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Critical ruptures in a bundle of slowly relaxing fibers

We study the damage enhanced creep rupture of disordered materials by means of a fiber bundle model. Broken fibers undergo a slow stress relaxation modeled by a Maxwell element whose stress exponent m can vary in a broad range. Under global load sharing we show that due to the strength disorder of fibers, the lifetime ʧ of the bundle has sample-to-sample fluctuations characterized by a log-normal distribution independent of the type of disorder. We determine the Monkman-Grant relation of the model and establish a relation between the rupture life tʄ and the characteristic time tm of the intermediate creep regime of the bundle where the minimum strain rate is reached, making possible reliable estimates of ʧ from short term measurements. Approaching macroscopic failure, the deformation rate has a finite time power law singularity whose exponent is a decreasing function of m. On the microlevel the distribution of waiting times is found to have a power law behavior with m-dependent exponents different below and above the critical load of the bundle. Approaching the critical load from above, the cutoff value of the distributions has a power law divergence whose exponent coincides with the stress exponent of Maxwell elements

© Physical Review E, 2008, vol. 73, núm. 3, p. 036102

American Physical Society

Author: Kovács, K.
Nagy, S.
Cruz Hidalgo, Raúl
Kun, F.
Herrmann, H.J.
Pagonabarraga Mora, Ignacio
Date: 2008
Abstract: We study the damage enhanced creep rupture of disordered materials by means of a fiber bundle model. Broken fibers undergo a slow stress relaxation modeled by a Maxwell element whose stress exponent m can vary in a broad range. Under global load sharing we show that due to the strength disorder of fibers, the lifetime ʧ of the bundle has sample-to-sample fluctuations characterized by a log-normal distribution independent of the type of disorder. We determine the Monkman-Grant relation of the model and establish a relation between the rupture life tʄ and the characteristic time tm of the intermediate creep regime of the bundle where the minimum strain rate is reached, making possible reliable estimates of ʧ from short term measurements. Approaching macroscopic failure, the deformation rate has a finite time power law singularity whose exponent is a decreasing function of m. On the microlevel the distribution of waiting times is found to have a power law behavior with m-dependent exponents different below and above the critical load of the bundle. Approaching the critical load from above, the cutoff value of the distributions has a power law divergence whose exponent coincides with the stress exponent of Maxwell elements
Format: application/pdf
ISSN: 1539-3755 (versió paper)
1550-2376 (versió electrònica)
Document access: http://hdl.handle.net/10256/7618
Language: eng
Publisher: American Physical Society
Collection: Reproducció digital del document publicat a: http://dx.doi.org/10.1103/PhysRevE.77.036102
Articles publicats (D-F)
Is part of: © Physical Review E, 2008, vol. 73, núm. 3, p. 036102
Rights: Tots els drets reservats
Subject: Mecànica de fractura
Fracture mechanics
Materials -- Fatiga
Materials -- Fatigue
Title: Critical ruptures in a bundle of slowly relaxing fibers
Type: info:eu-repo/semantics/article
Repository: DUGiDocs

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