Nucleation versus percolation: Scaling criterion for failure in disordered solids

Abstract

One of the major factors governing the mode of failure in disordered solids is the effective range $R$, over which the stress field is modified following a local rupture event. In random fiber bundle model, considered as a prototype of disordered solids, we show that the failure mode is nucleation dominated in the large system size limit, as long as $R$ scales slower than $L^{\zeta }$, with $\zeta =2/3$. For a faster increase in $R$, the failure properties are dominated by the mean-field critical point, where the damages are uncorrelated in space. In that limit, the precursory avalanches of all sizes are obtained even in the large system size limit. We expect these results to be valid for systems with finite (normalizable) disorder.

arXiv comment5 pages, 4 figures

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• Crack Localization and the Interplay between Stress Enhancement and Thermal Noise
• Failure time in heterogeneous systems
• Correlation between avalanches and emitted energies during fracture with variable stress release range
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• Influence of Roughness on Granular Avalanches
• An Insight of Heart-Like Systems with Percolation
• 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
• Modeling crack propagation in heterogeneous materials: Griffith's law, intrinsic crack resistance and avalanches