International Journal of Fracture

, Volume 193, Issue 2, pp 141–152 | Cite as

A self-affine geometrical model of dynamic RT-PMMA fractures: implications for fracture energy measurements

  • Jean-Benoit KoppEmail author
  • Jean Schmittbuhl
  • Olivier Noel
  • Christophe Fond
Original Paper


Profilometric imaging of fracture surfaces of rubber toughened polymer has been performed at two different resolutions (a) at large scales [10 \(\upmu \)m–25 mm] using an opto-mechanical profilometer and (b) at small scales [0.195 \(\upmu \)m–0.48 mm] using an interferometric optical microscope. We introduced a self-affine geometrical model using two parameters: the Hurst exponent and the topothesy. We showed that for rubber toughened materials the approximation of the created surface by a mean flat plane leads to a poor estimation of the dynamic fracture energy \(G_{Idc}\). The description of the created rough fracture surface by a self-affine model is shown to provide a significantly better approximation. A new and original geometrical method is introduced to estimate self-affine parameters: the 3D surface scaling method. Hurst exponents are shown to be unique, \(\chi =0.6\pm 0.1\) for the different fracture zones and measurement scales. Topothesy ratios indicate a significant difference of fracture surface roughness amplitude depending on the observation resolution when the detrending technique is not correctly introduced.


Dynamic fracture Polymers Surface roughness Self-affinity Hurst exponent Topothesy Fracture energy Rapid crack propagation 



The authors gratefully acknowledge the support of “Agence Nationale de la Recherche” and especially the collaborators of “Carenco”.


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Jean-Benoit Kopp
    • 1
    Email author
  • Jean Schmittbuhl
    • 2
  • Olivier Noel
    • 3
  • Christophe Fond
    • 4
  1. 1.I2M, Université de Bordeaux, CNRSTalenceFrance
  2. 2.EOST, Université de Strasbourg, CNRSStrasbourgFrance
  3. 3.IMMM, Université du Maine, CNRSLe MansFrance
  4. 4.ICube, Université du Strasbourg, CNRSStrasbourgFrance

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