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Scaling relationships of elastic-perfectly plastic film/coating materials from small scale sharp indentation

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Abstract

The scaling relationships of elastic-perfectly plastic film/coating materials during sharp indentation have been obtained using dimensional analysis and finite-element modeling. Besides the bulk substrate materials, a wide range of film/coating materials with different ratios in term of the Young’s modulus and yield strength were examined, namely different values of Ef/Es and Yf/Es. Based on these scaling relationships, the substrate effects on indentation response and deformed surface profile of residual imprint are given. Furthermore, the scaling relationship among the work of indentation, reduced elastic modulus and hardness has been found. It is found that the ratio of the indentation hardness to measurement of substrate elastic modulus could be used to characterize the wear resistance of film/coating materials. In addition, a novel method to acquire the intrinsic hardness and elastic modulus of film/coating materials is proposed combined with the well-known 10% critical indentation depth rule, which avoids the error caused by estimating the contact area. This work could be contributed for characterizing the mechanical properties of film/coating materials at micro- and nanoscale.

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References

  1. Wen W, Becker A A, Sun W. Determination of material properties of thin films and coatings using indentation tests: A review. J Mater Sci, 2017, 52: 12553–12573

    Article  Google Scholar 

  2. Wang S, Zhao H. Low temperature nanoindentation: Development and applications. Micromachines, 2020, 11: 407

    Article  Google Scholar 

  3. Ochoa Brezmes A, Breitkopf C. Influence of indenter tip diameter and film thickness on flat indentations into elastic-plastic films by means of the finite element method. Thin Solid Films, 2018, 653: 49–56

    Article  Google Scholar 

  4. Gupta A K, Porwal D, Dey A, et al. Evaluation of elasto-plastic properties of ITO film using combined nanoindentation and finite element approach. Ceramics Int, 2016, 42: 1225–1233

    Article  Google Scholar 

  5. Bhaskaran M, Sriram S, Ruffell S, et al. Nanoscale characterization of energy generation from piezoelectric thin films. Adv Funct Mater, 2011, 21: 2251–2257

    Article  Google Scholar 

  6. Wang Y B, Wang L F, Joyce H J, et al. Super deformability and Young’s modulus of GaAs nanowires. Adv Mater, 2011, 23: 1356–1360

    Article  Google Scholar 

  7. Oliver W C, Pharr G M. An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J Mater Res, 1992, 7: 1564–1583

    Article  Google Scholar 

  8. Doerner M F, Nix W D. A method for interpreting the data from depth-sensing indentation instruments. J Mater Res, 1986, 1: 601–609

    Article  Google Scholar 

  9. Cheng Y T, Cheng C M. Scaling approach to conical indentation in elastic-plastic solids with work hardening. J Appl Phys, 1998, 84: 1284–1291

    Article  Google Scholar 

  10. Cheng Y T, Cheng C M. Relationships between hardness, elastic modulus, and the work of indentation. Appl Phys Lett, 1998, 73: 614–616

    Article  Google Scholar 

  11. Cheng Y T, Cheng C M. Scaling relationships in indentation of power-law creep solids using self-similar indenters. Philos Mag Lett, 2001, 81: 9–16

    Article  Google Scholar 

  12. Cheng Y T, Cheng C M. Relationships between initial unloading slope, contact depth, and mechanical properties for conical indentation in linear viscoelastic solids. J Mater Res, 2005, 20: 1046–1053

    Article  Google Scholar 

  13. Cheng Y T, Cheng C M. Scaling, dimensional analysis, and indentation measurements. Mater Sci Eng-R-Rep, 2004, 44: 91–149

    Article  Google Scholar 

  14. Qu Z, Pei Y, He R, et al. Investigation of pile-up behavior for thermal barrier coatings under elevated-temperature indentation. J Appl Mech, 2016, 83: 041009

    Article  Google Scholar 

  15. Zhou H, Pei Y, Li F, et al. Electric-field-tunable mechanical properties of relaxor ferroelectric single crystal measured by nanoindentation. Appl Phys Lett, 2014, 104: 061904

    Article  Google Scholar 

  16. Zhou H, Zhang H, Pei Y, et al. Scaling relationship among indentation properties of electromagnetic materials at micro- and nanoscale. Appl Phys Lett, 2015, 106: 081904

    Article  Google Scholar 

  17. Yu Z J, Wei Y G. A study of indentation scaling relationships of elastic-perfectly plastic solids with an inclusion near the conical indenter tip. Sci China Tech Sci, 2019, 62: 721–728

    Article  MathSciNet  Google Scholar 

  18. Gamonpilas C, Busso E P. On the effect of substrate properties on the indentation behaviour of coated systems. Mater Sci Eng-A, 2004, 380: 52–61

    Article  Google Scholar 

  19. Korsunsky A M, Constantinescu A. Work of indentation approach to the analysis of hardness and modulus of thin coatings. Mater Sci Eng-A, 2006, 423: 28–35

    Article  Google Scholar 

  20. Ma Z S, Zhou Y C, Long S G, et al. An inverse approach for extracting elastic-plastic properties of thin films from small scale sharp indentation. J Mater Sci Tech, 2012, 28: 626–635

    Article  Google Scholar 

  21. Tunvisut K, O’Dowd N P, Busso E P. Use of scaling functions to determine mechanical properties of thin coatings from microindentation tests. Int J Solids Struct, 2001, 38: 335–351

    Article  MATH  Google Scholar 

  22. Tunvisut K, Busso E P, O’Dowd N P, et al. Determination of the mechanical properties of metallic thin films and substrates from indentation tests. Philos Mag A, 2002, 82: 2013–2029

    Article  Google Scholar 

  23. Qu Z, Zhang Q, He R, et al. Characterization of oxidation film on SiC ceramic substrate based on indentation method. Ceramics Int, 2017, 43: 4399–4404

    Article  Google Scholar 

  24. Liao Y, Zhou Y, Huang Y, et al. Measuring elastic-plastic properties of thin films on elastic-plastic substrates by sharp indentation. Mech Mater, 2009, 41: 308–318

    Article  Google Scholar 

  25. Ma Z S, Zhou Y C, Long S G, et al. On the intrinsic hardness of a metallic film/substrate system: Indentation size and substrate effects. Int J Plast, 2012, 34: 1–11

    Article  Google Scholar 

  26. Wang Z, Wang S, Zhou S, et al. Micro- and macroscopic plastic flow responses in high Nb-containing TiAl alloy by nanoindentation. Intermetallics, 2020, 127: 106958

    Article  Google Scholar 

  27. Kim B M, Lee C J, Lee J M. Estimations of work hardening exponents of engineering metals using residual indentation profiles of nano-indentation. J Mater Sci Technol, 2010, 24: 73–76

    Google Scholar 

  28. Mishnaevsky Jr. L L, Gross D. Deformation and failure in thin films/substrate systems: Methods of theoretical analysis. Appl Mech Rev, 2005, 58: 338–353

    Article  Google Scholar 

  29. Bucaille J L, Stauss S, Felder E, et al. Determination of plastic properties of metals by instrumented indentation using different sharp indenters. Acta Mater, 2003, 51: 1663–1678

    Article  Google Scholar 

  30. Wang Y. Effects of indenter angle and friction on the mechanical properties of film materials. Results Phys, 2016, 6: 509–514

    Article  Google Scholar 

  31. Hay J, Crawford B. Measuring substrate-independent modulus of thin films. J Mater Res, 2011, 26: 727–738

    Article  Google Scholar 

  32. Bowman K, Mechanical Behavior of Materials. New York: Wiley, 2004

    Google Scholar 

  33. Thomas S, Thomas R, Zachariah A K, et al. Microscopy Methods in Nanomaterials Characterization. Netherlands: Elsevier, 2017

    Google Scholar 

  34. Bhushan B. Nanotribology and Nanomechanics: An Introduction. Berlin: Springer Science & Business Media, 2008

    Google Scholar 

  35. Cabibbo M, Ciccarelli D, Spigarelli S. Nanoindentation hardness measurement in piling up SiO2 coating. Phys Procedia, 2013, 40: 100–112

    Article  Google Scholar 

  36. Wang J S, Zheng X J, Zheng H, et al. Evaluation of the substrate effect on indentation behavior of film/substrate system. Appl Surf Sci, 2010, 256: 5998–6002

    Article  Google Scholar 

  37. Li W, Liu P, Liaw P K. Microstructures and properties of high-entropy alloy films and coatings: A review. Mater Res Lett, 2018, 6: 199–229

    Article  Google Scholar 

  38. Yang R, Zhang T, Jiang P, et al. Experimental verification and theoretical analysis of the relationships between hardness, elastic modulus, and the work of indentation. Appl Phys Lett, 2008, 92: 231906

    Article  Google Scholar 

  39. Nix W D, Gao H. Indentation size effects in crystalline materials: a law for strain gradient plasticity. J Mech Phys Solids, 1998, 46: 411–425

    Article  MATH  Google Scholar 

  40. Cheng Y T, Cheng C M. Can stress-strain relationships be obtained from indentation curves using conical and pyramidal indenters? J Mater Res, 1999, 14: 3493–3496

    Article  Google Scholar 

  41. Zhao M, Chen X, Xiang Y, et al. Measuring elastoplastic properties of thin films on an elastic substrate using sharp indentation. Acta Mater, 2007, 55: 6260–6274

    Article  Google Scholar 

  42. Chen X, Ogasawara N, Zhao M, et al. On the uniqueness of measuring elastoplastic properties from indentation: The indistinguishable mystical materials. J Mech Phys Solids, 2007, 55: 1618–1660

    Article  MATH  Google Scholar 

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Correspondence to HongWei Zhao.

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This work was supported by the National Science Fund for Distinguished Young Scholars (Grant No. 51925504), the National Key R&D Program of China (Grant No. 2018YFF01012400), the National Science and Technology Innovation Leading Academic (Ten Thousand Talent Program), the National Defense Science and Technology Bureau Project (Grant No. JSJL2018110A001), the Pre-research of Equipment of the General Armaments Department (Grant No. 41422050301), and the Graduate Innovation Fund of Jilin University (Grant No. 101832020CX103).

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Wang, Z., Wang, J., Wang, W. et al. Scaling relationships of elastic-perfectly plastic film/coating materials from small scale sharp indentation. Sci. China Technol. Sci. 64, 1302–1310 (2021). https://doi.org/10.1007/s11431-020-1757-8

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  • DOI: https://doi.org/10.1007/s11431-020-1757-8

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