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

Abstract

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 à 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. K E Y W O R D Sfracture mechanics/

How the risk of failure in lifetime of tempered glass depends on the size of NiS inclusions and heat soak test duration

“…In this case, the present model presents no differences with the one already presented in Ref. [17].…”

“…On the other hand, when max ≥ cr,R min (Case B-No HST), the theory deviates from that of Ref. [17]. Reasoning as in Section 3.2.1, one finds where Λ *…”

“…Ref. [17] The probability of breakage in the LT takes the form (2) cr = 0 when 0 < cr,R min ; cr = cr,R min when 0 ≥ cr,R min .…”

“…In order to facilitate the comparison between the two different theories, this is the same case considered in Ref. [17].…”

“…It is important to observe that η can be estimated from field observations, by measuring the volume V 0 that on average contains only one NiS inclusion. 17 Hence, there is no need of a direct determination of R 0 and ΔV, on which η depends: such parameters have been introduced only for the micromechanical characterization of the model. To illustrate, recall that experimental campaigns consider large quantities of material and measure the number and size of inclusions that are there present.…”