Relationship between strain energy and fracture pattern morphology of thermally tempered glass for the prediction of the 2D macro-scale fragmentation of glass

This work deals with the prediction of glass breakage. A theoretical method based on linear elastic fracture mechanics (LEFM) merged with approaches from stochastic geometry is used to predict the 2D-macro-scale fragmentation of glass. In order to predict the fragmentation of glass the 2D Voronoi tesselation of distributed points based on spatial point processes is used. However, for the distribution of the points influence parameters of the fracture structure are determined. The approach is based on two influencing parameters of fragment size delta and fracture intensity lambda, which are described in this paper. The Fragment Size Parameter describes the minimum distance between the points and thus the size of a fragment. It is derived from the range of influence of the remaining elastic strain energy in a single fragment taking into account the LEFM based on the energy criterion of Griffith. It considers the extent of the initial elastic strain energy U-0 before fragmentation obtained from the residual stress as well as a ratio of the released energy eta due to fragmentation. The Fracture Intensity Parameter describes the intensity of the fragment distribution, and thus the empirical reality of a fracture pattern. It can be obtained by statistical evaluation of the fracture pattern. In this work, the fracture intensity is determined from the experimental data of fracture tests. The intensity of a fracture is the quotient of the number of fragments in an observation field and its area and is assumed to be constant in the observation filed. The fracture intensity and the correlation between a constant intensity and the Fragment Size Parameter was determined. The presented methodology can also generally be used for the prediction of fracture patterns in brittle materials using a Voronoi tesselation over random fields.