Polylactic acid (PLA) is a biodegradable polymer commonly used in 3D printing applications. Like many polymer melts, PLA exhibits non-Newtonian flow behavior, meaning that its viscosity depends on the applied shear rate. To model the viscosity of PLA as a non-Newtonian fluid, you can use a rheological model, which is a mathematical equation that describes the relationship between shear stress and shear rate.

Several rheological models can@@ be used to describe the non-Newtonian flow behavior of PLA, including:

τ = K γ^n

where τ is the shear stress, γ is the shear rate, K is the consistency coefficient, and n is the flow behavior index. The values of K and n can be determined by fitting the power law equation to experimental data.

τ = K (1 + (λγ)^2)^((n-1)/2)

where λ is a characteristic time constant and n is the flow behavior index. The values of K, λ, and n can be determined by fitting the Carreau-Yasuda equation to experimental data.

τ = K (1 + (λγ)^a)^((n-1)/a)

where a is a shape parameter. The values of K, λ, n, and a can be determined by fitting the Cross equation to experimental data.

To model the viscosity of PLA as a non-Newtonian fluid, you will need to perform rheological experiments to measure the shear stress and shear rate under various conditions. You can then fit the rheological model of your choice to the experimental data to determine the values of the model parameters. This will allow you to predict the viscosity of PLA under different shear rates and temperatures, which can be useful for optimizing 3D printing processes and understanding the flow behavior of PLA.

Bashar Aljawarneh Husam Bayoud

I want to apply the power rule to calculate viscosity and need exact values of 'K' and 'n' at 200 degrees centigrade for any sample to put in the Ansys simulation.

As M.A.H above, said the curve-fit used has to be determined experimentally, few non-newtonian fluids have viscosity correlations available, especially the temperature dependent aspects.

However, I note that you are looking at nozzle flows: if that is the case viscosity will probably not have a significant effect, as the flow is likely to be turbulent. Here: DP = K . Velocity head,

where K is the characteristic number of head losses for the orifice design used.

In general, PLA behaves as non-Newtonian fluid at molten phase, but NOT simply as a power-law fluid.

It follows the dependency of dynamic viscosity upon shear rate and temeprature follows a more complicated relationship, that is the Cross-WLF model (see: https://help.autodesk.com/view/MFIA/2023/ENU/?guid=MoldflowInsight_CLC_Ref_Materials_sim_math_models_Cross_WLF_viscosity_model_html).

If you have the Autodesk Moldflow Data Fitting, you can easily insert rheological data at different shear rates and temperatures in "Raw viscoity data" menu (see: attached figure) and select Your fitting model (Cross-WLF, by default).

Then, the program will perform the best fit; from my experience, this method is very fast and accurate (very high correlations).

Otherwise, you can also use the "fit" Matlab function, but the implementation is time consuming; if you still want to use the power-law model (only K and n parameters), then Matlab "fit" function is a good choice.

The correctness of simulation outcomes in polymer modeling depends a lot upon the rhelogical model you choose.

Best regards,

AP