arXiv subjects

Jean Schmittbuhl

Publications and source records attributed to Jean Schmittbuhl.

25 records · Page 2Linked to original sources

arXiv2002

Origin of the Universal Roughness Exponent of Brittle Fracture Surfaces: Correlated Percolation in the Damage Zone

We suggest that the observed large-scale universal roughness of brittle fracture surfaces is due to the fracture process being a correlated percolation process in a self-generated quadratic damage gradient. We use the quasi-static two-dimensional fuse model as a paradigm of a fracture model. We measure for this model, that exhibits a correlated percolation process, the correlation length exponent nu approximately equal to 1.35 and conjecture it to be equal to that of uncorrelated percolation, 4/3. We then show that the roughness exponent in the fuse model is zeta = 2 nu/(1+2 nu)= 8/11. This is in accordance with the numerical value zeta=0.75. As for three-dimensional brittle fractures, a mean-field theory gives nu=2, leading to zeta=4/5 in full accordance with the universally observed value zeta =0.80.

cond-mat↗

arXiv2001

Heterogeneous Interfacial Failure between Two Elastic Blocks

We investigate numerically the failure process when two elastic media, one hard and one soft that have been glued together thus forming a common interface, are pulled apart. We present three main results: (1) The area distribution of simultaneously failing glue (bursts) follows a power law consistent with the theoretically expected exponent 2.5, (2) the maximum load and displacement before catastrophic failure scale as L^2 and L^0 respectively, where L is the linear size of the system, and (3) the area distribution of failed glue regions (clusters) is a power law with exponent -1.6 when the system fails catstrophically.

cond-mat↗

arXiv2000

Elastic Response of Rough Surfaces in Partial Contact

We model numerically the partial normal contact of two elastic rough surfaces with highly correlated asperities. Facing surfaces are unmated and described as self-affine with a Hurst exponent H. The numerical algorithm is based on Fourier acceleration and allows efficient simulation of very large systems. The force, F, versus contact area, A, characteristics follows the law F = c A^[(1+H)/2] in accordance with the suggestion of Roux et al. (Europhys. Lett. 23, 277 (1993)). However finite size corrections are very large even for 512X512 systems where the effective exponent is still 20% larger than its asymptotic value.

cond-mat↗

arXiv2000

Distinguishing fractional and white noise in one and two dimensions

We discuss the link between uncorrelated noise and Hurst exponent for one and two-dimensional interfaces. We show that long range correlations cannot be observed using one-dimensional cuts through two-dimensional self-affine surfaces whose height distributions are characterized by a Hurst exponent lower than -1/2. In this domain, fractional and white noise are not distinguishable. A method analysing the correlations in two dimensions is necessary. For Hurst exponents larger than -1/2, a crossover regime leads to a systematic over estimate of the Hurst exponent.

cond-mat↗

arXiv2000

Normal Stress Distribution of Rough Surfaces in Contact

We study numerically the stress distribution on the interface between two thick elastic media bounded by interfaces that include spatially correlated asperities. The interface roughness is described using the self-affine topography that is observed over a very wide range of scales from fractures to faults. We analyse the correlation properties of the normal stress distribution when the rough surfaces have been brought into full contact. The self affinity of the rough surfaces is described by a Hurst exponent H. We find that the normal stress field is also self affine, but with a Hurst exponent H-1. Fluctations of the normal stress are shown to be important, especially at local scales with anti-persistent correlations.

cond-mat↗

arXiv1998

Anomalous roughening of wood fractured surfaces

Scaling properties of wood fractured surfaces are obtained from samples of three different sizes. Two different woods are studied: Norway spruce and Maritime pine. Fracture surfaces are shown to display an anomalous dynamic scaling of the crack roughness. This anomalous scaling behavior involves the existence of two different and independent roughness exponents. We determine the local roughness exponents $ζ_{loc}$ to be 0.87 for spruce and 0.88 for pine. These results are consistent with the conjecture of a universal local roughness exponent. The global roughness exponent is different for both woods, $ζ$ = 1.60 for spruce and $ζ$ = 1.35 for pine. We argue that the global roughness exponent $ζ$ is a good index for material characterization.

cond-mat↗

arXiv1998

Anomalous Scaling of Fracture Surfaces

We argue that fracture surfaces may exhibit anomalous dynamic scaling properties akin to what occurs in some models of kinetic roughening. We determine the complete scaling behavior of the local fluctuations of a brittle fracture in a granite block from experimental data. We obtain a global roughness exponent $χ= 1.2$ which differs from the local one, $χ_{loc} = 0.79$. Implications on fracture physics are discussed.

cond-mat.stat-mech↗