Maximum likelihood estimator method to estimate flaw parameters for different glass types

Abstract

Glass is commonly used in architectural applications, such as windows and in-fill panels and structural applications, such as beams and staircases. Despite the popularity of structural glass use in buildings, an engineering design standard to determine the required component or member strength for design loads does not exist. Glass is a brittle material that lacks a well-defined yield or ultimate stress, unlike ductile materials. The traditional engineering methods used to design a ductile material cannot be used to design a glass component. Glass fails in tension primarily due to the presence of microscopic flaws present on the surface that acts as stress concentrators. Hence, to accurately estimate the strength of glass, the presence of surface flaws need to be addressed. The glass failure prediction model is a probabilistic model that addresses the microscopic flaws in the form of two parameters, along with other factors such as load duration, environmental conditions, glass component geometry, and boundary condition to determine the strength of glass. The flaw parameters associated with the glass failure prediction model describes the size, shape, and number of surface flaws present on the surface of the glass. Due to the microscopic nature and variability of the surface flaws, it is impractical to attempt to measure the flaw parameters directly. Instead, the flaw parameters are numerically estimated from experimental failure test data. However, there is no universally recognized method to select the best flaw parameters and this omission leads to subjective approaches inducing variability. Recognizing a lack of a standardized and repeatable method to estimate flaw parameters, the universal, simple, and easy-to-use statistical tool, the maximum likelihood estimator method, is used in this work to estimate the surface flaw parameters for different glass failure prediction models such as glass failure prediction model for glass with holes, for annealed monolithic glass, and heat-treated monolithic glass. Published experimental data related to each model were collected and used to show the working principle of the maximum likelihood estimator method. Thus, the work herein removes variability associated with the historically subjective method and allows researchers to objectively and repeatably estimate flaw parameters for different glass failure prediction models consistently.