Performance of Standard Statistical Distributions for Modeling Glass Fracture

Abstract

Experimental data on the strength of new annealed float glass tested in an ambient environment was collected. A comparison was made between four standard distributions, the normal, lognormal, Gumbel and Weibull, with respect to the performance in modelling the strength. The Weibull distribution outperformed the normal and lognormal distributions when the data contained edge only failure origins. When the data was selected to contain surface only failure origins it is indicated that the extreme value distributions performed poorly. The Weibull model is known to have a basis in a failure-mechanism concept based on the weakest-link principle. The Gumbel distribution can also be derived from failure-based mechanics and be associated with certain types of flaw size distribution. The Weibull model, however, is a better choice for a failure model of glass edge strength compared to the normal and lognormal distributions and at least as good as a Gumbel distribution. The surface strength is complicated to model and none of the standard distributions which were examined are capable of producing a proper model. The sample size also has a profound impact on the performance of the surface strength models.