R'mili M, Godin N, Lamon J
CNRS/Institut National des Sciences Appliquées, CNRS, MATEIS Laboratory, Villeurbanne, France.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 May;85(5 Pt 1):051106. doi: 10.1103/PhysRevE.85.051106. Epub 2012 May 4.
The present paper investigates large sets of ceramic fibre failure strengths (500 to 1000 data) produced using tensile tests on tows that contained either 500 or 1000 filaments. The probability density function was determined through acoustic emission monitoring which allowed detection and counting of filament fractures. The statistical distribution of filament strengths was described using the normal distribution. The Weibull equation was then fitted to this normal distribution for estimation of statistical parameters. A perfect agreement between both distributions was obtained, and a quite negligible scatter in statistical parameters was observed, as opposed to the wide variability that is reported in the literature. Thus it was concluded that flaw strengths are distributed normally and that the statistical parameters that were derived are the true ones. In a second step, the conventional method of estimation of Weibull parameters was applied to these sets of data and, then, to subsets selected randomly. The influence of other factors involved in the conventional method of determination of statistical parameters is discussed. It is demonstrated that selection of specimens, sample size, and method of construction of so-called Weibull plots are responsible for statistical parameters variability.
本文研究了通过对包含500根或1000根细丝的丝束进行拉伸试验所产生的大量陶瓷纤维断裂强度数据（500至1000个数据）。通过声发射监测确定概率密度函数，该监测可检测和计数细丝断裂。细丝强度的统计分布用正态分布来描述。然后将威布尔方程拟合到该正态分布以估计统计参数。两种分布之间获得了完美的一致性，并且观察到统计参数中的散射相当可忽略不计，这与文献中报道的广泛变异性相反。因此得出结论，缺陷强度呈正态分布，并且所推导的统计参数是真实的参数。在第二步中，将传统的威布尔参数估计方法应用于这些数据集，然后应用于随机选择的子集。讨论了传统统计参数确定方法中涉及的其他因素的影响。结果表明，试样的选择、样本大小以及所谓威布尔图的构建方法是统计参数变异性的原因。
