Incollection,
Roughness of fracture surfaces: A tool to probe the mechanical heterogeneous properties of brittle materials
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)
Abstract
Understanding how a crack propagates within a disordered material is a challenging question.
Designed for this purpose, many studies since the pioneering work of Mandelbrot1,
have focused on the statistical properties of roughness of fracture surfaces,
with the hope to extract from their morphology the relevant physical ingredients of their failure.
An important step was recently achieved by Bonamy et al.2 that shown
that the roughness exponent, characterizing the self-affine geometry of crack roughness,
was reminiscent of the failure mechanism. A high exponent $0.8$
is the signature of damage and plastic mechanisms accompanying the failure of the material
while a lower exponent $0.4$ was shown to result from a perfectly
brittle failure. Interestingly, in this second case, all the irreversible damage and failure processes that have accompagnied the crack growth are localized on the fracture surface only. This suggests that their morphology could be used as a tool to
gain information on the disordered structure of the broken material. This study is the
first step in this direction.
As a starting point, we have developed a model of crack propagation within an
ideal elastic disordered material that is able to reproduce the main statistical
properties of experimental fracture surfaces of brittle materials.
This approach provides a path equation of the crack front involving various mechanical
parameters of the material such as its mean Poisson's ratio or properties reminiscent of
their disordered structure, such as the typical size of their heterogeneities
and their typical 'strength' compared to the mean properties of the material.
We will show that, using this equation, it is possible to estimate these parameters directly
from the statistical analysis of fracture roughness. In fact, a whole map of the material
disorder can be obtained within a cut plane of its 3D structure. The method will be validated on fracture surfaces of synthetic brittle glass ceramics that was shown to exhibit a low roughness exponent
$0.4$ 3, taking advantage of the a priori known disordered microstructure of
these materials that can be tuned on a controlled manner. The possible application of the method
to quasi-brittle materials will be then discussed.
1) B. B. Mandelbrot, D. E. Passoja, and A. J. Paullay, Fractal character of fracture surfaces of metals, Nature, 308, 721 (1984).\\
2) D. Bonamy, L. Ponson, S. Prades, E. Bouchaud, and C. Guillot, Scaling exponents for fracture surfaces in homogeneous glass and glassy ceramics, Phys. Rev. Lett., 97, 135504, (2006).\\
3) L. Ponson, H. Auradou, P. Vié and J.P. Hulin, Low self-affine exponents of fractured glass ceramics surfaces, Phys. Rev. Lett., 97, 125501, (2006).
