Finite element simulation for glass tempering
Resumen
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.
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