Modeling of Paste Extrusion in Semi-Solid State

A constitutive rheological equation is proposed for the paste extrusion of polytetrafluoroethylene (PTFE) that takes into account the continuous change of the microstructure during flow, through fibril formation. The mechanism of fibrillation is captured through a microscopic model for a structural parameter, ξ. This model essentially represents a balance of fibrillated and unfibrillated domains in the PTFE paste through a first-order kinetic differential equation. The rate of fibril formation is assumed to be a function of the strain rate and a flow type parameter, which describes the relative strength of straining and rotation in mixed type flows. The proposed constitutive equation consists of shear-thinning and shear-thickening terms, the relative contribution of the two being a function of ξ. Finite element simulations using the proposed constitutive relation predict correctly the variations of the extrusion pressure with the apparent shear rate and die geometrical parameters.