Statistical Properties of Fracture Precursors

Garcimartín, Ángel; Guarino, Alessio; Bellon, Ludovic; Ciliberto, S.

doi:10.1103/physrevlett.79.3202

Cited by 244 publications

(272 citation statements)

References 20 publications

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“…The presence of log-periodic correction to scaling in the elastic energy released has also been demonstrated numerically for the thermal fuse model [35,24] using a novel averaging procedure, called the "canonical ensemble averaging". A recent experimental study of rupture of fiber-glass composites has also confirmed the critical scenario [36].These results indicate that the "critical" behavior is not restricted to limited stress amplification but may well pertain to a much broader class of systems. This needs to be investigated more.…”

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Critical ruptures

2000

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The fracture of materials is a catastrophic phenomenon of considerable technological and scientific importance. Here, we analysed experiments designed for industrial applications in order to test the concept that, in heterogeneous materials such as fiber composites, rocks, concrete under compression and materials with large distributed residual stresses, rupture is a genuine critical point, i.e., the culmination of a self-organization of damage and cracking characterized by power law signatures. Specifically, we analyse the acoustic emissions recorded during the pressurisation of spherical tanks of kevlar or carbon fibers pre-impregnated in a resin matrix wrapped up around a thin metallic liner (steel or titanium) fabricated and instrumented by Aérospatiale-Matra Inc. These experiments are performed as part of a routine industrial procedure which tests the quality of the tanks prior to shipment and varies in nature. We find that the seven acoustic emission recordings of seven pressure tanks which was brought to rupture exhibit clear acceleration in agreement with a power law "divergence" expected from the critical point theory. In addition, we find strong evidence of log-periodic corrections that quantify the intermittent succession of accelerating bursts and quiescent phases of the acoustic emissions on the approach to rupture. An improved model accounting for the cross-over from the non-critical to the critical region close to the rupture point exhibits interesting predictive potential. * Corresponding author: D. Sornette, University of California, Los Angeles, 3845 Slichter Hall, Box 951567 Los Angeles, CA 90095-1567. Tel.: +1 (310) 825 28 63 Fax.: +1 (310) 206 3051-e-mail: sornette@moho.ess.ucla.edu. Plan of the studyIn this paper, we first present in section 2 a brief review of the "critical rupture" concept with an emphasis on the role of heterogeneity. Section 3 describes the experimental systems and the properties of the acoustic emission time series that we analyse with three theoretical formulas derived from the critical rupture concept. We present a brief justification for these three power laws. Section 4 gives the results obtained on the acoustic emission energy release rate on seven systems. Section 5 analyses the cumulative energy releases of these seven systems. Section 6 describes the relative merits of the three power law formulas for the prediction of the critical pressure of rupture and section 7 concludes.2 Review of the "critical rupture" concept BackgroundThe damage and fracture of materials is of enormous technological interest due to their economic and human cost. They cover a wide range of phenomena like, e.g., cracking of glass, aging of concrete, the failure of fiber networks in the formation of paper and the breaking of a metal bar subject to an external load. Failure of composite systems are of utmost importance in naval, aeronautics and space industry [1]. By the term composite, we refer to materials with heterogeneous microscopic structures and also to assemblages of macro...

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Critical ruptures

2000

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“…Experimental observations have been reported for several materials such as wood [12], cellular glass [13], concrete [14] and paper [15], but universality in the scaling exponents does not appear to be present.…”

Section: Introductionmentioning

confidence: 99%

Crack roughness and avalanche precursors in the random fuse model

2005

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We analyze the scaling of the crack roughness and of avalanche precursors in the two dimensional random fuse model by numerical simulations, employing large system sizes and extensive sample averaging. We find that the crack roughness exhibits anomalous scaling, as recently observed in experiments. The roughness exponents (ζ, ζ loc ) and the global width distributions are found to be universal with respect to the lattice geometry. Failure is preceded by avalanche precursors whose distribution follows a power law up to a cutoff size. While the characteristic avalanche size scales as s0 ∼ L D , with a universal fractal dimension D, the distribution exponent τ differs slightly for triangular and diamond lattices and, in both cases, it is larger than the mean-field (fiber bundle) value τ = 5/2.

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“…The cluster growth near the critical time also exhibits spatial scaling in addition to the temporal scaling, namely as fracture develops with time, the connectivity length of the clusters increases and diverges at t c . Recent experiments on the rupture of fiber-glass composites have also confirmed the critical scenario [19]. Johansen and Sornette [20] have recently re-analyzed the acoustic emissions recorded during the pressurization of spherical tanks of kevlar or carbon fibers impregnated in a resin matrix wrapped up around a thin metallic liner (steel or titanium) fabricated and instrumented by Aerospatiale-Matra Inc.…”

Section: Introductionmentioning

confidence: 99%

“…As we said above, the critical rupture concept establishes theoretically this law (1) as the result of the cooperative organization of precursory damage preparing the global rupture. If an observable such as the rate of acoustic emissions radiated during loading exhibit an acceleration close to rupture of the form (1) as documented in several experiments [15,19,20], it is clear that one can try to fit the data by (1) and get a prediction from the determination of t c .…”

Section: Introductionmentioning

confidence: 99%

Functional Renormalization Prediction of Rupture

Gluzman

Andersen

Sornette

2013

Selected Papers From Volume 32 of Vychislitel'naya Seysmologiya

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We develop theoretical formulas for the prediction of the rupture of systems which are known to exhibit a critical behavior, based solely on the knowledge of the early time evolution of an observable, such as the acoustic emission rate as a function of time or of stress. From the parameterization of such early time evolution in terms of a low-order polynomial, we use the functional renormalization approach introduced by Yukalov and Gluzman to transform this polynomial into a function which is asymptotically a power law. The value of the critical time t c , conditioned on the assumption that t c exists, is thus determined from the knowledge of the coefficients of the polynomials. We test with success this prediction scheme with respect to the order of the polynomials and as a function of noise.

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Statistical Properties of Fracture Precursors

Cited by 244 publications

References 20 publications

Critical ruptures

Critical ruptures

Crack roughness and avalanche precursors in the random fuse model

Functional Renormalization Prediction of Rupture

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