Modeling of delayed elasticity in glass

We have developed a numerical model based on finite element analysis (FEA) with a viscoelastic material model coupling stress relaxation and structural relaxation, using the Mauro-Allan-Potuzak (MAP) non-equilibrium viscosity equation as the shift function. A modeling study of the delayed elasticity behavior in glass under different equilibrium viscosity and non-equilibrium viscosity conditions is conducted. The delayed elastic response is found to be well described by a stretched exponential function with three parameters: the maximum delayed elasticity response, the retardation time of delayed elasticity response, and the stretching exponent of delayed elasticity response. The delayed elasticity magnitude is seen to increase with lower values of the stretching exponent bstress. At equilibrium viscosity, the retardation time shows a linear relationship with the stress relaxation time. However, when the temperature drops sharply in the non-equilibrium viscosity cases, the delayed elastic response may be frozen resulting in a lower magnitude for the delayed elasticity and the retardation time is not linear any more with the stress relaxation time. The delayed elasticity stretching exponent is seen to vary slightly at different relaxation times and normalized delayed elasticity response can roughly be collapsed into a single master curve. The impact of liquid fragility is also studied.