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An investigation of the interrelationships between strength, crack‐resistance ( R ‐curve) characteristics, and grain size for alumina ceramics has been carried out. Results of identation‐strength measurements on high‐density aluminas with uniform grain structures in the size range 2 to 80 μm are presented. A theoretical fit to the data, obtained by adjusting parameters of a constitutive frictional‐pullout relation in a grain‐bridging model, allows determination of the critical microstructural parameters controlling the R ‐curve behavior of these aluminas. The primary role of grain size in the toughness characteristic is to determine the scale of grain pullout at the bridged interface. It is shown that the strength properties are a complex function of the bridged microstructure, governed at all but the finest grain sizes by the stabilizing effect of the R ‐curve. The analysis confirms the usual negative dependence of strength on grain size for natural flaws that are small relative to the grain size, but the dependence does not conform exactly to the −1/2 power predicted on the basis of classical “Griffith‐Orowan” flaws. The analysis provides a self‐consistent account of the well‐documented transition from “Orowan” to “Petch” behavior.
Chantikul et al. (1990) studied this question.