Scaling Laws for Fracture of Heterogeneous Materials and Rock

Sahimi, Muhammad; Arbabi, Sepehr

doi:10.1103/physrevlett.77.3689

Cited by 104 publications

(65 citation statements)

References 18 publications

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“…These oscillations characterize the scaling regime up to the longest simulated time but they are not observed in the asymptotic solution presented in [13]. Given that log-time periodicity appears to be a rather common feature being observed, besides segregating fluids, during fracturing of heterogeneous solids [26,27] and in stock market indices [28] for instance, it would then be interesting to devise an analytical approach to enlighten the origin of this new phenomenon at least in the present model.…”

Section: Summary and Discussionmentioning

confidence: 99%

Structure and rheology of binary mixtures in shear flow

Corberi¹,

Gonnella²,

Lamura³

2000

Phys. Rev. E

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Results are presented for the phase separation process of a binary mixture subject to an uniform shear flow quenched from a disordered to a homogeneous ordered phase. The kinetics of the process is described in the context of the time-dependent Ginzburg-Landau equation with an external velocity term. The large-n approximation is used to study the evolution of the model in the presence of a stationary flow and in the case of an oscillating shear.For stationary flow we show that the structure factor obeys a generalized dynamical scaling. The domains grow with different typical lengthscales Rx and R ⊥ respectively in the flow direction and perpendicularly to it. In the scaling regime R ⊥ ∼ t α ⊥ and Rx ∼ γt αx (with logarithmic corrections), γ being the shear rate, with αx = 5/4 and α ⊥ = 1/4. The excess viscosity ∆η after reaching a maximum relaxes to zero as γ −2 t −3/2 . ∆η and other observables exhibit log-time periodic oscillations which can be interpreted as due to a growth mechanism where stretching and break-up of domains cyclically occur.In the case of an oscillating shear a cross-over phenomenon is observed: Initially the evolution is characterized by the same growth exponents as for a stationary flow. For longer times the phase separating structure cannot align with the oscillating drift and a different regime is entered with an isotropic growth and the same exponents of the case without shear.47.20.Hw; 05.70.Ln; 83.50.Ax

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Section: Summary and Discussionmentioning

confidence: 99%

Structure and rheology of binary mixtures in shear flow

Corberi¹,

Gonnella²,

Lamura³

2000

Phys. Rev. E

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“…This analogy has been the starting idea for extensive numerical simulations applied to the lattice models of fracture (Sahimi and Arbabi, 1996), which predicted the existence of scaling laws in the vicinity of fracture. With regard to real heterogeneous materials, it is important to emphasize two principal points:…”

Section: Physical Picture Of Rupturementioning

confidence: 99%

Self-similar law of energy release before materials fracture

Yukalov

Moura

Nechad

2004

Journal of the Mechanics and Physics of Solids

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A general law of energy release is derived for stressed heterogeneous materials, being valid from the starting moment of loading till the moment of materials fracture. This law is obtained by employing the extrapolation technique of the self-similar approximation theory. Experiments are accomplished measuring the energy release for industrial composite samples. The derived analytical law is confronted with these experimental data as well as with the known experimental data for other materials.

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“…Numerical simulations of Sahimi and Arbati [34] have recently confirmed that, near the global failure point, the cumulative elastic energy released during fracturing of heterogeneous solids with long-range elastic interactions follows a power law with log-periodic corrections to the leading term consistent with previous results [22][23][24][25][26][27][28][29][30]. 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".…”

Section: The Role Of Heterogeneitiesmentioning

confidence: 99%

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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Scaling Laws for Fracture of Heterogeneous Materials and Rock

Cited by 104 publications

References 18 publications

Structure and rheology of binary mixtures in shear flow

Structure and rheology of binary mixtures in shear flow

Self-similar law of energy release before materials fracture

Critical ruptures

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