Using a Hierarchical Weibull model to Predict Failure Strength of Different Glass Edge Profiles

Abstract

The edge strength of glass is analyzed using a Weibull statistical framework based on 78 data samples from a range of experiments recorded in literature. Based on the analysis, a 45 MPa strength value (computed as the lower bound in a one-sided confidence interval at the 75% level for the 5-percentile in the distribution) could be conservatively used with arrised, ground and polished edges when related to a reference length of 100 mm at an applied stress rate of 2 MPa/s. The size effect can be represented by the usual weakest-link scaling formula with the Weibull modulus taken to be 8.0, 12.0, 8.0 and 6.5, respectively, for as-cut, arrised, ground and polished edges. It is estimated that static fatigue is best accounted for with a value of stress corrosion parameter about n = 16. The results are obtained with random sampling MC in a hierarchical modelling approach with the Weibull parameters treated as nested random variables. By accounting for the influence of glass supplier as a mixed-effect in a linear statistical model, it is found that supplier effects are significant and important to consider along with others due to, e.g., stress rate and edge length exposed to maximum stress. The data samples which are limited to glass tested in an ambient environment using four-point bending fixture, show that Weibull statistics generally scatter considerably. Numerical investigations with random sampling show that shape parameter estimates scatter substantially when sample size is limited, which can explain some of the observed variability in shape more so for ground and polished edges than for as-cut and arrised. For the as-cut edge, it is suggested that the shape parameter is scale-dependent. The Weibull parameters are also estimated using a clustered likelihood estimator under the condition that the shape factor has constant value for each edge type.