# Croissance lente thermiquement activée et piégeage d'une fissure dans les matériaux structurés à une échelle mésoscopique : expériences et modèles

Abstract : This thesis presents an experimental and theoretical study of slow
growth mechanisms of a single crack under stress in a
bidimensional geometry.

We have performed traction experiments (creep tests) of
heterogeneous fibrous materials (paper samples) with an initial
macroscopic defect (mode 1). We have observed that the slow crack
growth is actually progressing by steps. The average dynamics of
the crack growth from an initial length $L_i$ to a critical length
$L_C$, where the fracture is rapid, shows an exponential law for
the crack growth defined by $2$ parameters : the rupture time
$\tau$ and a characteristic growth length $\zeta$. A measure of
the surface energy needed to open the crack permits to distinguish
the Griffith length $L_G$ and the critical length of rupture
$L_C$. A statistical study of the step size during the damaging
process reveals that the step size distribution follows a power
law truncated by an exponential, which is typical of a critical
point approach in a sub-critical process.

This complex dynamics can be predicted quantitatively by our
semi-analytical approach, which describes the slow crack growth in
a pure bi-dimensionnal elastic system in terms of an activation
process, where the statistical stress fluctuations allow to
overcome a breaking threshold through a series of irreversible
steps. Our theoretical approach based on a numerical model (a 2d
spring network describing a bi-dimensional elastic "discrete"
system) shows the importance of the irreversibility of the rupture
process and the crucial role of heterogeneities, which appear only
in our model as a characteristic mesoscopic length scale.
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Cited literature [46 references]

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Contributor : Stephane Santucci <>
Submitted on : Monday, April 25, 2005 - 11:46:52 AM
Last modification on : Monday, January 4, 2021 - 2:46:09 PM
Long-term archiving on: : Friday, September 14, 2012 - 12:40:12 PM

### Identifiers

• HAL Id : tel-00009085, version 1

### Citation

Stéphane Santucci. Croissance lente thermiquement activée et piégeage d'une fissure dans les matériaux structurés à une échelle mésoscopique : expériences et modèles. Physique [physics]. Ecole normale supérieure de lyon - ENS LYON, 2004. Français. ⟨tel-00009085⟩

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