Dynamics of cracks in disordered materials

Daniel Bonamy

doi:10.1016/j.crhy.2017.09.012

Prix Aniuta-Winter-Klein 2016 de l'Académie des sciences

Dynamics of cracks in disordered materials
[Dynamique des fissures dans les matériaux désordonnés]

Daniel Bonamy ¹

¹ SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette cedex, France

Comptes Rendus. Physique, Volume 18 (2017) no. 5-6, pp. 297-313.

Résumé
Abstract

Prévoir quand les matériaux cassent constitue un enjeu majeur dans de nombreux domaines industriels, géologiques et sociétaux. Cela reste une question largement ouverte : la concentration des contraintes par les fissures et défauts rend en effet la dynamique de rupture à l'échelle macroscopique très sensible au désordre de microstructure à des échelles très fines. Cela se traduit par des fluctuations statistiques importantes et des comportements sous homogénéisation non triviaux, difficiles à décrire dans le cadre des approches continues de l'ingénierie mécanique.

Nous examinons ici ces questions. Nous verrons :

– comment la mécanique linéaire élastique de la rupture contourne la difficulté en ramenant le problème à la déstabilisation d'une fissure unique dans un matériau effectif « moyen » sans défauts ;
– comment la fissuration lente présente, dans certains cas, une dynamique saccadée, composée d'événements violents et intermittents, incompatible avec l'approche précédente, mais qui peut s'expliquer par certains paradigmes issus de la physique statistique ;
– comment des fissures anormalement rapides émergent parfois du fait de la formation de microfissures à très petites échelles.

Predicting when rupture occurs or cracks progress is a major challenge in numerous fields of industrial, societal, and geophysical importance. It remains largely unsolved: stress enhancement at cracks and defects, indeed, makes the macroscale dynamics extremely sensitive to the microscale material disorder. This results in giant statistical fluctuations and non-trivial behaviors upon upscaling, difficult to assess via the continuum approaches of engineering.

These issues are examined here. We will see:

– how linear elastic fracture mechanics sidetracks the difficulty by reducing the problem to that of the propagation of a single crack in an effective material free of defects;
– how slow cracks sometimes display jerky dynamics, with sudden violent events incompatible with the previous approach, and how some paradigms of statistical physics can explain it;
– how abnormally fast cracks sometimes emerge due to the formation of microcracks at very small scales.

Publié le : 2017-05-01

DOI : 10.1016/j.crhy.2017.09.012

Keywords: Fracture, Disordered solids, Crackling, Scaling laws, Dynamic transition, Instabilities, Stochastic approach
Mot clés : Fracture, Solides désordonnés, Crackling, Lois d'échelle, Transition dynamique, Instabilités, Approche stochastique

Affiliations des auteurs :

Daniel Bonamy ¹

¹ SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette cedex, France

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Daniel Bonamy. Dynamics of cracks in disordered materials. Comptes Rendus. Physique, Volume 18 (2017) no. 5-6, pp. 297-313. doi : 10.1016/j.crhy.2017.09.012. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2017.09.012/

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