Size scaling of failure strength with fat-tailed disorder in a fiber bundle model

Abstract

We investigate the size scaling of the macroscopic fracture strength of heterogeneous materials when microscopic disorder is controlled by fat-tailed distributions. We consider a fiber bundle model where the strength of single fibers is described by a power law distribution over a finite range. Tuning the amount of disorder by varying the power law exponent and the upper cutoff of fibers' strength, in the limit of equal load sharing an astonishing size effect is revealed: For small system sizes the bundle strength increases with the number of fibers and the usual decreasing size effect of heterogeneous materials is only restored beyond a characteristic size. We show analytically that the extreme order statistics of fibers' strength is responsible for this peculiar behavior. Analyzing the results of computer simulations we deduce a scaling form which describes the dependence of the macroscopic strength of fiber bundles on the parameters of microscopic disorder over the entire range of system sizes.

arXiv comment6 pages, 4 figures, revtex

References in corpus (13)

• Statistical Models of Fracture
• Failure Processes in Elastic Fiber Bundles
• Tri-critical behavior in rupture induced by disorder
• Burst avalanches in solvable models of fibrous materials
• Fracture model with variable range of interaction
• Fracture in Three-Dimensional Fuse Networks
• Turning Statistical Physics Models Into Materials Design Engines
• Size effects in statistical fracture
• Role of disorder in the size-scaling of material strength
• Percolation and localization in the random fuse model
• Time evolution of damage under variable ranges of load transfer
• Breakdown of fiber bundles with stochastic load-redistribution
• Micro-structure of damage in thermally activated fracture of Lennard-Jones systems

Cited by in corpus (9)

• Modes of failures in disordered solids
• Record statistics of bursts signals the onset of acceleration towards failure
• Avalanche dynamics in higher dimensional fiber bundle models
• System-size-dependent avalanche statistics in the limit of high disorder
• Size scaling of failure strength at high disorder
• Failure process of fiber bundles with random misalignment
• From nucleation to percolation: the effect of system size when disorder and stress localization compete
• From nucleation to percolation: the effect of system size and system disorder
• Effect of localized loading on failure threshold of fiber bundles