On the Applicability of the Weibull Distribution to Model Annealed Glass Strength and Future Research Needs

Abstract

The applicability of the Weibull distribution to model the strength of glass, the existence of a size effect on the strength and the need for a non-destructive testing of the strength are discussed and reviewed. There are a growing number of studies that put into question the applicability of the Weibull distribution to model annealed glass fracture data. A recent study indicates that the breakage stresses are uncorrelated with the surface area, in violation of the size effect which entails the Weibull model. It is shown in this paper, however, that there is a size effect, as evidenced in an objective way by hypothesis testing using the likelihood ratio statistic. In numeric simulations it is shown that, given sample sizes of 30 specimens and the Weibull distribution being assumed, it is necessary to employ specimens which vary in surface area by a factor of about two at least, in order to detect the size effect with a success rate in excess of 0.95. To increase the use of soda-lime-silica glass in load-bearing components, however, there is a need for non-destructive testing methods, such as non-linear ultrasonic techniques. Non-destructive testing could be used not only to single out the weakest glass panes during manufacture, thus decreasing the variation in strength among as-received specimens, but also by other parties in the construction sector, such as in routine inspections on-site. Suitable stochastic models can be used together with such testing methods to develop a non-destructive strength grading of glass products.