1,450 research outputs found
Estimating Terminal Velocity of Rough Cracks in the Framework of Discrete Fractal Fracture Mechanics
In this paper we first obtain the order of stress singularity for a
dynamically propagating self-affine fractal crack. We then show that there is
always an upper bound to roughness, i.e. a propagating fractal crack reaches a
terminal roughness. We then study the phenomenon of reaching a terminal
velocity. Assuming that propagation of a fractal crack is discrete, we predict
its terminal velocity using an asymptotic energy balance argument. In
particular, we show that the limiting crack speed is a material-dependent
fraction of the corresponding Rayleigh wave speed
Intermittency and roughening in the failure of brittle heterogeneous materials
Stress enhancement in the vicinity of brittle cracks makes the macro-scale
failure properties extremely sensitive to the micro-scale material disorder.
Therefore: (i) Fracturing systems often display a jerky dynamics, so-called
crackling noise, with seemingly random sudden energy release spanning over a
broad range of scales, reminiscent of earthquakes; (ii) Fracture surfaces
exhibit roughness at scales much larger than that of material micro-structure.
Here, I provide a critical review of experiments and simulations performed in
this context, highlighting the existence of universal scaling features,
independent of both the material and the loading conditions, reminiscent of
critical phenomena. I finally discuss recent stochastic descriptions of crack
growth in brittle disordered media that seem to capture qualitatively - and
sometimes quantitatively - these scaling features.Comment: 38 pages, invited review for J. Phys. D cluster issue on "Fracture:
from the Atomic to the Geophysics Scale
Size effects in statistical fracture
We review statistical theories and numerical methods employed to consider the
sample size dependence of the failure strength distribution of disordered
materials. We first overview the analytical predictions of extreme value
statistics and fiber bundle models and discuss their limitations. Next, we
review energetic and geometric approaches to fracture size effects for
specimens with a flaw. Finally, we overview the numerical simulations of
lattice models and compare with theoretical models.Comment: review article 19 pages, 5 figure
Fracture strength: Stress concentration, extreme value statistics and the fate of the Weibull distribution
The fracture strength distribution of materials is often described in terms
of the Weibull law which can be derived by using extreme value statistics if
elastic interactions are ignored. Here, we consider explicitly the interplay
between elasticity and disorder and test the asymptotic validity of the Weibull
distribution through numerical simulations of the two-dimensional random fuse
model. Even when the local fracture strength follows the Weibull distribution,
the global failure distribution is dictated by stress enhancement at the tip of
the cracks and sometimes deviates from the Weibull law. Only in the case of a
pre-existing power law distribution of crack widths do we find that the failure
strength is Weibull distributed. Contrary to conventional assumptions, even in
this case, the Weibull exponent can not be simply inferred from the exponent of
the initial crack width distribution. Our results thus raise some concerns on
the applicability of the Weibull distribution in most practical cases
Rupture by damage accumulation in rocks
The deformation of rocks is associated with microcracks nucleation and
propagation, i.e. damage. The accumulation of damage and its spatial
localization lead to the creation of a macroscale discontinuity, so-called
"fault" in geological terms, and to the failure of the material, i.e. a
dramatic decrease of the mechanical properties as strength and modulus. The
damage process can be studied both statically by direct observation of thin
sections and dynamically by recording acoustic waves emitted by crack
propagation (acoustic emission). Here we first review such observations
concerning geological objects over scales ranging from the laboratory sample
scale (dm) to seismically active faults (km), including cliffs and rock masses
(Dm, hm). These observations reveal complex patterns in both space (fractal
properties of damage structures as roughness and gouge), time (clustering,
particular trends when the failure approaches) and energy domains (power-law
distributions of energy release bursts). We use a numerical model based on
progressive damage within an elastic interaction framework which allows us to
simulate these observations. This study shows that the failure in rocks can be
the result of damage accumulation
Scaling of Crack Surfaces and Implications on Fracture Mechanics
The scaling laws describing the roughness development of crack surfaces are
incorporated into the Griffith criterion. We show that, in the case of a
Family-Vicsek scaling, the energy balance leads to a purely elastic brittle
behavior. On the contrary, it appears that an anomalous scaling reflects a
R-curve behavior associated to a size effect of the critical resistance to
crack growth in agreement with the fracture process of heterogeneous brittle
materials exhibiting a microcracking damage.Comment: Revtex, 4 pages, 3 figures, accepted for publication in Physical
Review Letter
On the puzzling feature of the silence of precursory electromagnetic emissions
It has been suggested that fracture-induced MHz-kHz electromagnetic (EM)
emissions, which emerge from a few days up to a few hours before the main
seismic shock occurrence permit a real-time monitoring of the damage process
during the last stages of earthquake preparation, as it happens at the
laboratory scale. Despite fairly abundant evidence, EM precursors have not been
adequately accepted as credible physical phenomena. These negative views are
enhanced by the fact that certain 'puzzling features' are repetitively observed
in candidate fracture-induced pre-seismic EM emissions. More precisely, EM
silence in all frequency bands appears before the main seismic shock
occurrence, as well as during the aftershock period. Actually, the view that
'acceptance of 'precursive' EM signals without convincing co-seismic signals
should not be expected' seems to be reasonable. In this work we focus on this
point. We examine whether the aforementioned features of EM silence are really
puzzling ones or, instead, reflect well-documented characteristic features of
the fracture process, in terms of: universal structural patterns of the
fracture process, recent laboratory experiments, numerical and theoretical
studies of fracture dynamics, critical phenomena, percolation theory, and
micromechanics of granular materials. Our analysis shows that these features
should not be considered puzzling.Comment: arXiv admin note: text overlap with arXiv:cond-mat/0603542 by other
author
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