The in-plane expansion of fractured thermally pre-stressed glass panes -An equivalent temperature difference model for engineering glass design

The present paper is concerned with deriving simplified design equations and charts for modelling in-plane expansion of fractured thermally pre-stressed soda-lime-silica glass panes using the method of equivalent temperature differences (ETD) together with a thermal expansion analogy for strains. The starting point is a theoretical method based on linear elastic fracture mechanics merged with approaches from stochastic geometry to predict the 2D-macro-scale fragmentation of glass. The approach is based on two influencing parameters of glass: (i) fragment particle size, delta, and (ii) fracture particle intensity, lambda, which are related to the pre-stress induced strain energy density, U-D, before fracture. Further Finite Element (FE) analysis of single cylindrical glass particles allow for establishing functional relations of the glass fragment particle dimensions, the pre-stress level and the resulting maximum in-plane deformation. Combining the two parts of two-parameter fracture pattern modelling and FE results on fragment expansion, formulas and engineering design charts for quantifying the in-plane expansion of thermally pre-stressed glass panes due to fracturing via an ETD approach is derived and provided within this paper. Two examples from engineering practice serve as demonstrators on how to use our ETD approach to compute the equivalent temperature difference and resulting internal forces as well as deformations. This approach serves furthermore as a basis to estimate secondary effects (such as fracture-expansion-induced deformations or stresses) on support structures or remaining parts of glass laminates in form of handy ETD load cases within analytical as well as FE analysis.