Continuum Mechanics and Thermodynamics

, Volume 2, Issue 4, pp 279–299 | Cite as

An analytical approach for the calculation of stress-intensity factors in transformation-toughened ceramics

  • W. H. Müller


Stress-induced transformation toughening in Zirconia-containing ceramics is described analytically by means of a quantitative model: A Griffith crack which interacts with a transformed, circular Zirconia inclusion. Due to its volume expansion, a ZrO2-particle compresses its flanks, whereas a particle in front of the crack opens the flanks such that the crack will be attracted and finally absorbed. Erdogan's integral equation technique is applied to calculate the dislocation functions and the stress-intensity-factors which correspond to these situations. In order to derive analytical expressions, the elastic constants of the inclusion and the matrix are assumed to be equal.


Zirconia Integral Equation Analytical Approach Elastic Constant Volume Expansion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Stevens, R.: An Introduction to Zirconia. Magnesium Elektron Publication No. 113, 2nd Edn. 1986Google Scholar
  2. 2.
    Heuer, A. G.: Transformation Toughening in ZrO2-Containing Ceramics. J. Amer. Ceram. Soc. 70 (1987) 689Google Scholar
  3. 3.
    Claussen, N.: Umwandlungsverstärkte keramische Werkstoffe. Z. Werkstofftech. 13 (1982) 138Google Scholar
  4. 4.
    Claussen, N.; Rühle, M.: Design of ZrO2-Toughened Ceramics. Adv. in Cer., Vol. 3. Ohio: Columbus 1981Google Scholar
  5. 5.
    Evans, A. G.: Toughening Mechanisms in Zirconia Alloys. Adv. in Cer., Vol. 12. Ohio: Columbus 1984Google Scholar
  6. 6.
    Amazigo, J. C.; Budiansky, B.: Interaction of Particulate and Transformation Toughening. J. Mech. Phys. Sol. 36 (1988) 581Google Scholar
  7. 7.
    Müller, W. H.: Numerical Methods for the Description of “Ceramic Steels” (ZrO2 Containing Ceramics). Fracture Control of Engineering Structures, Vol. III. 2129, 1986Google Scholar
  8. 8.
    Müller, W. H.: The Exact Calculation of Stress Intensity Factors in Transformation Toughened Ceramics by Means of Integral Equations. Int. J. Fract. 41 (1989) 1Google Scholar
  9. 9.
    Isida, M.: Method of Laurent Series Expansion for Internal Crack Problems. In: Mechanics of Fracture I. Methods of Analysis and Solutions of Crack Problems. Ed. by G. C. Sih. Leyden: Noordhoff 1973Google Scholar
  10. 10.
    Erdogan, F.; Gupta, G. D.; Ratwani, M.: Interaction Between a Circular Inclusion and a Arbitrarily Oriented Crack. J. Appl. Mech. (1974) 1007Google Scholar
  11. 11.
    Erdogan, F.; Gupta, G. D.: The Inclusion Problem with a Crack Crossing the Boundary. Int. J. Fract. 11 (1975) 13Google Scholar
  12. 12.
    Schmeidler, W.: Integralgleichungen mit Anwendungen in Physik und Technik. Leipzig: AVG 1950Google Scholar
  13. 13.
    Erdogan, F.; Gupta, G. D.; Cook, T. S.: Numerical Solution of Singular Integral Equations. In: Methods of Analysis and Solutions of Crack Problems. Ed. by G. C. Sih. Leyden: Noordhoff 1973Google Scholar
  14. 14.
    Erdogan, F.; Biricikoglu, V.: Two Bonded Half Planes with a Crack Going Through the Interface. Int. J. Engng. Sci. 11 (1973) 745Google Scholar
  15. 15.
    Müller, W. H.: Quantitative Modelle zur Beschreibung der Phasenumwandlung und der Erhöhung des Bruchwiderstandes in zirkondioxidhaltigen Keramiken. Thesis. Berlin: TU 1986Google Scholar
  16. 16.
    Rossmanith, H. P.: Grundlagen der Bruchmechanik. Wien, New York: Springer 1982Google Scholar
  17. 17.
    Sih, G. C.: Handbook of Stress-Intensity-Factors. Bethlehem, Pa.: Lehigh-University 1973Google Scholar
  18. 18.
    Bronstein, I. N.; Semendjajew, K. A.: Taschenbuch der Mathematik. 16. Aufl. Zürich, Frankfurt/Main, Thun: Verlag Harri Deutsch 1976Google Scholar
  19. 19.
    Gradshteyn, I. S.; Ryzhik, I. M.: Table of Integrals, Series and Products. Second printing. London: Academic Press 1981Google Scholar

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • W. H. Müller
    • 1
  1. 1.Hermann-Föttinger-InstitutTechnische Universität BerlinBerlin 12

Personalised recommendations