Advertisement

Recent progresses in the phenomenological description for the indentation size effect in microhardness testing of brittle ceramics

  • 1146 Accesses

  • 9 Citations

Abstract

The indentation hardness of a given material is usually load-dependent and such a phenomenon is generally referred to as the indentation size effect (ISE). The existence of ISE means that, if hardness is used as a material selection criterion, it is clearly insufficient to quote a single hardness number. Several empirical or semi-empirical equations, including the Meyer’s law, the Hays-Kendall approach, the energy-balance approach, the proportional specimen resistance (PSR) model and the modified PSR model, etc., have been proposed for the description of the variation of the indentation size with the applied test load and for determining the so-called load-independent hardness. This paper reviews these existing empirical equations, with a special emphasis on the analysis and the application of the modified PSR model.

References

  1. [1]

    Michels BD, Frischa GH. Microhardness of chalcogenide glasses of the system Se-Ge-As. J Mater Sci 1982, 17: 329–334.

  2. [2]

    Hirao K, Tomozawa M. Microhardness of SiO2 glass in various environments. J Am Ceram Soc 1987, 70: 497–502.

  3. [3]

    Clinton DJ, Morrell R. Hardness testing of ceramic materials. Mater Chem Phys 1987, 17: 461–473.

  4. [4]

    Li H, Bradt RC. The microhardness indentation load/size effect in rutile and cassiterite single crystals. J Mater Sci 1993, 28: 917–926.

  5. [5]

    Quinn JB, Quinn GD. Indentation brittleness of ceramics: A fresh approach. J Mater Sci 1997, 32: 4331–4346.

  6. [6]

    Gong JH, Wu JJ, Z.D. Guan. Examination of the indentation size effect in low-load Vickers hardness testing of ceramics. J Europ Ceram Soc 1999, 19: 2625–2631.

  7. [7]

    Ullner C, Germak A, Le Doussal H, et al. Hardness testing on advanced technical ceramics. J Europ Ceram Soc 2001, 21: 439–451.

  8. [8]

    Sebastina S, Khadar M. Microhardness indentation size effect studies in 60B2O3=(40-x)PbO-xMcl2 (M = Pb, Cd) glasses. J Mater Sci 2005, 40: 1655–1659.

  9. [9]

    Mukhopadhyay NK, Paufler P. Micro- and nanoindentation techniques for mechanical characterization of materials. Inter Mater Rev 2006, 41: 209–245.

  10. [10]

    Sangwal K. Review: Indentation size effect, indentation cracks and microhardness measurement of brittle crystalline solids — some basic concepts and trends. Cryst Res Technol 2009, 44: 1019–1037.

  11. [11]

    Young CT, Rhee SK. Evaluation of correction methods for determining load-independent Knoop microhardness. J Test Eval 1978, 6: 221–230.

  12. [12]

    Mott BW. Micro-Indentation Hardness Testing. London, UK: Butterworths Scientific, 1956.

  13. [13]

    Bükle IH. Progress in micro-indentation hardness testing. Metall Rev 1959, 4: 49–100.

  14. [14]

    Blau PJ, Lawn BR, Eds. Microindentation Techniques in Materials Science and Engineering. Philadelphia: American Society for Testing and Materials, 1986.

  15. [15]

    Brown ARG, Ineson E. Experimental survey of low-load hardness testing instruments. J Iron Steel Institute 1957, 169: 376–388.

  16. [16]

    Mason W, Johnson PF, Varner JR. Importance of load cell sensitivity in determination of the load dependence of hardness in recording microhardness. J Mater Sci 1991, 26: 6576–6580.

  17. [17]

    Bückle IH. Use of the hardness test to determine other material properties. In: The Science of Hardness Testing and Its Research Application. Westbook JH, Conrad H, Eds. American Society for Metals, 1973: 453–494.

  18. [18]

    Tarkanian ML, Neumann JP, Raymond L. Determination of the temperature dependence of {100} and {112} slip in tungsten from Knoop hardness measurements. In: The Science of Hardness Testing and Its Research Application. Westbook JH, Conrad H, Eds. American Society for Metals, 1973: 187–198.

  19. [19]

    O’Neill H. The Hardness of Metals and Its Measurement. Cleveland: Sherwood, 1934.

  20. [20]

    Ma Q, Clarke DR. Size-dependent hardness of silver single-crystals. J Mater Res 1995, 10: 853–863.

  21. [21]

    Nix WD, Gao HJ. Indentation size effects in crystalline materials: A law of strain gradient plasticity. J Mech. Phys Solids 1998, 46: 411–425.

  22. [22]

    Gerberich WW, Tymiak NI, Grunlan JC, et al. Interpretations of indentation size effects. J Appl Mech Trans ASME 2002, 69: S433–442.

  23. [23]

    Sangwal K, Surowska B, Blaziak P. Analysis of the indentation size effect in the microhardness measurement of some cobalt-based alloys. Mater Chem Phys 2003, 77: 511–520.

  24. [24]

    Sahin O, Uzun O, Kolemen U, et al. Indentation size effect and microhardness study of beta-Sn single crystals. Chin Phys Lett 2005, 22: 3137–3140.

  25. [25]

    Kolemen U. Analysis of ISE in microhardness measurements of bulk MgB2 superconductors using different models. J Alloys Comp 2006, 425: 429–435.

  26. [26]

    Anandakumar VM, Khadar MA. Microhardness studies of nanocrystalline lead molybdate. Mater Sci Eng A 2009, 519: 141–146.

  27. [27]

    Terzioglu C. Investigation of some physical properties of Gd added Bi-2223 superconductors. J Alloys Comp 2011, 509: 87–93.

  28. [28]

    Meyer E. Investigations on hardness testing and hardness. VDI Zeitschriff 1908, 52: 2077–2078.

  29. [29]

    Hays C, Kendall EG. An analysis of Knoop microhardness. Metall 1973, 6: 275–282.

  30. [30]

    Fröhlich F, Grau P, Grellmann W. Performance and analysis of recording microhardness tests. Phys Status Solidi 1977, 42: 79–89.

  31. [31]

    Gong JH, Si WJ, Guan ZD. Effect of load-dependence of hardness on indentation toughness determination for soda-lime glass. J Non-Cryst Solids 2001, 282: 325–328.

  32. [32]

    Gong JH, Wu JJ, Guan ZD. Load dependence of the apparent hardness of silicon nitride ceramics in a wider range of loads. Mater Lett 1998, 35: 58–61.

  33. [33]

    Gong JH, Guan ZD. Load dependence of low-load Knoop hardness in ceramics: a modified PSR model. Mater Lett 2001, 47: 140–144.

  34. [34]

    Gong JH. Comment on “measurement of hardness on traditional ceramics”. J Europ Ceram Soc 2003, 23: 1769–1772.

  35. [35]

    Gong JH, Pan XT, Miao HZ, et al. Effect of metallic binder content on the microhardness of TiCN-based cermets. Mater Sci Eng A 2003, 359: 391–395.

  36. [36]

    Gong JH, Zhao Z, Guan ZD, et al. Load-dependence of Knoop hardness of Al2O3-TiC composites. J Europ Ceram Soc 2000, 20: 1895–1900.

  37. [37]

    Gong JH, Miao HZ, Hu BJ. Compositional dependence of hardness of (Ce,Y)-TZP/Al2O3 composites. Mater Sci Eng A 2004, 372: 207–212.

  38. [38]

    Peng ZJ, Gong JH, Miao HZ. On the description of indentation size effect in hardness testing for ceramics: analysis of the nanoindentation data. J Europ Ceram Soc 2004, 24: 2193–2201.

  39. [39]

    Dey A, Mukhopadhyay AK, Gangadharan S, et al. Nanoindentation study of microplasma sprayed hydroxyapatite coating. Ceram Int 2009, 35: 2295–2304.

  40. [40]

    Gong JH, Miao HZ, Zhao Z, et al. Load-dependence of the measured hardness of Ti(C,N)-based cermets. Mater Sci Eng A 2001, 303: 179–186.

  41. [41]

    Charkraborty D, Mukerji J. Characterization of silicon nitride single crystals and polycrystalline reaction sintered silicon nitride by microhardness measurements. J Mater Sci 1980, 15: 3051–3056.

  42. [42]

    Babini GN, Bellosi A, Galassi C. Characterization of hot-pressed silicon nitride-based materials by microhardness measurements. J Mater Sci 1987, 22: 1687–1693.

  43. [43]

    Sargent PM, Page TF. The influence on the microhardness of ceramic materials. Proc Brit Ceram Soc 1978, 26: 209–224.

  44. [44]

    Li H, Bradt RC. Knoop microhardness anisotropy of single crystal cassiterite (SnO2). J Am Ceram Soc 1991, 74: 1053–1060.

  45. [45]

    Gong JH, Guan ZD. Energy-balance relationship in Knoop hardness test for ceramics. J Chin Ceram Soc 1995, 23: 308–313.

  46. [46]

    Lawn BR, Evans AG, Marshall DB. Elastic/plastic indentation damage in ceramics: The median/radial crack system. J Am Ceram Soc 1980, 63: 574–581.

  47. [47]

    Gong JH, Yuan QM. Indentation size effect for Knoop hardness testing. J Tianjin Univ 1996, 29: 727–731.

  48. [48]

    Gong JH, Li LX. Indentation hardness of mullite based ceramics. J Inorg Mater 1996, 11: 375–380.

  49. [49]

    Mukhopadhyay NK. Analysis of microhardness data using the normalized power law equation and energy balance model. J Mater Sci 2005, 40: 241–244.

  50. [50]

    Liu Q, Yao YX, Zhou L. Theoretical analysis of indentation size effect. J Test Meas Technol 2009, 23: 1–6.

  51. [51]

    Gong JH. On the energy balance model for conventional Vickers microhardness testing of brittle ceramics. J Mater Sci Lett 2000, 19: 515–517.

  52. [52]

    Gong JH, Guan ZD. Effect of microcracking on the energy-balance relationship for hardness testing of ceramics. Mater Lett 2001, 49: 180–184.

  53. [53]

    Li Z, Ghosh A, Kobayashi AS, et al. Indentation fracture toughness of sintered silicon carbide in the Palmqvist crack regime. J Am Ceram Soc 1989, 72: 904–911.

  54. [54]

    Quinn GD, Green P, Xu L. Cracking and the indentation size effect for Knoop hardness of glasses. J Am Ceram Soc 2003, 86: 441–448.

  55. [55]

    Atkinson M, Shi H. Friction effect in low load hardness testing of iron. Mater Sci Technol 1989, 5: 613–614.

  56. [56]

    Shi H, Atkinson M. A friction effect in low-load hardness testing of copper and aluminum. J Mater Sci 1990, 25: 2111–2114.

  57. [57]

    Li H, Ghost A, Han YH, et al. The friction component of the indentation size effect in low load microhardness testing. J Mater Res 1993, 8: 1028–1032.

  58. [58]

    Gong JH, Wu JJ, Guan ZD. Description of the indentation size effect in hot-pressed silicon-nitride-based ceramics. J Mater Sci Lett 1998, 17: 473–475.

  59. [59]

    Lawn BR, Wilshaw TR. Indentation fracture: Principles and applications. J Mater Sci 1975, 10: 1049–1081.

  60. [60]

    Marshall DB, Lawn BR. Residual stress effects in sharp contact cracking: Part 1 Indentation fracture mechanics. J Mater Sci 1979, 14: 2001–2012.

  61. [61]

    Johnsonwalls D, Evans AG, Marshall DB, et al. Residual stresses in machined ceramic surfaces. J Am Ceram Soc 1986, 69: 44–47.

  62. [62]

    Li K, Liao TW. Surface/subsurface damage and the fracture strength of ground ceramics. J Mater Process Technol 1996, 57: 207–220.

  63. [63]

    Wu H, Roberts SG, Berby B. Residual stress and subsurface damage in machined alumina and alumina/silicon carbide nanocomposite ceramics. Acta Mater 2001, 49: 507–517.

  64. [64]

    Xie ZH, Hoffman M, Cheng YB. Microstructural tailoring and characterization fo a calcium αSiAlON composition. J Am Ceram Soc 2002, 85: 812–818.

  65. [65]

    Kolemen U, Uzun O, Yilmazlar M, et al. Hardness and microstructural analysis of Bi1.6Pb0.4Sr2Ca2-xSmxCu3Oy polycrystalline superconductors. J Alloys Comp 2006, 415: 300–306.

  66. [66]

    Sidjanin L, Rajnovic D, Ranogajec J, et al. Measurement of Vickers hardness on ceramic floor tiles. J Europ Ceram Soc 2007, 27: 1767–1773.

  67. [67]

    Wang K, Russel C, Liu CS. Preparation, mechanical properties and corrosion behaviors of oriented Ca(PO3)2 glass-ceramics. Mater Chem Phys 2008, 111: 106–113.

  68. [68]

    Sahin O, Uzun O, Sopicka-Lizer M, et al. Dynamic hardness and elastic modulus calculation of porous SiAlON ceramics using depth-sensing indentation technique. J Europ Ceram Soc 2008, 28: 1235–1242.

  69. [69]

    Filetin T, Solic S, Zmak I. The indentation size effect on the micro-hardness of sea mollusk shell structures. Mater Test 2011, 53: 48–53.

  70. [70]

    Chicot D, Roudet F, Soom A, et al. Interpretation of instrumented hardness measurements on stainless steel with different surface preparations. Surf Eng 2007, 23: 32–39.

  71. [71]

    Sidjanin L, Ranogajec J, Rajnovic D, et al. Influence of firing temperature on mechanical properties on roofing tiles. Mater Design 2007, 28: 941–947.

  72. [72]

    Nursoy M, Yilmazlar M, Terzioglu C, et al. Transport, microstructure and mechanical properties of Au diffusion-doped Bi-2223 superconductors. J Alloys Comp 2008, 459: 399–406.

  73. [73]

    Rios CT, Coelho AA, Batista WW, et al. ISE and fracture toughness evaluation by Vickers hardness testing of an Al3Nb-Nb2Al-AlNbNi in situ composite. J Alloys Comp 2009, 472: 65–70.

  74. [74]

    Feltham P, Banerjee R. Theory and application of microindentation in studies of glide and cracking in single crystals of elemental and compound semiconductors. J Mater Sci 1992, 27: 1626–1632.

  75. [75]

    Li H, Bradt RC. The effect of indentation-induced cracking on the apparent microhardness. J Mater Sci 1996, 31: 1065–1070.

  76. [76]

    Sakai T, Ghosh A, Bradt RC. The indentation fracture resistance of self-reinforced mullites. In: Fracture Mechanics of Ceramics, Vol. 10. Bradt RC, Hasselman DPH, Munz D, et al, Eds. New York: Plenum, 1992: 119–133.

  77. [77]

    Gong JH, Wu JJ, Guan ZD. Analysis of the indentation size effect on the apparent hardness for ceramics. Mater Lett 1999, 38: 197–201.

  78. [78]

    Bückle H. Mikrohärteprüfung. Stuttgart, Germany: Berliner Union Verlag, 1965.

Download references

Author information

Correspondence to Danyu Jiang.

Additional information

This article is published with open access at Springerlink.com

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and Permissions

About this article

Cite this article

Jiang, D. Recent progresses in the phenomenological description for the indentation size effect in microhardness testing of brittle ceramics. J Adv Ceram 1, 38–49 (2012) doi:10.1007/s40145-012-0004-2

Download citation

Key words

  • indentation
  • hardness
  • size effect
  • residual stress