In this report, we analysed the data of 3-point bending tests on Si3N4 and PSZ rectangular bar specimens and ZrO2 round bar specimens. The strength distributions of Si3N4 and PSZ and that of ZrO2 were representd by the multi-modal Weibull distribution and 2-parameter Weibull distribution (mono-modal), respectively. The parameters of the former were estimated with the multi-step maximum likelihood method, and those of the latter with the least square method. Using these parameters, the true stress (stress at the fracture origin) distributions were calculated on the basis of the statistical theory of stress and fracture location. As a result of comparison of the calculated distributions and experimental data, it was found that the both distributions showed good agreement. Furthermore, on the ZrO2 round bar specimens other bending tests were carried out, varying the specimen size and the loading method. Weibull moduli obtained in the tests were not constant. There was a tendency that they increased as the effective size decreased. We discussed the reason of this change, considering the experimental relationship between the crack size and the fracture strength.
In order to investigate the change of strength of ceramics due to the size effect, the strength distribution was simulated by the Monte-Carlo method. The tensile strength, 3-and 4-point bending strength of four kinds of specimens of different sizes were calculated, by using the model of specimens with a number of penny-shaped inner cracks of which diameters followed the prescribed distribution. The strength obtained was plotted on the Weibull probability papers and represented by the 2-parameter Weibull distribution. As some experimental data had indicated, the Weibull modulus had a tendency to increase as the effective size decreased. It became clear that this tendency was caused by the existence of the upper limit of crack strength. The strength distribution function for this model was also expressed and compared with the simulation results. Although the Weibull plot of that function was slightly concave, it showed good agreement with the simulation results. Furthermore, the relation between the mean strength and the effective volume was discussed, using the Weibull statistics. As a result, it was indicated that the Weibull statistics could not explain the change of strength due to the size effect satisfactorily.
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