Viscosity Model dialog

This dialog allows the fitting and/or entry of the shear viscosity and juncture loss model coefficients. These models directly influence the material's behavior within the flow simulation. The following sections describe the both the models and fitting of its coefficients.

Cross-WLF Viscosity Model

The Cross-WLF viscosity model describes the temperature, shear rate, and pressure dependency of the shear viscosity for thermoplastic materials.

The viscosity model is given by the following equation:

where:

• is the melt viscosity (Pa s)
• is the zero shear viscosity or the 'Newtonian limit' in which the viscosity approaches a constant at very low shear rates,
• is the shear rate (1/s)
• is the critical stress level (called Tau* in the dialog) at the transition to shear thinning, determined by curve fitting, and
• is the power law index in the high shear rate regime, determined by curve fitting.

The zero shear viscosity is given by the equation:

where

• is the temperature (K)
• is the glass transition temperature, determined by curve fitting,
• 
• is the pressure (Pa), and where
• , , , and are data-fitted coefficients.

The glass transition temperature is given by the equation: where is a data-fitted coefficient.

Note: Tau* is related to the relaxation time of the material, D1 is related to the Tg, and A1 and A2 can be used to determine the thermal expansion coefficient.

Cross-WLF Viscosity Fitting

The values of D1, D2, D3, A1, A2, Tau* and n are the Cross-WLF coefficients used to control the shear viscosity fit. If enabled, the Fit Viscosity button will vary the coefficients to minimize the RMS error and produce the optimum fit to the raw viscosity data entered in the Viscosity Input dialog.

If you do not want a coefficient to vary during the fitting process, you can select the adjacent Keep Constant Fixed checkbox.

Note: Fitting of the D3 parameter used to capture the materials pressure dependency requires viscosity measured at elevated exit pressure levels. So the fitting of this parameter requires non-zero exit pressures to be present in the Viscosity Input data.

Viscosity Plot

Plots the viscosity versus shear rate at specific temperature groupings. If multiple Die L/D are present the plot will also be grouped by the Die L/D values.

Pressure Plot

If enabled this will plot the pressure calculated from the raw viscosity data versus shear rate at specific temperature groupings.

Juncture Loss

This is the pressure drop that occurs when the melt passes through a large change in path diameter, such as from the end of the runner to the gate. The software can calculate this loss, using the Bagley correction constants, C1 and C2, where the following equation is used:

where:

• Pe is the entrance pressure

• is the wall shear stress

Note: Juncture Loss coefficients can only be fit using Capillary viscosity data generated with multiple Die L/D ratios. If entrance pressures have been supplied, then the Juncture Loss will be fit to these values based on the above equation. If they have not been supplied then the C1 and C2 values will be used together with the Cross-WLF coefficients to fit the Capillary viscosity values.

For materials that do not have juncture loss data supplied, appropriate values can be estimated from the following table and entered into the material data:

Juncture Loss Plot

If enabled the Juncture Loss plot button will show the raw Capillary Entrance Pressures versus Wall Shear Stress. The fit of the Juncture Loss model is also shown in the plot. This fit can be manually altered by moving the ends of the line, which will modify the C1 and C2 parameters to suit this manually moved fit.

Note: If the Capillary viscosity inputted was not Bagley corrected, then the Cross-WLF coefficients should be refit after any adjustments of C1 and C2. This updates the shear viscosity fit based on the new Juncture Loss coefficients.

RMS

This is the error percentage used when optimising the data fit.