Size effect of the modulus of rupture in float glass plates

Abstract

This paper investigates the modulus of rupture of float glass plates of different sizes aiming at determining the effect of the plate area on its flexural tensile strength. Currently, the Weibull statistical distribution expression, which is calibrated with test data, is used for estimating the area dependent size effect. The present investigation is based on a theoretical stochastic model that is independent of test data. The numerical analysis simulates large size samples of plates and is based on the glass plate geometry, the boundary conditions, the specific loading data and implements the glass properties through a flaw distribution model characterizing the glass plate material. Very large size samples are required to obtain a converged solution. The model analysis yields higher strengths for smaller plates and the predicted tensile strength depends on the loading method. To eliminate the effect of the loading system on the size effect it was hypothesized that the fracture origin area, rather than the entire plate area, dominates the behavior. The fracture origin area for typical loading systems was determined from the model analyses. Implementation of this hypothesis shows that all tensile strength results for large samples of plates subjected to different loading systems follow a single common size-effect curve, which depends on the fracture origin area and is independent of the loading system. The calculated nonlinear stress ratio spans over almost five orders of magnitude of the plate area, considerably beyond the limited range of plate areas appearing in the literature. Comparison of the theoretically based size effect function with the empirical Weibull based data in the literature, shows similar results for relatively large area plates but an increasing difference for smaller areas, where the extrapolated empirical stress ratio law considerably underpredicts the theoretical results. Comparison of the calculated stress ratio results with test data shows very good agreement.