Prony series spectra of structural relaxation in N-BK7 for finite element modeling.

Structural relaxation behavior of N-BK7 glass was characterized at temperatures 20 °C above and below T(12) for this glass, using a thermo mechanical analyzer (TMA). T(12) is a characteristic temperature corresponding to a viscosity of 10(12) Pa·s. The glass was subject to quick temperature down-jumps preceded and followed by long isothermal holds. The exponential-like decay of the sample height was recorded and fitted using a unique Prony series method. The result of his method was a plot of the fit parameters revealing the presence of four distinct peaks or distributions of relaxation times. The number of relaxation times decreased as final test temperature was increased. The relaxation times did not shift significantly with changing temperature; however, the Prony weight terms varied essentially linearly with temperature. It was also found that the structural relaxation behavior of the glass trended toward single exponential behavior at temperatures above the testing range. The result of the analysis was a temperature-dependent Prony series model that can be used in finite element modeling of glass behavior in processes such as precision glass molding (PGM).