Abstract.
Some materials, and in particular some polymer materials, can display an important range of stress levels for which slow and progressive damage can be observed before they finally break. In creep or fatigue experiments, final rupture can happen after very long times, during which the mechanical properties have progressively decayed. We model here some generic features of the long-time damage evolution of disordered elastic materials under constant load, characterized by a progressive decrease of the elastic modulus. We do it by studying a two-dimensional electric random fuse network with quenched disorder and thermal noise. The time evolution of global quantities (conductivity or, equivalently, elastic modulus) is characterized by different regimes ranging from faster than exponential to slower than logarithmic, which are governed by the stress level and the relative magnitude of disorder with respect to temperature. A region of widely distributed rupture times exists where the modulus decays (more slowly than) logarithmically for not too small values of the disorder and for not too large values of the load. A detailed analysis of the dynamical regimes is performed and presented through a phase diagram.
Graphical abstract
Similar content being viewed by others
References
S. Roux, H.J. Herrmann (Editors), Statistical Models for the Fracture of Disordered Media (North-Holland, Amsterdam, 1990)
B.K. Chakrabarti, L.G. Benguigui, Statistical Physics of Fracture and Breakdown in Disordered Systems (Clarendon Press, Oxford, 1997)
M.J. Alava, P.K.V.V. Nukala, S. Zapperi, Adv. Phys. 55, 349 (2006)
L. Vanel, S. Ciliberto, P.-P. Cortet, S. Santucci, J. Phys. D: Appl. Phys. 42, 214007 (2009)
R.W. Hertzberg, John A. Manson, Fatigue of Engineering Plastics (Academic Press, New York, 1980)
E. Mourglia, PhD Thesis, Laboratoire de Polymères et Matériaux Avancés, CNRS/Rhodia, Lyon, France (2010)
E. Mourglia, D. Long, L. Odoni, P. Sotta, C. Rochas, in Book of Abstracts, 14th International Conference on Deformation, Yield and Fracture of Polymers, Rolduc Abbey, Kerkrade, The Netherlands, 6-9 April 2009
P.K. Mallick, Y. Zhou, Int. J. Fatigue 26, 941 (2004)
J.J. Horst, J. Spoormaker, Polym. Eng. Sci. 36, 2718 (1996)
Y. Zhou, P.K. Mallick, Polym. Composite 27, 230 (2006)
V. Bellenger, A. Tcharkhtchi, P. Castaing, Int. J. Fatigue 28, 1348 (2006)
A. Bernasconi, M. Kulin, Polym. Composite 30, 154 (2009)
J.W. Dally, Polym. Eng. Sci. 9, 434 (1969)
S. Castagnet, S. Girault, J.L. Gacougnolle, P. Dang, Polymer 41, 7523 (2000)
A. Pawlak, A. Galeski, Macromolecules 38, 9688 (2005)
J.F. Mandell, D.D. Huang, F.J. McGarry, Polym. Composite 2, 137 (1981)
A.J. Lesser, J. Appl. Polym. Sci. 58, 869 (1995)
P.B. Bowden, J.A. Jukes, J. Mater. Sci. 7, 52 (1972)
V.S. Kuksenko, V.P. Tamuzs, Fracture micromechanics of polymer materials (Martinus Nijhoff Publishers, The Hague, 1981)
D.D. Joseph, J. Fluid Mech. 366, 367 (1998)
B. Kahng, G.G. Batrouni, S. Redner, L. De Arcangelis, H.J. Herrmann, Phys. Rev. B 37, 7625 (1988)
S. Zapperi, P. Ray, H.E. Stanley, A. Vespignani, Phys. Rev. E 59, 5049 (1999)
J.V. Andersen, D. Sornette, K.-T. Leung, Phys. Rev. Lett. 78, 2140 (1997)
P.-P. Cortet, L. Vanel, S. Ciliberto, Europhys. Lett. 74, 602 (2006)
S. Santucci, L. Vanel, A. Guarino, R. Scorretti, S. Ciliberto, Europhys. Lett. 62, 320 (2003)
R. Toussaint, A. Hansen, Phys. Rev. E 73, 046103 (2006)
D. De Tommasi, S. Marzano, G. Puglisi, G. Saccomandi, Continuum Mech. Thermodyn. 22, 47 (2010)
F. Reurings, M.J. Alava, Eur. Phys. J. B 47, 85 (2005)
A. Guarino, L. Vanel, R. Scorretti, S. Ciliberto, J. Stat. Mech. P06020, (2006)
S. Roux, Phys. Rev. E 62, 6164 (2000)
S. Ciliberto, A. Guarino, R. Scorretti, Physica D 158, 83 (2001)
R. Scorretti, S. Ciliberto, A. Guarino, Europhys. Lett. 55, 626 (2001)
A. Politi, S. Ciliberto, R. Scorretti, Phys. Rev. E 66, 026107 (2002)
A. Saichev, D. Sornette, Phys. Rev. E 71, 016608 (2005)
A. Guarino, S. Ciliberto, S. Eur. Phys. J. B 83, 215 (2011)
N. Shahidzadeh-Bonn, P. Vi, X. Chateau, J.-N. Roux, D. Bonn, Phys. Rev. Lett. 95, 175501 (2005)
N. Mallick, S. Ciliberto, S.G. Roux, P. Di Stefano, L. Vanel, Proceedings of the $12^{th}$ International Conference on Fracture, 12-17 juillet 2009, Ottawa, communication T48.003
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Fusco, C., Vanel, L. & Long, D.R. Long-time damage under creep experiments in disordered materials: Transition from exponential to logarithmic fracture dynamics. Eur. Phys. J. E 36, 34 (2013). https://doi.org/10.1140/epje/i2013-13034-y
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epje/i2013-13034-y