Failure mechanisms and surface roughness statistics of fractured Fontainebleau sandstone

Ponson, Laurent; Auradou, Harold; Pessel, Marc; Lazarus, V.; Hulin, Jean-Pierre

doi:10.1103/physreve.76.036108

Cited by 68 publications

(76 citation statements)

References 26 publications

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“…This is consistent with the observation of a conserved Gaussian distribution at large scales (see Fig. 2), and in agreement with previous findings [10,15,16]. The mono-affine behavior is very clear for the mortar and the ceramic fracture surface.…”

supporting

confidence: 93%

Turbulent Fracture Surfaces: A Footprint of Damage Percolation?

Vernède¹,

Ponson

Bouchaud

2015

Phys. Rev. Lett.

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We show that a length scale ξ can be extracted from the spatial correlations of the "steep cliffs" that appear on fracture surface. Above ξ, the slope amplitudes are uncorrelated and the fracture surface is mono-affine. Below ξ, long-range spatial correlation lead to a multi-fractal behavior of the surface, reminiscent of turbulent flows. Our results support a unifying conjecture for the geometry of fracture surfaces: for scales > ξ the surface is the trace left by an elastic line propagating in a random medium, while for scales < ξ the highly correlated patterns on the surface result from the merging of interacting damage cavities.After thirty years of research, it is now well established that fracture surfaces exhibit robust universal fractal statistical properties, first reported in [1] and recently reviewed in [2]. Yet, identifying the physical mechanisms that lead to such fractal structures is still an open problem [3]. The most commonly used approach to characterize the roughness of fractal cracks is to study the scaling of the off-plane height variation δh of the fracture surface with the observation scale δr. The variance of this distribution shows a scaling law δh 2 ∼ δr 2ζ where ζ is the so-called roughness exponent. For purely brittle failure, the roughness exponent is reported to be ζ ≈ 0.45 [5,6] whereas for materials that undergo damage during failure, ζ ≈ 0.75 [7,8]. It has been conjectured that these exponents are the signature of the fracture mechanism above and below the size of the process zone [4]. However, standard methods for extracting roughness exponents are not able to elicit the differences between the fracture mechanisms in the two regimes.Here we propose a different approach for characterizing crack roughness statistics by focusing on the local slopes of the fracture surfaces and their spatial correlations. This allows us to identify unambiguously two scaling regimes: above some length scale ξ, the slope amplitudes are uncorrelated and the fracture surface displays a mono-affine Gaussian behavior with a roughness exponent of ζ ≈ 0.45. Below ξ, long-range spatial correlations do appear and lead to a multi-fractal behavior of the surface. Our findings show that the presence of two distinct regimes of roughness first reported in Refs. [9, 10] is a generic feature of fracture surfaces and is reminiscient of the brittle mode of failure that takes place at large scale and of the damage mechanisms present in the tip vicinity. In addition, it reveals the subtle organization of crack roughness at small length scales δx < ξ, reminiscent of the phenomenology of turbulent flows [11]. In particular, we relate quantitatively the multi-fractal spectrum measured at these length scales with the spatial correlations of the local slopes, and show that the largest slopes organize into a network of lines or "steep cliffs" that exhibit universal statistics. This new approach to Top: h, height of the measured fracture surface. Bottom: ω transformation providing the field of local slopes computed at a scale ...

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supporting

confidence: 93%

Turbulent Fracture Surfaces: A Footprint of Damage Percolation?

Vernède¹,

Ponson

Bouchaud

2015

Phys. Rev. Lett.

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“…The slope of the log-log relation for local distribution determines the fractal exponent of the surface [33]. Note that white noise in the PSD (present for long wavelengths) is omitted during the linear representation [34].…”

Section: Methodsmentioning

confidence: 99%

Wear Characteristics of Metallic Counterparts under Elliptical-Locus Ultrasonic Vibration

Zhang

Wang

2016

Applied Sciences

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Wear behavior is influential to improve friction drive and wear lifespan of actuators or motors, which work at an elliptical locus vibration. Sliding wear tests of metallic friction pairs are conducted by a laboratory rig of ultrasonic vibration. Surfaces of the different metallic sliders are characterized using surface roughness, Abbott curves and fractal dimension. Results show that surface roughness is reduced to varying degrees in the metallic sliders due to ultrasonic polishing and/or micro-rolling effect. Variations in the fractal dimensions of contact surfaces are consistent with that of surface roughness. Wear traces demonstrate that plastic deformation and cracking are the primary failure modes. Where the driving tip on the slider is in intermittent contact followed by impact effects, ripples of 3~5 µm traces suggest the occurrence of fretting in duralumin sliders. Nodular cast iron showed a favorable performance during running of ultrasonic motor, exhibiting a stable output performance and durable wear life.

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“…9 as a function The ductile crack profiles studied here exhibit a more complex behavior than brittle fracture surfaces. Indeed, in brittle materials, distributions of height variations follow a Gaussian behavior at all scales (Ponson 2007;Ponson et al 2007). In our description based on Student's t distribution, this corresponds to k → ∞, or equivalently, to √ k/(k − 2) = 1, for any value of δx.…”

Section: Non-gaussian Statistics Of Height Fluctuationsmentioning

confidence: 98%

Statistics of ductile fracture surfaces: the effect of material parameters

Ponson

Cao

Bouchaud

et al. 2014

Fracture Phenomena in Nature and Technology

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The effect of material parameters on the statistics of fracture surfaces is analyzed under small scale yielding conditions. Three dimensional calculations of ductile crack growth under mode I plane strain, small scale yielding conditions are carried out using an elastic-viscoplastic constitutive relation for a progressively cavitating plastic solid with two populations of void nucleating second phase particles represented. Large particles that result in void nucleation at an early stage are modeled discretely while small particles that require large strains to nucleate are homogeneously distributed. The three dimensional analysis permits modeling of a three dimensional material microstructure and of the resulting three dimensional stress and deformation states that develop in the fracture process region. Material parameters characterizing void nucleation are varied and the statistics of the resulting fracture surfaces is investigated. All the frac- ture surfaces are found to be self-affine over a size range of about two orders of magnitude with a very similar roughness exponent of 0.56 ± 0.03. In contrast, the full statistics of the fracture surfaces is found to be more sensitive to the material microscopic fracture properties: height fluctuations are shown to crossover from a Student's distribution with power law tails at small scales to a Gaussian behavior at large scales, but this transition occurs at a material dependent length scale. Using the family of Student's distributions, this transition can be described introducing an additional exponent μ = 0.15 ± 0.02, the value of which compares well with recent experimental findings. The description of the roughness distribution used here gives a more complete quantitative characterization of the fracture surface morphology which allows a better comparison with experimental data and an easier interpretation of the roughness properties in terms of microscopic failure mechanisms.

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Failure mechanisms and surface roughness statistics of fractured Fontainebleau sandstone

Cited by 68 publications

References 26 publications

Turbulent Fracture Surfaces: A Footprint of Damage Percolation?

Turbulent Fracture Surfaces: A Footprint of Damage Percolation?

Wear Characteristics of Metallic Counterparts under Elliptical-Locus Ultrasonic Vibration

Statistics of ductile fracture surfaces: the effect of material parameters

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