# DYNAMICS OF RESIDUAL STRESS FORMATION IN GLASS AND ITS MODELING

2018;
: 38-43
Authors:
1
Lviv Polytechnic National University

For the purpose of mathematical modeling of the process ofstressformation in glass, 6x25x100 mmfloat glasssampleswere tempered. During thetemperingthe change ofstresses and thetemperature ofinner and outer layers of glasswerefilmed witha digital camera.Obtainedresults almost completely coincided with the results obtained by R. Gardon.

The analysis of literary data showed that the dynamics of changes of residual stresses cantake placeby twodifferent mechanisms: with the change of the sign of surface stresses and the gradual increase of theirvaluewithout the signchange. The first (low-temperature) mechanism occurs when the glass is cooled atthetemperaturethat islower than the softeningone, and the second (high temperature) occurs when the glass is cooled atthetemperature that is greater than the specified temperature.

It is shown thatthe development of themathematical model requiresthe consideration ofdifferential values of thermal expansion and modulus of elasticity of glass atthegiven temperature. It was noted that the TCLE ofglass gainsthemaximum value at thesofteningtemperature of glass and subsequently decreases when the glass transition temperatureis reached. The modulus of elasticity, on the contrary, atthesoftening temperature is equal to zero, andlaterit acquires a certain value, which is almost unchanged after the glass transition temperature.

The calculation formulas and values ofphysical parameters that were usedduring thedevelopingof themathematical model are presented in the work. The obtained results of the calculation showed that the change of the sign of instant stressesoccurswhenthe temperature ofglasssurfaceis lowerthanTg (the firstsecond ofcooling). Total transient stresses change their sign when the temperature of the middle layer is close to the temperatureofTg (the3rdsecond ofcooling). The maximumvalueofinstantstressescorresponds to the maximum difference between the temperatures of the middle and the surface layer, which occurs when the temperature of the middle layer reaches the valueofTg (3.2seconds ofcooling).

The obtained results of calculations almost coincide with the values of surface stresses obtained experimentally.

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