陶瓷断裂强度Weibull统计分析的可靠性  

Onthe Reliability of Weibull Statistical Analysis for Fracture Strength of Ceramics

作　　者：龚江宏[1] GONG Jiang-Hong(Key Laboratory of New Ceramics and Fine Processing,Tsinghua University,Beijing 100084,China)

机构地区：[1]清华大学新型陶瓷与精细工艺国家重点实验室,北京100084

出　　处：《现代技术陶瓷》2022年第5期335-352,共18页Advanced Ceramics

摘　　要：脆性陶瓷材料的断裂强度通常表现出显著的离散性,其统计性质需要借助于一个Weibull分布函数加以描述;而作为Weibull分布函数中的一个重要参数,Weibull模数则通常用于描述断裂强度实测值的离散程度。从统计学上说,对于同一种材料,采用点估计方法由不同的强度样本得到的Weibull模数估计值之间总是会存在一些偏差,这就导致了两个基本问题的出现,即:(1)如何评估Weibull模数估计值与其真实值之间的差异?(2)采用多大容量的强度样本才可能获得较为可靠的Weibull模数值?此外,断裂强度服从Weibull分布这一说法仅仅是一个假设,在断裂强度并不服从Weibull分布的情况下,采用Weibull分布描述强度数据是否可以对材料的可靠性给出准确评价?在过去几十年间,学者们借助于MonteCarlo模拟技术对上述问题进行了较为深入的研究。本文简要回顾了这些研究所取得的成果,以期对Weibull分布在陶瓷材料断裂强度统计性质研究中应用的可靠性做出一个较为完整的描述。For brittle ceramics,Weibull distribution is generally adopted for the description of the statistical property of the measured fracture strength,which usually exhibits a large scatter.As an important parameter of Weibull distribution,Weibull modulus is considered to be an index of the dispersion extent of the measured fracture strength.From the viewpoint of statistics,different values of Weibull modulus would be obtained with one of the conventional point-estimation methods by analyzing different strength sample measured for a given material,thereby resulting in two basic issues which need to be understood:(1)how to evaluate the difference between the estimated value of Weibull modulus and its true value?(2)how many strength data are enough for the reliable determination of Weibull modulus?In addition,it is only an assumption that the measured fracture strength of ceramics follows Weibull distribution.If this assumption is not true,then another issue arises:if the reliability of the examined materials can be evaluated accurately by using Weibull distribution to describe the measured strength?During the past decades,these above-mentioned issues have been studied extensively based on Monte Carlo simulations.This paper gave a brief summary for the main results obtained in these studies,in order to establish a complete description for the reliability of applying Weibull distribution to describe the statistical properties of the measured fracture strength ofceramics.

关 键 词：WEIBULL分布 MONTECARLO模拟 统计性质 断裂强度 

分 类 号：TQ174[化学工程—陶瓷工业]