1. Flexural Fracture Strength, Fracture Locations, and Monte Carlo Predictions for a Silicon Nitride by Ten U.S. Laboratories
- Author
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Mattison K. Ferber, V. J. Tennery, Kristin Breder, and Michael G. Jenkins
- Subjects
Flexural strength ,Consistency (statistics) ,Linear regression ,Monte Carlo method ,Statistics ,Materials Chemistry ,Ceramics and Composites ,Fracture (geology) ,Forensic engineering ,Range (statistics) ,Estimator ,Weibull distribution - Abstract
The work reported was conducted to provide a basis for a number of structural ceramic mechanical property standardization activities in the United States, Germany, Japan, and Sweden. A comparison of key property values of a commercial silicon nitride determined in a number of laboratories was a major objective. The work reported was conducted by 10 U.S. laboratories on GN-10 silicon nitride, and represented the U.S. work within an International Energy Agency program including the United States, Germany, Japan, and Sweden. Fracture location analyses showed that fracture location within the inner span often was not a linear function of location within the span. Some of this behavior was explained by random sampling effects based upon simulation predictions, but some was apparently dependent upon friction within the fixtures in spite of efforts to minimize it. Flexural strengths were measured at 25° and 1250°C in air and were analyzed using the two-parameter Weibull model in terms of m and σΘ using both linear regression (LR) and maximum likelihood (ML) methods. Under the measurement conditions for the 10 room-temperature strength sets, the value of the ML estimator for m varied by as much as 36%, while the value for the σΘ parameter estimator varied only 3.3%. The LR estimator for m varied by about 54%. For the high-temperature specimens, the ML estimator for m varied by 48% while the LR estimator varied by 38%. Ranked fracture location analysis showed that the high-temperature fracture locations were more random than those in the room-temperature specimens, and was probably due to friction in the high-temperature fixtures. There was little pin rolling ability in many of the high-temperature fixtures used. Monte Carlo and one-way analysis-of-variance (ANOVA) methods provided insight into the consistency of the strength values. Monte Carlo predictions showed that for room-temperature strength, the maximum likelihood estimator m for all 10 laboratories fit within the 10% and 90% confidence bounds for 30 specimen sets. The dispersion of the high-temperature data was such that the m estimator satisfied the model only at the 1% and 99% confidence levels for the 15 specimen sets. ANOVA results showed that for the room-temperature flexural strength, data from all 10 laboratories were not distinguishable for this evaluator at the 95% confidence level and that scatter within individual data sets was a larger effect than was the variation between the data sets. For the high-temperature data, the results from one laboratory were clearly outside the allowable range at this confidence level.
- Published
- 2004
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