A statistical model for the failure of glass plates due to nickel sulfide inclusions

Nickel Sulfide (NiS) inclusions can provoke the rupture of thermally treated glass due to a phase transformation with volume increase that stresses the surrounding glass. Starting from a Pareto statistics for the population of inclusion sizes, from an assumed kinetics of the phase transformation, a micro-mechanically motivated model provides the statistical characterization of the probability of spontaneous failure of glass during lifetime. A distinction based upon the composition of NiS is used to discuss the effects of the heat soak test (HST), where glass remains at high temperature for a certain time to speed-up the phase transformation and destroy those elements with critical inclusions. Three functions a la Weibull for the probability of spontaneous rupture during lifetime are theoretically derived for the case of no HST, short HST, and long HST. In particular, the probability of collapse for long HSTs depends upon the holding time in the oven. An explanatory example shows the potentiality of the model for optimizing the HST parameters toward a target probability of failure, but experimental campaigns are needed for a proper calibration.