Time-dependent fiber bundles with local load sharing. II. General Weibull fibers

2009 ◽  
Vol 80 (6) ◽  
Author(s):  
S. Leigh Phoenix ◽  
William I. Newman
Keyword(s):  
Load Sharing ◽  
Time Dependent ◽  
Local Load ◽  
Fiber Bundles

scholarly journals Crossover of Failure Time Distributions in a Model of Time-Dependent Fracture

2021 ◽  
Vol 9 ◽  
Author(s):  
Mikko J. Alava
Keyword(s):  
External Load ◽  
Failure Time ◽  
Load Sharing ◽  
System Size ◽  
Time Dependent ◽  
Local Load ◽  
Extreme Statistics ◽  
Lifetime Distributions ◽  
One Dimensional ◽  
Failure Time Distributions

An important question in the theory of fracture is what kind of lifetime distributions may exist for materials under load. Here, this is studied in the context of a one-dimensional fracture model with local load sharing under a constant external load, “creep.” Simulations of the system with Weibull distributed initial lifetimes for the elements show that the limiting distribution follows from extreme statistics and takes the Gumbel form eventually, with longer and longer crossovers in the system size from a Weibull-like distribution, depending on the initial Weibull exponent.

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.

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

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.

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.

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