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Characterization of materials’ elasticity and yield strength through micro-/nano-indentation testing with a cylindrical flat-tip indenter

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Abstract

Material property measurements at the micro-/nanoscale are required for within many materials systems, such as thin-films, coatings, nanostructured materials, and interface/interphase. An innovative approach through micro-/nano-indentation testing with a cylindrical flat-tip indenter and coupled with computer modeling was proposed to characterize the material’s elastic–plastic properties. A mechanical model proposed for directly extracting the yield strength of the tested materials, based on the hemi-spherical stress–strain distribution assumption, was analytically derived and numerically validated. Specimens being tested are aluminum alloy, low carbon steel, and alloy steel. A micro-/nano-indentation solid model was constructed and computer modeling was conducted. The load point in the indentation load–depth curve and the modifier for extracting the yield strength were identified through computer modeling and validated by indentation tests. The material properties measured by indentation were compared with tensile tests. The indentation testing errors induced by residual stresses in specimens were investigated by a residual stress measurement system.

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References

  1. A.C. Fischer-Cripps: Nanoindentation, 3rd ed. (Springer, New York, 2011).

    Google Scholar 

  2. A.C. Fischer-Cripps: The IBIS Handbook of Nanoindentation (Fischer-Cripps Laboratories Pty Ltd, Forestville, Australia, 2009).

    Google Scholar 

  3. American Society for Testing and Materials: ASTM E2546-07 Standard Practice for Instrumented Indentation Testing (ASTM International, West Conshohocken, PA, 2007).

    Google Scholar 

  4. K. Szilágyi, A. Borosnyói, and I. Zsigovics: Surface hardness and related properties of concrete. Concr. Struct. 12, 51–57 (2010).

    Google Scholar 

  5. H. Hertz: Über die Berührung fester elastischer Körper. J. Reine. Angew. Math. 5, 12–23 (1881).

    Google Scholar 

  6. J.A. Brinell: Mémoire sur les épreaves á bille en acier, II. Cong. Int. Methodes d′Essai, A. Wahlberg, Paris, 1900.

    Google Scholar 

  7. A.C. Fischer-Cripps: Introduction to Contact Mechanics, 2nd ed. (Springer, New York, 2007).

    Google Scholar 

  8. P. Zhang, S.X. Li, and Z.F. Zhang: General relationship between strength and hardness. Mater. Sci. Eng., A 529, 63–67 (2011).

    Google Scholar 

  9. D. Tabor: Hardness of Metals (Clarendon Press, Oxford, UK, 1951).

    Google Scholar 

  10. B.W. Mott: Micro-Indentation Hardness Testing (Butterworths, London, 1956).

    Google Scholar 

  11. M. Bauccio: ASM Metals Reference Book (ASM International, Materials Park, OH, 1993).

    Google Scholar 

  12. International Organization for Standardization: ISO/DIS 14577-1, Metallic Materials—Instrumented Indentation Test for Hardness and Materials Parameters—Part 1: Test Method, 2002.

  13. J. Datsko: Material Properties and Manufacturing Processes (Wiley, New York, 1966).

    Google Scholar 

  14. J. Datsko: Materials in Design and Manufacturing (Malloy, Ann Arbor, Michigan, 1977).

    Google Scholar 

  15. J.A.H. Ramaekers and P.C. Veenstra: The relation between effective deformation and micro-hardness in a state of large plastic deformation. CIRP Ann. XVIII, 541 (1970).

    Google Scholar 

  16. G.M. Pharr, W.C. Oliver, and F.R. Brotzen: On the generality of the relationship among contact stiffness, contact area, and elastic modulus during indentation. J. Mater. Res. 7 (3), 613 (1992).

    CAS  Google Scholar 

  17. W.C. Oliver and G.M. Pharr: An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J. Mater. Res. 7 (6), 1564 (1992).

    CAS  Google Scholar 

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

    CAS  Google Scholar 

  19. S.C. Wright, Y. Huang, and N.A. Fleck: Deep penetration of polycarbonate by a cylindrical punch. Mech. Mater. 13, 277 (1992).

    Google Scholar 

  20. L. Cheng, X. Xia, W. Yu, L.E. Scriven, and W.W. Gerberich: Flat-punch indentation of viscoelastic material. J. Polym. Sci., Part B: Polym. Phys. 38, 10 (2000).

    CAS  Google Scholar 

  21. J.I. Eldridge, D. Zhu, and R.A. Miller: Mesoscopic nonlinear elastic modulus of thermal barrier coatings determined by cylindrical punch indentation. J. Am. Ceram. Soc. 84 (11), 2737 (2001).

    CAS  Google Scholar 

  22. B.X. Xu, B. Zhao, and Z.F. Yue: Finite element analysis of the indentation stress characteristics of the thin film/substrate systems by flat cylindrical indenters. Materialwiss. Werkstofftech. 37 (8), 681 (2006).

    Google Scholar 

  23. A. Gisario, M. Barletta, and A. Boschetto: Characterization of laser treated steels using instrumented indentation by cylindrical flat punch. Surf. Coat. Technol. 202, 2557 (2008).

    CAS  Google Scholar 

  24. Y.C. Lu and D.M. Shinozaki: Characterization and modeling of large displacement micro/nano-indentation of polymeric solids. J. Eng. Mater. Technol. 130 (4), 041001 (2008).

    Google Scholar 

  25. Y.C. Lu, S.N.V.R.K. Kurapati, and F. Yang: Finite element analysis of cylindrical indentation for determining plastic properties of materials in small volumes. J. Phys. D: Appl. Phys. 41, 115415 (2008).

    Google Scholar 

  26. C.L. Slaboch and T. Ovaert: Mechanical characterization and simulation of murine thrombi. Presented at ASME 2011 Summer Bioengineering Conference, Parts A and B, Farmington, Pennsylvania, 783–784, June 22–25, 2011; Paper No. SBC2011-53190.

  27. Z. Hu, K.J. Lynne, S.P. Markondapatnaikuni, and F. Delfanian: Material elastic-plastic property characterization by nanoindentation testing coupled with computer modeling. Mater. Sci. Eng., A 587, 268 (2013).

    CAS  Google Scholar 

  28. M.S. Kashani: Sources of error in relating nanoindentation results to material properties. Ph.D. Thesis, Wichita State University, 2010.

  29. D.J. Strange and A.K. Varshneya: Finite element simulation of microindentation on aluminum. J. Mater. Sci. 36 (8), 1943 (2001).

    CAS  Google Scholar 

  30. T.A. Laursen and J.C. Simo: A study of the mechanics of microindentation using finite elements. J. Mater. Res. 7 (3), 618 (1992).

    CAS  Google Scholar 

  31. N. Panich: Nanoindentation of silicon (100) studied by experimental and finite element method. KMUTT Research & Development Journal 27 (3), 271(2004).

    Google Scholar 

  32. P.C.B. Poon: A critical appraisal of nanoindentation with application to elastic-plastic solids and soft materials. Ph.D. Thesis, California Institute of Technology, Pasadena, California, 2009.

    Google Scholar 

  33. X. Huang and A.A. Pelegri: Mechanical characterization of thin film materials with nanoindentation measurement and finite element analysis. J. Compos. Mater. 40 (15), 1393 (2006).

    CAS  Google Scholar 

  34. F.Y. Chen, R.C. Chang, and L.H. Chen: Determining the plastic-viscoplastic mechanical properties of thin films by nanoindentation and finite element method. In Proceedings of the Seventh International Congress on Thermal Stresses, TS2007, Taipei, Taiwan, June 4–7, 2007.

  35. H. Song: Selected mechanical problems in load and depth sensing indentation testing. Ph.D. Thesis, Rice University, Houston, Texas, 1999.

    Google Scholar 

  36. Z. Liu, E. Harsono, and S. Swaddiwudhipong: Material characterization based on instrumented and simulated indentation tests. Int. J. Appl. Mech. 1 (1), 61 (2009).

    Google Scholar 

  37. E. Harsono: Material characterization via simulated indentation test including effect of friction. Ph.D. Thesis, National University of Singapore, 2009.

  38. T.H. Fang, S.R. Jian, and D.S. Chuu: Nanomechanical properties of TiC, TiN and TiCN thin films using scanning probe microscopy and nanoindentation. Appl. Surf. Sci. 228, 365 (2004).

    CAS  Google Scholar 

  39. C.A. Schuh: Nanoindentation studies of materials. Mater. Today 9 (5), 32 (2006).

    CAS  Google Scholar 

  40. N. Panich and S. Yong: Improved method to determine the hardness and elastic moduli using nano-indentation. KMITL Sci. J. 5 (2), 483 (2005).

    Google Scholar 

  41. H. Li and J.J. Vlassak: Determining the elastic modulus and hardness of an ultrathin film on a substrate using nanoindentation. J. Mater. Res. 24 (3), 1114 (2009).

    CAS  Google Scholar 

  42. B. Bhushan: Handbook of Micro/Nano Tribology, 2nd ed. (CRC Press, Boca Raton, Florida, 1999), p. 433.

    Google Scholar 

  43. B. Bhushan and X. Li: Nanomechanical characterization of solid surfaces and thin films. Int. Mater. Rev. 48 (3), 125 (2003).

    CAS  Google Scholar 

  44. X.H. Wang, S. Jacobsen, J.Y. He, Z.L. Zhang, S.F. Lee, and H.L. Lein: Application of nanoindentation testing to study of the interfacial transition zone in steel fiber reinforced mortar. Cem. Concr. Res. 39 (8), 701 (2009).

    CAS  Google Scholar 

  45. X. Huang: Mechanical characterization of thin film materials with nanoindentation measurement and finite element analysis. Ph.D. Thesis, Rutgers, The State University of New Jersey, 2005.

  46. E.B. Tadmor, R. Miller, R. Phillips, and M. Ortiz: Nanoindentation and incipient plasticity. J. Mater. Res. 14 (6), 2233 (1999).

    CAS  Google Scholar 

  47. A.M. Minor, S.A.S. Asif, Z. Shan, E.A. Stach, E. Cyrankowski, J. Thomas, T.J. Wyrobek, and O.L. Warren: A new view of the onset of plasticity during the nanoindentation of aluminum. Nat. Mater. 5, 697 (2006).

    CAS  Google Scholar 

  48. Z.Q. Feng, Q.C. He, Q.F. Zeng, and P. Joli: Theory of nanoindentation. In Handbook of Nanophysics, K. Sattler ed. (Taylor & Francis, Boca Raton, FL, 2010); pp.26-1-26-15.

    Google Scholar 

  49. A.C. Lund, A.M. Hodge, and C.A. Schuh: Incipient plasticity during nanoindentation at elevated temperatures. Appl. Phys. Lett. 85 (8), 1362 (2004).

    CAS  Google Scholar 

  50. S. Swaddiwudhipong, L.H. Poh, J. Hua, Z.S. Liu, and K.K. Tho: Modeling nano-indentation tests of glassy polymers using finite elements with strain gradient plasticity. Mater. Sci. Eng., A 404, 179 (2005).

    Google Scholar 

  51. J.J. Guo, K. Wang, T. Fujita, J.W. McCauley, and J.P. Singh: Nanoindentation characterization of deformation and failure of aluminum oxynitride. Acta Mater. 59, 1671 (2011).

    CAS  Google Scholar 

  52. B. Poon, D. Rittel, and G. Ravichandran: An analysis of nanoindentation in elasto-plastic solids. Int. J. Solids Struct. 45 (25–26), 6399 (2008).

    Google Scholar 

  53. J. Wang and T.C. Ovaert: Computational mechanical property determination of viscoelastic/plastic materials from nanoindentation creep test data. J. Mater. Res. 24 (3), 1245 (2009).

    CAS  Google Scholar 

  54. Z. Shan and S.K. Sitaraman: Elastic-plastic characterization of thin films using nanoindentation technique. Thin Solid Films 437, 176 (2003).

    CAS  Google Scholar 

  55. C. Zhang: Characterization of the mechanical properties of visco-elastic and visco-elastic-plastic materials by nanoindentation tests. Ph.D. Thesis, Tongji University, Shanghai, China, 2007.

    Google Scholar 

  56. L.M. Jiang, Y.C. Zhou, and Y.L. Huang: Elastic-plastic properties of thin film on elastic-plastic substrates characterized by nanoindentation test. Trans. Nonferrous Met. Soc. China 20 (12), 2345 (2010).

    Google Scholar 

  57. I.N. Sneddon: Boussinesq’s problem for a flat-ended cylinder. Math. Proc. Cambridge Philos. Soc. 42 (1), 29 (1946).

    Google Scholar 

  58. J.W. Harding and I.N. Sneddon: The elastic stresses produced by the indentation of the plane surface of a semi-infinite elastic solid by a rigid punch. Math. Proc. Cambridge Philos. Soc. 41 (1), 16 (1945).

    Google Scholar 

  59. M. Barquins and D. Maugis: Adhesive contact of axisymmetric punches on an elastic half-space: The modified Hertz-Huber stress tensor for contacting spheres. J. Mec. Theor. Appl. 1 (2), 331 (1982).

    Google Scholar 

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

    Google Scholar 

  61. R. Hill: The Mathematical Theory of Plasticity, 2nd ed. (Clarendon Press, Oxford, UK, 1950).

    Google Scholar 

  62. S. Timoshenko: Theory of Elasticity (Mc Graw Hill, New York, 1934).

    Google Scholar 

  63. American Society for Testing and Materials: ASTM E8/E8M-11 Standard Test Methods for Tension Testing of Metallic Materials (ASTM International, 2011).

  64. ANSYS Inc.: ANSYS theory reference manual—ANSYS version14.5, 2013.

  65. K.L. Johnson: The correlation of indentation experiments. J. Mech. Phys. Solids 18 (2), 115 (1970).

    Google Scholar 

  66. A.L. Yurkov, V.N. Skvortsov, I.A. Buyanovsky, and R.M. Matvievsky: Sliding friction of diamond on steel, sapphire, alumina and fused silica with and without lubricants. J. Mater. Sci. Lett. 16 (16), 1370 (1997).

    CAS  Google Scholar 

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ACKNOWLEDGMENTS

This work was supported by the Materials Evaluation and Testing Lab (METLAB), the Department of Mechanical Engineering at South Dakota State University, and the State of South Dakota. Help from Zachary J. Rykhus for measuring residual stresses and computational facility support from Bryan Rieger at University High Performance Computing, the College of Engineering at South Dakota State University are gratefully acknowledged.

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  1. Department of Mechanical Engineering, South Dakota State University, Brookings, South Dakota, 57007, USA

    Zhong Hu, Kevin Lynne & Fereidoon Delfanian

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  1. Zhong Hu
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Correspondence to Zhong Hu.

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Hu, Z., Lynne, K. & Delfanian, F. Characterization of materials’ elasticity and yield strength through micro-/nano-indentation testing with a cylindrical flat-tip indenter. Journal of Materials Research 30, 578–591 (2015). https://doi.org/10.1557/jmr.2015.4

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