Comptes Rendus
Prix Aniuta-Winter-Klein 2016 de l'Académie des sciences
Dynamics of cracks in disordered materials
Comptes Rendus. Physique, Volume 18 (2017) no. 5-6, pp. 297-313.

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.

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.

Published online:
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

Daniel Bonamy 1

1 SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette cedex, France
@article{CRPHYS_2017__18_5-6_297_0,
     author = {Daniel Bonamy},
     title = {Dynamics of cracks in disordered materials},
     journal = {Comptes Rendus. Physique},
     pages = {297--313},
     publisher = {Elsevier},
     volume = {18},
     number = {5-6},
     year = {2017},
     doi = {10.1016/j.crhy.2017.09.012},
     language = {en},
}
TY  - JOUR
AU  - Daniel Bonamy
TI  - Dynamics of cracks in disordered materials
JO  - Comptes Rendus. Physique
PY  - 2017
SP  - 297
EP  - 313
VL  - 18
IS  - 5-6
PB  - Elsevier
DO  - 10.1016/j.crhy.2017.09.012
LA  - en
ID  - CRPHYS_2017__18_5-6_297_0
ER  - 
%0 Journal Article
%A Daniel Bonamy
%T Dynamics of cracks in disordered materials
%J Comptes Rendus. Physique
%D 2017
%P 297-313
%V 18
%N 5-6
%I Elsevier
%R 10.1016/j.crhy.2017.09.012
%G en
%F CRPHYS_2017__18_5-6_297_0
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/

[1] W. Weibull A statistical theory of the strength of the materials, Proc. R. Swed. Inst. Eng. Res. (1939), p. 151

[2] K. Ravi-Chandar Dynamic fracture of nominally brittle materials, Int. J. Fract., Volume 90 (1998), pp. 83-102 | DOI

[3] J. Fineberg; M. Marder Instability in dynamic fracture, Phys. Rep., Volume 313 (1999), pp. 1-108

[4] Inglis Stresses in a plate due to the presence of cracks and sharp corners, Trans. Inst. Nav. Archit., Volume 55 (1913), p. 219

[5] A.A. Griffith The phenomena of rupture and flow in solids, Philos. Trans. R. Soc. Lond. A, Volume 221 (1920), p. 163

[6] G.R. Irwin Analysis of stresses and strains near the end of a crack traversing a plate, J. Appl. Mech., Volume 24 (1957), p. 361

[7] B. Lawn Fracture of Brittle Solids, Cambridge Solide State Science, 1993

[8] L.B. Freund Crack propagation in an elastic solid subjected to general loading – I. Constant rate of extension, J. Mech. Phys. Solids, Volume 20 (1972) no. 3, pp. 129-140

[9] L.B. Freund Crack propagation in an elastic solid subjected to general loading – II. Non-uniform rate of extension, J. Mech. Phys. Solids, Volume 20 (1972) no. 3, pp. 141-152

[10] L.B. Freund Crack propagation in an elastic solid subjected to general loading – III. Stress wave loading, J. Mech. Phys. Solids, Volume 21 (1973) no. 2, pp. 47-61

[11] L.B. Freund Dynamic Fracture Mechanics, Cambridge University Press, 1990

[12] K. Ravi-Chandar Dynamic Fracture, Elsevier Ltd., 2004

[13] T. Goldman; A. Livne; J. Fineberg Acquisition of inertia by a moving crack, Phys. Rev. Lett., Volume 104 (2010)

[14] H. Kanomori The energy release in great earthquakes, J. Geophys. Res., Volume 82 (1977), pp. 2981-2987

[15] P. Bak; K. Christensen; L. Danon; T. Scanlon Unified scaling law for earthquakes, Phys. Rev. Lett., Volume 88 (2002) no. 17 http://prl.aps.org/pdf/PRL/v88/i17/e178501

[16] F. Omori On after-shocks of eartquakes, J. Coll. Sci., Imp. Univ. Tokyo, Volume 7 (1894), pp. 111-200

[17] T. Utsu; Y. Ogata; R. Matsu'ura The centenary of the omori formula for dacay law of aftershock activity, J. Phys. Earth, Volume 43 (1995), pp. 1-33

[18] T. Utsu Aftershocks and eartquakes statistics (iii), J. Fac. Sci., Hokkaido Univ., Ser. VII, Volume 3 (1971), pp. 380-441

[19] A. Helmstetter Is earthquake triggering driven by small earthquakes?, Phys. Rev. Lett., Volume 91 (2003) no. 5

[20] M. Bath Lateral inhomogeneities of the upper mantle, Tectonophysics, Volume 2 (1965) no. 6, pp. 483-514 http://www.sciencedirect.com/science/article/pii/004019516590003X

[21] S. Deschanel; L. Vanel; N. Godin; E. Maire; G. Vigier; S. Ciliberto Mechanical response and fracture dynamics of polymeric foams, J. Phys., Appl. Phys., Volume 42 (2009)

[22] A. Petri; G. Paparo; A. Vespignani; A. Alippi; M. Costantini Experimental evidence for critical dynamics in microfracturing processes, Phys. Rev. Lett., Volume 73 (1994), p. 3423

[23] L.I. Salminen; A.I. Tolvanen; M.J. Alava Acoustic emission from paper fracture, Phys. Rev. Lett., Volume 89 (2002) no. 18

[24] T. Mäkinen; A. Miksic; M. Ovaska; M.J. Alava Avalanches in wood compression, Phys. Rev. Lett., Volume 115 (2015) no. 5 | DOI

[25] H.V. Ribeiro; L.S. Costa; L.G.A. Alves; P.A. Santoro; S. Picoli; E.K. Lenzi; R.S. Mendes Analogies between the cracking noise of ethanol-dampened charcoal and earthquakes, Phys. Rev. Lett., Volume 115 (2015) no. 2 | DOI

[26] J. Baro; A. Corral; X. Illa; A. Planes; E.K.H. Salje; W. Schranz; D.E. Soto-Parra; E. Vives Statistical similarity between the compression of a porous material and earthquakes, Phys. Rev. Lett., Volume 110 (2013) | arXiv

[27] J. Rosti; X. Illa; J.K.M.J. Alava Crackling noise and its dynamics in fracture of disordered media, J. Phys. D, Appl. Phys., Volume 42 (2009)

[28] D. Bonamy Intermittency and roughening in the failure of brittle heterogeneous materials, J. Phys. D, Appl. Phys., Volume 42 (2009) no. 21 http://stacks.iop.org/0022-3727/42/i=21/a=214014

[29] M. Minozzi; G. Caldarelli; L. Pietronero; S. Zapperi Dynamic fracture model for acoustic emission, Eur. Phys. J. B, Volume 36 (2003), pp. 203-207

[30] K.J. Målø y; J. Schmittbuhl Dynamical event during slow crack propagation, Phys. Rev. Lett., Volume 87 (2001)

[31] K.J. Målø y; S. Santucci; J. Schmittbuhl; R. Toussaint Local waiting time fluctuations along a randomly pinned crack front, Phys. Rev. Lett., Volume 96 (2006)

[32] S. Santucci; L. Vanel; S. Ciliberto Subcritical statistics in rupture of fibrous materials: experiments and model, Phys. Rev. Lett., Volume 93 (2004)

[33] T. Cambonie; J. Bares; M.L. Hattali; D. Bonamy; V. Lazarus; H. Auradou Effect of the porosity on the fracture surface roughness of sintered materials: from anisotropic to isotropic self-affine scaling, Phys. Rev. E, Volume 91 (2015) no. 1 | DOI

[34] J. Barés; M.L. Hattali; D. Dalmas; D. Bonamy Fluctuations of global energy release and crackling in nominally brittle heterogeneous fracture, Phys. Rev. Lett., Volume 113 (2014) no. 26 | DOI

[35] J. Barés, A. Dubois, L. Hattali, D. Dalmas, D. Bonamy, Aftershock sequences and seismic-like organization of acoustic events produced by a single propagating tensile crack, submitted for publication.

[36] J.P. Sethna; K.A. Dahmen; C.R. Myers Crackling noise, Nature, Volume 410 (2001), pp. 242-250 | arXiv

[37] J.-P. Bouchaud Power laws in economics and finance: some ideas from physics, Quant. Finance, Volume 1 (2001), pp. 105-112

[38] P. Houle; J.P. Sethna Acoustic emission from crumpling paper, Phys. Rev. E, Volume 54 (1996) no. 1, p. 278

[39] J. Chen; J.S. Thorp; I. Dobson Cascading dynamics and mitigation assessment in power system disturbances via a hidden failure model, Int. J. Electr. Power Energy Syst., Volume 27 (2005) no. 4, pp. 318-326

[40] H. Gao; J.R. Rice A first order perturbation analysis on crack trapping by arrays of obstacles, J. Appl. Mech., Volume 56 (1989), p. 828

[41] J.-P. Bouchaud; E. Bouchaud; G. Lapasset; J. Planès Models of fractal cracks, Phys. Rev. Lett., Volume 71 (1993), pp. 2240-2243

[42] J. Schmittbuhl; S. Roux; J.-P. Vilotte; K.J. Måløy Interfacial crack pinning: effect of nonlocal interactions, Phys. Rev. Lett., Volume 74 (1995), pp. 1787-1790

[43] H. Larralde; R.C. Ball The shape of slowly growing cracks, Europhys. Lett., Volume 30 (1995), pp. 87-92

[44] S. Ramanathan; D. Ertas; D.S. Fisher Quasistatic crack propagation in heterogeneous media, Phys. Rev. Lett., Volume 79 (1997), p. 873

[45] D. Bonamy; L. Ponson; S. Prades; E. Bouchaud; C. Guillot Scaling exponents for fracture surfaces in homogeneous glass and glassy ceramics, Phys. Rev. Lett., Volume 97 (2006)

[46] D. Bonamy; E. Bouchaud Failure of heterogeneous materials: a dynamic phase transition?, Phys. Rep., Volume 498 (2011), pp. 1-44

[47] A. Movchan; H. Gao; J. Willis On perturbations of plane cracks, Int. J. Solids Struct., Volume 35 (1998) no. 26–27, pp. 3419-3453 http://www.sciencedirect.com/science/article/pii/S002076839700231X

[48] J.R. Rice 1st-order variation in elastic fields due to variation in location of a planar crack front, J. Appl. Mech., Volume 52 (1985), pp. 571-579

[49] D. Ertas; M. Kardar Critical dynamics of contact line depinning, Phys. Rev. E, Volume 49 (1994)

[50] J.-F. Joanny; P.-G. de Gennes A model for contact-angle hysteresis, J. Chem. Phys., Volume 81 (1984), pp. 552-562

[51] J.S. Urbach; R.C. Madison; J.T. Markert Interface depinning, self-organized criticality, and the barkhausen effect, Phys. Rev. Lett., Volume 75 (1995), pp. 276-279

[52] G. Durin; S. Zapperi Scaling exponents for barkhausen avalanches in polycrystalline and amorphous ferromagnets, Phys. Rev. Lett., Volume 84 (2000), pp. 4705-4708

[53] D.S. Fisher Interface fluctuations in disordered systems: 5-ε expansion and failure of dimensional reduction, Phys. Rev. Lett., Volume 56 (1986) no. 18, p. 1964

[54] P. Chauve; P.L. Doussal; K.J. Wiese Renormalization of pinned elastic systems: how does it work beyond one loop?, Phys. Rev. Lett. (2001), p. 1785

[55] A. Rosso; P.L. Doussal; K.J. Wiese Avalanche-size distribution at the depinning transition: a numerical test of the theory, Phys. Rev. B, Volume 80 (2009)

[56] A. Dobrinevski; P.L. Doussal; K.J. Wiese Nonstationary dynamics of the Alessandro–Beatrice–Bertotti–Montorsi model, Phys. Rev. E, Volume 85 (2012)

[57] D. Bonamy; S. Santucci; L. Ponson Crackling dynamics in material failure as the signature of a self-organized dynamic phase transition, Phys. Rev. Lett., Volume 101 (2008) no. 4 http://prl.aps.org/pdf/PRL/v101/i4/e045501

[58] J. Barés; M. Barlet; C.L. Rountree; L. Barbier; D. Bonamy Nominally brittle cracks in inhomogeneous solids: from microstructural disorder to continuum-level scale, Front. Phys., Volume 2 (2014) | DOI

[59] J. Barés; L. Barbier; D. Bonamy Crackling versus continuumlike dynamics in brittle failure, Phys. Rev. Lett., Volume 111 (2013)

[60] J. Astrom; P.D. Stefano; F. Probst; L. Stodolsky; J. Timonen; C. Bucci; S. Cooper; C. Cozzini; F. Feilitzsch; H. Kraus; J. Marchese; O. Meier; U. Nagel; Y. Ramachers; W. Seidel; M. Sisti; S. Uchaikin; L. Zerle Fracture processes observed with a cryogenic detector, Phys. Lett. A, Volume 356 (2006), pp. 262-266

[61] J. Scheibert; C. Guerra; F. Célarié; D. Dalmas; D. Bonamy Brittle–quasibrittle transition in dynamic fracture: an energetic signature, Phys. Rev. Lett., Volume 104 (2010) no. 4 http://prl.aps.org/pdf/PRL/v104/i4/e045501

[62] D. Dalmas; C. Guerra; J. Scheibert; D. Bonamy Damage mechanisms in the dynamic fracture of nominally brittle polymers, Int. J. Fract., Volume 184 (2013) no. 1–2, pp. 93-111 | DOI

[63] Smekal Zum bruchvorgang bei sprodem stoffverhalten unter ein-and mehrachsigen beanspruchungen, Osterr. Ing. Arch., Volume 7 (1953), pp. 49-70

[64] K. Ravi-Chandar; B. Yang On the role of microcracks in the dynamic fracture of brittle materials, J. Phys. Mech. Solids, Volume 45 (1997), pp. 535-563

[65] C. Guerra Dynamic Fracture in Brittle Amorphous Materials: Dissipation Mechanisms and Dynamically-Induced Microcracking in Polymethylmethalcrylate (PMMA), École Polytechnique, 2009 (Ph.D. thesis)

[66] P. Du; B. Xue; Y. Song; M. Zuo; S. Lu; Q. Zheng; J. Yu Experimental observation and computer simulation of conic markings on fracture surfaces of polymers, J. Mater. Sci., Volume 45 (2010), p. 3088

[67] T.J. Ahrens; A.M. Rubin Impact-induced tensional failure in rocks, J. Geophys. Res., Planets, Volume 98 (1993), p. 1185

[68] C.L. Rountree; D. Bonamy; D. Dalmas; S. Prades; R.K. Kalia; C. Guillot; E. Bouchaud Fracture in glass via molecular dynamics simulations and atomic force microscopy experiments, Phys. Chem. Glasses B, Volume 51 (2010), p. 127

[69] C.L. Rountree; R.K. Kalia; E. Lidorikis; A. Nakano; L.V. Brutzel; P. Vashishta Atomistic aspects of crack propagation in brittle materials: multimillion atom molecular dynamics simulations, Annu. Rev. Mater. Res., Volume 32 (2002), pp. 377-400

[70] P. Murali; T. Guo; Y. Zhang; R. Narasimhan; Y. Li; H. Gao Atomic scale fluctuations govern brittle fracture and cavitation behavior in metallic glasses, Phys. Rev. Lett., Volume 107 (2011)

[71] C. Guerra; J. Scheibert; D. Bonamy; D. Dalmas Understanding fast macroscale fracture from microcrack post mortem patterns, Proc. Natl. Acad. Sci. USA, Volume 109 (2012), pp. 390-394 http://www.pnas.org/content/109/2/390.full

[72] B. Tarasov Intersonic shear rupture mechanism, Int. J. Rock Mech. Min. Sci., Volume 45 (2008) no. 6, pp. 914-928 | DOI

[73] S. Osovski; A. Srivastava; L. Ponson; E. Bouchaud; V. Tvergaard; K. Ravi-Chandar; A. Needleman The effect of loading rate on ductile fracture toughness and fracture surface roughness, J. Mech. Phys. Solids, Volume 76 (2015), pp. 20-46 | DOI

[74] J. Fineberg; S.P. Gross; M. Marder; H.L. Swinney Instability in dynamic fracture, Phys. Rev. Lett., Volume 67 (1991), pp. 457-460

[75] E. Sharon; J. Fineberg Confirming the continuum theory of dynamic brittle fracture for fast cracks, Nature, Volume 397 (1999) no. 6717, pp. 333-335 http://www.nature.com/nature/journal/v397/n6717/full/397333a0.html

[76] A. Livne; G. Cohen; J. Fineberg Universality and hysteretic dynamics in rapid fracture, Phys. Rev. Lett., Volume 94 (2005) no. 22 | DOI

[77] T.G. Boué; G. Cohen; J. Fineberg Origin of the microbranching instability in rapid cracks, Phys. Rev. Lett., Volume 114 (2015) no. 5 | DOI

[78] A. Livne; E. Bouchbinder; J. Fineberg Breakdown of linear elastic fracture mechanics near the tip of a rapid crack, Phys. Rev. Lett., Volume 101 (2008)

[79] E. Bouchbinder; A. Livne; J. Fineberg Weakly nonlinear theory of dynamic fracture, Phys. Rev. Lett., Volume 101 (2008)

[80] D. Leguillon A criterion for crack nucleation at a notch in homogeneous materials, C. R. Acad. Sci., IIB, Volume 329 (2001) no. 2, pp. 97-102

[81] D. Leguillon Strength or toughness? A criterion for crack onset at a notch, Eur. J. Mech. A, Solids, Volume 21 (2002) no. 1, pp. 61-72

[82] J.-F. Boudet; S. Ciliberto Interaction of sound with fast crack propagation, Phys. Rev. Lett., Volume 80 (1998), pp. 341-344

[83] E. Sharon; G. Cohen; J. Fineberg Propagating solitary waves along a rapidly moving crack front, Nature, Volume 410 (2001), pp. 68-71

[84] D. Bonamy; K. Ravi-Chandar Interaction of shear waves and propagating cracks, Phys. Rev. Lett., Volume 91 (2003)

[85] D. Bonamy; K. Ravi-Chandar Dynamic crack response to a localized shear pulse perturbation in brittle amorphous materials: on crack surface roughening, Int. J. Fract., Volume 134 (2005), pp. 1-22

[86] J.R. Willis; A.B. Movchan Dynamic weight functions for a moving crack. I. Mode I loading, J. Mech. Phys. Solids, Volume 43 (1995), pp. 319-341

[87] J.R. Willis; A.B. Movchan Three-dimensional dynamic perturbation of a propagating crack, J. Mech. Phys. Solids, Volume 45 (1997), pp. 591-610

[88] S. Ramanathan; D.S. Fisher Dynamics and instabilities of planar tensile cracks in heterogeneous media, Phys. Rev. Lett., Volume 79 (1997), p. 877

[89] E. Bouchaud; J.-P. Bouchaud; D.S. Fisher; S. Ramanathan; J.R. Rice Can crack front waves explain the roughness of cracks?, J. Phys. Mech. Solids, Volume 50 (2002), pp. 1703-1725

[90] M. Adda-Bedia; R.E. Arias; E. Bouchbinder; E. Katzav Dynamic stability of crack fronts: out-of-plane corrugations, Phys. Rev. Lett., Volume 110 (2013) no. 1 | DOI

Cited by Sources:

Comments - Policy