Extraction of Weibull Parameters of Fiber Strength from Means and Standard Deviations of Failure Loads and Fiber Diameters

• Published in: Journal of the American Ceramic Society Vol. 84; no. 3; pp. 588 - 592
• Main Author: Parthasarathy, Triplicane A.
• Format: Journal Article
• Language: English
• Published: Westerville, Ohio American Ceramics Society 01-03-2001; Blackwell; Wiley Subscription Services, Inc
• Subjects: Applied sciences; Building materials. Ceramics. Glasses; Ceramic and carbon fibers; Ceramic industries; Chemical industry and chemicals; Exact sciences and technology; fibers; simulation; Technical ceramics; Weibull statistics; Silicon Carbides; Mechanical properties; Standard deviation; Fracture load; Mean error; Weibull distribution; Diameter; Ceramic fiber
• ISSN: 0002-7820; 1551-2916
• DOI: 10.1111/j.1151-2916.2001.tb00703.x

The errors in using an average fiber diameter to calculate the mean strength (ςm), Weibull reference strength (ς0), and Weibull modulus (m) from failure loads of fibers were examined experimentally. Although the use of an average diameter gave very good estimates of ςm, the error in the Weibull parameters (ς0 and m) was significant, which supported the recent simulation results. Computational approaches to reduce these errors have been considered, and a numerical procedure to extract the Weibull parameters from the means and standard deviations of the load and fiber diameter has been proven feasible, provided the sample population is large. Parametric studies have shown that sample populations of ∼175 are required to obtain results within an error of 10%. The recommended sample populations for commercial fibers are 75–200, depending on the scatter in the fiber diameter and the acceptable error.