Finite element simulation for glass tempering

Abstract

The production of tempered glass for screen protectors has aroused enormous interest in the growing smartphone market, requiring the use of technologies to prevent fractures during production. The Finite Element Method (FEM) was used mainly because of its effectiveness and the possibility of simulating models with complex geometries. In order to cover as many applications as possible, the material chosen for the simulation was soda-lime glass, the most commonly produced glass. The tempering simulation was successfully performed in AbaqusTM software using the Fortran subroutine UEXPAN to estimate the thermal expansion coefficients of each element during cooling in the glass transition range. Analysis of the stress history during hardening proved useful in preventing the material from fracturing, since the maximum tensile and compressive stresses appear long before the sample reaches room temperature. Residual stresses at the end of hardening represent only around 1-10% of these maximum stresses. The analysis also showed that the stresses generated depend on the geometry of the sample and the cooling rate. Furthermore, it was observed that the higher the surface/volume ratio, the higher the critical cooling rate, at which the mechanical limits of the glass are reached, and the easier it is to perform tempering without fracturing the sample. In the end, it was possible to obtain a critical cooling rate of ~7 °C/s for the production of smartphone screen protectors, meaning that air-tempering is possible (1-10 °C/s). An interesting aspect of the work was the possibility of visually studying, step by step, the evolution of stresses. Initially, there was greater thermal contraction on the outside of the sample, followed by greater thermal contraction in the bulk, resulting in the well-known profile of compressive stresses on the surface and tensile stresses in the bulk. Finally, the finite element model developed in this work showed good qualitative representation, exhibiting some phenomena predicted by theory, such as the inversion of stresses during tempering, or that occur in practice, such as stress striations in voluminous samples. Thus, the FEM proved to be a powerful tool for simulating glass tempering, being possible to improve the model by including the phenomenon of stress relaxation during the glass transition phase and the variation of glass transition temperature as a function of cooling rate.