A5 Residual Stress and Spontaneous Fracture (NiS Inclusions)

Topic

A nickel sulfide inclusion trapped within this tempered glass since its manufacture undergoes a phase transformation over time—from its alpha form to its beta form. The alpha form, in which the inclusion is trapped during glass production, is metastable at room temperature; consequently, over months or even years, it transforms into the beta form, which is the stable form at that temperature. The fact that this transformation takes so long explains why the fracture described by this model can occur with a delay—long after the tempered glass has been installed and put into service.

The transformation of the nickel sulfide inclusion from the alpha to the beta form causes the inclusion to expand; the beta form occupies a larger specific volume than the alpha form, and because the inclusion is rigidly encased by the surrounding glass, this expansion cannot occur freely. As the inclusion attempts to expand within the rigid surrounding glass, a localized stress field is generated around it, consistent with Eshelby's theory regarding an inclusion undergoing a volume change within an elastic matrix.

Furthermore, the fact that this expansion occurs within the tempered glass's core tensile zone—a zone established in another model in this series describing the tempering process—can trigger spontaneous fracture. The additional stress generated by the inclusion's expansion combines with the tensile stress already present in the core zone due to the tempering process itself; if the sum of these stresses exceeds the glass's tolerance limit, the glass fractures spontaneously, without any external load acting upon it. For this reason, this model—which centers on the inclusion of nickel sulfide—depends directly on another model within the same set: the one defining the core tension zone of the tempered glass. The existence of this core tension zone is a necessary condition for the expansion of an inclusion—at the precise point where it is trapped—to meet the spontaneous fracture criteria described by the model. Since the location of the inclusion within the glass is, in practice, impossible to predict beforehand, the timing and location of the resulting spontaneous fracture—should it occur—are equally unpredictable.

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