Acta Mechanica Solida Sinica

, Volume 28, Issue 3, pp 221–234 | Cite as

Determination of Fracture Toughness of Brittle Materials by Indentation

Article

Abstract

Fracture toughness is one of the crucial mechanical properties of brittle materials such as glasses and ceramics which demonstrate catastrophic failure modes. Conventional standardized testing methods adopted for fracture toughness determination require large specimens to satisfy the plane strain condition. As for small specimens, indentation is a popular, sometimes exclusive testing mode to determine fracture toughness for it can be performed on a small flat area of the specimen surface. This review focuses on the development of indentation fracture theories and the representative testing methods. Cracking pattern dependent on indenter geometry and material property plays an important role in modeling, and is the main reason for the diversity of indentation fracture theories and testing methods. Along with the simplicity of specimen requirement is the complexity of modeling and analysis which accounts for the semi-empirical features of indentation fracture tests. Some unresolved issues shaping the gap between indentation fracture tests and standardization are also discussed.

Key Words

indentation fracture toughness indenter geometry cracking patterns 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Palmqvist, S., A method to determine the toughness of brittle materials, especially hard metals. Jerkontorets Ann., 1957, 141: 303–307.Google Scholar
  2. 2.
    Palmqvist, S., The work for the formation of a crack during Vickers indentation as a measure of the toughness of hard metals. Arch. Einsenhuttenwes, 1962, 33: 629–634.Google Scholar
  3. 3.
    Palmqvist, S., The work for the formation of a crack as a measure of hard metals. Jernkontorets Ann., 1963, 147: 107–110.Google Scholar
  4. 4.
    Cook, R.F. and Pharr, G.M., Direct observation and analysis of indentation cracking in glasses and ceramics. Journal of The American Ceramic Society, 1990, 73(4): 787–817.CrossRefGoogle Scholar
  5. 5.
    Ostojic, P. and McPherson, R., A review of indentation fracture theory: Its development, principles and limitations. International Journal of Fracture, 1987, 33(4): 297–312.CrossRefGoogle Scholar
  6. 6.
    Ponton, C.B. and Rawlings, R.D., Vickers indentation fracture toughness test part 1 review of literature and formulation of standardised indentation toughness equations. Materials Science And Technology, 1989, 5(9): 865–872.CrossRefGoogle Scholar
  7. 7.
    Ponton, C.B. and Rawlings, R.D., Vickers indentation fracture toughness test—Part 2: Application and critical evaluation of standardised indentation toughness equations. Materials Science And Technology, 1989, 5(10): 961–976.CrossRefGoogle Scholar
  8. 8.
    Chen, J.J., Indentation-based methods to assess fracture toughness for thin coatings. Journal of Physics D-Applied Physics, 2012, 45: 203001.CrossRefGoogle Scholar
  9. 9.
    ISO14577:2002, Metallic materials — instrumented indentation test for hardness and materials parameters. International Organization for Standardization, Geneva, Switzerland.Google Scholar
  10. 10.
    Dukino, R.D. and Swain, M.V., Comparative measurement of indentation fracture toughness with Berkovich and Vickers indenters. Journal of the American Ceramic Society, 1992, 75(12): 3299–3304.CrossRefGoogle Scholar
  11. 11.
    Tandon, R., A technique for measuring stresses in small spatial regions using cube-corner indentation: application to tempered glass plates. Journal of The European Ceramic Society, 2007, 27(6): 2407–2414.CrossRefGoogle Scholar
  12. 12.
    Schiffmann, K.I., Determination of fracture toughness of bulk materials and thin films by nanoindentation: comparison of different models. Philosophical Magazine, 2011, 91(7–9): 1163–1178.CrossRefGoogle Scholar
  13. 13.
    Laugier, M.T., New formula for indentation toughness in ceramics. Journal of Materials Science Letters, 1987, 6(3): 355–356.CrossRefGoogle Scholar
  14. 14.
    Lawn, B.R., Evans, A.G. and Marshall, D.B., Elastic/plastic indentation damage in ceramics: the median/radial crack system. Journal of The American Ceramic Society, 1980, 63(9–10): 574–581.CrossRefGoogle Scholar
  15. 15.
    Marshall, D.B. and Lawn, B.R., Residual-stress effects in sharp contact cracking—1. Indentation fracture mechanics. Journal of Materials Science, 1979, 14(8): 2001–2012.CrossRefGoogle Scholar
  16. 16.
    Morris, D.J. and Cook, R.F., In situ cube-corner indentation of soda-lime glass and fused silica. Journal of The American Ceramic Society, 2004, 87(8): 1494–1501.CrossRefGoogle Scholar
  17. 17.
    Roesler, F.C., Brittle fractures near equilibrium. Proceedings of the Physical Society, Section B, 1956, 69(10): 981–992.CrossRefGoogle Scholar
  18. 18.
    Frank, F.C. and Lawn, B.R., On the theory of Hertzian fracture. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1967, 299: 291–306.CrossRefGoogle Scholar
  19. 19.
    Zeng, K., Breder, K. and Rowcliffe, D.J., The Hertzian stress field and formation of cone cracks—ii. determination of fracture toughness. Acta Metallurgica et Materialia, 1992, 40(10): 2601–2605.CrossRefGoogle Scholar
  20. 20.
    Zeng, K., Breder, K., Rowcliffe, D.J. and Herrström, C., Elastic modulus determined by Hertzian indentation. Journal of Materials Science, 1992, 27(14): 3789–3792.CrossRefGoogle Scholar
  21. 21.
    Warren, P.D., Determining the fracture toughness of brittle materials by Hertzian indentation. Journal Of The European Ceramic Society, 1995, 15(3): 201–207.CrossRefGoogle Scholar
  22. 22.
    Evans, A.G. and Charles, E.A., Fracture toughness determinations by indentation. Journal of The American Ceramic Society, 1976, 59(7–8): 371–372.CrossRefGoogle Scholar
  23. 23.
    Yoffe, E., Elastic stress fields caused by indenting brittle materials. Philosophical Magazine, A, 1982, 46(4): 617–628.CrossRefGoogle Scholar
  24. 24.
    Tabor, D., The Hardness of Metals. London, UK: Oxford University Press, 1951.Google Scholar
  25. 25.
    Hill, R., The Mathematical Theory of Plasticity. New York, USA: Oxford University Press, 1998.MATHGoogle Scholar
  26. 26.
    Rooke, D.P. and Cartwright, D.J., Compendium of Stress Intensity Factors. London: Her Majesty’s Stationery Office, 1975.Google Scholar
  27. 27.
    Laugier, M.T., The elastic/plastic indentation of ceramics. Journal of Materials Science Letters, 1985, 4(12): 1539–1541.CrossRefGoogle Scholar
  28. 28.
    Oore, M. and Burns, D.J., Estimation of stress intensity factors for embedded irregular cracks subjected to arbitrary normal stress fields. Journal of Pressure Vessel Technology, 1980, 102(2): 202–211.CrossRefGoogle Scholar
  29. 29.
    Ouchterlony, F., Stress intensity factors for the expansion loaded star crack. Engineering Fracture Mechanics, 1976, 8(2): 447–448.CrossRefGoogle Scholar
  30. 30.
    Anstis, G.R., Chantikul, P., Lawn, B.R. and Marshall, D.B., A critical evaluation of indentation techniques for measuring fracture toughness—I. Direct crack measurements. Journal of the American Ceramic Society, 1981, 64(9): 533–538.CrossRefGoogle Scholar
  31. 31.
    Pharr, G.M., Harding, D.S. and Oliver, W.C., Measurement of fracture toughness in thin films and small volumes using nanoindentation methods. In: Mechanical Properties and Deformation Behavior of Materials Having Ultra-fine Microstructures, Edited by Nastasi, M., Parkin, D.M. and Gleiter, H., Kluwer Academic Publishers, Dordrecht, the Netherlands, 1993: 449–461.CrossRefGoogle Scholar
  32. 32.
    Harding, D.S., Oliver, W.C. and Pharr, G.M., Cracking during nanoindentation and its use in the measurement of fracture toughness. Materials Research Society Symposium Proceedings, 1995, 356: 663–668.CrossRefGoogle Scholar
  33. 33.
    Pharr, G.M., Measurement of mechanical properties by ultra-low load indentation. Materials Science and Engineering A, 1998, 253(1–2): 151–159.CrossRefGoogle Scholar
  34. 34.
    Zhang, T.H., Feng, Y.H., Yang, R. and Jiang, P., A method to determine fracture toughness using cube-corner indentation. Scripta Materialia, 2010, 62(4): 199–201.CrossRefGoogle Scholar
  35. 35.
    Feng, Y.H., Zhang, T.H. and Yang, R., A work approach to determine Vickers indentation fracture toughness. Journal of The American Ceramic Society, 2011, 94(2): 332–335.CrossRefGoogle Scholar
  36. 36.
    Fett, T., Computation of the crack opening displacements for Vickers indentation cracks. Report FZKA 6757, Forschungszentrum Karlsruhe, Karlsruhe, Germany, 2002.Google Scholar
  37. 37.
    Fett, T., Kounga, A.B. and Rödel, J., Stresses and stress intensity factor from cod of Vickers indentation cracks. Journal of Materials Science, 2004, 39(6): 2219–2221.CrossRefGoogle Scholar
  38. 38.
    Shetty, D.K., Rosenfield, A.R. and Duckworth, W., Analysis of indentation crack as a wedge-loaded half-penny crack. Journal of The American Ceramic Society, 1985, 68(2): C65–C67.CrossRefGoogle Scholar
  39. 39.
    Shetty, D.K., Wright, I.G., Mincer, P.N. and Clauer, A.H., Indentation fracture of wc-co cermets. Journal of Materials Science, 1985, 20(5): 1873–1882.CrossRefGoogle Scholar
  40. 40.
    Niihara, K., Morena, R. and Hasselman, D.P.H., Evaluation of Kic of brittle solids by the indentation method with low crack-to-indent ratios. Journal of Materials Science Letters, 1982, 1(1): 13–16.CrossRefGoogle Scholar
  41. 41.
    Niihara, K., A fracture mechanics analysis of indentation-induced Palmqvist crack in ceramics. Journal of Materials Science Letters, 1983, 2(5): 221–223.CrossRefGoogle Scholar
  42. 42.
    Lankford, J., Indentation microfracture in the Palmqvist crack regime: implications for fracture toughness evaluation by the indentation method. Journal of Materials Science Letters, 1982, 1(11): 493–495.CrossRefGoogle Scholar
  43. 43.
    Liang, K.M., Orange, G. and Fantozzi, G., Evaluation by indentation of fracture toughness of ceramic materials. Journal of Materials Science, 1990, 25(1): 207–214.CrossRefGoogle Scholar
  44. 44.
    Johnson, K.L., Contact Mechanics. Cambridge, UK: Cambridge University Press, 1985.CrossRefMATHGoogle Scholar
  45. 45.
    Zeng, K., Breder, K. and Rowcliffe, D.J., The Hertzian stress field and formation of cone cracks—I. Theoretical approach. Acta Metallurgica et Materialia, 1992, 40(10): 2595–2600.CrossRefGoogle Scholar
  46. 46.
    Lawn, B.R., Hertzian fracture in single crystals with the diamond structure. Journal of Applied Physics, 1968, 39(10): 4828–4836.CrossRefGoogle Scholar
  47. 47.
    Geandier, G., Denis, S. and Mocellin, A., Float glass fracture toughness determination by Hertzian, contact: experiments and analysis. Journal of Non-crystalline Solids, 2003, 318(3): 284–295.CrossRefGoogle Scholar
  48. 48.
    Faisal, N.H., Ahmed, R. and Reuben, R.L., Indentation testing and its acoustic emission response: applications and emerging trends. International Materials Reviews, 2011, 56(2): 98–142.CrossRefGoogle Scholar
  49. 49.
    Quinn, G.D. and Bradt, R.C., On the Vickers indentation fracture toughness test. Journal of The American Ceramic Society, 2007, 90(3): 673–680.CrossRefGoogle Scholar
  50. 50.
    Oliver, W.C. and Pharr, G.M., Improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. Journal of Materials Research, 1992, 7(6): 1564–1583.CrossRefGoogle Scholar
  51. 51.
    King, R.B., Elastic analysis of some punch problems for a layered medium. International Journal of Solids And Structures, 1987, 23(12): 1657–1664.CrossRefMATHGoogle Scholar
  52. 52.
    Cheng, Y.T. and Cheng, C.M., Relationships between hardness, elastic modulus, and the work of indentation. Applied Physics Letters, 1998, 73(5): 614–616.CrossRefGoogle Scholar
  53. 53.
    Yang, R., Zhang, T.H., Jiang, P. and Bai, Y.L., Experimental verification and theoretical analysis of the relationships between hardness, elastic modulus, and the work of indentation. Applied Physics Letters, 2008, 92(23): 231906.Google Scholar
  54. 54.
    Yang, R., Zhang, T.H. and Feng, Y.H., Theoretical analysis of the relationships between hardness, elastic modulus, and the work of indentation for work-hardening materials. Journal of Materials Research, 2010, 25(11): 2072–2077.CrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2015

Authors and Affiliations

  1. 1.State Key Laboratory of Nonlinear Mechanics, Institute of MechanicsChinese Academy of SciencesBeijingChina
  2. 2.College of Mechanical EngineeringZhejiang University of TechnologyHangzhouChina

Personalised recommendations