Remaining stress-state and strain-energy in tempered glass fragments

When tempered glass breaks, it shatters into relatively small pieces depending on the residual stress state in the glass. This has been known for centuries and is currently used in standards for classifying whether a piece of glass is tempered or not. However, the process of fragmentation is complex and only a few, relatively simple, models have been suggested for predicting the fragment size. The full theoretical explanation is still to be found and this work aims at providing another brick to the puzzle. The strain-energy present in tempered glass is obviously contributing to the fragmentation process and some authors e.g. Barsom (J Am Ceram Soc 51(2):75, 1968), Gulati (Glass processing days, Tamglass Engineering Oy, Tampere, 1997), Warren (Fractography of glasses and ceramics IV, Alfred University, Alfred, 2001) and Tandon and Glass (Fracture mechanics of ceramics—active materials, nanoscale materials, composites, glass and fundamentals, Springer, Houston, 2005) have proposed models for the fragments size based on an energy approach. Often an estimate of the remaining strain energy in the fragment is used; which leaves the questions: (a) what parameters are important for the remaining strain energy? (b) what is the magnitude of the remaining strain energy? (c) is there a simple way to estimate the remaining strain energy?
The present paper applies a quasi-static finite element model in order to answer these questions. In the present paper an example on the deformation and the stress redistribution in a fragment is given. Furthermore, a parametric investigation on the strain energy remaining in cylindrical- and prismatic fragments is given. It is shown, that there exists a simple relation between the thickness of the glass pane and the remaining strain energy in the fragment. A simple method for estimating the remaining strain energy in a fragment of a given shape and initial residual stress state is presented.