849 research outputs found
Autonomy and Singularity in Dynamic Fracture
The recently developed weakly nonlinear theory of dynamic fracture predicts
corrections to the standard asymptotic linear elastic
displacement-gradients, where is measured from the tip of a tensile crack.
We show that the singularity does not automatically conform with the
notion of autonomy (autonomy means that any crack tip nonlinear solution is
uniquely determined by the surrounding linear elastic fields) and
that it does not automatically satisfy the resultant Newton's equation in the
crack parallel direction. We show that these two properties are interrelated
and that by requiring that the resultant Newton's equation is satisfied,
autonomy of the singular solution is retained. We further show that the
resultant linear momentum carried by the singular fields vanishes
identically. Our results, which reveal the physical and mathematical nature of
the new solution, are in favorable agreement with recent near tip measurements.Comment: 4 pages, 2 figures, related papers: arXiv:0902.2121 and
arXiv:0807.486
On the Self-Affine Roughness of a Crack Front in Heterogeneous Media
The long-ranged elastic model, which is believed to describe the evolution of
a self-affine rough crack-front, is analyzed to linear and non-linear orders.
It is shown that the nonlinear terms, while important in changing the front
dynamics, are not changing the scaling exponent which characterizes the
roughness of the front. The scaling exponent thus predicted by the model is
much smaller than the one observed experimentally. The inevitable conclusion is
that the gap between the results of experiments and the model that is supposed
to describe them is too large, and some new physics has to be invoked for
another model.Comment: 4 pages, 4 figure
The dynamics of cracks in torn thin sheets
Motivated by recent experiments, we present a study of the dynamics of cracks
in thin sheets. While the equations of elasticity for thin plates are well
known, there remains the question of path selection for a propagating crack. We
invoke a generalization of the principle of local symmetry to provide a
criterion for path selection and demonstrate qualitative agreement with the
experimental findings. The nature of the singularity at the crack tip is
studied with and without the interference of nonlinear terms.Comment: 7 pages, 11 figure
Some exact results for the velocity of cracks propagating in non-linear elastic models
We analyze a piece-wise linear elastic model for the propagation of a crack
in a stripe geometry under mode III conditions, in the absence of dissipation.
The model is continuous in the propagation direction and discrete in the
perpendicular direction. The velocity of the crack is a function of the value
of the applied strain. We find analytically the value of the propagation
velocity close to the Griffith threshold, and close to the strain of uniform
breakdown. Contrary to the case of perfectly harmonic behavior up to the
fracture point, in the piece-wise linear elastic model the crack velocity is
lower than the sound velocity, reaching this limiting value at the strain of
uniform breakdown. We complement the analytical results with numerical
simulations and find excellent agreement.Comment: 9 pages, 13 figure
Supersonic crack propagation in a class of lattice models of Mode III brittle fracture
We study a lattice model for mode III crack propagation in brittle materials
in a stripe geometry at constant applied stretching. Stiffening of the material
at large deformation produces supersonic crack propagation. For large
stretching the propagation is guided by well developed soliton waves. For low
stretching, the crack-tip velocity has a universal dependence on stretching
that can be obtained using a simple geometrical argument.Comment: 4 pages, 3 figure
Cracks Cleave Crystals
The problem of finding what direction cracks should move is not completely
solved. A commonly accepted way to predict crack directions is by computing the
density of elastic potential energy stored well away from the crack tip, and
finding a direction of crack motion to maximize the consumption of this energy.
I provide here a specific case where this rule fails. The example is of a crack
in a crystal. It fractures along a crystal plane, rather than in the direction
normally predicted to release the most energy. Thus, a correct equation of
motion for brittle cracks must take into account both energy flows that are
described in conventional continuum theories and details of the environment
near the tip that are not.Comment: 6 page
Frictional sliding without geometrical reflection symmetry
The dynamics of frictional interfaces play an important role in many physical
systems spanning a broad range of scales. It is well-known that frictional
interfaces separating two dissimilar materials couple interfacial slip and
normal stress variations, a coupling that has major implications on their
stability, failure mechanism and rupture directionality. In contrast,
interfaces separating identical materials are traditionally assumed not to
feature such a coupling due to symmetry considerations. We show, combining
theory and experiments, that interfaces which separate bodies made of
macroscopically identical materials, but lack geometrical reflection symmetry,
generically feature such a coupling. We discuss two applications of this novel
feature. First, we show that it accounts for a distinct, and previously
unexplained, experimentally observed weakening effect in frictional cracks.
Second, we demonstrate that it can destabilize frictional sliding which is
otherwise stable. The emerging framework is expected to find applications in a
broad range of systems.Comment: 14 pages, 5 figures + Supplementary Material. Minor change in the
title, extended analysis in the second par
Velocity Fluctuations in Dynamical Fracture: the Role of Microcracks
We address the velocity fluctuations of fastly moving cracks in stressed
materials. One possible mechanism for such fluctuations is the interaction of
the main crack with micro cracks (irrespective whether these are existing
material defects or they form during the crack evolution). We analyze carefully
the dynamics (in 2 space dimensions) of one macro and one micro crack, and
demonstrate that their interaction results in a {\em large} and {\em rapid}
velocity fluctuation, in qualitative correspondence with typical velocity
fluctuations observed in experiments. In developing the theory of the dynamical
interaction we invoke an approximation that affords a reduction in mathematical
complexity to a simple set of ordinary differential equations for the positions
of the cracks tips; we propose that this kind of approximation has a range of
usefulness that exceeds the present context.Comment: 7 pages, 7 figure
Drying Patterns: Sensitivity to Residual Stresses
Volume alteration in solid materials is a common cause of material failure.
Here we investigate the crack formation in thin elastic layers attached to a
substrate. We show that small variations in the volume contraction and
substrate restraint can produce widely different crack patterns ranging from
spirals to complex hierarchical networks. The networks are formed when there is
no prevailing gradient in material contraction whereas spirals are formed in
the presence of a radial gradient in the contraction of a thin elastic layer.Comment: 4 pages, 4 figure
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