Simulation of Glass Fracture using Voronoi Random Field Tessellations

Within this paper the mathematical foundation, deduction, calibration and application of a Machine Learning inspired simulation approach for the prediction of fracture patterns of thermally pre-stressed glass via tessellations over stochastic point processes is shown. The method is called ‘BREAK'(Bayesian Reconstruction and Prediction of Glass Breakage Patterns) and allows the fast simulation of glass fracture patterns under preservation of certain fracture pattern statistics. The model is based on the combination of an energy criterion of linear elastic fracture mechanics (LEFM) and the statistical analysis of the fracture pattern of tempered glass in order to determine characteristics of the fragmentation pattern (e.g. fragment size, fracture intensity, etc.) within an observation field. The modelling approach consists of the idea, that the final fracture pattern is a Voronoi tessellation induced by a stochastic point process, whose parameters can be inferred by statistical evaluation of pictures of several fractured glass specimen. By calibration of a stochastic point process and consecutive tessellation of the region of interest statistically identically distributed realisations of fracture patterns can be generated. Within this article, the application of the method is shown for different levels of thermal pre-stress for certain glasses. It is found, that the proposed method is superior in wall-clock time and statistical accuracy over existing methods.