Critical behavior in fiber bundle model: A study on brittle to quasi-brittle transition
The Institute of Mathematical Sciences, CIT Campus - Taramani, Chennai 600113, India
Received: 18 August 2015
Accepted: 22 October 2015
We report a critical behavior in the breakdown of an equal-load-sharing fiber bundle model at a dispersion of the breaking threshold of the fibers. For , there is a finite probability Pb, that rupturing of the weakest fiber leads to the failure of the entire system. For , . At , with , where L is the size of the system. As , the relaxation time τ diverges obeying the finite-size scaling law: with . At , the system fails, at the critical load, in avalanches (of rupturing fibers) of all sizes s following the distribution , with . 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