Failure of heterogeneous materials: A dynamic phase transition?

Physics Reports

Volumn 498, Issue 1, 2011, Pages 1-44

  Bonamy, D ^a   Bouchaud, E ^a  

^a CNRS UMR 3299   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 78650677567     PISSN: 03701573     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physrep.2010.07.006     Document Type: Review

References (190)

1. François D., Pineau A., Zaoui A. Comportement mécanique des matériaux, volume I: élasticité plasticité 1991, Hermès.
2. François D., Pineau A., Zaoui A. Comportement mécanique des matériaux 1995, Hermès.
3. Corté L., Beaume F., Leibler L. Crystalline organization and toughening: example of polyamide-12. Polymer 2005, 46:2748-2757.
4. Corté L., Leibler L. Analysis of polymer blend morphologies from transmission electron micrographs. Polymer 2005, 46:6360-6368.
5. Leonforte F., Tanguy A., Wittmer J.P., Barrat J.L. Continuum limit of amorphous elastic bodies ii: linear response to a point source force. Phys. Rev. B 2004, 70:014203.
6. Leonforte F., Tanguy A., Wittmer J.-P., Barrat J.-L. Inhomogeneous elastic response of silica glass. Phys. Rev. Lett. 2006, 97(5):055501.
7. Célarié F., Prades S., Bonamy D., Ferrero L., Bouchaud E., Guillot C., Marliere C. Glass breaks like metal, but at the nanometer scale. Phys. Rev. Lett. 2003, 90:075504.
8. A.A. Griffith, J. Waltamn Jr., The theory of rupture, in: C.B. Biezeno, J.M. Burgers (Eds.), Proc. First Internat. Congr. Appl. Mech., 1924, p. 55.
9. Freund L.B. Dynamic Fracture Mechanics 1990, Cambridge University Press.
10. Bergkvist H. Some experiments on crack motion and arrest in polymethylmethacrylate. Eng. Fracture Mech. 1974, 6:621-626.
11. Boudet J.-F., Ciliberto S. Interaction of sound with fast crack propagation. Phys. Rev. Lett. 1998, 80:341-344.
12. Sharon E., Fineberg J. Confirming the continuum theory of dynamic brittle fracture for fast cracks. Nature 1999, 397:333-335.
13. Scheibert J., Guerra C., Clari F., Dalmas D., Bonamy D. Brittle/quasi-brittle transition in the dynamic fracture of nominally brittle materials: an energetic signature. Phys. Rev. Lett. 2010, 104:045501.
14. Livne A., Bouchbinder E., Svetlizky I., Fineberg J. The near-tip fields of fast cracks. Science 2010, 327:1359.
15. Ravi-Chandar K. Dynamic fracture of nominally brittle materials. Int. J. Frac. 1998, 90:83-102.
16. Fineberg J., Marder M. Instability in dynamic fracture. Phys. Rep. 1999, 313:1-108.
17. Movchan A.B., Gao H., Willis J.R. On perturbations of plane cracks. Int. J. Solids Struct. 1998, 26:3419-3453.
18. Meade K.P., Keer L.M. Stress-intensity factor for a semi-infinite plane crack with a wavy front. J. Elasticity 1984, 14:79-92.
19. Rice J.R. 1st-order variation in elastic fields due to variation in location of a planar crack front. J. Appl. Mech. 1985, 52:571-579.
20. Schmittbuhl J., Roux S., Vilotte J.P., Måløy K.J. Interfacial crack pinning: effect of nonlocal interactions. Phys. Rev. Lett. 1995, 74:1787-1790.
21. Ramanathan S., Ertas D., Fisher D.S. Quasistatic crack propagation in heterogeneous media. Phys. Rev. Lett. 1997, 79:873.
22. Schmittbuhl J., Måløy K.J. Direct observation of self-affine crack propagation. Phys. Rev. Lett. 1997, 78:3888-3891.
23. Delaplace A., Schmittbuhl J., Måløy K.J. High-resolution description of crack front in heterogeneous plexiglas block. Phys. Rev. E 1999, 60:1337-1343.
24. Adda-Bedia M., Katzav E., Vandembroucq D. Second-order variation in elastic fields of a tensile planar crack with a curved front. Phys. Rev. E 2006, 73:035106.
25. Cotterell B., Rice J.R. Slightly curved or kinked cracks. Int. J. Frac. 1980, 16:155-169.
26. Larralde H., Ball R.C. The shape of slowly growing cracks. Europhys. Lett. 1995, 30:87-92.
27. Ball R.C., Larralde H. 3-dimensional stability analysis of planar straight cracks propagating quasi-statically under type-i-loading. Int. J. Fract. 1995, 71:365-377.
28. Willis J.R., Movchan A.B. Dynamic weight functions for a moving crack. i. mode i loading. J. Mech. Phys. Solids 1995, 43:319-341.
29. Willis J.R., Mochvan A.B. Three dimensional dynamic perturbation of a dynamic propagating crack. J. Mech. Phys. Solids 1997, 45:591.
30. Ramanathan S., Fisher D.S. Dynamics and instabilities of planar tensile cracks in heterogeneous media. Phys. Rev. Lett. 1997, 79:877.
31. Morrissey J.W., Rice J.R. Crack front waves. J. the Mech. and Physics of Solids 1998, 46:467-487.
32. Morrissey J.W., Rice J.R. Perturbative simulations of crack front waves. J. the Mech. and Physics of Solids 2000, 48:1229-1251.
33. Sharon E., Cohen G., Fineberg J. Propagating solitary waves along a rapidly moving crack front. Nature 2001, 410:68-71.
34. Bouchaud E., Bouchaud J.P., Fisher D.S., Ramanathan S., Rice J.R. Can crack front waves explain the roughness of cracks?. J. Mech. Phys. Solids 2002, 50:1703-1725.
35. Sharon E., Cohen G., Fineberg J. Crack front waves and the dynamics of a rapidly moving crack. Phys. Rev. Lett. 2002, 88(8):085503.
36. Bonamy D., Ravi-Chandar K. Interaction of shear waves and propagating cracks. Phys. Rev. Lett. 2003, 91:235502.
37. Bonamy D., Ravi-Chandar K. Dynamic crack response to a localized shear pulse perturbation in brittle amorphous materials: on crack surface roughening. Int. J. Fract. 2005, 134:1-22.
38. Sharon E., Cohen G., Fineberg J. Comment on: "interaction of shear waves and propagating cracks". Phys. Rev. Lett. 2004, 93. 099601-1.
39. Bonamy D., Ravi-Chandar K. Reply on: interaction of shear waves and propagating cracks. Phys. Rev. Lett. 2004, 93:099602.
40. Goldstein R.V., Salganik R.L. Brittle fracture of solids with arbitrary cracks. Int. J. Frac. 1974, 10:507-523.
41. Sommer E. Formation of fracture 'lances' in glass. Eng. Frac. Mech. 1969, 1:539-540.
42. Bouchaud E., Paun F. Fracture and damage at a microstructural scale. Comp. Sci. Eng. 1999, September-October(1).
43. Morel S., Mourot G., Schmittbuhl J. Influence of the specimen geometry on r-curve behavior and roughening of fracture surfaces. Int. J. Frac. 2003, 121:23-42.
44. Prades S., Bonamy D., Dalmas D., Bouchaud E., Guillot C. Nano-ductile crack propagation in glasses understress corrosion: spatiotemporal evolution of damage in the vicinity of the crack tip. Int. J. Solid Struct. 2005, 42:637-645.
45. Rountree C.L., Kalia R.K., Lidorikis E., Nakano A., Van Brutzel L., Vashishta P. Atomistic aspects of crack propagation in brittle materials: multimillion atom molecular dynamics simulations. Ann. Rev. Mater. Res. 2002, 32:377-400.
46. Guin J.P., Wiederhorn S.M. Fracture of silicate glasses: Ductile or brittle?. Phys. Rev. Lett. 2004, 92. 215502/1-4.
47. Guin J.P., Wiederhorn S.M. Surfaces formed by subcritical crack growth in silicate glasses. Int. J. Fract. 2006, 140:15-26.
48. Han K., Ciccotti M., Roux S. Measuring nanoscale stress intensity factors with an atomic force microscope. Eur. Phys. Lett. 2010, 89:66003.
49. Wiederehorn S., Lopez-Cepero J, Wallace J., Guin J.-P., Fett T. Roughness of glass surfaces formed by sub-critical crack growth. J. Non-Cryst. Solids 2007, 353:1582-1591.
50. Lechenault F., Pallares G., George M., Rountree C., Bouchaud E., Ciccotti M. Effects of finite probe size on self-affine roughness measurements. Phys. Rev. Lett. 2010, 104:025502.
51. Ponson L., Bonamy D., Auradou H., Mourot G., Morel S., Bouchaud E., Guillot C., Hulin J.-P. Anisotropic self-affine properties of experimental fracture surfaces. Int. J. Frac. 2006, 140:27-37.
52. Ponson L., Bonamy D., Bouchaud E. 2d scaling properties of experimental fracture surfaces. Phys. Rev. Lett. 2006, 96:035506.
53. Mandelbrot B.B., Passoja D.E., Paullay A.J. Fractal character of fracture surfaces of metals. Nature 1984, 308:721-722.
54. Kertész J., Horv'ath V.K., Weber F. Self-affine rupture lines in paper sheets. Fractals 1993, 1:67-74.
55. Santucci S., Måløy K.J., Delaplace A., Mathiesen J., Hansen A., Bakke J., Schmittbuhl J., Vanel L., Ray P. Statistics of fracture surfaces. Phys. Rev. E 2007, 75:016104-1-016104-6.
56. Salminen L.I., Alava M.J., Niskanen K.J. Analysis of long crack lines in paper webs. Eur. Phys. J. B 2003, 32:369-374.
57. Mallick N., Cortet P.-P., Santucci S., Roux S.G., Vanel L. Discrepancy between subcritical and fast rupture roughness: a cumulant analysis. Phys. Rev. Lett. 2007, 98:255502.
58. Bouchbinder E., Procaccia I., Santucci S., Vanel L. Fracture surfaces as multiscaling graphs. Phys. Rev. Lett. 2006, 96(5):055509.
59. Måløy K.J., Santucci S., Schmittbuhl J., Toussaint R. Local waiting time fluctuations along a randomly pinned crack front. Phys. Rev. Lett. 2006, 96:045501.
60. S. Santucci, M. Grob, A. Hansen, R. Toussaint, J. Schmittbuhl, K.J. Måløy, Fracture roughness scaling: a case study on planar cracks, 2010. [cond-mat.mtrl-sci]. arxiv:1007.1188v1.
61. Marchenko A., Fichou D., Bonamy D., Bouchaud E. Time resolved observation of fracture events in mica crystal using scanning tunneling microscope. Appl. Phys. Lett. 2006, 89:093124.
62. Obreimoff J.-W. The splitting strength of mica. Proc. Roy. Soc. Lond. A 1930, 127:290-297.
63. Daguier P., Bouchaud E., Lapasset G. Roughness of crack front pinned by microstructural obstacles. Europhys. Lett. 1995, 31:367-372.
64. Bouchaud E., Lapasset G., Planes J. Fractal dimension of fractured surfaces: A universal value?. Europhys. Lett. 1990, 13:73-79.
65. Feder J. Fractals 1988, Plenum.
66. Måløy K.J., Hansen A., Hinrichsen E.L., Roux S. Experimental measurements of the roughness of brittle cracks. Phys. Rev. Lett. 1992, 68:213-215.
67. Daguier P., Hénaux S., Bouchaud E., Creuzet F. Quantitative analysis of a fracture surface by atomic force microscopy. Phys. Rev. E 1996, 53:5637.
68. Daguier P., Nghiem B., Bouchaud E., Creuzet F. Pinning and depinning of crack fronts in heterogeneous materials. Phys. Rev. Lett. 1997, 78:1062-1065.
69. M. Hinojosa, E. Bouchaud, B. Nghiem, Long distance roughness of fracture surfaces in heterogeneous materials, in: G.E. Beltz, R.L. Blumberg Selinger, M.P. Marder, K.-S. Kim (Eds.), Materials Research Society Proceedings, MRS Fall Meeting 1998, vol. 539, 1999, pp. 203-208.
70. Schmittbuhl J., Schmitt F., Scholz C. Scaling invariance of crack surfaces. J. Geophys. Res. 1995, 100:5953-5973.
71. Boffa J.M., Allain C., Hulin J.P. Experimental analysis of fracture rugosity in granular and compact rocks. Eur. Phys. J. AP. 1998, 2:281-289.
72. Boffa J.-M., Allain C., Hulin J.-P. Experimental analysis of self-affine fractured rock surfaces through shadow length measurements. Physica A 2000, 278:65-86.
73. Ponson L., Auradou H., Vié P., Hulin J.P. Low self-affine exponents of fractured glass ceramics surfaces. Phys. Rev. Lett. 2006, 97:125501.
74. Ponson L. Crack propagation in disordered materials: how to decypher fracture surfaces. Annales de Physique 2007, 32:1.
75. Ponson L., Auradou H., Pessel M., Lazarus V., Hulin J.P. Failure mechanisms and surface roughness statistics of fractured fontainebleau sandstone. Phys. Rev. E 2008, 76:036108.
76. López J.M., Schmittbuhl J. Anomalous scaling of fracture surfaces. Phys. Rev. E 1998, 57:6405-6408.
77. Bouchaud E., Naveos S. From quasi-static to rapid fracture. J. Phys. I France 1995, 5:547.
78. Bouchaud E., Boivin D., Pouchou J.-L., Bonamy D., Poon B., Ravichandran G. Fracture through cavitation in a metallic glass. Europhys. Lett. 2008, 83:66006.
79. Bouchaud E., Lapasset G., Planes J., Navéos S. Statistics of branched fracture surfaces. Phys. Rev. B 1993, 48:2917-2928.
80. Engoy T., Måløy K.J., Hansen A., Roux S. Roughness of two-dimensional cracks in wood. Phys. Rev. Lett. 1994, 73:834.
81. Morel S., Schmittbuhl J., López J.M., Valentin G. Anomalous roughening of wood fractured surfaces. Phys. Rev. E 1998, 58:6999-7005.
82. Morel S., Schmittbuhl J., Bouchaud E., Valentin G. Scaling of crack surfaces and implications for fracture mechanics. Phys. Rev. Lett. 2000, 85:1678-1681.
83. Morel S., Bouchaud E., Valentin G. Size effect in fracture: roughening of crack surfaces and asymptotic analysis. Phys. Rev. B 2002, 65:104101.
84. Bouchaud E. Scaling properties of cracks. J. Phys. Condens. Matter 1997, 9:4319-4344.
85. Mourot G., Morel S., Bouchaud E., Valentin G. Anomalous scaling of mortar fracture surfaces. Phys. Rev. E 2005, 71. 016136-1-016136-7.
86. Bouchaud J.P., Bouchaud E., Lapasset G., Planes J. Models of fractal cracks. Phys. Rev. Lett. 1993, 71:2240-2243.
87. Ammann J.J., Bouchaud E. Characterization of self-affine surfaces from 3d digital reconstruction. Eur. Phys. J. B Appl. Phys. 1998, 4:133-142.
88. Célarié F., Prades S., Bonamy D., Dickelé A., Bouchaud E., Guillot C., Marlière C. Surface fracture of glassy materials as detected by real-time atomic force microscopy (afm) experiments. Appl. Surf. Sci. 2003, 212:92-96.
89. Family F., Vicsek T. Dynamic of Fractal Surfaces 1991, World Scientific.
90. Ponson L., Bonamy D., Barbier L. Cleaved surface of i-alpdmn quasicrystals: influence of the local temperature elevation at the crack tip on the fracture surface roughness. Phys. Rev. B 2006, 74:184205.
91. Bouchbinder E., Procaccia I., Sela S. Disentangling scaling properties in anisotropic fracture. Phys. Rev. Lett. 2005, 95:255503.
92. G. Pallares, L. Ponson, S. Chapuliot, E. Bouchaud, (Unpublished).
93. Morel S., Bonamy D., Ponson L., Bouchaud E. Transient damage spreading and anomalous scaling in mortar crack surfaces. Phys. Rev. E 2008, 78. 016112-1-016112-5.
94. C. Guerra-Amaro, D. Bonamy, S. Chapuliot, E. Bouchaud, Process zone size determination from the morphology of steel fracture surfaces (Unpublished).
95. Schmittbuhl J., Gentier S., Roux S. Field-measurements of the roughness of fault surfaces. Geophys. Lett. 1993, 20:639-641.
96. Dalmas D., Lelarge A., Vandembroucq D. Crack propagation through phase-separated glasses: effect of the characteristic size of disorder. Phys. Rev. Lett. 2008, 101:255501.
97. Bouchaud E. The morphology of fracture surfaces: a tool for understanding crack propagation in complex materials. Surf. Rev. Lett. 2003, 10:797-814.
98. Falk M.L. Molecular-dynamics study of ductile and brittle fracture in model noncrystalline solids. Phys. Rev. B 1999, 60:7062-7070.
99. Schall P., Weitz D.A., Spaepen F. Structural rearrangements that govern flow in colloidal glasses. Science 2007, 318(5858):1895-1899.
100. Besseling R., Weeks E.R., Schofield A.B., Poon W.C.K. Three-dimensional imaging of colloidal glasses under steady shear. Phys. Rev. Lett. 2007, 99(2):028301.
101. Falk M.L., Langer J.S. Dynamics of viscoplastic deformation in amorphous solids. Phys. Rev. E 1998, 57:7192-7205.
102. Argon A.S. Plastic deformation in metallic glasses. Acta Met. 1979, 27:47-58.
103. L. Van Brutzel, E. Bouchaud, Molecular dynamics simulations of crack propagation mode in silica, in: School on Physics of Glass - Structure and Dynamics, May 10-22, 1999, Institut d'Etudes Scientifiques de Cargse, France, Physics of Glasses - Structure and Dynamics, in: P. Jund, R. Jullien (Eds.), AIP Conference Proceedings, vol. 489, 1999, pp. 231-235.
104. Vashishta P., Kalia R.K., Rino J.P., Ebbsjo I. Interaction potential for SiO2: a molecular-dynamics study of structural correlations. Phys. Rev. B 1990, 41:12197-12210.
105. Rountree C.L., Prades S., Bonamy D., Bouchaud E., Kalia R.K., Guillot C. A unified study of crack propagation in amorphous silica: Using experiments and simulations. J. Alloys Compd. 2007, 434-435:60-63.
106. Kalia R.K., Nakano A., Tsuruta K., Vashishta P. Morphology of pores and interfaces and mechanical behavior of nanoclustered-assembled silicon nitride ceramic. Phys. Rev. Lett. 1997, 78:689.
107. Nakano A., Kalia R.K., Vashishta P. Dynamics and morphology of brittle cracks: a molecular-dynamics study of silicon-nitride. Phys. Rev. Lett. 1995, 75:3138-3141.
108. Chen Y.-C., Lu Z., Nomura K., Wang W., Kalia R.K., Nakano A., Vashishta P. Interaction of voids and nanoductility in silica glass. Phys. Rev. Lett. 2007, 99:155506.
109. Chen Y.C., Nomura K., Kalia R.K., Nakano A., Vashishta P. Void deformation and breakup in shearing silica glass. Phys. Rev. Lett. 2009, 103:035501.
110. Lawn B. Fracture of Brittle Solids 1993, Cambridge University Press.
111. Ciccotti M. Stress-corrosion mechanisms in silicate glasses. J. Phys. D: Appl. Phys. 2009, 42. 214006(1-18).
112. Tomozawa M., Han W.-T., Lanford W.A. Water entry into silica glass during slow crack growth. J. Am. Ceram. Soc. 1991, 74:2573-2576.
113. Tomozawa M. Fracture of glasses. Ann. Rev. Mat. Sci. 1996, 26:43-74.
114. Grimaldi A., George M., Pallares G., Ciccotti M. The crack tip: a nanolab for studying confined liquids. Phys. Rev. Lett. 2008, 100:165505.
115. Michalske T.A., Freiman S.W. A molecular mechanism for stress corrosion in vitreous silica. J. Am. Ceram. Soc. 1983, 68:284-288.
116. Bonamy D., Prades S., Rountree C.L., Ponson L., Dalmas D., Bouchaud E., Ravi-Chandar K., Guillot C. Nanoscale damage during fracture in silica glass. Int. J. Fract. 2006, 140:3-14.
117. Bonamy D., Prades S., Ponson L., Dalmas D., Rountree C.L., Bouchaud E., Guillot C. Experimental investigation of damage and fracture in glassy materials at the nanometer scale. Int. J. Prod. Tech. 2006, 26:339-353.
118. Bouchbinder E., Mathiesen J., Procaccia I. Roughening of fracture surfaces: the role of plastic deformation. Phys. Rev. Lett. 2004, 92(24):245505.
119. Bouchbinder E., Mathiesen J., Procaccia I. Stress field around arbitrarily shaped cracks in two-dimensional elastic materials. Phys. Rev. E 2004, 69(2 Part 2):026127.
120. Afek I., Bouchbinder E., Katzav E., Mathiesen J., Procaccia I. Void form and roughening in slow fracture. Phys. Rev. E 2005, 71:066127.
121. Santucci S., Vanel L., Ciliberto S. Subcritical statistics in rupture of fibrous materials: experiments and model. Phys. Rev. Lett. 2004, 93:095505.
122. Pierce F.T. Tensile tests for cotton yarns. v. the weakest link-theorems on the strength of long and short composite specimens. J. Textile Institute Trans. 1926, 17:355-368.
123. Hemmer P.C., Hansen A., Pradhan S. Rupture processes in fibre bundle models. Lecture Notes in Physics 2006, 705:27-55.
124. Kun F., Raischel F., Hidalgo R.C., Herrmann H.J. Extensions of fibre bundle models. Lecture Notes in Phys. 2006, 705:57-92.
125. Daniels H.E. The statistical theory of the strength of bundles and threads. Proc. Roy. Soc. Lond. Ser. A Math.. Phys. Sci. 1945, 183:405-435. 995.
126. Sornette D. Mean-field solution of a block-spring model of earthquakes. J. Phys. I France 1992, 2:2089-2096.
127. de Arcangelis L., Redner S., Herrmann H.J. A random fuse model for breaking processes. J. Phys. Lett. (Paris) 1985, 46:585-590.
128. Herrmann H.J., Roux S. Statistical Model for the Fracture and Breakdown for Disordered Media 1990, North Holland, Amsterdam.
129. Alava M.J., Nukala P.K.V.V., Zapperi S. Statistical models of fracture. Adv. Phys. 2006, 55:349-476.
130. Li Y.S., Duxbury P.M. Crack arrest by residual bonding in resistor and spring networks. Phys. Rev. B Condensed Matter 1988, 38(13):9257-9260.
131. Zapperi S., Vespignani A., Stanley H.E. Plasticity and avalanche behaviour in microfracturing phenomena. Nature 1997, 388:658-660.
132. de Arcangelis L., Hansen A., Herrmann H.J., Roux S. Scaling laws in fracture. Phys. Rev. B Condens. Matter 1989, 40(1):877-880.
133. Sahimi M., Arbabi S. Mech. of disordered solids. iii. fracture properties. Phys. Rev. B Condens. Matter 1993, 47(2):713-722.
134. Duxbury P.M., Beale P.D., Leath P.L. Size effect of electrical breakdown in quenched random media. Phys. Rev. Lett. 1986, 57:1052-1055.
135. Nukala P.K.V.V., Simunovic S. Scaling of fracture strength in disordered quasi-brittle materials. Eur. Phys. J. B 2004, 37:91-100.
136. Zapperi S., Nukala P.K.V.V. Fracture statistics in the three-dimensional random fuse model. Int. J. Frac. 2006, 140:99-111.
137. Hansen A., Hemmer P.C. Burst avalanches in bundles of fibers - local versus global load-sharing. Phys. Lett. A 1994, 184:394-396.
138. Zapperi S., Nukala P.K.V.V., Simunovic S. Crack roughness and avalanche precursors in the random fuse model. Phys. Rev. E 2005, 71:026106.
139. Zapperi S., Nukala P.K.V.V., Simunovic S. Crack avalanches in the three-dimensional random fuse model. Physica A 2005, 357:129-133.
140. Deschanel S., Vanel L., Godin N., Vigier G., Ciliberto S. Experimental study of crackling noise: conditions on power law scaling correlated with fracture precursors. J. Stat. Mech.: Theor. Exp. 2009, P01018:1-13.
141. Utsu T. Representation and analysis of the earthquake size distribution: A historical review and some new approaches. Pure Appl. Geophys. 1999, 155:509-535.
142. Minozzi M., Caldarelli G., Pietronero L., Zapperi S. Dynamic fracture model for acoustic emission. Eur. Phys. J. B 2003, 36:203-207.
143. B. Pant, S. Morel, E. Bouchaud, Acoustic emission tracking of failure precursors in cement.
144. Salminen L.I., Tolvanen A.I., Alava M.J. Acoustic emission from paper fracture. Phys. Rev. Lett. 2002, 89(18):185503.
145. Hansen A., Hinrichsen H., Roux S. Roughness of crack interfaces. Phys. Rev. Lett. 1991, 66(19):2476-2479.
146. Batrouni G.C., Hansen A. Fracture in three-dimensional fuse networks. Phys. Rev. Lett. 1998, 80:325-328.
147. Raisanen V.I., Seppala E.T., Alava M.J., Duxbury P.M. Quasistatic cracks and minimal energy surfaces. Phys. Rev. Lett. 1998, 80:329-332.
148. Raisanen V.I., Alava M.J., Nieminen R.M. Fracture of three-dimensional fuse networks with quenched disorder. Phys. Rev. B 1998, 58:14288-14295.
149. Seppala E.T., Raisanen V.I., Alava M.J. Scaling of interfaces in brittle fracture and perfect plasticity. Phys. Rev. E 2000, 61(6 Pt A):6312-6319.
150. Nukala P.K.V.V., Zapperi S., Simunovic S. Crack surface roughness in three-dimensional random fuse networks. Phys. Rev. E August 2006, 74(2 Pt 2):026105.
151. Nukala P.K.V.V., Zapperi S., Alava M.J., Simunovic S. Effect of disorder and notches on crack roughness. Phys. Rev. E 2007, 76(5 Pt 2):056111.
152. Roux S., Hansen A. Perfect plasticity in a random medium. J. Phys. II (France) 1992, 2:1007-1021.
153. Halpin-Healy T. Directed polymers in random media: Probability distributions. Phys. Rev. A 1991, 44. R3415-R3418.
154. Kardar M., Parisi G., Zhang Y.-C. Dynamic scaling of growing interfaces. Phys. Rev. Lett. 1986, 56:889.
155. Middleton A.A. Numerical results for the ground-state interface in a random medium. Phys. Rev. E 1995, 52. R3337-R3340.
156. Hinojosa M., Reyes-Melo E., Guerra C., Gonzalez V., Ortiz U. Scaling properties of slow fracture in glass: from deterministic to irregular topography. Int. J. Frac. 2008, 151:81-93.
157. Hansen A., Schmittbuhl J. Origin of the universal roughness exponent of brittle fracture surfaces: stress weighted percolation in the damage zone. Phys. Rev. Lett. 2003, 90:45504.
158. Schmittbuhl J., Hansen A. Roughness of interfacial crack fronts: stress-weighted percolation in the damage zone. Phys. Rev. Lett. 2003, 90:045505.
159. Toussaint R., Pride S.R. Fracture of disordered solids in compression as a critical phenomenon. i. statistical mechanics formalism. Phys. Rev. E 2002, 66(3 Part 2A):036135.
160. Toussaint R., Pride S.R. Fracture of disordered solids in compression as a critical phenomenon. ii. model hamiltonian for a population of interacting cracks. Phys. Rev. E 2002, 66(3 Part 2A):036136.
161. Toussaint R., Pride S.R. Fracture of disordered solids in compression as a critical phenomenon. iii. analysis of the localization transition. Phys. Rev. E 2002, 66(3 Part 2A):036137.
162. Zapperi S., Herrmann H.J., Roux S. Planar cracks in the fuse model. Eur. Phys. J. B 2000, 17:131-136.
163. Nukala P.K.V., Zapperi S., Alava M.J., Simunovic S. Crack roughness in the two-dimensional random threshold beam model. Phys. Rev. E 2008, 78. 046105 (1-8).
164. Gao H., Rice J.R. A first order perturbation analysis on crack trapping by arrays of obstacles. J. Appl. Mech. 1989, 56:828.
165. Bertotti G., Durin G., Magni A. Scaling aspects of domain wall dynamics and barkhausen effect in ferromagnetic materials. J. Appl. Phys. 1994, 75:5490-5492.
166. Durin G., Zapperi S. Scaling exponents for barkhausen avalanches in polycrystalline and amorphous ferromagnets. Phys. Rev. Lett. 2000, 84:4705-4708.
167. Ertas D., Kardar M. Critical dynamics of contact line depinning. Phys. Rev. E 1994, 49:R2532.
168. Rolley E., Guthmann C., Gombrowicz R., Repain V. Roughness of the contact line on a disordered substrate. Phys. Rev. Lett. 1998, 80:2865-2868.
169. Le Doussal P., Wiese K.J., Moulinet S., Rolley E. Height fluctuations of a contact line: a direct measurement of the renormalized disorder correlator. EPL 2009, 87. 56001p1-p6.
170. Kardar M. Nonequilibrium dynamics of interfaces and lines. Phys. Reports 1998, 301:85-112.
171. Chauve P., Le Doussal P., Wiese K.J. Renormalization of pinned elastic systems: how does it work beyond one loop?. Phys. Rev. Lett. 2001, 86:1785-1788.
172. Duemmer O., Krauth W. Depinning exponents of the driven long-range elastic string. J. Statist. Mech. 2007, 1:01019.
173. L. Ponson, Depinning transition in failure of disordered brittle materials, in: 2008 APS March Meeting, 2008.
174. Ponson L. Depinning transition in the failure of inhomogeneous brittle materials. Phys. Rev. Lett. 2009, 103:055501.
175. Feigelman M.V., Geshkenbein V.B., Larkin A.I., Vinokur V.M. Theory of collective flux creep. Phys. Rev. Lett. 1989, 63:2303-2306.
176. Kolton A.B, Rosso A., Giamarchi T. Creep motion of an elastic string in a random potential. Phys. Rev. Lett. 2005, 94(4):047002.
177. Koivisto J., Rosti J., Alava M.J. Creep of a fracture line in paper peeling. Phys. Rev. Lett. 2007, 99:145504.
178. Roux S., Vandembroucq D., Hild F. Effective toughness of heterogeneous brittle materials. Eur. J. Mech. A/Solids 2003, 22:743-749.
179. Charles Y., Vandembroucq D., Hild F., Roux S. Material-independent crack arrest statistics. J. Mech. Phys. Sol. 2004, 52:1651-1669.
180. Charles Y., Hild F., Roux S., Vandembroucq D. Material-independent crack arrest statistics: application to indentation experiments. Int. J. Fract. 2006, 142:51-67.
181. Bak P., Tang C., Wiesenfield K. Self-organized criticality: an explanation of 1/f noise. Phys. Rev. Lett. 1987, 59:381-384.
182. Bonamy D., Santucci S., Ponson L. Crackling dynamics in material failure as the signature of a self-organized dynamic phase transition. Phys. Rev. Lett. 2008, 101:045501.
183. Kolton A.B, Rosso A., Giamarchi T., Krauth W. Dynamics below the depinning threshold in disordered elastic systems. Phys. Rev. Lett. 2006, 97(5):057001.
184. Rosso A., Krauth W. Roughness at the depinning threshold for a long-range elastic string. Phys. Rev. E 2002, 65:25101.
185. Leshhorn H., Nattermann T., Sepanow S., Tang L.-H. Driven interface depinning in a disordered medium. Ann. Phys. 1997, 6:1-34.
186. Ertas D., Kardar M. Dynamic roughening of directed lines. Phys. Rev. Lett. 1992, 69:929.
187. Bonamy D., Ponson L., Prades S., Bouchaud E., Guillot C. Scaling exponents for fracture surfaces in homogeneous glass and glassy ceramics. Phys. Rev. Lett. 2006, 97:135504.
188. Katzav E., Adda-Bedia M., Derrida B. Fracture surfaces of heterogeneous materials: a 2d solvable model. Eur. Phys. Lett. 2007, 78:46006.
189. Tanguy A., Gounelle M., Roux S. From individual to collective pinning: effect of long-range elastic intercations. Phys. Rev. E 1998, 58:1577-1590.
190. Mosayebi M., Del Gado E., Ilg P., Ottinger H.C. Probing a critical length scale at the glass transition. Phys. Rev. Lett. 2010, 104:205704.