A rapidly moving crack in a brittle material is often idealized as a one-dimensional object moving through an ideal two-dimensional material, where the crack tip is a singular point. In real three-dimensional materials, however, tensile cracks are planar objects whose tip forms a propagating one-dimensional singular front. Let us now consider a crack front propagating through a heterogeneous medium populated by an ensemble of localized inhomogeneities (asperities). The front is distorted by its interaction with each asperity. Can the crack front, after many such interactions, still be considered a single coherent entity, or, must the dynamics of failure be described by ensemble of individual cracks, in all but the most homogeneous materials? Here we present laboratory measurements of a new type of wave, crack front waves, CFW, which are generated by asperities and propagate along the crack fronts in tensile fracture. CFW play a major role in the fracture process. They serve to both transport and distribute the energy fluctuations, induced by asperities, throughout the entire front. In this way, these waves allow a crack front to retain its coherence despite repeated interactions with randomly dispersed material inhomogeneities. We will show that CFW are nonlinear entities that have the following interesting characteristic properties.
1.They propagate along the front at approximately the Rayleigh wave speed, relative to the material.
2.CFW are both highly localized with a characteristic, inherently nonlinear shape, reminiscent of solitons. This shape is independent of both their scale and the form of the initial perturbation
3.CFW are long-lived and, upon interaction, retain both their shape and amplitude.
4.CFW are generated either by asperities or, intrinsically, by the spontaneous formation of micro-branches [1].
Recent theoretical work [2,3], has predicted a similar type of (in-plane) elastic wave that exists within the plane defined by the crack front and propagation direction. In addition to having an in-plane component, CFW create structure normal to the fracture plane that can be observed as characteristic tracks on the fracture surface. CFW dynamics, as described above, may have important ramifications in the interpretation of these fracture surface markings and, hence, in the identification of the dynamic processes that created a given surface. Examples include failure analysis and geophysical interpretation of field data. The existence of CFW also calls into question the accuracy of two-dimensional descriptions of fracture. Their long lifetimes introduce an inertial element (where a crack is "aware" of its space-time history) that is absent in current theories of fracture.
1. see e.g. J. Fineberg and M. Marder, Phys. Rep. 313, 1 (1999).
2. S. Ramanathan, D.S. Fisher, Phys. Rev. Lett. 79, 877-880 (1997).
3. J. W. Morrissey, J. R. Rice, J. Mech. Phys. Sol. 46: (3)
467-487 (1998).
[N20.002] Studies of deformation and fracture in model noncrystalline solids
Michael L. Falk (Dept. of Materials Science and Engineering, University of Michigan)
Fracture and deformation have long been areas of active
study in mechanical engineering and materials physics. Yet,
despite centuries of effort,unanswered fundamental questions
continue to prevent accurate detailed predictions of how
materials crack and bend. Open questions include the
relationship between micro-scale and macro-scale plasticity,
the physics of the brittle-ductile transition and
spontaneous branching in dynamic fracture. Recently attempts
have been made to model experiments of dynamic brittle
fracture in PMMA, an amorphous polymer, via finite element
methods. However, these methods run into serious problems
modeling crack branching behavior and may not be well posed
in the standard continuum mechanics sense. More reliable
models require a detailed understanding of crack tip
dynamics. Molecular simulations of fracture in
noncrystalline solids clearly indicate that the fracture
toughness depends quite sensitively on the dynamics of the
material response near the crack tip. The detailed kinetics
of these deformation processes in noncrystalline solids can
be investigated using simple computer models. These models
provide insight into the deformation which goes on in the
vicinity of the crack tip. Including such effects into our
theories of fracture helps to bridge the gap between
molecular processes and crack tip dynamics.
[N20.003] Fracture and Friction
Eric Gerde (Computational and Applied Mathematics), Michael Marder (Department of Physics, The University of Texas at Austin)
We present an atomic scale description of a self-healing
crack steadily traveling along a compressed interface
between dissimilar solids. The motion is similar to the
wrinkle-like Weertman pulse observed by Anooshehpoor in
recent foam-rubber sliding experiments. In contrast to the
theoretical models of Weertman and Adams, and the numerical
calculations of Andrews and Ben-Zion, we do not employ a
frictional constitutive law on the interface. Yet the
restrictive conditions under which these cracks can
propagate make the interface appear to have a static
coefficient of friction. By analytically linking atomic and
continuum fields, we are able to efficiently and
exhaustively explore the conditions under which self-healing
cracks can propagate. To a good approximation, they are
sustainable only when the interfacial shear stresses are 0.4
times the compressive stresses.
[N20.004] Transition from Straight to Oscillating Cracks in Dynamic Fracture
Paul Petersan, Robert Deegan, Michael Marder (Center for Nonlinear Dynamics, University of Texas at Austin)
The propagation of a crack in a biaxially stretched latex
sheet provides a novel test bed for investigating the crack
path selection problem in dynamic fracture. We have found
that these cracks undergo a transition from straight to
oscillating paths as the extensions applied to the system
along two perpendicular axes are varied. The growth of this
oscillation from its onset and implications to the problem
of path selection will be discussed.
[N20.005] The Effect of Damping Propagating Stress Waves during Brittle Fracture
A. Johns, R. Morahan, J. Paoluccio, L.C. Krysac (Dept. of Physics, University of the Pacific)
There is growing evidence that brittle fracture may be some
kind of phase transition, where the amount of disorder in
the material determines whether the transition is first
order or continuous. Other properties of materials, such as
the amplitude of propagating stress waves, may also affect
the statistics of brittle fracture. The failure under
tensile stress of a brittle carbon foam has been found to be
forewarned by bond breaking activity produced by propagating
stress waves. Results from experiments damping the activity
of the stress waves by submerging the foam in a ferrofluid
are presented, and the implications for the description of
fracture as a phase transition discussed.
[N20.006] Effective elastic constants of a two dimensional solid under an oscillatory applied stress
Rodrigo Arias (Universidad de Chile, Santiago, Chile)
The response of a two dimensional solid, populated by
thermally excited dislocation pairs, to an oscillatory
applied stress is studied in an infinite medium. A low
population of dislocation pairs is assumed, i.e. the
temperature is lower than the Kosterlitz-Thouless
dislocation pairs unbinding transition temperature. A
linearized Fokker-Planck equation for the dislocations
distribution is solved in the limit of a long wavelength and
low frequency weak applied stress. Frequency and wavelength
dependent elastic constants describe the linear response of
this defect populated medium to the oscillatory applied
stress.
[N20.007] Multiscale approach to intergranular fracture in polycrystals
Thierry Cretegny (LASSP, Cornell University), Chuin-Shan Chen (Cornell Theory Center), Erin Iesulauro (Civil and Environmental Engineering, Cornell University), Christopher R. Myers (Cornell Theory Center), Anthony R. Ingraffea (Civil and Environmental Engineering, Cornell University), James P. Sethna (LASSP, Cornell University)
We present atomistic measurements of traction-separation laws and fracture toughness at grain boundaries with a variety of misorientations and inclinations. We use the quasicontinuum approach, combining molecular dynamics and finite element portions of our Digital Material framework. Our measurements will feed into finite element models investigating the effects of texture and grain-boundary toughness anisotropy on intergranular fracture in polycrystals.