Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

A model for crack initiation in elastic/plastic indentation fields

  • 1293 Accesses

  • 374 Citations

Abstract

A model is proposed for the initiation of microfracture beneath sharp indenters. Using a simple approximation for the tensile stress distribution in the elastic/plastic indentation field, in conjunction with the principle of geometrical similarity, fracture mechanics procedures are applied to determine critical conditions for the growth of penny-like “median cracks” from sub-surface flaws. The analysis provides a functional relationship between the size of the critical flaw and the indentation load necessary to make this flaw extend. Initiation is well defined (unstable) only if the critical flaw lies within a certain size range; outside this range, large flaws can extend stably but small flaws can not extend at all. No flaws can extend below a characteristic minimum load, values of the indentation variables at this load accordingly providing useful threshold parameters. These quantities involve the intrinsic deformation/fracture parameters, hardness and toughness, in a fundamental way, thereby establishing a basis for materials selection in fracture-sensitive applications.

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

References

  1. 1.

    B. R. Lawn andT. R. Wilshaw,J. Mater. Sci. 10 (1975) 1049.

  2. 2.

    A. G. Evans andT. R. Wilshaw,Acta. Met. 24 (1976) 939.

  3. 3.

    Idem, J. Mater. Sci.,12 (1977) 97.

  4. 4.

    F. C. Frank andB. R. Lawn,Proc. Roy. Soc. Lond. A299 (1967) 291.

  5. 5.

    B. R. Lawn andM. V. Swain,J. Mater. Sci. 10 (1975) 113.

  6. 6.

    B. R. Lawn andE. R. Fuller,ibid. 10 (1975) 2016.

  7. 7.

    B. R. Lawn, T. Jensen andA. Arora,ibid. 11 (1976) 575.

  8. 8.

    A. G. Evans andE. A. Charles,J. Amer. Ceram. Soc. 59 (1976) 371.

  9. 9.

    R. Hill, “Plasticity” (Clarendon Press, Oxford, 1950) p. 97.

  10. 10.

    D. Tabor, “The Hardness of Metals” (Clarendon Press, Oxford, 1951).

  11. 11.

    G. C. Sih, “Handbook of Stress Intensity Factors” (Lehigh University Press, Lehigh, 1973).

  12. 12.

    B. R. Lawn andT. R. Wilshaw, “Fracture of Brittle Solids” (Cambridge University Press, Cambridge, 1975) Chs. 1–3.

Download references

Author information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Lawn, B.R., Evans, A.G. A model for crack initiation in elastic/plastic indentation fields. J Mater Sci 12, 2195–2199 (1977). https://doi.org/10.1007/BF00552240

Download citation

Keywords

  • Tensile Stress
  • Stress Distribution
  • Crack Initiation
  • Simple Approximation
  • Large Flaw