384 research outputs found
The Breakdown of Linear Elastic Fracture Mechanics near the Tip of a Rapid Crack
We present high resolution measurements of the displacement and strain fields
near the tip of a dynamic (Mode I) crack. The experiments are performed on
polyacrylamide gels, brittle elastomers whose fracture dynamics mirror those of
typical brittle amorphous materials. Over a wide range of propagation
velocities (), we compare linear elastic fracture mechanics (LEFM)
to the measured near-tip fields. We find that, sufficiently near the tip, the
measured stress intensity factor appears to be non-unique, the crack tip
significantly deviates from its predicted parabolic form, and the strains ahead
of the tip are more singular than the divergence predicted by LEFM.
These results show how LEFM breaks down as the crack tip is approached.Comment: 4 pages, 4 figures, first of a two-paper series (experiments); no
change in content, minor textual revision
Arrested Cracks in Nonlinear Lattice Models of Brittle Fracture
We generalize lattice models of brittle fracture to arbitrary nonlinear force
laws and study the existence of arrested semi-infinite cracks. Unlike what is
seen in the discontinuous case studied to date, the range in driving
displacement for which these arrested cracks exist is very small. Also, our
results indicate that small changes in the vicinity of the crack tip can have
an extremely large effect on arrested cracks. Finally, we briefly discuss the
possible relevance of our findings to recent experiments.Comment: submitted to PRE, Rapid Communication
Steady-State Cracks in Viscoelastic Lattice Models
We study the steady-state motion of mode III cracks propagating on a lattice
exhibiting viscoelastic dynamics. The introduction of a Kelvin viscosity
allows for a direct comparison between lattice results and continuum
treatments. Utilizing both numerical and analytical (Wiener-Hopf) techniques,
we explore this comparison as a function of the driving displacement
and the number of transverse sites . At any , the continuum theory misses
the lattice-trapping phenomenon; this is well-known, but the introduction of
introduces some new twists. More importantly, for large even at
large , the standard two-dimensional elastodynamics approach completely
misses the -dependent velocity selection, as this selection disappears
completely in the leading order naive continuum limit of the lattice problem.Comment: 27 pages, 8 figure
Crack Front Waves and the dynamics of a rapidly moving crack
Crack front waves are localized waves that propagate along the leading edge
of a crack. They are generated by the interaction of a crack with a localized
material inhomogeneity. We show that front waves are nonlinear entities that
transport energy, generate surface structure and lead to localized velocity
fluctuations. Their existence locally imparts inertia, which is not
incorporated in current theories of fracture, to initially "massless" cracks.
This, coupled to crack instabilities, yields both inhomogeneity and scaling
behavior within fracture surface structure.Comment: Embedded Latex file including 4 figure
An intrinsic nonlinear scale governs oscillations in rapid fracture
When branching is suppressed, rapid cracks undergo a dynamic instability from
a straight to an oscillatory path at a critical velocity . In a systematic
experimental study using a wide range of different brittle materials, we first
show how the opening profiles of straight cracks scale with the size
of the nonlinear zone surrounding a crack's tip. We then show, for
all materials tested, that is both a fixed fraction of the shear speed
and, moreover, that the instability wavelength is proportional to .
These findings directly verify recent theoretical predictions and suggest that
the nonlinear zone is not passive, but rather is closely linked to rapid crack
instabilities.Comment: 4 pages, 4 figures + supplementary informatio
Quasi-Static Fractures in Disordered Media and Iterated Conformal Maps
We study the geometrical characteristic of quasi-static fractures in
disordered media, using iterated conformal maps to determine the evolution of
the fracture pattern. This method allows an efficient and accurate solution of
the Lam\'e equations without resorting to lattice models. Typical fracture
patterns exhibit increased ramification due to the increase of the stress at
the tips. We find the roughness exponent of the experimentally relevant
backbone of the fracture pattern; it crosses over from about 0.5 for small
scales to about 0.75 for large scales, in excellent agreement with experiments.
We propose that this cross-over reflects the increased ramification of the
fracture pattern.Comment: submitted to Physical Review Letter
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
Phase-Field Model of Mode III Dynamic Fracture
We introduce a phenomenological continuum model for mode III dynamic fracture
that is based on the phase-field methodology used extensively to model
interfacial pattern formation. We couple a scalar field, which distinguishes
between ``broken'' and ``unbroken'' states of the system, to the displacement
field in a way that consistently includes both macroscopic elasticity and a
simple rotationally invariant short scale description of breaking. We report
two-dimensional simulations that yield steady-state crack motion in a strip
geometry above the Griffith threshold.Comment: submitted to PR
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
Nonequilibrium brittle fracture propagation: Steady state, oscillations and intermittency
A minimal model is constructed for two-dimensional fracture propagation. The
heterogeneous process zone is presumed to suppress stress relaxation rate,
leading to non-quasistatic behavior. Using the Yoffe solution, I construct and
solve a dynamical equation for the tip stress. I discuss a generic tip velocity
response to local stress and find that noise-free propagation is either at
steady state or oscillatory, depending only on one material parameter. Noise
gives rise to intermittency and quasi-periodicity. The theory explains the
velocity oscillations and the complicated behavior seen in polymeric and
amorphous brittle materials. I suggest experimental verifications and new
connections between velocity measurements and material properties.Comment: To appear in Phys. Rev. Lett., 6 pages, self-contained TeX file, 3
postscript figures upon request from author at [email protected] or
[email protected], http://cnls-www.lanl.gov/homepages/rafi/rafindex.htm
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