Introduction
Thermoplastic polyurethane (TPU) is a class of highly non-linear polymers with great properties for many modern applications that require a sustainable material. In this article I will demonstrate how you can find and calibrate a suitable material model for one specific material of this class, viz. Elastollan from BASF. What is really cool is that I was able to find lots of high-quality freely available experimental data for the material. The majority of the experimental data consisted of long-term creep, but as I will show below, the traditional creep models were not very accurate. The most accurate material model instead was the TNV model from the PolyUMod library.
Experimental Data for Elastollan 1164D
The CAMPUS Plastics material database contains experimental data for a large number of different polymers. For Elastollan 1164D from BASF the data include the following: compression set, DMA temperature sweep, stress-strain as a function of temperature, and creep modulus as a function of time. In my example I will focus on the room temperature behavior. In needed, I could have repeated the approach presented here for other temperatures. The CAMPUS Plastics database allows you to see the control points for the different graphs in table format. It is very easy to use this data in MCalibration, you just need to select the table data, copy it to the clipboard, and then past it into the MCalibration Data tab. There is no need to type any values or extract any data from a graph. Once the data is in MCalibration I recommend clicking on the “Change Number of Data Points” button and selecting “Cubic spline interpolate the data points” in order to increase the number of data points in a smooth way. Figure 1 shows the experimental stress-strain response.
Figure 1. Experimental uniaxial tension data for Elastollan 1164D.
The CAMPUS Plastics database also contains creep modulus data as a function of time for Elastollan 1164D. I don’t fully understand why the creep data is in the form of creep modulus as a function of time. I think it isย more interesting to see the creep strain as a function of time. As I think about, if the material was linear viscoelastic then the creep modulus would be independent of the applied stress, which is clearly is not in this case, so perhaps that is a reason to plot creep modulus data. Fortunately it is super easy to convert creep modulus to creep strain using Hook’s law. I performed this conversion using a Google sheet, and then copied the creep data into the MCalibration Data tab. That is quick and easy. Figure 2 shows the experimental creep data that I used for the study. Note that the creep data goes from 1 hr to 11 years. Not too bad!
Figure 2. Expermimental creep data for Elastollan 1164D,
Results: Ansys Linear Elastic with Strain-Hardening Creep
Figure 3 compares the best fit of the Ansys linear elastic model with strain-hardening creep to the available experimental data for Elastollan. I discussed this model in more detail in this article. The average error for the model predictions is 16.2%. Not very good.
Figure 3. Predictions from the Ansys linear elastic model with strain-hardening creep.
Results: Ansys Linear Elastic with Time-Hardening Creep
Figure 4 compares the best fit of the Ansys linear elastic model with time-hardening creep to the available experimental data for Elastollan. I discussed this model in more detail in this article. The average error for the model predictions is 16.7%. Not very good.
Fig 4. Predictions from the Ansys linear elastic model with time-hardening creep.
Results: PolyUMod Bergstrom-Boyce (BB)
Figure 5 compares the best fit of the PolyUMod Bergstrom-Boyce (BB) model to the available experimental data for Elastollan. The average error for the model predictions is 15.2%. Not very good.
Figure 5. Predictions from the PolyUMod BB model.
Results: Abaqus Parallel Rhelological Framework (PRF)
Figure 6 compares the best fit of the Abaqus PRF model to the available experimental data for Elastollan. The average error for the model predictions is 11.7%. The model predicts the creep trends better, but the predictions are still not very good.
Figure 6. Predictions from the Abaqus PRF model
Results: PolyUMod TN Model
Figure 7 compares the best fit of the PolyUMod TN model to the available experimental data for Elastollan. The average error for the model predictions is 9.4%. The model predicts the creep trends even better than the Abaqus PRF model, but as will be shown in the next section the TNV model is even better.
Figure 7. Predictions from the PolyUMod TN model.
Results: PolyUMod TNV Model
I saved the most accurate material model to the last! Figure 8 compares the best fit of the PolyUMod TNV model to the available experimental data for Elastollan. This model consists of two parallel networks, each having a yeoh hyperelastic element in series with a power-flow element. The average error for the model predictions is 5.1%. The predictions are really good. This is the material model that I recommend for this material.
Figure 8. Predictions from the PolyUMod TNV model.
Summary Elastollan Creep Study
Here is a comparison between the different material models. The PolyUMod TNV models is the most accurate models for Elastollan 1164D. If you have not tried the PolyUMod models, then request a free trial license.
