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Effects of strain hardening and residual stress in impression on the instrumented indentation technique

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Abstract

Finite element analyses were carried out to simulate the loading, unloading, and reloading processes of indentation tests. It was found that the validity of applying the elastic contact theory to the indentation unloading process is strongly related to the strain hardening and residual stress in impression. It is the combination of strain hardening and residual stress that causes the unloading or reloading curves to show elastic loading in the range from zero to the maximum load whereas the reloading curve on the impression without strain hardening and residual stress shows elastic–plastic loading in the same range. These computations indicate that applying the elastic contact theory to the unloading or reloading processes, the fundamental prerequisite of the instrumented indentation technique, is valid because of the existence of strain hardening and residual stress. The mechanism of this hardening effect is discussed through energy analysis.

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References

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

    Article  Google Scholar 

  2. M. Dao, N. Chollacoop, K.J. Van Vliet, T.A. Venkatesh, S. Suresh: Computational modeling of the forward and reverse problems in instrumented sharp indentation. Acta Mater. 49, 3899 (2001).

    Article  CAS  Google Scholar 

  3. W.Y. Ni, Y.T. Cheng, C.M. Cheng, D.S. Grummon: An energy-based method for analyzing instrumented spherical indentation experiments. J. Mater. Res. 19, 149 (2004).

    Article  CAS  Google Scholar 

  4. G.M. Pharr, A. Bolshakov: Understanding nanoindentation unloading curves. J. Mater. Res. 17, 2660 (2002).

    Article  CAS  Google Scholar 

  5. N. Schwarzer: Elastic surface deformation due to indenters with arbitrary symmetry of revolution. J. Phys. D Appl. Phys. 37, 2761 (2004).

    Article  CAS  Google Scholar 

  6. J. Woirgard, J.C. Dargenton: An alternative method for penetration depth determination in nanoindentation measurements. J. Mater. Res. 12, 2455 (1997).

    Article  CAS  Google Scholar 

  7. F.M. Borodich: The Hertz frictional contact between nonlinear elastic anisotropic bodies (the similarity approach). Int. J. Solids Struct. 30, 1513 (1993).

    Article  Google Scholar 

  8. Y.W. Bao, W. Wang, Y.C. Zhou: Investigation of the relationship between elastic modulus and hardness based on depth-sensing indentation measurements. Acta Mater. 52, 5397 (2004).

    Article  CAS  Google Scholar 

  9. W.D. Nix, H.J. Gao: Indentation size effects in crystalline materials: A law for strain gradient plasticity. J. Mech. Phys. Solids 46, 411 (1998).

    Article  CAS  Google Scholar 

  10. M.F. Doerner, W.D. Nix: A method for interpreting the data from depth-sensing indentation instruments. J. Mater. Res. 1, 601 (1986).

    Article  Google Scholar 

  11. W.C. Oliver, G.M. Pharr: An improved technique for determining hardness and elastic-modulus using load and displacement sensing indentation experiments. J. Mater. Res. 7, 1564 (1992).

    Article  CAS  Google Scholar 

  12. 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 

  13. W.C. Oliver, 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 

  14. J.H. Gong, H.Z. Miao, Z.J. Peng: Analysis of the nanoindentation data measured with a Berkovich indenter for brittle materials: Effect of the residual contact stress. Acta Mater. 52, 785 (2004).

    Article  CAS  Google Scholar 

  15. F.M. Borodich, L.M. Keer: Contact problems and depth-sensing nanoindentation for frictionless and frictional boundary conditions. Int. J. Solids Struct. 41, 2479 (2004).

    Article  Google Scholar 

  16. A. Bolshakov, W.C. Oliver, G.M. Pharr: Influences of stress on the measurement of mechanical properties using nanoindentation: Part II. Finite element simulations. J. Mater. Res. 11, 760 (1996).

    Article  CAS  Google Scholar 

  17. M. Mata, J. Alcalá: The role of friction on sharp indentation. J. Mech. Phys. Solids 52, 145 (2004).

    Article  Google Scholar 

  18. ANSYS theory manual version 7.0 ANSYS Inc.

  19. K.L. Johnson: The correlation of indentation experiments. J. Mech. Phys. Solids 18, 115 (1970).

    Article  Google Scholar 

  20. M. Mata, O. Casals, and J. Alcalá: The plastic zone size in indentation experiments: The analogy with the expansion of a spherical cavity. Int. J. Solids Struct. (2005) available online at www.sciencedirect.com.

    Google Scholar 

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Liu, L.Z., Bao, Y.W. & Zhou, Y.C. Effects of strain hardening and residual stress in impression on the instrumented indentation technique. Journal of Materials Research 21, 1680–1686 (2006). https://doi.org/10.1557/jmr.2006.0213

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  • DOI: https://doi.org/10.1557/jmr.2006.0213

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