Quasistatic Crack Propagation in Heterogeneous Media

Ramanathan, Sharad; Ertaş, Deniz; Fisher, Daniel S.

doi:10.1103/physrevlett.79.873

Cited by 157 publications

(169 citation statements)

References 19 publications

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“…We believe that this is an important aspect in the success of model A in reproducing a correlated roughening, quantitatively close to the experimental observations. It also explains why models which used the linear approximation of a straight crack plus a perturbed K II achieved scaling exponents different from those observed in experiments [15,16].…”

Section: Resultsmentioning

confidence: 96%

Random and correlated roughening in slow fracture by damage nucleation

2006

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We address the role of the nature of material disorder in determining the roughness of cracks which grow by damage nucleation and coalescence ahead of the crack tip. We highlight the role of quenched and annealed disorders in relation to the length scales d and ξc associated with the disorder and the damage nucleation respectively. In two related models, one with quenched disorder in which d ≃ ξc, the other with annealed disorder in which d ≪ ξc, we find qualitatively different roughening properties for the resulting cracks in 2-dimensions. The first model results in random cracks with an asymptotic roughening exponent ζ ≈ 0.5. The second model shows correlated roughening with ζ ≈ 0.66. The reasons for the qualitative difference are rationalized and explained.

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Section: Resultsmentioning

confidence: 96%

Random and correlated roughening in slow fracture by damage nucleation

2006

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“…In certain conditions, the problem can be directly related to models and theories of interface depinning in random media and the roughness exponent computed by numerical simulations and renormalization group calculations [16,17]. Unfortunately, the numerical agreement between this theoretical approach and experiments is quite poor [18,19,20].…”

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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“…Examples include interfaces between two fluids in porous media [2] or between oppositely magnetized ferromagnetic domains, vortex lines and lattices in type II superconductors [3], [4], charge density waves [5], and planar crack fronts in solids [6].…”

Section: Introductionmentioning

confidence: 99%

Depinning with dynamic stress overshoots: A hybrid of critical and pseudohysteretic behavior

Schwarz

Fisher

2003

Phys. Rev. E

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A model of an elastic manifold driven through a random medium by an applied force F is introduced and studied. The focus is on the effects of inertia and elastic waves, in particular stress overshoots in which motion of one segment of the manifold causes a temporary stress on its neighboring segments in addition to the static stress. Such stress overshoots decrease the critical force for depinning and make the depinning transition hysteretic with static and pinned configurations coexisting with the steadily moving phase for a range of F . We find that the steady state velocity of the moving phase is, nevertheless, history independent and the critical behavior as the force is decreased is in the same universality class as in the absence of stress overshoots -the dissipative limit in which hysteresis cannot occur and theoretical analysis has been possible. To reach this conclusion, finite-size scaling analyses have been performed and a variety of quantities studied, including velocities, roughnesses, distributions of critical forces, and universal amplitude ratios.If the force is increased slowly from zero, the behavior is complicated with a spectrum of avalanche sizes occurring that seems to be quite different from the dissipative limit. Related behavior is seen as the force is increased back up again to restart the motion of samples that have been stopped from the moving phase. The restarting process itself involves both fractal and bubble-like nucleation. Hysteresis loops in small and intermediate size samples can be understood in terms of a depletion layer caused by the stress overshoots. Surprisingly, in the limit of very large samples the hysteresis loops vanish. Although complicated crossovers complicate the analysis, we argue that the underlying universality class governing this pseudohysteresis and avalanches is again that of the apparently-very-different dissipative limit. But there are history dependent amplitudes -associated with the depletion layer -that cause striking differences over wide ranges of length scales. Consequences of this picture for the statistics and dynamics of earthquakes on geological faults are briefly discussed.

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Quasistatic Crack Propagation in Heterogeneous Media

Cited by 157 publications

References 19 publications

Random and correlated roughening in slow fracture by damage nucleation

Random and correlated roughening in slow fracture by damage nucleation

Crack roughness and avalanche precursors in the random fuse model

Depinning with dynamic stress overshoots: A hybrid of critical and pseudohysteretic behavior

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