Failure properties of fiber bundle models

Abstract

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.

18 pages and 10 figs, to be published as DMTAS conf. proc. (held in Chennai India) in IJMPB

References in corpus (6)

• Bursts in a fiber bundle model with continuous damage
• Dynamic critical behavior of failure and plastic deformation in the random fiber bundle model
• Precursors of catastrophe in the BTW, Manna and random fiber bundle models of failure
• Phase transition in fiber bundle models with recursive dynamics
• Failure due to fatigue in fiber bundles and solids
• Time evolution of damage under variable ranges of load transfer

Cited by in corpus (22)

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• Failure properties of loaded fiber bundles having a lower cutoff in fiber threshold distribution
• Crossover behavior in a mixed mode fiber bundle model
• A simple beam model for the shear failure of interfaces
• A Fiber Bundle Model of Traffic Jams
• Effect of discontinuity in threshold distribution on the critical behaviour of a random fiber bundle
• Gravity-driven instabilities: interplay between state-and-velocity dependent frictional sliding and stress corrosion damage cracking
• Attack vulnerability of power systems under an equal load redistribution model
• Phase transition in the modified fiber bundle model
• A random fiber bundle with many discontinuities in the threshold distribution
• Robustness of flow networks against cascading failures under partial load redistribution
• Crossover behaviors in one and two dimensional heterogeneous load sharing fiber bundle models
• Self-organized dynamics in local load sharing fiber bundle models
• Creep-like behavior in athermal threshold dynamics: Effects of disorder and stress
• Random neighbour model for yielding
• Fiber bundle model under heterogeneous loading
• Fractal Dimensionof the El Salvador Earthquake (2001) time Series
• Stability in fiber bundle model : Existence of strong links and the effect of disorder