Skip to main content

Calculation of Crack Tip Phase Transformation Zones in TZP with the Weight Function Method

  • Chapter
Fracture Mechanics of Ceramics

Abstract

Stabilized zirconia ceramics can undergo a stress-induced tetragonal-to-monoclinic phase transformation. This way, a transformation zone with compressive stresses develops around crack tips, leading to an increase in fracture toughness. The increase in fracture toughness depends on the size of the transformation zone. Therefore, the ability to compute the phase transformation zone at a crack tip is crucial to determine the transformation toughening due to phase transformation. In the case of subcritical phase transformation, the crack tip phase transformation zone has been calculated using the finite element method. In some zirconia ceramics, like ceria-stabilized TZP zirconia ceramics, an autocatalytic phase transformation takes place, leading to large, elongated transformation zones. As this supercritical phase transformation cannot be computed with finite elements, several methods for investigating supercritical phase transformation have been developed. In this paper, a method based on the weight function method will be described.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R.M. McMeeking, A.G. Evans, Mechanics of transformation toughening in brittle materials, J. Am. Ceram. Soc., 65, 242–246 (1982).

    Article  Google Scholar 

  2. B. Budiansky, J.W. Hutchinson, J.C. Lambropoulos, Continuum theory of dilatant transformation toughening in ceramics, Int. J. Sol. Struct., 19, 337–356 (1983).

    Article  Google Scholar 

  3. D.M. Stump, B. Budiansky, Crack-growth resistance in transformation-toughened ceramics, Int. J. Solids Struct., 25, 635–646 (1989).

    Article  Google Scholar 

  4. G.T.M. Stam, E. van der Giessen, P. Meijers, Effect of transformation-induced shear strains on crack growth in zirconia-containing ceramics, Int. J. Sol. Struct., 31, 1923–1948 (1994).

    Article  Google Scholar 

  5. C.S. Yu, D.K. Shetty, M.C. Shaw, D.B. Marshall, Transformation zone shape effects on crack shielding in ceria-partially-stabilized zirconia (Ce-TZP)-alumina composites, J. Am. Ceram. Soc., 75, 2991–2994 (1992).

    Article  CAS  Google Scholar 

  6. S.A. Silling, Numerical studies of loss of ellipticity near singularities in an elastic material, J. Elasticity, 19, 213–239 (1988).

    Article  Google Scholar 

  7. D.M. Stump, The role of shear stresses and shear strains in transformation toughening, Phil. Mag., A 64, 879–902 (1991).

    Article  Google Scholar 

  8. J.D. Eshelby, The determination of the elastic field of an ellipsoidal inclusion, and related problems, Proc. R. Soc. London, A 241, 376–396 (1957).

    Article  Google Scholar 

  9. T. Fett, Application of the weight function and boundary collocation method to the calculation of initial phase transformation zones, Engng. Frac. Mech., 52, 853–863 (1995).

    Article  Google Scholar 

  10. G. Rauchs, Untersuchungen zur tetragonal-monoklinen Phasenumwandlung in Ce02stabilisiertem Zirkonoxid bei mehrachsiger Belastung, PhD-Thesis, University of Karlsruhe, Germany, (1998).

    Google Scholar 

  11. I.W. Chen, P.E. Reyes-Morel, Implication of transformation plasticity in Zr02containing ceramics: Shear and dilatation effects, J. Am. Ceram. Soc., 69, 181–189 (1986).

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer Science+Business Media New York

About this chapter

Cite this chapter

Rauchs, G., Munz, D., Fett, T. (2002). Calculation of Crack Tip Phase Transformation Zones in TZP with the Weight Function Method. In: Bradt, R.C., Munz, D., Sakai, M., Shevchenko, V.Y., White, K. (eds) Fracture Mechanics of Ceramics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-4019-6_1

Download citation

  • DOI: https://doi.org/10.1007/978-1-4757-4019-6_1

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-3370-6

  • Online ISBN: 978-1-4757-4019-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics