ISO 20501:2019 pdf – Fine ceramics (advanced ceramics, advanced technical ceramics)一Weibull statistics for strength data.
1 Scope This document covers the reporting of uniaxial strength data and the estimation of probability distribution parameters for advanced ceramics which fail in a brittle fashion. The failure strength of advanced ceramics is treated as a continuous random variable. Typically, a number of test specimens with well-defined geometry are brought to failure under well-defined isothermal loading conditions. The load at which each specimen fails is recorded. The resulting failure stresses are used to obtain parameter estimates associated with the underlying population distribution. This document is restricted to the assumption that the distribution underlying the failure strengths is the two-parameter Weibull distribution with size scaling. Furthermore, this document is restricted to test specimens (tensile, flexural, pressurized ring, etc.] that are primarily subjected to uniaxial stress states. Subclauses 6.4 and 6.5 outline methods of correcting for bias errors in the estimated Weibull parameters, and to calculate confidence bounds on those estimates from data sets where all failures originate from a single flaw population (i.e. a single failure mode). In samples where failures originate from multiple independent flaw populations (e.g. competing failure modes), the methods outlined in 6.4 and 6.5 for bias correction and confidence bounds are not applicable. 2 Normative references There are no normative references in this document. 3 Terms and definitions For the purposes of this document, the following terms and definitions apply. ISO and IEC maintain terminological databases for use in standardization at the following addresses: -ISO Online browsing platform: available at https://ww.iso.org/obp – IEC Electropedia: available at http://www.electropedia.org/
3.1.2 censored data strength measurements (i.e. a sample) containing suspended observations such as that produced by multiple competing or concurrent flaw populations Note 1 to entry: Consider a sample where fractography clearly established the existence of three concurrent flaw distributions (although this discussion is applicable to a sample with any number of concurrent flaw distributions). The three concurrent flaw distributions are referred to here as distributions A, B, and C. Based on fractographic analyses, each specimen strength is assigned to a flaw distribution that initiated failure. In estimating parameters that characterize the strength distribution associated with flaw distribution A, all specimens (and not just those that failed from type-A flaws) shall be incorporated in the analysis to ensure efficiency and accuracy of the resulting parameter estimates. The strength of a specimen that failed by a type-B (or type-C) flaw is treated as a right censored observation relative to the A flaw distribution. Failure due to a type-B [or type-C) flaw restricts, or censors, the information concerning type-A flaws in a specimen by suspending the test before failure occurs by a type-A flaw. The strength from the most severe type-A flaw in those specimens that failed from type-B (or type-C) flaws is higher than (and thus to the right of) the observed strength. However, no information is provided regarding the magnitude of that difference. Censored data analysis techniques incorporated in this document utilize this incomplete information to provide efficient and relatively unbiased estimates of the distribution parameters. 3.1.3 competing failure modes distinguishably different types of fracture initiation events that result from concurrent (competing) flaw distributions 3.1.4 compound flaw distribution any form of multiple flaw distribution that is neither pure concurrent, nor pure exclusive
5.2 This document provides two approaches, method A and method B, which are appropriate for different purposes. Method A provides a simple analysis for circumstances in which the nature of strength-defining flaws is either known or assumed to be from a single population. Fractography to identify and group test items with given flaw types is thus not required. This method is suitable for use for simple material screening. . Method B provides an analysis for the general case in which competing flaw populations exist. This method is appropriate for final component design and analysis. The method requires that fractography be undertaken to identify the nature of strength-limiting flaws and assign failure data to given flaw population types. 5.3 In method A, a strength data set can be analysed and values of the Weibull modulus and characteristic strength (m, σθ] are produced, together with confidence bounds on these parameters. If necessary, the estimate of the mean strength can be computed. Finally, a graphical representation of the failure data along with a test report can be prepared. It should be noted that the confidence bounds are frequently widely spaced, which indicates that the results of the analysis should not be used to extrapolate far beyond the existing bounds of probability of failure. A necessary assumption for a valid extrapolation (with respect to the tested effective volume Veff and/or small probabilities of failure) is that the flaw populations in all considered strength test pieces are of the same type.