Estimation of flaw parameters for holes in glass using maximum likelihood estimator

Currently, a widely accepted, objective, and repeatable procedure for determining the flaw parameters used in the glass failure prediction model does not exist. Historically flaw parameters were primarily based on statistical measures and the researchers’ interpretation of experimental data. This paper advances a procedure to calculate the flaw parameters used in the two-parameter form of the glass failure prediction model for holes based on the well-known maximum likelihood estimator method based on destructive testing. Additionally, the paper presents a three-parameter form of the glass failure prediction model for holes to incorporate the residual compressive surface stress for heat-treated glass into the load resistance. The paper also advances a procedure to calculate the flaw parameters for the three-parameter form of the glass failure prediction model based on the maximum likelihood estimator method. The work herein uses failure test data from a set of historical four-point bending tests of glass beams with a hole located at the geometric center to illustrate the procedure to determine flaw parameters. Because the flaw parameters for the three-parameter glass failure prediction model are a function of the residual compressive surface stress, a method is presented to choose the residual compressive surface stress value to base the other two parameters upon. An example design scenario provides insight into the variations between the two- and three-parameter glass failure prediction models and the effect the residual compressive surface stress has on the load resistance.