Model
The model predicts the frictional properties between a woven fabric embedded in a molten thermoplastic material and a flat rigid surface. The model calculates the the friction force (or the average shear stress) as a function of the normal force (or the average pressure), the sliding velocity and the temperature. The woven fabric and the tool surface are considered undeformable, separated by a generalised Newtonian fluid. For each bundle contour, the Reynolds' equation can be solved:
where p is the pressure, h the bundle contour, η the viscosity, x the spatial coordinate and U the sliding velocity. The model results in a bearing and friction force per unit width for a single surface contour. Extension to a general model for fabric-tool friction is now straightforward. First, the scheme has to be applied to both the warp and weft bundle contours of the fabric. Second, the forces per unit width must be multiplied with the corresponding bundle widths and third, the forces must be multiplied with the corresponding number of bundles present in the unit cell area.
The next figure shows the scheme of the full model:
Schematics of the model
It starts with extracting the bundle contour properties from the weave geometry and selecting an appropriate rheological model that
calculates the viscosity of the matrix material. Then the meso model solver routine is entered. This routine uses a Newton Raphson (NR) procedure to find the bearing force of a unit cell. Inside the meso model solver, the Reynolds' equation solver ensures that the Reynolds'
equation fulfills the applied boundary conditions.
The model implementation requires the specification of the geometry. The model uses the conceptually simple elliptic description:
This is only a very brief explanation of the model. For more details, have a look at:
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