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International Journal of Fracture

, Volume 184, Issue 1–2, pp 137–149 | Cite as

Statistics of ductile fracture surfaces: the effect of material parameters

  • Laurent Ponson
  • Yuanyuan Cao
  • Elisabeth Bouchaud
  • Viggo Tvergaard
  • Alan Needleman
Article

Abstract

The effect of material parameters on the statistics of fracture surfaces is analyzed under small scale yielding conditions. Three dimensional calculations of ductile crack growth under mode I plane strain, small scale yielding conditions are carried out using an elastic-viscoplastic constitutive relation for a progressively cavitating plastic solid with two populations of void nucleating second phase particles represented. Large particles that result in void nucleation at an early stage are modeled discretely while small particles that require large strains to nucleate are homogeneously distributed. The three dimensional analysis permits modeling of a three dimensional material microstructure and of the resulting three dimensional stress and deformation states that develop in the fracture process region. Material parameters characterizing void nucleation are varied and the statistics of the resulting fracture surfaces is investigated. All the fracture surfaces are found to be self-affine over a size range of about two orders of magnitude with a very similar roughness exponent of \(0.56\,\pm \,0.03\). In contrast, the full statistics of the fracture surfaces is found to be more sensitive to the material microscopic fracture properties: height fluctuations are shown to crossover from a Student’s distribution with power law tails at small scales to a Gaussian behavior at large scales, but this transition occurs at a material dependent length scale. Using the family of Student’s distributions, this transition can be described introducing an additional exponent \(\mu = 0.15\,\pm \,0.02\), the value of which compares well with recent experimental findings. The description of the roughness distribution used here gives a more complete quantitative characterization of the fracture surface morphology which allows a better comparison with experimental data and an easier interpretation of the roughness properties in terms of microscopic failure mechanisms.

Keywords

Fracture surfaces Roughness statistics Ductile fracture Crack growth Scaling behavior Finite elements 

Notes

Acknowledgments

The financial support provided by the U.S. National Science Foundation through Grant CMMI-1200203 and by the European Union through the ToughBridge Marie Curie Grant (LP) is gratefully acknowledged. We also thank Jean-Philippe Bouchaud and Stéphane Vernède for fruitful discussions

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Laurent Ponson
    • 1
  • Yuanyuan Cao
    • 1
  • Elisabeth Bouchaud
    • 2
  • Viggo Tvergaard
    • 3
  • Alan Needleman
    • 4
  1. 1.Institut Jean le Rond d’Alembert (UMR 7190), CNRSUniversité Pierre et Marie CurieParisFrance
  2. 2.CEA-Saclay and ESPCIParis TechParisFrance
  3. 3.Department of Mechanical EngineeringThe Technical University of DenmarkLyngbyDenmark
  4. 4.Department of Materials Science and EngineeringUniversity of North TexasDentonUSA

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