A Simple Estimation Method of Weibull Modulus and Verification with Strength Data

Abstract

This study examines methods for simplifying estimation of the Weibull modulus. This parameter is an important instrument in understanding the statistical behavior of the strength of materials, especially those of brittle solids. It is shown that a modification of Robinson’s approximate expression can provide good estimates of Weibull modulus values (m) in terms of average strength (<σ>) and standard deviation (S): m = 1.10 <σ>/S. This modified Robinson relation is verified on the basis of 267 Weibull analyses accompanied by <σ> and S measurements. Estimated m values matched normally obtained m values on average within 1%, and each pair of m values was within ± 20%, except for 11 cases. Applications are discussed, indicating that the above relation can offer a quantitative tool based on the Weibull theory to engineering practice. This survey suggests a rule of thumb: ductile metal alloys have Weibull moduli of 10 to 200.

Keywords

• Weibull modulus
• estimation methods
• modified Robinson relation
• strength data
• observed datasets
• large-scale data