Skip to main content
SpringerLink
Log in

Correlating interfacial fracture toughness to surface roughness in polymer-based interfaces

  • Article
  • Focus Issue: Multiscale Materials Modeling of Interface-mediated Thermomechanical Behavior
  • Published:
Journal of Materials Research Aims and scope Submit manuscript

Abstract

Statistical fractal characteristics are examined for polymer-based interfaces. Interfacial fracture behavior is modulated via exposure to varying levels of chemical contaminant concentration so as not to affect the initial interface roughness. The results of 1D height–height correlation analysis show a strong correlation between the interfacial fracture toughness and the resulting fracture surface roughness, and a toughness-independent roughness exponent; \(\beta \approx\) 0.35 ± 0.04, which is the slope of the self-affine domain. The cut-off length scale of the self-affinity is found to scale with interface toughness, and equal the combined length scales of interfacial cohesive length and plastic zone size within the adhesive layer. The reported statistical characteristics of interfacial fracture surfaces is among the first to show the quantitative inter-correlation between interfacial adhesion and the resulting fracture surface roughness. With additional examination of other systems, the observed correlations have the potential to assess the interfacial fracture toughness for a wide range of polymer-based interfaces.

Graphic abstract

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7

Similar content being viewed by others

Data availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

References

  1. D. Hull, Fractography: Observing, Measuring and Interpreting Fracture Surface Topography (Cambridge University Press, Cambridge, 1999).

    Google Scholar 

  2. B.B. Mandelbrot, R. Pignoni, The Fractal Geometry of Nature, vol. 173 (WH freeman, New York, 1983).

    Google Scholar 

  3. B.B. Mandelbrot, D.E. Passoja, A.J. Paullay, Fractal character of fracture surfaces of metals. Nature 308, 721–722 (1984)

    Article  CAS  Google Scholar 

  4. E.E. Underwood, K. Banerji, Fractals in fractography. Mater. Sci. Eng. 80(1), 1–14 (1986)

    Article  Google Scholar 

  5. Z.Q. Mu, C.W. Lung, Studies on the fractal dimension and fracture toughness of steel. J. Phys. D 21(5), 848 (1988)

    Article  CAS  Google Scholar 

  6. R.E. Williford, Multifractal fracture. Scr. Metall. 22(11), 1749–1754 (1988)

    Article  CAS  Google Scholar 

  7. G.M. Lin, J.K.L. Lai, Fractal characterization of fracture surfaces in a resin-based composite. J. Mater. Sci. Lett. 12(7), 470–472 (1993)

    Article  CAS  Google Scholar 

  8. C.S. Pande, L.E. Richards, N. Louat, B.D. Dempsey, A.J. Schwoeble, Fractal characterization of fractured surfaces. Acta Metall. 35(7), 1633–1637 (1987)

    Article  CAS  Google Scholar 

  9. E. Bouchaud, G. Lapasset, J. Planes, Fractal dimension of fractured surfaces: a universal value? Europhys. Lett. 13, 73 (1990)

    Article  CAS  Google Scholar 

  10. K.J. Maloy, A. Hansen, E.L. Hinrichsen, S. Roux, Experimental measurements of the roughness of brittle cracks. Phys. Rev. Lett. 68, 213 (1992)

    Article  CAS  Google Scholar 

  11. J. Schmittbuhl, S. Gentier, S. Roux, Field measurements of the roughness of fault surfaces. Geophys. Res. Lett. 20(8), 639–641 (1993)

    Article  Google Scholar 

  12. P. Daguier, B. Nghiem, E. Bouchaud, F. Creuzet, Pinning and depinning of crack fronts in heterogeneous materials. Phys. Rev. Lett. 78(6), 1062 (1997)

    Article  CAS  Google Scholar 

  13. M.A. Issa, M.A. Issa, M.S. Islam, A. Chudnovsky, Fractal dimension––a measure of fracture roughness and toughness of concrete. Eng. Fract. Mech. 70(1), 125–137 (2003)

    Article  Google Scholar 

  14. L. Ponson, A. Srivastava, S. Osovski, E. Bouchaud, V. Tvergaard, A. Needleman, Correlating toughness and roughness in ductile fracture. arXiv preprint arXiv:abs/1307.4413. (2013)

  15. S. Santucci, K.J. Måløy, A. Delaplace, J. Mathiesen, A. Hansen, J.Ø.H. Bakke, J. Schmittbuhl, L. Vanel, P. Ray, Statistics of fracture surfaces. Phys. Rev. E 75(1), 016104 (2007)

    Article  Google Scholar 

  16. L. Ponson, H. Auradou, P. Vié, J.P. Hulin, Low self-affine exponents of fractured glass ceramics surfaces. Phys. Rev. Lett. 97(12), 125501 (2006)

    Article  Google Scholar 

  17. J.M. Boffa, C. Allain, J.P. Hulin, Experimental analysis of fracture rugosity in granular and compact rocks. Eur. Phys. J. 2(3), 281–289 (1998)

    Article  Google Scholar 

  18. D. Bonamy, L. Ponson, S. Prades, E. Bouchaud, C. Guillot, Scaling exponents for fracture surfaces in homogeneous glass and glassy ceramics. Phys. Rev. Lett. 97(13), 135504 (2006)

    Article  CAS  Google Scholar 

  19. S. Morel, D. Bonamy, L. Ponson, E. Bouchaud, Transient damage spreading and anomalous scaling in mortar crack surfaces. Phys. Rev. E 78(1), 016112 (2008)

    Article  Google Scholar 

  20. E. Saborowski, P. Steinert, A. Dittes, T. Lindner, A. Schubert, T. Lampke, Introducing fractal dimension for interlaminar shear and tensile strength assessment of mechanically interlocked polymer-metal interfaces. Materials 13(9), 2171 (2020)

    Article  CAS  Google Scholar 

  21. A.G. Evans, J.W. Hutchinson, Effects of non-planarity on the mixed mode fracture resistance of bimaterial interfaces. Acta Metall. 37(3), 909–916 (1989)

    Article  CAS  Google Scholar 

  22. K.M. Liechti, Y.S. Chai, Asymmetric shielding in interfacial fracture under in-plane shear. J. Appl. Mech. 59(2), 295–304 (1992)

    Article  CAS  Google Scholar 

  23. D. Yavas, X. Shang, W. Hong, A.F. Bastawros, Utilization of nanoindentation to examine bond line integrity in adhesively bonded composite structures. Int. J. Fract. 204(1), 101–112 (2016)

    Article  Google Scholar 

  24. D. Yavas, A.F. Bastawros, Prediction of interfacial surface energy and effective fracture energy from contaminant concentration in polymer-based interfaces. ASME. J. Appl. Mech. 84(4), 044501 (2017)

    Article  Google Scholar 

  25. D. Yavas, X. Shang, A.F. Bastawros, Mode-I fracture toughness and surface morphology evolution for contaminated adhesively bonded composite structures. Compos. Struct. 203, 513–522 (2018)

    Article  Google Scholar 

  26. M. Lane, R.H. Dauskardt, A. Vainchtein, H. Gao, Plasticity contributions to interface adhesion in thin-film interconnect structures. J. Mater. Res. 15(12), 2758–2769 (2000)

    Article  CAS  Google Scholar 

  27. H. Chai, On the correlation between the mode I fracture of adhesive joints and laminated composites. Eng. Fract. Mech. 24(3), 413–431 (1986)

    Article  Google Scholar 

  28. H. Chai, Observation of deformation and damage at the tip of cracks in adhesive bonds loaded in shear and assessment of a criterion for fracture. Int. J. Fract. 60(4), 311–326 (1993)

    CAS  Google Scholar 

  29. D. Bonamy, E. Bouchaud, Failure of heterogeneous materials: a dynamic phase transition? Phys. Rep. 498(1), 1–44 (2011)

    Article  CAS  Google Scholar 

  30. V. Tvergaard, J.W. Hutchinson, Toughness of an interface along a thin ductile layer joining elastic solids. Philos. Mag. A 70(4), 641–656 (1994)

    Article  CAS  Google Scholar 

  31. A. Hillerborg, M. Modéer, P.E. Petersson, Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cem. Concr. Res. 6(6), 773–781 (1976)

    Article  Google Scholar 

  32. G. Bao, Z. Suo, Remarks on crack-bridging concepts. Appl. Mech. Rev. 45(8), 355–366 (1992)

    Article  Google Scholar 

  33. I. Mohammed, K.M. Liechti, Cohesive zone modeling of crack nucleation at bimaterial corners. J. Mech. Phys. Solids 48(4), 735–764 (2000)

    Article  Google Scholar 

  34. C. Wu, R. Huang, K.M. Liechti, Simultaneous extraction of tensile and shear interactions at interfaces. J. Mech. Phys. Solids 125, 225–254 (2019)

    Article  CAS  Google Scholar 

  35. S. Jain, S.R. Na, K.M. Liechti, R.T. Bonnecaze, A cohesive zone model and scaling analysis for mixed-mode interfacial fracture. Int. J. Solids Struct. 129, 167–176 (2017)

    Article  Google Scholar 

  36. MIL-STD-1246C, Product cleanliness levels and contamination control program (1994)

  37. ASTM-D5528-13, Standard Test Method for Mode-I Interlaminar Fracture Toughness of Unidirectional Fiber-Reinforced Polymer Matrix Composites (ASTM International, West Conshohocken, 2013).

    Google Scholar 

Download references

Acknowledgments

This work was supported by National Science Foundation under contract No. DMR-1807545, and by the Office of Naval Research (ONR) under Contract No. 104728. The authors would also like to acknowledge Redwood Scientific, Inc. on grades of contamination. Special thanks to an anonymous reviewer who has greatly helped in integrating the presentation of the paper.

Author information

Authors and Affiliations

  1. Department of Aerospace Engineering, Iowa State University, Ames, IA, 50011-2271, USA

    Denizhan Yavas & Ashraf F. Bastawros

Authors
  1. Denizhan Yavas
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ashraf F. Bastawros
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ashraf F. Bastawros.

Ethics declarations

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yavas, D., Bastawros, A.F. Correlating interfacial fracture toughness to surface roughness in polymer-based interfaces. Journal of Materials Research 36, 2779–2791 (2021). https://doi.org/10.1557/s43578-021-00218-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1557/s43578-021-00218-1

Keywords

Search

Navigation