmayr

Cohen

2013

JGR Solid Earth

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[1] We conducted a series of strain-controlled experiments to study the characteristics of a shear zone forming in dense flow of confined dry granular media. The primary objective was to link force fluctuations due to jamming and force network reformation with episodic release of elastic energy as passively monitored by acoustic emission sensors. Under constant deformation rate, the shear stress exhibits a characteristic sawtooth behavior reflecting the strong influence of micromechanical processes on the macroscopic stress-strain behavior. Measured shear stress jumps were highly correlated with low-frequency (< 20 kHz) acoustic emission events. High-frequency (30 kHz-80 kHz) acoustic signals that were measured with different sensors appear to be directly linked to continual grain-scale interactions (e.g., friction, rolling). A conceptual mechanical fiber bundle model (FBM) was used to represent dynamics at the shear zone of large granular assemblies. The model was capable of reproducing the dynamics of stress jumps and associated elastic energy release events. The combination of acoustic emission (AE) measurements and FBM framework offers new insights into the behavior of shear failure and enhances capabilities for resolving grain-scale mechanical processes and for predicting rapid mass movement such as shallow landslides and debris flows.

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Codetection of acoustic emissions during failure of heterogeneous media: New perspectives for natural hazard early warning

Faillettaz

Reiweger³

2016

Geophysical Research Letters

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A simple method for real‐time early warning of gravity‐driven rupture that considers both the heterogeneity of natural media and characteristics of acoustic emissions attenuation is proposed. The method capitalizes on codetection of elastic waves emanating from microcracks by multiple and spatially separated sensors. Event codetection is considered as surrogate for large event size with more frequent codetected events marking imminence of catastrophic failure. Using a spatially explicit fiber bundle numerical model with spatially correlated mechanical strength and two load redistribution rules, we constructed a range of mechanical failure scenarios and associated failure events (mapped into acoustic emission) in space and time. Analysis considering hypothetical arrays of sensors and consideration of signal attenuation demonstrate the potential of the codetection principles even for insensitive sensors to provide early warning for imminent global failure.

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Failure processes in elastic fiber bundles

Cited by 331 publications

References 177 publications

Fiber-bundle model with time-dependent healing mechanisms to simulate progressive failure of snow

Fiber-bundle model with time-dependent healing mechanisms to simulate progressive failure of snow

Shear‐induced force fluctuations and acoustic emissions in granular material

Codetection of acoustic emissions during failure of heterogeneous media: New perspectives for natural hazard early warning

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