Asymptotic bounds on the time to fatigue failure of bundles of fibers under local load sharing

1982 ◽  
Vol 14 (01) ◽  
pp. 95-121 ◽  
Author(s):  
Luke Tierney
Keyword(s):  
Fatigue Failure ◽  
General Framework ◽  
Applied Load ◽  
Tensile Load ◽  
Load Sharing ◽  
Local Load ◽  
Fiber Bundles ◽  
Asymptotic Bounds ◽  
Parallel Arrangement ◽  
A Chain

A fiber bundle is a parallel arrangement of fibers. Under a steady tensile load, fibers fail randomly in time in a manner that depends on how they share the applied load. The bundle fails when all its fibers have failed in a specified region.In this paper we consider the fatigue failure of such a bundle in a fiber load-sharing setting appropriate for composite materials, that is, to bundles impregnated with a flexible matrix. The bundle is actually modelled as a chain of short bundles, and local load sharing is assumed for the fibers within each short bundle. The chain of bundles fails once all the fibers in one of the short bundles have failed.Reasonable assumptions are made on the stochastic failure of individual fibers. A general framework for describing fiber bundles is developed and is used to derive the limiting distribution of the time to the first appearance of a set ofkor more adjacent failed fibers as the number of fibers in the bundle grows large. These results provide useful bounds on the distribution of the time to total bundle failure. Some implications and extensions of these results are discussed.

Asymptotic bounds on the time to fatigue failure of bundles of fibers under local load sharing

1982 ◽  
Vol 14 (1) ◽  
pp. 95-121 ◽  
Author(s):  
Luke Tierney
Keyword(s):  
Fatigue Failure ◽  
General Framework ◽  
Applied Load ◽  
Tensile Load ◽  
Load Sharing ◽  
Local Load ◽  
Fiber Bundles ◽  
Asymptotic Bounds ◽  
Parallel Arrangement ◽  
A Chain

A fiber bundle is a parallel arrangement of fibers. Under a steady tensile load, fibers fail randomly in time in a manner that depends on how they share the applied load. The bundle fails when all its fibers have failed in a specified region.In this paper we consider the fatigue failure of such a bundle in a fiber load-sharing setting appropriate for composite materials, that is, to bundles impregnated with a flexible matrix. The bundle is actually modelled as a chain of short bundles, and local load sharing is assumed for the fibers within each short bundle. The chain of bundles fails once all the fibers in one of the short bundles have failed.Reasonable assumptions are made on the stochastic failure of individual fibers. A general framework for describing fiber bundles is developed and is used to derive the limiting distribution of the time to the first appearance of a set of k or more adjacent failed fibers as the number of fibers in the bundle grows large. These results provide useful bounds on the distribution of the time to total bundle failure. Some implications and extensions of these results are discussed.

Burst-size distribution in fiber-bundles with local load-sharing

1994 ◽  
Vol 193 (5-6) ◽  
pp. 425-430 ◽  
Author(s):  
S.D. Zhang ◽  
E.J. Ding
Keyword(s):  
Size Distribution ◽  
Burst Size ◽  
Load Sharing ◽  
Local Load ◽  
Fiber Bundles

scholarly journals Local load sharing fiber bundles with a lower cutoff of strength disorder

2006 ◽  
Vol 74 (3) ◽  
Author(s):  
Frank Raischel ◽  
Ferenc Kun ◽  
Hans J. Herrmann
Keyword(s):  
Load Sharing ◽  
Local Load ◽  
Fiber Bundles ◽  
Lower Cutoff

Failure of fiber bundles with local load sharing

1996 ◽  
Vol 53 (2) ◽  
pp. 646-654 ◽  
Author(s):  
Shu-dong Zhang ◽  
E-Jiang Ding
Keyword(s):  
Load Sharing ◽  
Local Load ◽  
Fiber Bundles

scholarly journals FAILURE PROPERTIES OF FIBER BUNDLE MODELS

2003 ◽  
Vol 17 (29) ◽  
pp. 5565-5581 ◽  
Author(s):  
SRUTARSHI PRADHAN ◽  
BIKAS K. CHAKRABARTI
Keyword(s):  
Critical Stress ◽  
Finite Interval ◽  
Fiber Strength ◽  
Load Sharing ◽  
Higher Dimensions ◽  
Strength Distribution ◽  
Local Load ◽  
Fiber Bundles ◽  
Magnetic Model ◽  
Failure Properties

We study the failure properties of fiber bundles when continuous rupture goes on due to the application of external load on the bundles. We take the two extreme models: equal load sharing model (democratic fiber bundles) and local load sharing model. The strength of the fibers are assumed to be distributed randomly within a finite interval. The democratic fiber bundles show a solvable phase transition at a critical stress (load per fiber). The dynamic critical behavior is obtained analytically near the critical point and the critical exponents are found to be universal. This model also shows elastic-plastic like nonlinear deformation behavior when the fiber strength distribution has a lower cut-off. We solve analytically the fatigue-failure in a democratic bundle, and the behavior qualitatively agrees with the experimental observations. The strength of the local load sharing bundles is obtained numerically and compared with the existing results. Finally we map the failure phenomena of fiber bundles in terms of magnetic model (Ising model) which may resolve the ambiguity of studying the failure properties of fiber bundles in higher dimensions.

Scaling law in avalanche breaking of composite materials

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Ahmed Hader ◽  
Hicham Sbiaai ◽  
Mohammed Tanasehte ◽  
Layla Amallah ◽  
Yahia Boughaleb
Keyword(s):  
Composite Materials ◽  
External Load ◽  
Fiber Bundle ◽  
Applied Load ◽  
Scaling Law ◽  
Load Sharing ◽  
Local Load ◽  
Vicsek Model ◽  
Content Type ◽  
Fiber Bundle Model

PurposeThe fibers are loaded by the cosine component of the external load, when a fiber fails, and due to the local load-sharing nature, its force is shared by surviving neighboring fibers. The results show that the system presents a greater resistance and toughness toward the applied load compared to the classical one.Design/methodology/approachIn this paper, the authors adopt the dynamics of a local load-sharing fiber bundle model in two dimensions under an external load to study scaling law in failure process of composite materials with randomly oriented fibers. The model is based on the fiber bundle model where the fibers are randomly oriented. The system is different to the classical one where the fibers are arranged in parallel with the applied load direction.FindingsThe evolution time of the fraction of broken fiber is described by an exponential law with two characteristic times. The latter decrease linearly and exponentially respectively with both applied load and temperature.Originality/valueScaling behavior of the broken fiber numbers with the size system shows that the system exhibits a scaling law of Family–Vicsek model with universal exponents.

scholarly journals Size Distribution of Emitted Energies in Local Load Sharing Fiber Bundles

2021 ◽  
Vol 9 ◽  
Author(s):  
Subhadeep Roy ◽  
Soumyajyoti Biswas
Keyword(s):  
Size Distribution ◽  
Power Law ◽  
Linear Relation ◽  
Fiber Bundle ◽  
Average Energy ◽  
Load Sharing ◽  
Local Load ◽  
Fiber Bundles ◽  
Avalanche Size ◽  
Fiber Bundle Model

We study the local load sharing fiber bundle model and its energy burst statistics. While it is known that the avalanche size distribution of the model is exponential, we numerically show here that the avalanche size (s) and the corresponding average energy burst (〈E〉) in this version of the model have a non-linear relation (〈E〉 ~ sγ). Numerical results indicate that γ ≈ 2.5 universally for different failure threshold distributions. With this numerical observation, it is then possible to show that the energy burst distribution is a power law, with a universal exponent value of −(γ + 1).

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