Role of damage in the selection of the scaling properties of fracture surfaces: Experimental evidences and theoretical interpretation

Laurent PONSON, Silke PRADES, Daniel BONAMY, Elisabeth BOUCHAUD, Claude GUILLOT

In the two previous sections, the statistical scaling properties of fracture surfaces in heterogeneous materials were shown to obey Family-Viseck scaling, characterized by *two* set of critical exponents, namely ζ=0.75, β =0.6 and Z= ζ/β=1.2 in glass, metallic alloys, mortar and wood, and ζ=0.4, β =0.5 and Z= ζ/β=0.8 in sandstone and packing of sintered glass beads.*x* of these anisotropic self-affine regimes was found to coincide with the size of the process zone where damage cavities can be observed (see Figure). Moreover, in silica glass, the size of the process zone and x were found to decay both as the logarithm of the crack growth velocity (see Figure). In packing of sintered glass beads, the scaling properties were observed from 100µm (microstructure scale) to 10mm, i.e. at scales three orders of magnitudes larger than the size of the process zone (about 100 nm as in homogeneous glass). This leads us to conjecture that the two series of critical exponents are obtained whether fracture surfaces are observed at scales *below* or *above *the size of the process zone /1/.

To uncover the origin of these two distinct universality classes we focused more specifically on the range of *length-scales* over which the scaling properties are observed. In metallic alloys and oxide glasses, the cut-off length

The large scale regime can be successfully captured by deriving a model of crack propagation within Linear Elastic Fracture Mechanics. Within this framework, we showed that the crack roughness development can been described as an elastic string with nonlocal interactions creeping in a 2D random media - the spatial coordinate along which the crack globally grows playing the role of time. This approach predicts in particular fracture surfaces with a morphology *independent of* the average loading and of the crack growth velocity, with Family-Viseck scaling properties characterized by ζ=0.4; β =0.5 and Z= ζ/β=0.8, as observed for packings of sintered glass beads. The set of exponents {ζ=0.75; β =0.6; Z= ζ/β=1.2} observed for length-scales below the size of the process zone is conjectured to reflect the screening of elastic interactions through the presence of damage cavities.

Top: Damage cavities in metallic alloys from /2/. Center: Same for Aluminosilicate glass from /3/ The process zone is found to be about 100µm in metallic alloys and 100nm in oxide glasses to be compared to the self-affine cutoff length ξ ~ 100µm and ξ ~ 100nm respectively. In silica glass, the size of the process zone Rc and ξ were found to decay both as the logarithm of the crack growth velocity v (Bottom, from /1/)

**REFERENCES:**

[1] D. Bonamy, L. Ponson, S. Prades, E. Bouchaud, C. Guillot, Phys. Rev. Lett. **97** 135504, (2006)

[2] E. Bouchaud and F. Paun, Comp. Sci. Eng. **1**, 32-38 (1999)

[3] F. Célarié, S. Prades, D. Bonamy, L. Ferrero, E. Bouchaud, C. Guillot and C. Marlière,* *Phys. Rev. Lett. **90** 075504, (2003)

#780 - Màj : 15/04/2007

• Systèmes complexes et transition énergétique › Statistical physics in mechanics

• Laboratory of Physics and Chemistry of Surfaces and Interfaces • UMR 3680 - Service de Physique de l'Etat Condensé (SPEC) • Service de Physique et Chimie des Surfaces et des Interfaces

• Laboratory of Nano-Objects and Complex Systems (LNOSC) • SPHYNX • GMT-MSIN : Modélisation des Surfaces Interfaces et Nanostructures