%0 Book Section %1 statphys23_0643 %A Mallick, N. %A Cortet, P.P. %A Santucci, S. %A Roux, S.G. %A Vanel, L. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K analysis fracture growth instability roughness scaling statphys23 topic-4 %T Inluence of growth dynamics on fracture roughness %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=643 %X Since the early description of rough fractures as self-affine surfaces, the existence of universal roughness exponents has been strongly debated. There are now many experimental evidences for a non-universal value of the roughness exponent of fracture surfaces (influence of the heterogenity of the material structure, the anisotropy of the fracturation process...). Also, a recent analysis suggests that in rupture of paper, the crack interface would be multifractal. We study the roughness of a crack interface in a sheet of paper during a creep experiment. The paper sheet is loaded with an initial crack at its center in a tensile machine with a constant force (mode I). This force is chosen in order to have a stable crack. Nevertheless, the crack grows very slowly (about $10^-4\,m.s^-1$) by a thermal activation process (subcritical growth), and when it reaches a critical length, there is a transition in the growth regime, which becomes very fast (about $300\,m.s^-1$) and is driven by mechanical instability. After digitization of the post mortem sample, we are able to extract subcritical and fast growth parts of the signal and analyse them comparatively. Roughness exponents are reliably estimated using the first order cumulant, a quantity recently introduced in the turbulence literature. We show that this quantity should be a beter estimator of the roughness exponent than the second order structure function usually used. Using a large data set, we find a significant difference in fracture roughness between the slow (sub-critical) and the fast growth regime. In the subcritical growth part we find a roughness exponent of about $0.70$ while in the fast growth part this exponent is about $0.64$. We also study the influence of paper structure, sample geometry and loading. Finally, we discuss the relevance of multifractality, by reviewing very recent signal processing tools that have been developped to characterize scaling properties.

@incollection{statphys23_0643, abstract = {Since the early description of rough fractures as self-affine surfaces, the existence of universal roughness exponents has been strongly debated. There are now many experimental evidences for a non-universal value of the roughness exponent of fracture surfaces (influence of the heterogenity of the material structure, the anisotropy of the fracturation process...). Also, a recent analysis suggests that in rupture of paper, the crack interface would be multifractal. We study the roughness of a crack interface in a sheet of paper during a creep experiment. The paper sheet is loaded with an initial crack at its center in a tensile machine with a constant force (mode I). This force is chosen in order to have a stable crack. Nevertheless, the crack grows very slowly (about $10^{-4}\,\rm{m.s}^{-1}$) by a thermal activation process (subcritical growth), and when it reaches a critical length, there is a transition in the growth regime, which becomes very fast (about $300\,\rm{m.s}^{-1}$) and is driven by mechanical instability. After digitization of the \textit{post mortem} sample, we are able to extract subcritical and fast growth parts of the signal and analyse them comparatively. Roughness exponents are reliably estimated using the first order cumulant, a quantity recently introduced in the turbulence literature. We show that this quantity should be a beter estimator of the roughness exponent than the second order structure function usually used. Using a large data set, we find a significant difference in fracture roughness between the slow (sub-critical) and the fast growth regime. In the subcritical growth part we find a roughness exponent of about $0.70$ while in the fast growth part this exponent is about $0.64$. We also study the influence of paper structure, sample geometry and loading. Finally, we discuss the relevance of multifractality, by reviewing very recent signal processing tools that have been developped to characterize scaling properties.}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Mallick, N. and Cortet, P.P. and Santucci, S. and Roux, S.G. and Vanel, L.}, biburl = {https://www.bibsonomy.org/bibtex/278bb94a8a995f41f87b886037d4dc145/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {f8b1d729b03d28bbd9b2ea1b9ebd7ba4}, intrahash = {78bb94a8a995f41f87b886037d4dc145}, keywords = {analysis fracture growth instability roughness scaling statphys23 topic-4}, month = {9-13 July}, timestamp = {2007-06-20T10:16:25.000+0200}, title = {Inluence of growth dynamics on fracture roughness}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=643}, year = 2007 }