Weibull silicon nitrides

Fig. 1 a) Strength data of a silicon nitride ceramic tested in four point bending (4PB) in a Weibull plot and b) the relative frequency distribution of flaw sizes. The data points were determined by fracture experiments. 

Additionally, the insitu-reinforced silicon nitride materials exhibit an increased Weibull modulus [86]. This has two reasons firstly, the concentration of the large, strength-limiting grains is so high that the defect size has a narrow size distribution and secondly, these materials exhibit pronounced R-curve behaviour, which makes the material tolerant of larger cracks. The high thermal shock resistance of these materials also seems to be connected with this fact [30]. 

N. Hirosaki, Y, Akimune and M. Mitomo, Effect of Grain Growth of P-Silicon Nitride on Strength, Weibull Modulus and Fracture Toughness , J. Am. Ceram. Soc., 76, 1993, 1892-94. 

Another feature of this material is its narrow distribution of the fracture strength. When the strength distribution was expressed in Weibull statistics, the Weibull modulus was 46 - substantially higher than the value of 26 obtained for a conventional, self-reinforced silicon nitride. Thus, the seeded and tape-cast silicon nitride showed a synergistic improvement in all of the important fracture attributes, such as fracture strength, fracture toughness, and strength stability (Weibull modulus). 

Figure 12.8 Bending strength test results for a silicon nitride ceramic. Plotted is the probability of failure versus the strength. The straight lines represent Weibull distributions. The measured Weibull distribution has a mod ulus of m = 15.5, and the characteristic strength is 844 MPa. Also...

Figure 12.11 Strength distribution of a silicon nitride ceramic (same data as in Figure 12.8). A Weibull distribution function (solid curve) and a Gaussian distribution function (dashed curve) are fitted to the data. The data are plotted (a) in...

This example, involving a heavy-duty diesel ceramic exhaust valve (Corum et al. ), was selected to contrast failure probability predictions for power law. Walker law and a proof test condition. The valves were made of NT-551 silicon nitride material. Table 1 contains a summary of the Weibull and SCG parameters obtained from four-point flexure bars at three different temperatures (Andrews et al. ). CARES/Life was used to obtain these parameters using the raw data listed in Andrews et al.. Data to obtain values for the Walker law parameters did not exist, so assumed values for Qv and A2/A1 were used. 

A log-log plot of failure probability versus stress will have a slope of m, the Weibull modulus. Figure 1.2 shows the failure distributions of silicon carbide and silicon nitride at room and elevated temperatures. 

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