Calendering of thermoplastics: models and computations

John Vlachopoulos (JV) started his polymer processing career with the process of calendering. In two landmark papers with Kiparissides, C. and Vlachopoulos, J. (1976). Finite element analysis of calendering. Polym. Eng. Sci. 16: 712–719; Kiparissides, C. and Vlachopoulos, J. (1978). A study of viscous dissipation in the calendering of power-law fluids. Polym. Eng. Sci. 18: 210–214 he introduced the Finite Element Method (FEM) to solve the governing equations of mass, momentum, and energy based on the Lubrication Approximation Theory (LAT). This early work was followed by the introduction of wall slip (with Vlachopoulos, J. and Hrymak, A.N. (1980). Calendering poly(vinyl chloride): theory and experiments. Polym. Eng. Sci. 20: 725–731). The first 2-D simulations for calendering PVC were carried out with Mitsoulis, E., Vlachopoulos, J., and Mirza, F.A. (1985). Calendering analysis without the lubrication approximation. Polym. Eng. Sci. 25: 6–18. In the intervening 35 years, other works have emerged, however our understanding has not been drastically improved since JV’s early works. Results have also been obtained for pseudoplastic and viscoplastic fluids using the general Herschel-Bulkley constitutive model. The emphasis was on finding possible differences with LAT regarding the attachment and detachment points of the calendered sheet (hence the domain length), and the extent and shape of yielded/unyielded regions. The results showed that while the former is well predicted by LAT, the latter is grossly overpredicted. More results have been obtained for 3-D simulations, showing intricate patterns in the melt bank. Also, the transient problem has been solved using the ALE-FEM formulation for moving free-boundary problems. The results are compared with the previous simulations for the steady-state and show a good agreement. The transient simulations capture the movement of the upstream and downstream free surfaces, and also provide the attachment and detachment points, which are unknown a priori. Finding these still remains the prevailing challenge in the modeling of the calendering process.

Experiments and Modelling of Calender Processing for Shear Thinning Thermoplastics between Counter Rotating Rolls with Differential Velocities

This paper is concerned with a floor application calendering processing using both a PVC and a Polyolefin formulation within a two roll calender. The rheology of both formulations was measured using the Rheoplast, a specific capillary rheometer. Experiments with various velocity differentials were performed and the roll separating force and the sheet exit temperature were measured for each case. An isothermal model based on the lubrication approximations hypothesis together with a power-law behavior for the molten polymer has been developed. Due to the difference between the rotation velocities of the two cylinders, the problem is no longer symmetric and the integration of the generalized Reynolds equation requires taking into account various velocity profiles. The resulting pressure profile enables computation of the roll separating force. The agreement between the model and experiments performed with the PVC formulation at various velocity differentials is fair; however for the Polyolefin formulation there is a significant difference which means that the model for this new formulation needs to be improved.

Influence of the Calendering Step on the Adhesion Properties of Coextruded Structures

The coupled coextrusion calendering process of multilayer thermoplastic sheets has been studied. The structure of the film has been observed, the density of chemical links at the interface and the adhesion between the coextruded layers have been measured. There are some controversial features about the influence of calendering parameters. Several models of increasing complexity are proposed to master the process and its influence on adhesion. A multilayer thermal model accounting for the crystallization kinetics of both polymers allows defining qualitatively the temperature field especially at the interface between the two layers. A multilayer thermo-mechanical model provides quantitative figures on the stress, shear, elongation and temperature fields in the coextruded film and especially at the interface. Relationships between these parameters, density of chemical links at the interface, crystalline structure of the sample and peeling forces are discussed.