Rheological behaviour and modelling of semi-solid Sn-15% Pb alloy

Abstract

The rheological behaviour and modelling of a semi-solid, Sn-15% Pb alloy characterized by a special coaxial-cylinder rheometer over a wide range of process conditions is reported. In particular, the effect of shear rate $$\left( {\dot \gamma } \right)$$ , volume fraction of solid (f s), and cooling rate on the apparent viscosity (η) of the semi-solid Sn-15% Pb alloy under isothermal and various cooling conditions was studied. Based on the experimental data, the shear rate used in preparing the semi-solid alloy as well as the volume fraction of solid have the most dominant effects on the rheological properties of the semi-solid Sn-15% Pb alloy. A viscosity model expressed as $$\eta \left( {\dot \gamma ,f_s } \right) = \left( {1 - f_s /f_s^* } \right)^{ - m\left( {\dot \gamma } \right)} \eta _\infty \left( {f_s } \right)\left\{ {1 + \left[ {\dot \gamma ^ * \left( {f_s } \right)/\dot \gamma } \right]^a } \right\}^{n/a}$$ is proposed in which f s * is the critical solid fraction at which the apparent viscosity goes to infinity, η∞ (F s) corresponds to the asymptotic viscosity at infinity shear rate, and $$\dot \gamma ^ * \left( {f_s } \right)$$ characterizes the transition shear rate between the power-law and Newtonian regions. finally, measurements with a differential scanning calorimeter were made and used to correlate the temperature and volume fraction of solid which, in turn, was corroborated with available data from the literature.