434 research outputs found
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
Fracture through cavitation in a metallic glass
The fracture surfaces of a Zr-based bulk metallic glass exhibit exotic multi-affine isotropic scaling properties. The study of the mismatch between the two facing fracture surfaces as a function of their distance shows that fracture occurs mostly through the growth and coalescence of damage cavities. The fractal nature of these damage cavities is shown to control the roughness of the fracture surfaces
Electrical conductance of a 2D packing of metallic beads under thermal perturbation
Electrical conductivity measurements on a 2D packing of metallic beads have
been performed to study internal rearrangements in weakly pertubed granular
materials. Small thermal perturbations lead to large non gaussian conductance
fluctuations. These fluctuations are found to be intermittent and gathered in
bursts. The distributions of the waiting time between to peaks is found to be a
power law inside bursts. The exponent is independent of the bead network, the
intensity of the perturbation and external stress. these bursts are interpreted
as the signature of individual bead creep rather than collective vaults
reorganisations. We propose a simple model linking the exponent of the waiting
time distribution to the roughness exponent of the surface of the beads.Comment: 7 pages, 6 figure
Relevance of visco-plastic theory in a multi-directional inhomogeneous granular flow
We confront a recent visco-plastic description of dense granular flows [P.
Jop et al, Nature, {\bf 441} (2006) 727] with multi-directional inhomogeneous
steady flows observed in non-smooth contact dynamics simulations of 2D
half-filled rotating drums. Special attention is paid to check separately the
two underlying fundamental statements into which the considered theory can be
recast, namely (i) a single relation between the invariants of stress and
strain rate tensors and (ii) the alignment between these tensors.
Interestingly, the first prediction is fairly well verified over more than four
decades of small strain rate, from the surface rapid flow to the quasi-static
creep phase, where it is usually believed to fail because of jamming. On the
other hand, the alignment between stress and strain rate tensors is shown to
fail over the whole flow, what yields an apparent violation of the
visco-plastic rheology when applied without care. In the quasi-static phase,
the particularly large misalignment is conjectured to be related to transient
dilatancy effects
Understanding fast macroscale fracture from microcrack post mortem patterns
Dynamic crack propagation drives catastrophic solid failures. In many
amorphous brittle materials, sufficiently fast crack growth involves
small-scale, high-frequency microcracking damage localized near the crack tip.
The ultra-fast dynamics of microcrack nucleation, growth and coalescence is
inaccessible experimentally and fast crack propagation was therefore studied
only as a macroscale average. Here, we overcome this limitation in
polymethylmethacrylate, the archetype of brittle amorphous materials: We
reconstruct the complete spatio-temporal microcracking dynamics, with
micrometer / nanosecond resolution, through post mortem analysis of the
fracture surfaces. We find that all individual microcracks propagate at the
same low, load-independent, velocity. Collectively, the main effect of
microcracks is not to slow down fracture by increasing the energy required for
crack propagation, as commonly believed, but on the contrary to boost the
macroscale velocity through an acceleration factor selected on geometric
grounds. Our results emphasize the key role of damage-related internal
variables in the selection of macroscale fracture dynamics.Comment: 9 pages, 5 figures + supporting information (15 pages
Scaling exponents for fracture surfaces in homogenous glass and glassy ceramics
We investigate the scaling properties of post-mortem fracture surfaces in
silica glass and glassy ceramics. In both cases, the 2D height-height
correlation function is found to obey Family-Viseck scaling properties, but
with two sets of critical exponents, in particular a roughness exponent
in homogeneous glass and in glassy
ceramics. The ranges of length-scales over which these two scalings are
observed are shown to be below and above the size of process zone respectively.
A model derived from Linear Elastic Fracture Mechanics (LEFM) in the
quasistatic approximation succeeds to reproduce the scaling exponents observed
in glassy ceramics. The critical exponents observed in homogeneous glass are
conjectured to reflect damage screening occurring for length-scales below the
size of the process zone
Experimental study of granular surface flows via a fast camera: a continuous description
Depth averaged conservation equations are written for granular surface flows.
Their application to the study of steady surface flows in a rotating drum
allows to find experimentally the constitutive relations needed to close these
equations from measurements of the velocity profile in the flowing layer at the
center of the drum and from the flowing layer thickness and the static/flowing
boundary profiles. The velocity varies linearly with depth, with a gradient
independent of both the flowing layer thickness and the static/flowing boundary
local slope. The first two closure relations relating the flow rate and the
momentum flux to the flowing layer thickness and the slope are then deduced.
Measurements of the profile of the flowing layer thickness and the
static/flowing boundary in the whole drum explicitly give the last relation
concerning the force acting on the flowing layer. Finally, these closure
relations are compared to existing continuous models of surface flows.Comment: 20 pages, 11 figures, submitted to Phys. FLuid
Diphasic non-local model for granular surface flows
Considering recent results revealing the existence of multi-scale rigid
clusters of grains embedded in granular surface flows, i.e. flows down an
erodible bed, we describe here the surface flows rheology through a non-local
constitutive law. The predictions of the resulting model are compared
quantitatively to experimental results: The model succeeds to account for the
counter-intuitive shape of the velocity profile observed in experiments, i.e. a
velocity profile decreasing exponentially with depth in the static phase and
remaining linear in the flowing layer with a velocity gradient independent of
both the flowing layer thickness, the angle between the flow and the
horizontal, and the coefficient of restitution of the grains. Moreover, the
scalings observed in rotating drums are recovered, at least for small rotating
speed.Comment: 7 pages, submitted to Europhys. Let
Reconfiguring Independent Sets in Claw-Free Graphs
We present a polynomial-time algorithm that, given two independent sets in a
claw-free graph , decides whether one can be transformed into the other by a
sequence of elementary steps. Each elementary step is to remove a vertex
from the current independent set and to add a new vertex (not in )
such that the result is again an independent set. We also consider the more
restricted model where and have to be adjacent
Cleaved surface of i-AlPdMn quasicrystals: Influence of the local temperature elevation at the crack tip on the fracture surface roughness
Roughness of i-AlPdMn cleaved surfaces are presently analysed. From the
atomic scale to 2-3 nm, they are shown to exhibit scaling properties hiding the
cluster (0.45 nm) aperiodic structure. These properties are quantitatively
similar to those observed on various disordered materials, albeit on other
ranges of length scales. These properties are interpreted as the signature of
damage mechanisms occurring within a 2-3 nm wide zone at the crack tip. The
size of this process zone finds its origin in the local temperature elevation
at the crack tip. For the very first time, this effect is reported to be
responsible for a transition from a perfectly brittle behavior to a nanoductile
one.Comment: 8 page
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