Skip to main content
Log in

Determination of Fracture Toughness of Brittle Materials by Indentation

  • Published:
Acta Mechanica Solida Sinica Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Palmqvist, S., A method to determine the toughness of brittle materials, especially hard metals. Jerkontorets Ann., 1957, 141: 303–307.

    Google Scholar 

  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. 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. 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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  8. Chen, J.J., Indentation-based methods to assess fracture toughness for thin coatings. Journal of Physics D-Applied Physics, 2012, 45: 203001.

    Article  Google Scholar 

  9. ISO14577:2002, Metallic materials — instrumented indentation test for hardness and materials parameters. International Organization for Standardization, Geneva, Switzerland.

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  13. Laugier, M.T., New formula for indentation toughness in ceramics. Journal of Materials Science Letters, 1987, 6(3): 355–356.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  17. Roesler, F.C., Brittle fractures near equilibrium. Proceedings of the Physical Society, Section B, 1956, 69(10): 981–992.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  23. Yoffe, E., Elastic stress fields caused by indenting brittle materials. Philosophical Magazine, A, 1982, 46(4): 617–628.

    Article  Google Scholar 

  24. Tabor, D., The Hardness of Metals. London, UK: Oxford University Press, 1951.

    Google Scholar 

  25. Hill, R., The Mathematical Theory of Plasticity. New York, USA: Oxford University Press, 1998.

    MATH  Google Scholar 

  26. Rooke, D.P. and Cartwright, D.J., Compendium of Stress Intensity Factors. London: Her Majesty’s Stationery Office, 1975.

    Google Scholar 

  27. Laugier, M.T., The elastic/plastic indentation of ceramics. Journal of Materials Science Letters, 1985, 4(12): 1539–1541.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  29. Ouchterlony, F., Stress intensity factors for the expansion loaded star crack. Engineering Fracture Mechanics, 1976, 8(2): 447–448.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Chapter  Google Scholar 

  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.

    Article  Google Scholar 

  33. Pharr, G.M., Measurement of mechanical properties by ultra-low load indentation. Materials Science and Engineering A, 1998, 253(1–2): 151–159.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  36. Fett, T., Computation of the crack opening displacements for Vickers indentation cracks. Report FZKA 6757, Forschungszentrum Karlsruhe, Karlsruhe, Germany, 2002.

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  41. Niihara, K., A fracture mechanics analysis of indentation-induced Palmqvist crack in ceramics. Journal of Materials Science Letters, 1983, 2(5): 221–223.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

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

    Book  MATH  Google Scholar 

  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.

    Article  Google Scholar 

  46. Lawn, B.R., Hertzian fracture in single crystals with the diamond structure. Journal of Applied Physics, 1968, 39(10): 4828–4836.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  MATH  Google Scholar 

  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.

    Article  Google Scholar 

  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. 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.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Taihua Zhang.

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 11302231, 11025212 and 11272318).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Feng, Y., Zhang, T. Determination of Fracture Toughness of Brittle Materials by Indentation. Acta Mech. Solida Sin. 28, 221–234 (2015). https://doi.org/10.1016/S0894-9166(15)30010-0

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1016/S0894-9166(15)30010-0

Key Words

Navigation