Failure properties of fiber bundle models

TL;DR

This paper investigates the failure behavior of fiber bundle models under load, analyzing both equal and local load sharing scenarios, deriving critical behavior analytically, and relating the phenomena to magnetic models for higher-dimensional insights.

Contribution

It provides analytical solutions for phase transition and failure in democratic fiber bundles and maps failure phenomena to magnetic models for higher-dimensional understanding.

Findings

Universal critical exponents near the phase transition

Elastic-plastic nonlinear deformation behavior observed

Qualitative agreement with experimental fatigue-failure data

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.