9.5.3. Recommended Models and Parameters

Consider the typical wall shear rate in the extrusion process. If a constant viscosity is observed around , the Maxwell or Oldroyd-B model is recommended. If shear thinning occurs around , the PTT or Giesekus model is recommended. If qualitative information on the macromolecular behavior is required, it can also be interesting to consider using the DCPP model.

For filled materials, such as rubber, the Leonov model can also be considered, but the large number of unknowns involved warns against having unrealistic modeling ambitions.

Both single- and multi-mode models are acceptable for a 2D model, but a single-mode model is strongly recommended for a 3D model.

For a single-mode model, select a relaxation time on the order of . For a two-mode model, select one relaxation time < and one > , with no more than one decade between relaxation times. For a three-mode (or more) model, select relaxation times < and > , with no more than one decade between relaxation times.

For a strain-hardening material (for example, LDPE), a low value can be specified for the PTT model’s ε or the Giesekus model’s α. Values of 10-3 to 10-2 are typical. For strain-thinning or moderate strain-hardening materials (for example, LLDPE or HDPE), a higher value—typically about 0.1—can be specified. Also, for strain hardening materials, the DCPP model can be used with a large enough value of q (number of arms).

For the simulation of the flow of filled materials, the use of the Leonov model can be a good idea. The model involves several parameters, and have received reasonable default values. It is worth mentioning that the Leonov model involves the calculation of several tensors, and that the use of a multi-mode model can be computationally expensive.

Finally, for very large flow simulations, it may be relevant to consider the “simplified viscoelastic model" suggested in Simplified Viscoelastic Model, suited for extrusion simulation. Here, the identification of parameters is based on rheometric information, such as viscosity and swelling versus the flow rate. Typically, the first normal viscosity equals the shear viscosity by default, while a relaxation time function and a weighting factor have to be identified in order to reproduce the swelling behavior. That is, a 2D axisymmetric flow simulation is required for parameters identification.

In the automatic fitting procedure, it is preferable to consider the data in the range of shear rates of interest, typically one decade above and one below. If data extrapolation is necessary, it should be done over no more than one decade. Also, use appropriate weighting factors (see Weighting Measured Data) if some data are more reliable than others.

The whole shear viscosity curve for the model may differ from measurements at low shear rates, but this can generally be disregarded. Indeed, low shear rates are encountered only in a few areas of the flow, and involve usually a fraction of the total flow rate, such that the total impact on the momentum is negligible.