Skip to main content
SpringerLink
Log in

Numerical investigation of indentation fatigue on polycrystalline copper

  • Published:
Journal of Materials Research Aims and scope Submit manuscript

Abstract

The dynamic indentation response of polycrystalline copper under cyclic fatigue loading is studied with a flat cylindrical indenter. First, a simple analytical model shows that in a purely elastic solid, the indentation depth responds with the same wavelength and frequency as the applied sinusoidal fatigue load. Next, a numerical simulation of an indentation fatigue test on an elastic-plastic solid (polycrystalline copper) is performed. Finite element analyses reveal that the mean indentation depth is controlled by both the mean of the indentation fatigue load and the load amplitude, while the amplitude of the indentation depth is independent of the mean load. Further investigations indicate that with an increased number of cycles, the increment of indentation depth reaches a constant rate. The steady state indentation depth rate is dependent not only on the amplitude of indentation fatigue load but also on the fatigue mean load, which is similar to strain accumulation during a conventional fatigue test. A parallel indentation experiment on annealed polycrystalline copper also confirms the effect of the fatigue mean load, indicating consistency with numerical results.

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

Similar content being viewed by others

References

  1. W.C. Oliver and G.M. Pharr: Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding and refinements to methodology., J. Mater. Res. 19, 3 (2004).

    Article  CAS  Google Scholar 

  2. Y.T. Cheng and C.M. Cheng: Scaling dimensional analysis and indentation measurements. Mater. Sci. Eng., R 44, 91 (2004).

    Article  Google Scholar 

  3. X. Chen, N. Ogasawara, M. Zhao, and N. Chiba: On the uniqueness of measuring elastoplastic properties from indentation: The indistinguishable mystical materials., J. Mech. Phys. Solids 55, 1618 (2007).

    Article  Google Scholar 

  4. Z.H. Xia, W.A. Curtin, and B.W. Sheldon: A new method to evaluate the fracture toughness of thin films. Acta Mater. 52, 3507 (2004).

    Article  CAS  Google Scholar 

  5. X. Chen, Y. Xiang, and J.J. Vlassak: A novel technique to measure mechanical properties of porous materials by nanoindentation. J. Mater. Res. 21, 715 (2006).

    Article  CAS  Google Scholar 

  6. J.K. Mason, A.C. Lund, and C.A. Schuh: Determining the activation energy and volume for the onset of plasticity during nanoindentation. Phys. Rev. B 73, 054102 (2006).

    Article  Google Scholar 

  7. A. Gouldstone, N. Chollacoop, M. Dao, J. Li, A.M. Minor, and Y.L. Shen: Indentation across size scales and disciplines: Recent developments in experimentation and modeling. Acta Mater. 55, 4015 (2007).

    Article  CAS  Google Scholar 

  8. M.H. Zhao, X. Chen, J. Yan, and A.M. Karlsson: Determination of uniaxial residual stress and mechanical properties by instrumented indentation. Acta Mater. 54, 2823 (2006).

    Article  CAS  Google Scholar 

  9. I. Pane and E. Blank: Role of plasticity on indentation behavior: Relations between surface and subsurface responses. Int. J. Solids Struct. 43, 2014 (2006).

    Article  Google Scholar 

  10. X.D. Li and B. Bhushan: A review of nanoindentation continuous stiffness measurement technique and its applications. Mater. Charact. 48, 11 (2002).

    Article  CAS  Google Scholar 

  11. A.C. Fischer-Cripps: Multiple-frequency dynamic nanoindentation testing. J. Mater. Res. 19, 2981 (2004).

    Article  CAS  Google Scholar 

  12. E.A. Ossa, V.S. Deshpande, and D. Cebon: Spherical indentation behaviour of bitumen. Acta Mater. 53, 3103 (2005).

    Article  CAS  Google Scholar 

  13. T. Saraswati, T. Sritharan, S. Mhaisalkar, C.D. Breach, and F. Wulf: Cyclic loading as an extended nanoindentation technique. Mater. Sci. Eng., A 423, 14 (2006).

    Article  Google Scholar 

  14. K.J. VanVliet and S. Suresh: Simulations of cyclic normal indentation of crystal surfaces using the bubble-raft model. Philos. Mag. A 82, 1993 (2002).

    Article  CAS  Google Scholar 

  15. B. Shiari and R.E. Miller: Multiscale modeling of ductile crystals at the nanoscale subjected to cyclic indentation. Acta Mater. 56, 2799 (2008).

    Article  CAS  Google Scholar 

  16. J.M. Cairney, R. Tsukano, M.J. Hoffman, and M. Yang: Degradation of TiN coatings under cyclic loading. Acta Mater. 52, 3229 (2004).

    Article  CAS  Google Scholar 

  17. T.D. Raju, K. Nakasa, and M. Kato: Relation between delamination of thin films and backward deviation of load–displacement curves under repeating nanoindentation. Acta Mater. 51, 457 (2003).

    Article  CAS  Google Scholar 

  18. Y.T. Cheng, W.Y. Ni, and C.M. Cheng: Nonlinear analysis of oscillatory indentation in elastic and viscoelastic solids. Phys. Rev. Lett. 97, 075506 (2006).

    Article  Google Scholar 

  19. J. Mencik, G. Rauchs, J. Bardon, and A. Riche: Determination of elastic modulus and hardness of viscoelastic-plastic materials by instrumented indentation under harmonic load. J. Mater. Res. 20, 2660 (2005).

    Article  CAS  Google Scholar 

  20. G.M. Odegard, T.S. Gates, and H.M. Herring: Characterization of viscoelastic properties of polymeric materials through nanoindentation. Exp. Mech. 45, 2005130 (2005).

    Article  Google Scholar 

  21. M.R. VanLandingham, N.K. Chang, P.L. Drzal, C.C. White, and S.H. Chang: Viscoelastic characterization of polymers using instrumented indentation. I. Quasi-static testing. J. Polym. Sci., Part B: Polym. Phys. 43, 1794 (2005).

    Article  CAS  Google Scholar 

  22. J.C.M. Li and S.N.G. Chu: Impression fatigue. Scr. Mater. 13, 1021 (1979).

    CAS  Google Scholar 

  23. B.X. Xu and Z.F. Yue: A study of the ratcheting by the indentation fatigue method with a flat cylindrical indenter: Part I. Experimental study., J. Mater. Res. 21, 1793 (2006).

    Article  CAS  Google Scholar 

  24. B.X. Xu and Z.F. Yue: A study of the ratcheting by the indentation fatigue method with a flat cylindrical indenter: Part II. Finite element simulation. J. Mater. Res. 22, 186 (2007).

    Article  CAS  Google Scholar 

  25. I.N. Sneddon: The relation between load and penetration in the axisymmetric Boussinesq problem for a punch of arbitrary profile. Int. J. Eng. Sci. 3, 47 (1965).

    Article  Google Scholar 

  26. ABAQUS User’s Manual, Version 6.2 (Hibbitt, Karlsson and Sor-ensen, Inc., Pawtucket, RI, 2001).

    Google Scholar 

  27. J.L. Chaboche and D. Nouaihas: Constitutive modelling of ratchetting effects—Part I: Experimental facts and properties of the classical models. J. Eng. Mater. Technol. 111, 384 (1989).

    Article  Google Scholar 

  28. J.L. Chaboche and D. Nouaihas: Constitutive modelling of ratchetting effects—Part II: Possibilities of some additional kinematic rules., J. Eng. Mater. Technol. 111, 409 (1989).

    Article  Google Scholar 

  29. N. Ohno and J.D. Wang: On modelling of kinematic hardening for retcheting behaviour. Nucl. Eng. Des. 153, 205 (1995).

    Article  CAS  Google Scholar 

  30. P. Delobelle, P. Robinet, and L. Bocher: Experimental study and phenomenological modelization of ratchet under uniaxial and biaxial loading on an austenitic stainless steel. Int. J. Plast. 11, 295 (1995).

    Article  CAS  Google Scholar 

  31. Y. Jiang and P. Kurath: Characteristics of the Armstrong-Frederick type plasticity models. Int. J. Plast. 12, 387 (1996).

    Article  CAS  Google Scholar 

  32. J.C. Moosbrugger and D.J. Morrison: Nonlinear kinematic hardening rule parameters—Direct determination from completely reversed proportional cycling. Int. J. Plast. 13, 633 (1997).

    Article  CAS  Google Scholar 

  33. M. Abdel-Karim and N. Ohno: Kinematic hardening model suitable for ratchetting with steady-state. Int. J. Plast. 16, 225 (2000).

    Article  CAS  Google Scholar 

  34. D. Mclean: Mechanical Properties of Metals (Wiley, New York, 1965), p. 112.

    Google Scholar 

  35. Y. Yokouchi, I.G. Greenfield, T.W. Chou, and E.B. Iturbe: Elastic-plastic analysis of indentation damage: Cyclic loading of copper. J. Mater. Sci. 22, 3087 (1987).

    Article  CAS  Google Scholar 

  36. B.X. Xu, X.M. Wang, and Z.F. Yue: Indentation behavior of polycrystalline copper under fatigue peak overloading. J. Mater. Res. 22, 1585 (2007).

    Article  CAS  Google Scholar 

  37. B.X. Xu, Z.F. Yue, and J. Wang: Indentation fatigue behaviour of polycrystalline copper. Mech. Mater. 39, 1066 (2007).

    Article  Google Scholar 

  38. H.D. Chandlera and S. Kwofie: A description of cyclic creep under conditions of axial cyclic and mean stresses. Int. J. Fatigue 27, 541 (2005).

    Article  Google Scholar 

  39. M. Megahed, A.R.S. Ponter, and C.J. Morrison: Experimental investigations into the influence of cyclic phenomena of metals on structural ratchetting behavior. Int. J. Mech. Sci. 26, 625 (1984).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, i’an, 710072, People’s Republic of China

    B. X. Xu

  2. Columbia Nanomechanics Research Center, Department of Civil Engineering and Engineering Mechanics, Columbia University, New York, New York, 10027-6699, USA

    B. X. Xu

  3. School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi’an, 710072, People’s Republic of China

    Z. F. Yue & X. Chen

Authors
  1. B. X. Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Z. F. Yue
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. X. Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to B. X. Xu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Xu, B.X., Yue, Z.F. & Chen, X. Numerical investigation of indentation fatigue on polycrystalline copper. Journal of Materials Research 24, 1007–1015 (2009). https://doi.org/10.1557/jmr.2009.0107

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1557/jmr.2009.0107

Search

Navigation