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.

Uncertainty Assessment for the Buckling Analysis of Glass Columns with Random Parameters

“…Based on Table 1, the major design issue for glass can be thus expected in the well-known, high natural variability of prestress and strength parameters for such a vulnerable constructional material. Several studies of literature (Nurhuda et al, 2010;Lamela et al, 2014;Veer et al, 2018;Pisano and Carfagni, 2017;Mognato et al, 2017;Kinsella et al, 2018) have been dedicated to the measurement and assessment of these nondeterministic and size-dependent material parameters, hence resulting in specific recommendations and limitation for structural design.…”

“…For all the examined glass columns, the failure configuration is numerically detected as the first attainment of a maximum tensile stress in bending at least equal to the nominal resistance of AN, HS or FT glass respectively, thus 45, 70 and 120 MPa (Table 1). In this study, any kind of variability in the material resistance is disregarded (Kinsella et al, 2018), while imposing random mechanical and geometrical parameters to the set of 800 members (3 glass types).…”

Volume 2: …and SGAMR Goes!

“…Besides, the high variability in the tensile resistance of glass still represents one of the major issues for optimized design of glass structures. In this regard, (Kinsella et al, 2018) focus on the available modeling approaches for the fracture of glass and in particular on the standard statistical distributions.…”