]. S. Batdorf and H. L. Heinisch-jr, Weakest Link Theory Reformulated for Arbitrary Fracture Criterion, Journal of the American Ceramic Society, vol.8, issue.4, pp.61-68, 1978.
DOI : 10.1007/BF00116368

. Beyerlein, Statistics of fracture for an elastic notched composite lamina containing Weibull fibers??? Part I. Features from Monte-Carlo simulation, Engineering Fracture Mechanics, vol.57, issue.2-3, pp.241-265, 1997.
DOI : 10.1016/S0013-7944(97)00012-X

. Beyerlein, Statistics of fracture for an elastic notched composite lamina containing weibull fibers???Part II. Probability models of crack growth, Engineering Fracture Mechanics, vol.57, issue.2-3, pp.267-299, 1997.
DOI : 10.1016/S0013-7944(97)00013-1

. Bouchaud, Models of fractal cracks, Physical Review Letters, vol.71, issue.14, pp.71-2240, 1993.
DOI : 10.1103/PhysRevLett.71.2240

. Bouchaud, Can crack front waves explain the roughness of cracks?, Journal of the Mechanics and Physics of Solids, vol.50, issue.8, pp.1703-1725, 2000.
DOI : 10.1016/S0022-5096(01)00137-5

URL : https://hal.archives-ouvertes.fr/hal-00130574

. Bower, ]. A. Ortiz-1991, M. Bower, and . Ortiz, A three-dimensional analysis of crack trapping and bridging by tough particles, Journal of the Mechanics and Physics of Solids, vol.39, issue.6, pp.815-858, 1991.
DOI : 10.1016/0022-5096(91)90026-K

. Bower, ]. A. Ortiz-1993, M. Bower, and . Ortiz, The Influence of Grain Size on the Toughness of Monolithic Ceramics, Journal of Engineering Materials and Technology, vol.115, issue.3, pp.228-236, 1993.
DOI : 10.1115/1.2904212

]. W. Curtin, Stochastic Damage Evolution and Failure in Fiber-Reinforced Composites, Adv. Appl. Mech, vol.36, issue.164, 1998.
DOI : 10.1016/S0065-2156(08)70186-8

]. D. Davies, The Statistical Approach to Engineering Design in Ceramics, Proc. Brit, pp.22-429, 1973.

. Delaplace, High resolution description of a crack front in a heterogeneous Plexiglas block, Physical Review E, vol.60, issue.2, pp.1337-1343, 1999.
DOI : 10.1103/PhysRevE.60.1337

]. K. Eriksson, The effective fracture toughness of structural components obtained with the blend rule, Nuclear Engineering and Design, vol.182, issue.2, pp.123-129, 1998.
DOI : 10.1016/S0029-5493(97)00355-5

]. A. Evans, A General Approach for the Statistical Analysis of Multiaxial Fracture, Journal of the American Ceramic Society, vol.381, issue.3, pp.61-68, 1978.
DOI : 10.1016/0079-6425(76)90006-2

]. D. Fisher, Sliding charge-density waves as a dynamic critical phenomenon, Physical Review B, vol.31, issue.3, pp.1396-1427, 1985.
DOI : 10.1103/PhysRevB.31.1396

]. H. Gao and J. R. Rice, A First-Order Perturbation Analysis of Crack Trapping by Arrays of Obstacles, Journal of Applied Mechanics, vol.56, issue.4, pp.56-828, 1989.
DOI : 10.1115/1.3176178

]. A. Hansen and J. Schmittbuhl, Origin of the Universal Roughness Exponent of Brittle Fracture Surfaces:Stress-Weighted Percolation in the Damage Zone, Physical Review Letters, vol.90, issue.4, pp.45504-45505, 2003.
DOI : 10.1103/PhysRevLett.90.045504

T. Jayatilaka, ]. A. De, S. Jayatilaka, and K. Trustrum, Statistical approach to brittle fracture, Journal of Materials Science, vol.229, issue.7, pp.1426-1430, 1977.
DOI : 10.1007/BF00540858

]. E. Kroener, Elastic moduli of perfectly disordered composite materials, Journal of the Mechanics and Physics of Solids, vol.15, issue.5, pp.319-329, 1967.
DOI : 10.1016/0022-5096(67)90026-9

. Landis, Micromechanical simulation of the failure of fiber reinforced composites, Journal of the Mechanics and Physics of Solids, vol.48, issue.3, pp.621-648, 2000.
DOI : 10.1016/S0022-5096(99)00051-4

R. W. Morrissey, J. R. Morrissey, and . Rice, Perturbative simulations of crack front waves, Journal of the Mechanics and Physics of Solids, vol.48, issue.6-7, pp.1229-1251, 2000.
DOI : 10.1016/S0022-5096(99)00069-1

]. A. Movchan and J. R. Willis, Dynamic weight functions for a moving crack. II. Shear loading, Journal of the Mechanics and Physics of Solids, vol.43, issue.9, pp.1369-1383, 1995.
DOI : 10.1016/0022-5096(95)00041-G

. Movchan, On perturbations of plane cracks, International Journal of Solids and Structures, vol.35, issue.26-27, pp.3419-3453, 1998.
DOI : 10.1016/S0020-7683(97)00231-X

]. D. Munz and T. Fett, Scatter of Mechanical Properties, Ceramics, pp.137-158, 1999.
DOI : 10.1007/978-3-642-58407-7_8

]. G. Perrin and J. R. Rice, Disordering of a dynamic planar crack front in a model elastic medium of randomly variable toughness, Journal of the Mechanics and Physics of Solids, vol.42, issue.6, pp.1047-1064, 1994.
DOI : 10.1016/0022-5096(94)90083-3

]. S. Ramanathan and D. S. Fisher, Dynamics and Instabilities of Planar Tensile Cracks in Heterogeneous Media, Physical Review Letters, vol.79, issue.5, pp.877-880, 1997.
DOI : 10.1103/PhysRevLett.79.877

. Ramanathan, ]. S. Fisher, D. S. Ramanathan, and . Fisher, Onset of propagation of planar cracks in heterogeneous media, Physical Review B, vol.58, issue.10, pp.6026-6046, 1998.
DOI : 10.1103/PhysRevB.58.6026

]. K. Ranjith and J. R. Rice, Slip dynamics at an interface between dissimilar materials, Journal of the Mechanics and Physics of Solids, vol.49, issue.2, pp.341-361, 2001.
DOI : 10.1016/S0022-5096(00)00029-6

J. R. Rice, Some Studies of Crack Dynamics, Proceedings Physical Aspects of Fracture, pp.3-11, 2001.
DOI : 10.1007/978-94-010-0656-9_1

. Schmittbuhl, Pinning of interfacial crack: Effect of non-local interactions, Phys. Rev. Lett, pp.74-1787, 1995.

]. J. Schmittbuhl and K. J. Måløy, Direct Observation of a Self-Affine Crack Propagation, Physical Review Letters, vol.78, issue.20, pp.3888-3891, 1997.
DOI : 10.1103/PhysRevLett.78.3888

. Skoe, FRONT PROPAGATION IN RANDOM MEDIA: FROM EXTREMAL TO ACTIVATED DYNAMICS, International Journal of Modern Physics C, vol.13, issue.06, pp.751-757, 2002.
DOI : 10.1142/S0129183102003565

. Tanguy, From individual to collective pinning: Effect of long-range elastic interactions, Physical Review E, vol.58, issue.2, pp.1577-1590, 1998.
DOI : 10.1103/PhysRevE.58.1577

J. R. Willis, On methods for bounding the overall properties of nonlinear composites, Journal of the Mechanics and Physics of Solids, vol.39, issue.1, pp.73-86, 1991.
DOI : 10.1016/0022-5096(91)90031-I

M. Willis, ]. J. Willis, and A. B. Movchan, Dynamic weight functions for a moving crack. I. Mode I loading, Journal of the Mechanics and Physics of Solids, vol.43, issue.3, pp.319-341, 1995.
DOI : 10.1016/0022-5096(94)00075-G

]. S. Woolfries and J. R. Willis, Perturbation of a dynamic planar crack moving in a model elastic solid, Journal of the Mechanics and Physics of Solids, vol.47, issue.8, pp.1633-1661, 1999.
DOI : 10.1016/S0022-5096(98)00121-5