Universal Log-Periodic Correction to Renormalization Group Scaling for Rupture Stress
Prediction From Acoustic Emissions

Anifrani, J.-C.; Floc’h, C. Le; Sornette, Didier; Souillard, B.

doi:10.1051/jp1:1995156

Cited by 168 publications

(257 citation statements)

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“…From a general view point, log-periodic oscillations are the hallmark of a discrete hierarchical structure obeying a discrete scale invariance symmetry [24]. Expression (2) has been proposed previously on the basis of a discrete renormalization group approach to rupture [20,24]. Detailed theoretical and numerical analysis of ensemble of interacting cracks have shown that such discrete hierarchy can self-organize from a cascade of Mullins-Sekerka instabilities [23].…”

Section: Theorymentioning

confidence: 99%

“…Another application of the thermal fuse model is damage by electro-migration of polycrystalline metal films [19]. See also [17] for relations with dendrites and fronts propagation.In 1991-1995, it was proposed and tested on a real engineering composite structure the concept that failure in fiber composites may be described similarly, namely that the rate of damage would exhibit a "critical" behavior [20]. This critical behavior corresponds to an acceleration of the rate of energy release or to a deceleration, depending on the nature and range of the stress transfer mechanism and on the loading procedure.…”

mentioning

confidence: 99%

“…This critical behavior corresponds to an acceleration of the rate of energy release or to a deceleration, depending on the nature and range of the stress transfer mechanism and on the loading procedure. Based on general consideration on the nature of the experimental signatures of critical rupture, it was proposed that the power law behavior of the time-to-failure analysis should be corrected for the presence of log-periodic modulations [20] as signatures of a hierarchy of characteristic scales in the rupture process. This method is now been used by the French Aerospace company Aérospatiale-Matra on pressure tanks made of kevlar-matrix and carbon-matrix composites embarked on the European Ariane 4 and 5 rockets.…”

mentioning

confidence: 99%

“…This is the fundamental representation of rupture seen as a critical point in the time-to-failure analysis. The second formulacontains an additional term with relative weight C/B, describing a so-called log-periodic correction to scaling [20,24]. Basically, this formula means that the power law acceleration is modulated by downs and ups organized as a geometrical series converging to p c .…”

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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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Section: Theorymentioning

confidence: 99%

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2000

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“…Although science still seems to be far from the guaranteed decision of this problem there exist some interesting approaches based on the peculiar properties of precursory phenomena [3][4][5][6][7][8][9]. Another important problem is recognition and differentiation of weak earthquakes and technogenic underground explosion signals.…”

Section: Introductionmentioning

confidence: 99%

Universal approach to overcoming nonstationarity, unsteadiness and non-Markovity of stochastic processes in complex systems

Yulmetyev¹,

Мокшин²,

Hänggi

2005

Physica A: Statistical Mechanics and its Applications

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In the present paper, we suggest a new universal approach to study complex systems by microscopic, mesoscopic and macroscopic methods. We discuss new possibilities of extracting information on nonstationarity, unsteadiness and non-Markovity of discrete stochastic processes in complex systems. We consider statistical properties of the fast, intermediate and slow components of the investigated processes in complex systems within the framework of microscopic, mesoscopic and macroscopic approaches separately. Among them theoretical analysis is carried out by means of local noisy time-dependent parameters and the conception of a quasi-Brownian particle (QBP) (mesoscopic approach) as well as the use of wavelet transformation of the initial row time series. As a concrete example we examine the seismic time series data for strong and weak earthquakes in Turkey (1998; 1999) in detail, as well as technogenic explosions. We propose a new possible solution to the problem of forecasting strong earthquakes. Besides we have found out that an unexpected restoration of the first two local noisy parameters in weak earthquakes and technogenic explosions is determined by exponential law. In this paper we have also carried out the comparison and ARTICLE IN PRESS have discussed the received time dependence of the local parameters for various seismic phenomena. r

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Non-Destructive Evaluation of Damage and Failure of Fibre Reinforced Polymer Composites Using Ultrasonic Waves and Acoustic Emission

Guerjouma¹,

Baboux

Ducret

et al. 2001

Adv. Eng. Mater.

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In this communication we have reported experimental evidence of a change of behavior in plastic deformation with the structure dimension. It appears that dislocation activity is less localized as material confinement increases. An analytical model providing deformation mechanism maps is proposed, which is further investigated by using numerical simulation of dislocation dynamics. With decreasing layer thickness, both the effect of more and more discrete pile ups of dislocations and a decrease in the interface strength can explain the deviation at small scale from the Hall±Petch law. The softening observed in ultrafine Cu/Ni (h < 50 ) is explained by interdiffusion effects. ExperimentalIn-situ reflective high-energy electron diffraction was used in an original way to access both in-plane and out-of-plane lattice parameters during growth [15], and therefore to give information about the stress relaxation state of the layer. These measurements were in good agreement with the in-situ laser curvature method for residual stress measurements [7]. Local probe microscopy such as scanning tunneling microscopy (STM) and atomic force microscopy (AFM) was used to characterize the roughness and the grain size of the deposited films. Auger spectroscopy on wedge deposited films was used to measure the composition profile across the interfaces. This was coupled with X-ray diffraction techniques using the Bragg±Brentano setup. The periodicity of the layer structure give rises to a satellite peak and the fit to experimental data of the recorded spectrum gives access to layer roughness and composition profiles. We used high-resolution TEM to study the interface structure (misfit dislocations) and the layer structure (Cu is BCC in a Cu/Nb multilayer for h £ 2 nm) [16]. TEM in-situ deformation observations were also carried out on these small-scale structures to study deformation mechanisms [17].The mechanical properties were measured by nanoindentation techniques using an MTS Nanoindenter in continuous stiffness mode. For testing films, stiff and hard substrates are required: hence the use of Si in our experiments, so that there should be no interference from the substrate. The Berkovich indenters (triangular prism) were calibrated on Al and fused silica using the Oliver±Pharr procedure [18]. AFM was used to image the remaining indent and characterize the area of contact. Nanoindentation was used in different ways: to measure elastic and plastic properties (Young's modulus and hardness), and to determine the strain-rate sensitivity at room temperature. Moreover, we designed specific experiments to observe the slip patterns of deep indents in the films. Tensile tests on free standing films were also performed [19] and dedicated experiments on dislocation injections from single crystal substrates were done [6].Applications of reinforced composites and heterogeneous solids are widespread, spanning technological areas of various aerospace and mechanical industries. A real challenge concerning these materials is their life time predictio...

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Universal Log-Periodic Correction to Renormalization Group Scaling for Rupture Stress Prediction From Acoustic Emissions

Cited by 168 publications

References 4 publications

Critical ruptures

Critical ruptures

Universal approach to overcoming nonstationarity, unsteadiness and non-Markovity of stochastic processes in complex systems

Non-Destructive Evaluation of Damage and Failure of Fibre Reinforced Polymer Composites Using Ultrasonic Waves and Acoustic Emission

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