Prediction of PA12 melt viscosity in Laser Sintering by a Time and Temperature dependent rheological model

Abstract

A rheological model was derived from experimental data and has been proposed to predict the viscosity of a Polyamide 12 (PA12) melt as a function of time, temperature and shear rate. In a first step, the rheological model was derived that is mainly based on the well-known three parameter Carreau model. In addition, two shift factors were introduced to the model. The shift factor aT by Arrhenius considers the temperature dependence of the viscosity. A second shift factor aSC (SC: Structural Change) is proposed. This factor describes the structural change that was observed as a significant viscosity build-up, concluded as molar mass build-up and understood as post condensation of PA12 at LS process conditions. In fact, at temperatures and times investigated, the effect on viscosity was found to be of exponential, limited and irreversible growth behaviour. The rate of post condensation is time and temperature dependent. It is assumed that powder bed temperature leads to molar mass build-up of PA12 because of consumption of molecular chains into molecular chain extension. Moreover, the progressing formation of extended molecular chains however decreases molecular movement and finally freezes post condensation. This physiochemical model assumption is expressed in the form of the structural change shift factor aSC that introduces two additional parameters to the rheological model. The parameter aSC,UL corresponds to the upper limit whereas k0 is correlated to the rate of structural change. Furthermore, it was found to be suitable to use individual activation energies for aT and aSC calculation, i.e. to differentiate between flow activation and structural change activation energy. Based on experimental data, rheological model parameters were optimised using a genetic algorithm. The comparison of predicted viscosity with experimental data was found to be in good agreement. Hence, the rheological model is suitable to predict the viscosity of a PA12 as result of a combined LS process time and temperature influences. In a second step, the model was applied in order to calculate the viscosity during the laser sintering process as a function of energy density, by using data for the melt temperature and laser exposure time which were measured on-line with a high-speed-thermal imaging system. Moreover, the effect of structural change on the viscosity of PA12 is shown with respect to LS process time and temperature.