Critical behavior in fiber bundle model: A study on brittle to quasi-brittle transition

Subhadeep Roy; Purusattam Ray

doi:10.1209/0295-5075/112/26004

All issues

Volume 112 / No 2 (October 2015)

EPL, 112 2 (2015) 26004

Abstract

Issue		EPL Volume 112, Number 2, October 2015


Article Number		26004
Number of page(s)		5
Section		Condensed Matter: Structural, Mechanical and Thermal Properties
DOI		https://doi.org/10.1209/0295-5075/112/26004
Published online		16 November 2015

EPL, 112 (2015) 26004

Critical behavior in fiber bundle model: A study on brittle to quasi-brittle transition

Subhadeep Roy and Purusattam Ray

The Institute of Mathematical Sciences, CIT Campus - Taramani, Chennai 600113, India

Received: 18 August 2015
Accepted: 22 October 2015

Abstract

We report a critical behavior in the breakdown of an equal-load-sharing fiber bundle model at a dispersion $\delta_c$ of the breaking threshold of the fibers. For $\delta < \delta_c$ , there is a finite probability P_b, that rupturing of the weakest fiber leads to the failure of the entire system. For $\delta \geq \delta_c$ , $P_b = 0$ . At $\delta_c, P_b \sim L^{-\eta}$ , with $\eta \approx 1/3$ , where L is the size of the system. As $\delta \rightarrow \delta_c$ , the relaxation time τ diverges obeying the finite-size scaling law: $\tau \sim L^{\beta}(|\delta-\delta_c| L^{\alpha})$ with $\alpha = \beta \approx 1/3$ . At $\delta_c$ , the system fails, at the critical load, in avalanches (of rupturing fibers) of all sizes s following the distribution $P(s) \sim s^{-\kappa}$ , with $\kappa \approx 1/2$ . We relate this critical behavior to the brittle to quasi-brittle transition in the model. For the local-load-sharing scheme, the system is found to be always brittle for sufficiently large system sizes.

PACS: 64.60.av – Cracks, sandpiles, avalanches, and earthquakes / 62.25.Mn – Fracture/brittleness / 62.20.fk – Ductility, malleability

© EPLA, 2015

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