Numerical simulation of viscoplastic material flow through extrusion dies.

Abstract

Various flows through extrusion dies have been studied for viscoplastic materials exhibiting a yield stress (Bingham fluids). These include entry flows from a reservoir into a die and exit flows from a die into the atmosphere under the influence of a pressure gradient. The materials are modelled by a constitutive equation of Bingham fluids with yield stress, as modified by Papanastasiou to include an exponential term for low strain rates and to avoid discontinuities. This equation applies everywhere in the flow field in both yielded and practically unyielded regions. The Finite Element method is used to discretize the domain and solve the set of conservation and constitutive equations along with the proper boundary conditions. The results are given as a function of a dimensionless Bingham number (Bi) or yield stress ($\tau\sbsp{y}{*}$). The emphasis is on determining the extent and shape of unyielded/yielded regions as well as the extrudate swell for planar and axisymmetric geometries. It is found that reduction in swelling occurs as the amount of yield increases, which becomes contraction and then it asymptotically increases to reach 1 as Bi $\to \infty$. The results for the pressure necessary to push the material through are used to determine the excess pressure losses over and above the Newtonian values, giving rise to entrance, exit and the total end correction. These are found to be substantially higher than the Newtonian values as Bi increases, reaching values close to 4 times their Newtonian counterparts. The results correctly capture the location and extent of solid and fluid regions in such flows, which is of considerable interest for industrial purposes. The combined effect of entry and exit flow under non-isothermal conditions has been also studied in an effort to simulate a visco-elastico-plastic material for which experimental data are available in the literature. (Abstract shortened by UMI.)