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When a heterogeneous material is broken,
the fracture surfaces are rough. That roughness has already been widely
studied experimentally, and strong geometrical properties have been observed.
But it is the first time that researchers have managed to achieve a numerical
simulation that corresponds to experiment, and to explain the physical
origin of the phenomenon. This research, conducted by George Batrouni,
from the “Institut non linéaire de Nice” (Non-Linear
Institute of Nice, CNRS and Université de Nice) with Jean Schmittbuhl,
from the “Laboratoire de géologie” (Geology Laboratory)
of the Ecole Normale Supérieure of Paris, associated with CNRS,
and Alex Hansen (Physics dept, NTNU, Trondheim, Norway), provides essential
information for mastering resistance of materials. It could also help
seismologists to gain a better understanding of the behavior of faults
during earthquakes, and thus to produce better forecasts for seismic risks.
A crack that develops in a wall or along the
ground in a sidewalk, for example, never forms in a straight line: the
energy is dispersed and passes through the many defects in the material,
giving rise to a coalescence of micro-cracks that finally lead to a rough
fracture. This property is common to all heterogeneous materials. In 1984,
Benoît Mandelbrot1 observed that fracture surfaces had scale invariance
properties: the same patterns are to be found at different scales of magnitude.
Later, it was shown that that scale invariance was verified over a very
wide range of scales and is relatively insensitive to the type of the
material or to its fracture mode.
Several physicists have sought to understand the physical origin of experimental
observations, in particular the values measured in the case of an interfacial
fracture, in situ optical observation of which was obtained for the first
time in Oslo in 1997. This achievement was finally made by George Batrouni,
Jean Schmittbuhl and Alex Hansen. Their work has been published in Physical
Review Letters2 . “We propose a novel theory that we are verifying
with a highly original simulation algorithm. In this case of interfacial
fracture, we show that the roughness of the crack front does not come
from the crack front itself, but rather form the micro-cracking that develops
ahead of the crack front.” The elastic interactions that appear between
the micro-cracks can be described by a particular percolation process.
The scientists have thus succeeded in explaining the dynamics of this
phenomenon. Other recent work shows that these results can be extended
to the case of fracture surfaces, and thus solve the mystery of their
geometry.
There are many potential applications of this research work. For example,
it is possible to imagine strong points which, placed judiciously, would
block the micro-cracks in a material. For example, that could be a way
of further improving the reliability of the joins between the wings and
the fuselage of an airplane. In seismology, roughness is also an important
parameter. Earthquakes occur mainly at the borders between tectonic plates.
The mechanical state along faults is heavily influenced by their roughness
and by the stress fluctuations that they generate. The research, which
improves understanding of that roughness and above all of the processes
whereby earthquakes are triggered, should be invaluable for seismologists.
“I don’t claim it will be possible to predict the extensions
of future earthquakes,” points out George Batrouni, “but it
should offer better understanding of the processes whereby earthquakes
are initiated, and therefore improved forecasting of future earthquakes
in any given region.”
1 - Benoît Mandelbrot, a French
mathematician who was born in Poland in 1924, is famous for his work on
fractal curves which he studied particularly at IBM. He coined the term
“fractal” in 1975 from the Latin adjective fractus (fragmented
or irregular) which comes from the verb frangere (to break or to create
irregular fragments). The irregularities in nature, which appear to be
chaotic, are in fact expressions of a very complex geometry of the infinitely
small where the concept of fractional dimensions is substituted for the
concept of Euclidian dimension. For example, his work applies to the study
of coastlines, cloud shapes, a tree, a fern leaf, etc.
2 - Roughness of Interfacial Cracks Fronts: Stress-Weighted Percolation
in the Damage Zone, Physical Review Letters, March 31, 2003.
Researcher contacts:
George Batrouni
Institut non lineaire de Nice (INLN),
Tel.: +33 4 92 96 73 18
George.Batrouni@inln.cnrs.fr
Communication contact for the Department of
Mathematics and Physical Sciences:
Frédérique Laubenheimer
+33 1 44 96 42 63
frederique.laubenheimer@cnrs-dir.fr
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