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The goal of research into fracture at the Center for Nonlinear
Dynamics is to study fracture as a dynamical system; to understand
how dynamics at small scales works out in phenomena at the
macroscopic scale.
The research has experimental, theoretical, and numerical components.
Experiments: Many of our experiments have concerned the fracture of Plexiglas, glass, and other brittle amorphous materials. The question on which we focused was Why do cracks propagate at only a fraction of the ultimate speed predicted by theory? The experiments led us to answer that crack speeds are limited by dynamical instabilities of the tip. We have performed many experiments to characterize the instability, and find its consequences. Recently, we have been carrying out experiments in crystalline silicon, so as to be able to obtain quantitative comparisons with theoretical and numerical work. We are in the process of performing a new series of experiments at liquid nitrogen temperatures. We are also investigating fracture instabilities in rubber, and quasi-static crack waves in silicon
Theory: The main accomplishments of theory have been to develop complete analytical solutions for the fracture of crystals. We have shown that there is a forbidden band of velocities in low-temperature crystals where crack propagation is impossible, that above this band cracks propagate stably, and that above a critical energy flux they become unstable to a micro-cracking instability surprisingly reminiscent of the experiments in amorphous materials. We have also worked out a detailed statistical mechanics of fracture. Current work involves self-healing cracks along interfaces, and the connection between fracture and friction.
Numerics: We have developed a molecular dynamics code in MPI specially suited to studying fracture of materials with three-body interactions. Making use of scaling ideas from analytical solutions, we use the molecular dynamics to make predictions about laboratory-scale phenomena. The numerical work has been focusing upon silicon, so as to make direct comparison with our laboratory experiments.
To find out more about our work visit the following links:
Physical
Review Focus story on popping balloons
Physical
Review Focus Story on fracture experiments in single crystals of
silicon
HTML
version of a paper on How Things Break that appeared in Physics Today
Details
on the experiments in PMMA
Quicktime
movies and results from the simulations in silicon
MPEG movie (6.5 MB) showing a supersonic
crack in numerical simulation of rubber
List of
reprints on fracture that can be ordered from the Center for
Nonlinear DynamicsCracks
Cleave Crystals (pdf, 820K), cond-mat/0403159 . Cracks can follow
crystal planes even if they must violate the conventional rule for
crack motion -- the principle of local symmetry -- to do so.
Lectures
delivered in Spring 2003 at Les Houches Winter school (1800K ,
pdf)
Friction
and Fracture, (120K, pdf) How self-healing fractures
between two objects can lead to sliding. Published in Nature.
Eric
Gerde's Thesis on Friction and Fracture, (2700K,
PostScript) How self-healing fractures between two objects can lead
to sliding; this time with all the math included.
Oscillating
Fracture Paths in Rubber (300K, pdf) Why the edges of a
balloon are wiggly. Published in Physical Review Letters, and
featured in Physical
Review Focus
Molecular
dynamics of cracks (900K, pdf) Almost nontechnical review for
Computers in Science and Engineering, has a new qualitative
argument for the velocity gap.
Cracks
and atoms (1700K, pdf) Slightly caustic description of
molecular dynamics simulations by Dominic Holland and Marder,
published in Advanced Materials.
Dynamic
fracture in single crystal silicon (316 K, pdf) Article by
Jens Hauch, Marder, Dominic Holland, and Harry Swinney, comparing
experiment and computations for rapid fracture in silicon, published
in PRL. This article was featured in Physical
Review Focus.
Instability
in dynamic fracture (4.1 MB, pdf) Review article by J
Fineberg and M Marder published in Physics Reports. Summary of
results on instabilities in dynamic fracture, with an emphasis upon
experiment, but also containing pedagogical material on dynamic
fracture from both continuum and atomic viewpoints.
Energies
of a kinked crack line (7 MB, pdf) Article from J Stat Phys.
on kink configurations that allow cracks to creep.
Ideal
fracture of silicon studied with molecular dynamics (1.3 MB,
pdf) 1998 paper by D Holland and M Marder in Physical Review Letters,
vol 80, pp 746-749. Shows how to use molecular dynamics to obtain
experimentally measurable features of fracture. WARNING: We no
longer trust the interatomic potentials we used for these studies!
Statistical
mechanics of cracks (0.2 MB, pdf) 1996 paper by M Marder in
Physical Review E, vol 54, pp 3442-3454. Contains reformulation of
classical statistical mechanics in terms of functional integral,
variational solution, demonstration that time-reversed paths play a
crucial role in activated processes, laborious calculation of
prefactor.
Origin
of crack-tip instabilities (0.3 MB, pdf) 1995 paper in by M
Marder and S Gross in Journal of Mechanics and Physics of Solids, vol
43, pp. 1-48. Contains theory of lattice fracture in one-dimensional
models, Mode III, and Mode I; demonstrates velocity gap, linear
stability, microcracking instability.
