Thermal effects in the numerical simulation of the thermoforming of multilayered polymer sheets

This paper mainly treats the thermal effects during the thermoforming process while most of the previous analyses consider an isothermal deformation. A non isothermal three dimensional finite element model of the thermoforming process is proposed. It couples the thermal equations in the thickness and mechanical equations on the mean surface of the sheet. The mechanical resolution is done by a finite element method using a membrane approximation. The deformation is driven by a pressure difference through the sheet. The thermal resolution uses a one dimension finite element method in the thickness with convection or conduction at the surface and dissipation of mechanical energy. The polymer cooling is very efficient during the contact with the tools. The coupling is done by the thermal dependent rheology. The respective contributions of friction and thermal effects in the thickness of the part during the process are discussed. The model also considers a possible multilayered material, with specific rheological parameters inside each layer. The rheology of a polystyrene was measured under elongation as a function of temperature, strain and strain-rate and described by a visco-plastic law. The predictions of the model were compared with measurements on an instrumented thermoforming machine and with the local thickness of axisymmetrical parts and with 3-D parts thermoformed with the same polystyrene.