35 research outputs found
Pinning/depinning of crack fronts in heterogeneous materials
The fatigue fracture surfaces of a metallic alloy, and the stress corrosion
fracture surfaces of glass are investigated as a function of crack velocity. It
is shown that in both cases, there are two fracture regimes, which have a well
defined self-affine signature. At high enough length scales, the universal
roughness index 0.78 is recovered. At smaller length scales, the roughness
exponent is close to 0.50. The crossover length separating these two
regimes strongly depends on the material, and exhibits a power-law decrease
with the measured crack velocity , with . The exponents and characterising the dependence of
and upon the pulling force are shown to be close to and
.Comment: 4 pages, latex, and 4 encapsulated postscript figure
Roughness of tensile crack fronts in heterogenous materials
The dynamics of planar crack fronts in heterogeneous media is studied using a
recently proposed stochastic equation of motion that takes into account
nonlinear effects. The analysis is carried for a moving front in the
quasi-static regime using the Self Consistent Expansion. A continuous dynamical
phase transition between a flat phase and a dynamically rough phase, with a
roughness exponent , is found. The rough phase becomes possible due
to the destabilization of the linear modes by the nonlinear terms. Taking into
account the irreversibility of the crack propagation, we infer that the
roughness exponent found in experiments might become history-dependent, and so
our result gives a lower bound for .Comment: 7 page
Fracture Roughness Scaling: a case study on planar cracks
Using a multi-resolution technique, we analyze large in-plane fracture fronts
moving slowly between two sintered Plexiglas plates. We find that the roughness
of the front exhibits two distinct regimes separated by a crossover length
scale . Below , we observe a multi-affine regime and the
measured roughness exponent is in
agreement with the coalescence model. Above , the fronts are
mono-affine, characterized by a roughness exponent , consistent with the fluctuating line model. We relate the
crossover length scale to fluctuations in fracture toughness and the stress
intensity factor
Dynamical stability of the crack front line
Dynamical stability of the crack front line that propagates between two
plates is studied numerically using the simple two-dimensional mass-spring
model. It is demonstrated that the straight front line is unstable for low
speed while it becomes stable for high speed. For the uniform model, the
roughness exponent in the slower speed region is fairly constant around 0.4 and
there seems to be a rough-smooth transition at a certain speed. For the
inhomogeneous case with quenched randomness, the transition is gradual.Comment: 14 pages, 7 figure
Anomalous roughening of wood fractured surfaces
Scaling properties of wood fractured surfaces are obtained from samples of
three different sizes. Two different woods are studied: Norway spruce and
Maritime pine. Fracture surfaces are shown to display an anomalous dynamic
scaling of the crack roughness. This anomalous scaling behavior involves the
existence of two different and independent roughness exponents. We determine
the local roughness exponents to be 0.87 for spruce and 0.88
for pine. These results are consistent with the conjecture of a universal local
roughness exponent. The global roughness exponent is different for both woods,
= 1.60 for spruce and = 1.35 for pine. We argue that the global
roughness exponent is a good index for material characterization.Comment: 7 two columns pages plus 8 ps figures, uses psfig. To appear in
Physical Review
Dynamics and Instabilities of Planar Tensile Cracks in Heterogeneous Media
The dynamics of tensile crack fronts restricted to advance in a plane are
studied. In an ideal linear elastic medium, a propagating mode along the crack
front with a velocity slightly less than the Rayleigh wave velocity, is found
to exist. But the dependence of the effective fracture toughness on
the crack velocity is shown to destabilize the crack front if
. Short wavelength radiation due to weak random
heterogeneities leads to this instability at low velocities. The implications
of these results for the crack dynamics are discussed.Comment: 12 page
Quasi-static cracks and minimal energy surfaces
We compare the roughness of minimal energy(ME) surfaces and scalar
``quasi-static'' fracture surfaces(SQF). Two dimensional ME and SQF surfaces
have the same roughness scaling, w sim L^zeta (L is system size) with zeta =
2/3. The 3-d ME and SQF results at strong disorder are consistent with the
random-bond Ising exponent zeta (d >= 3) approx 0.21(5-d) (d is bulk
dimension). However 3-d SQF surfaces are rougher than ME ones due to a larger
prefactor. ME surfaces undergo a ``weakly rough'' to ``algebraically rough''
transition in 3-d, suggesting a similar behavior in fracture.Comment: 7 pages, aps.sty-latex, 7 figure
Scaling of interfaces in brittle fracture and perfect plasticity
The roughness properties of two-dimensional fracture surfaces as created by
the slow failure of random fuse networks are considered and compared to yield
surfaces of perfect plasticity with similar disorder. By studying systems up to
a linear size L=350 it is found that in the cases studied the fracture surfaces
exhibit self-affine scaling with a roughness exponent close to 2/3, which is
asymptotically exactly true for plasticity though finite-size effects are
evident for both. The overlap of yield or minimum energy and fracture surfaces
with exactly the same disorder configuration is shown to be a decreasing
function of the system size and to be of a rather large magnitude for all cases
studied. The typical ``overlap cluster'' length between pairs of such
interfaces converges to a constant with increasing.Comment: Accepted for publication in Phys. Rev.
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