Failure time in heterogeneous systems

Abstract

We show that the failure time ${\tau }_f$ in fiber bundle model, taken as a prototype of heterogeneous materials, depends crucially on the strength of the disorder $\delta$ and the stress release range $R$ in the system. For $R$ beyond a critical value $R_c$ the distribution of ${\tau }_f$ follows Weibull form. In this region, the average ${\tau }_f$ shows the variation ${\tau }_f\sim L^{\alpha }$ where $L$ is the system size. For $R<R_c$, ${\tau }_f\sim L/R$. We find that the crossover length scale has the scaling form $R_c\sim L^{1-\alpha }$. This scaling has been found to be valid for various disorder distributions. For $\delta <{\delta }_c$, $\alpha$ is an increasing function of $\delta$. For all $\delta \ge {\delta }_c$, $\alpha$=1/3.

4 pages, 4 figures

References in corpus (5)

• From damage percolation to crack nucleation through finite size criticality
• Modes of failures in disordered solids
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• Scaling forms for Relaxation Times of the Fiber Bundle model
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Cited by in corpus (4)

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• Failure process of fiber bundles with random misalignment