Numerical investigation of spherical indentation on elastic-power-law strain-hardening solids with non-equibiaxial residual stresses

Abstract

The finite element simulations show that non-equibiaxial residual stresses (RS) can shift the load-depth curve from the unstressed curve and cause elliptical remnant indentation in spherical indentation. Thus the relative load change between stressed and unstressed samples and the asymmetry of elliptical remnant indentation were employed as characteristic parameters to evaluate the magnitude and directionality of RS. Through theoretical and numerical analysis, the effects of RS on indentation load and remnant impression as well as the affect mechanism were systematically discussed. Finally, two equations which could provide foundations for establishing spherical indentation method to evaluate non-equibiaxial RS were obtained.

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References

  1. 1.

    J. Lu: Handbook of Measurement of Residual Stresses (The Fairmont Press, Lilburn, Georgia, 1996).

    Google Scholar 

  2. 2.

    S. Suresh and A.E. Giannakopoulos: A new method for estimating residual stresses by instrumented sharp indentation. Acta Mater. 46, 5755 (1998).

    CAS  Article  Google Scholar 

  3. 3.

    T.Y. Tsui, W.C. Oliver, and G.M. Pharr: Influences of stress on the measurement of mechanical properties using nanoindentation: Part I. Experimental studies in an aluminum alloy. J. Mater. Res. 11, 752 (1996).

    CAS  Article  Google Scholar 

  4. 4.

    B. Taljat and G.M. Pharr: Measurement of residual stress by load and depth sensing spherical indentation. Mater. Res. Soc. Symp. Proc. 594, 519 (2000).

    Article  Google Scholar 

  5. 5.

    S. Carlsson and P.-L Larsoon: On the determination of residual stress and strain fields by sharp indentation testing. Part I: Theoretical and numerical analysis. Acta Mater. 49, 2179 (2001).

    CAS  Article  Google Scholar 

  6. 6.

    J.G. Swadener, B. Taljat, and G.M. Pharr: Measurement of residual stress by load and depth sensing indentation with spherical indenters. J. Mater. Res. 16, 2091 (2001).

    CAS  Article  Google Scholar 

  7. 7.

    A.E. Giannakopoulos: The Influence of Initial elastic surface stresses on instrumented sharp indentation. J. Appl. Mech. 70, 638 (2003).

    Article  Google Scholar 

  8. 8.

    Z.K. Lu, Y.H. Feng, G.J. Peng, R. Yang, Y. Huan, and T.H. Zhang: Estimation of surface equi-biaxial residual stress by using instrumented sharp indentation. Mater. Sci. Eng. A 614, 264 (2014).

    CAS  Article  Google Scholar 

  9. 9.

    L. Xiao, D. Ye, and C. Chen: A further study on representative models for calculating the residual stress based on the instrumented indentation technique. Comput. Mater. Sci. 82, 476 (2014).

    Article  Google Scholar 

  10. 10.

    M. He, C.H. Huang, X.X. Wang, F. Yang, N. Zhang, and F.G. Li: Assessment of the Local Residual Stresses of 7050-T7452 Aluminum Alloy in microzones by the instrumented indentation with the Berkovich Indenter. J. Mater. Eng. Perform. 26, 4923 (2017).

    CAS  Article  Google Scholar 

  11. 11.

    T.-H. Pham and S.-E. Kim: Determination of equi-biaxial residual stress and plastic properties in structural steel using instrumented indentation. Mater. Sci. Eng. A 688, 352 (2017).

    CAS  Article  Google Scholar 

  12. 12.

    V.P. Fardin, E.A. Bonfante, P.G. Coelho, M.N. Janal, N. Tovar, L. Witek, D. Bordin, and G. Bonfante: Residual stress of porcelain-fused to zirconia 3-unit fixed dental prostheses measured by nanoindentation. Dent. Mater. 34, 260 (2018).

    CAS  Article  Google Scholar 

  13. 13.

    G. Peng, Z. Lu, Y. Ma, Y. Feng, Y. Huan, and T. Zhang: Spherical indentation method for estimating equibiaxial residual stress and elastic-plastic properties of metals simultaneously. J. Mater. Res. 33, 884 (2018).

    CAS  Article  Google Scholar 

  14. 14.

    J. Chen, J. Liu, and C. Sun: Residual stress measurement via digital image correlation and sharp indentation testing. Opt. Eng. 55, 124102 (2016).

    Article  Google Scholar 

  15. 15.

    Y.-C. Kim, M.-J. Choi, D. Kwon, and J.-Y. Kim: Estimation of principal directions of Bi-axial residual stress using instrumented Knoop indentation testing. Met. Mater. Int. 21, 850 (2015).

    Article  Google Scholar 

  16. 16.

    F. Rickhey, J.H. Lee, and H. Lee: A contact size-independent approach to the estimation of biaxial residual stresses by Knoop indentation. Mater. Des. 84, 300 (2015).

    CAS  Article  Google Scholar 

  17. 17.

    Y.-H. Lee and D. Kwon: Estimation of biaxial surface stress by instrumented indentation with sharp indenters. Acta Mater. 52, 1555 (2004).

    CAS  Article  Google Scholar 

  18. 18.

    L. Shen, Y. He, D. Liu, Q. Gong, B. Zhang, and J. Lei: A novel method for determining surface residual stress components and their directions in spherical indentation. J. Mater. Res. 30, 1078 (2015).

    CAS  Article  Google Scholar 

  19. 19.

    Y.-C. Kim, H.-J. Ahn, D. Kwon, and J.-Y. Kim: Modeling and experimental verification for non-equibiaxial residual stress evaluated by Knoop indentations. Met. Mater. Int. 22, 12 (2006).

    Article  Google Scholar 

  20. 20.

    H.-J. Ahn, J.-H. Kim, H. Xu, J. Lee, J.-Y. Kim, Y.-C. Kim, and D. Kwon: Directionality of residual stress evaluated by instrumented indentation testing using wedge indenter. Met. Mater. Int. 23, 465 (2017).

    Article  Google Scholar 

  21. 21.

    J.H. Han, J.S. Lee, Y.H. Lee, M.J. Choi, G. Lee, K.H. Kim, and D. Kwon: Residual stress estimation with identification of stress directionality using instrumented indentation technique. Key Eng. Mater. 345-346, 1125 (2007).

    Article  Google Scholar 

  22. 22.

    M.-J. Choi, S.-K. Kang, I. Kang, and D. Kwon: Evaluation of nonequibiax-ial residual stress using Knoop indenter. J. Mater. Res. 27, 121 (2011).

    Article  Google Scholar 

  23. 23.

    H. Hertz: Miscellaneous Papers (Macmillan, London, 1896).

    Google Scholar 

  24. 24.

    K.L. Johnson: Contact Mechanics (Cambridge University Press, Cambridge, UK, 1985).

    Google Scholar 

  25. 25.

    L. Brand: The Pi theorem of dimensional analysis. Arch. Ration. Mech. Anal. 1, 35 (1957).

    Article  Google Scholar 

  26. 26.

    C. Yu, Y.H. Feng, R. Yang, G.J. Peng, Z.K. Lu, and T.H. Zhang: An integrated method to determine elastic-plastic parameters by instrumented spherical indentation. J. Mater. Res. 29, 1095 (2014).

    CAS  Article  Google Scholar 

  27. 27.

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

    CAS  Article  Google Scholar 

  28. 28.

    T. Zhang, C. Yu, G. Peng, and Y. Feng: Identification of the elastic-plastic constitutive model for measuring mechanical properties of metals by instrumented spherical indentation test. MRS Commun. 7, 221 (2017).

    CAS  Article  Google Scholar 

Download references

Acknowledgments

The authors would like to gratefully acknowledge the support from the National Natural Science Foundation of China (Grant Nos. 11727803, 11772302, 11672356, 11402233, and 11502235) and Public Welfare Project of Zhejiang Province (2015C31074).

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Correspondence to Guangjian Peng.

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The supplementary material for this article can be found at https://doi.org/10.1557/mrc.2018.240

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Zhang, T., Cheng, W., Peng, G. et al. Numerical investigation of spherical indentation on elastic-power-law strain-hardening solids with non-equibiaxial residual stresses. MRS Communications 9, 360–369 (2019). https://doi.org/10.1557/mrc.2018.240

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