The Efficiency of Normal Distribution in Statistical Characterization of the Experimentally Measured Strength for Cerami
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JMEPEG https://doi.org/10.1007/s11665-020-05352-1
The Efficiency of Normal Distribution in Statistical Characterization of the Experimentally Measured Strength for Ceramics Jianghong Gong
, Bin Deng, and Danyu Jiang
Submitted: 9 June 2020 / Revised: 2 November 2020 / Accepted: 8 November 2020 It has been assumed that the measured strength of ceramics follows a Weibull distribution. However, there is still no sound evidence to confirm this assumption. On the contrary, some studies have shown that other distributions such as normal distribution may describe more appropriately the measured strength data than Weibull distribution. In this paper, an extensive comparison between the efficiencies of normal and Weibull distributions in describing the strength variations was performed based on the analyses of 27 strength datasets, each containing 30 data measured on different ceramics. It was shown based on Anderson–Darling (A–D) test that, in most cases, normal distribution may give a satisfactory description for the data. The analysis results reveal that, at least for the small datasets generally used in laboratory evaluation, it seems to be unnecessary to perform a Weibull analysis because a simple normal distribution analysis is accurate enough for the statistical characterization of strength for the examined materials. Keywords
failure analysis, mechanical testing, normal distribution, strength variation, structural ceramics, Weibull distribution
1. Introduction It has been well known that the measured strength of a given ceramic exhibits a larger scatter (Ref 1, 2). Such scatter may be attributed mainly to the intrinsic brittleness of ceramics. According to Griffith theory (Ref 3), the largest, most severe stresses and the most sharp defects, i.e., the dominant crack, in the test specimen or the component will initial fracture. For the brittle ceramics, the natural variability in size, location, and severity of the dominant crack would result in an inherent scatter in the measured strength. Another important factor which results in the scatter in measured strength is the manufacture of the test specimen or the component (Ref 4-7). Cutting, grinding, and polishing, the usually adopted procedure for specimen preparation, may introduce residual stresses and cracks in the surface and near-surface of the test specimen, thereby altering the distribution of the defects (Ref 8, 9). In addition, the measured strength also depends on the test conditions, such as specimen size, stress distribution, stress state, etc. (Ref 4, 10, 11).
Jianghong Gong, State Key Laboratory of New Ceramics and Fine Processing, School of Materials Science and Engineering, Tsinghua University, Beijing 100084, China; Bin Deng, Department of the Prosthodontics, The General Hospital of Chinese PLA, Beijing 100853, China; and Danyu Jiang, State Key Laboratory of High Performance Ceramics and Superfine Microstructure, Shanghai Institute of Ceramics, Shanghai 200050, China. Contact e-mail: [email protected].
Journal of Materials Engineering and Perfor
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