Journal of Materials Science

, Volume 17, Issue 1, pp 235–239 | Cite as

Transformation toughening

Part 2 Contribution to fracture toughness
  • F. F. Lange


Two approaches are taken to determine the contribution of a stress-induced phase transformation to the fracture toughness of a brittle material. Both approaches result in an expression for the critical stress intensity factor,Kc, of
$$K_c = \left[ {K_0^2 + \frac{{2RE_c V_i (|\Delta G^c | - \Delta U_{se} f)}}{{(1 - v_c^2 )}}} \right]^{1/2} ,$$
whereK0 is the critical stress intensity for the material without the transformation phenomenon, (¦ΔGc¦−Usef) is the work done per unit volume by the stress field to induce the transformation,Ec andνc are the elastic properties,Vi is the volume-fraction of retained, high-temperature phase andR is the size of the transformation zone associated with the crack. It is assumed that only those inclusions (or grains) close to the free surface of the crack will contribute to the fracture toughness; thus,R the inclusion size. The chemical free-energy change associated with the transformation, ¦ΔGc¦, will govern the temperature and alloying dependence of the fracture toughness.


Brittle Free Surface Phase Transformation Fracture Toughness Intensity Factor 
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Copyright information

© Chapman and Hall Ltd 1982

Authors and Affiliations

  • F. F. Lange
    • 1
  1. 1.Structural Ceramics GroupRockwell International Science CenterThousand OaksUSA

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