## Introduction

This article examines how accurately many modern material models can predict the large-strain stress response of a polyether ether ketone (PEEK) material. As you will see, the traditional plasticity model are **not** capable of accurately predicting the response of this industrially important material. Only some of the more modern viscoplastic material models have a chance at capturing the experimental response of PEEK, and can be considered a suitable material model for PEEK.

Also see our 4-part article series: “PEEK Calibration Tutorial“.

PolyUMod TNV Model Predictions of PEEK. The TNV model is the most accurate model in the study 🏆

## Experimental Data Used for the PEEK Material Model Study

In this study I used monotonic uniaxial tension data obtained at an engineering strain rate of 0.1/s, and cyclic uniaxial compression data obtained at engineering strain rates of -0.1/s and -0.001/s. To make the data easier to interpret I plotted the approximate true stress-strain response, even thought raw experimental data is engineering stress and strain. All results from the study were generated using MCalibration®. As expected, PEEK exhibits a strain-rate dependent response, and the yield stress softens after macroscopic yield has been reached.

## Results #10: Abaqus Johnson-Cook

The Johnson-Cook predictions have an average error of 36.5%. That is bad, and not surprising since the Johnson-Cook model does not predict the unloading or yield softening response of thermoplastics very well.

## Results #9: Ansys Bergstrom-Boyce

The Ansys Bergstrom-Boyce (BB) model predictions have an average error of 33%. I developed this model for rubber-like materials, and it is not surprising that it is not more accurate for a stiff thermoplastic material like PEEK.

## Results #8: Abaqus Elastic-Plastic Combined Hardening

Since the experimental data contains cyclic data, it is interesting to explore the use of a kinematic hardening plasticity model. Here I tried the Abaqus elastic-plastic model with combined hardening. The average error of this model is 29%. The results look qualitatively better, but the accuracy is still not good.

## Results #7: Abaqus PRF Model with 3 Networks (Yeoh and Power Flow)

The Abaqus PRF models are sometimes accurate for thermoplastics. In this case I tried a 3 network model with Yeoh hyperelasticity and power flow. This is the representation that I use the most when analyzing thermoplastics. See my PRF model summary for more details. The accuracy of this model is 14%, which is not too bad. But as I will show below, other models are even better.

## Results #6: Abaqus PRF Model with 4 Networks (Yeoh and Power Flow)

Switching to a 4 network PRF model improves the average error to a value of 12%. The details of the prediction, however, are not very accurate around the yield point.

## Results #5: Ansys TNM

Since 2021, Ansys has supported the Three Network Model (TNM). This is an advanced viscoplastic material model that often works well for thermoplastics. In this case the average error of the TNM is 11%. This is better than the native Abaqus PRF model.

## Results #4: PolyUMod TN Model

The PolyUMod TN model is very similar to the Ansys TNM. In this case both of these models have an average error of about 11%.

## Results #3: Abaqus PRF Model with 3 Networks (Yeoh and PowerwYEP Flow)

## Results #2: PolyUMod Flow Evoluation Networks (FEN) Model

The FEN model is a PolyUMod material model that is somewhat obsolete. The TNV model is typically more accurate and also runs faster. In this example I calibrated a 4 network FEN model that gives and average error of 8.2%. The predictions look really good.

## Results #1: PolyUMod TNV Model

The winner of the Most Accurate Material Model award goes to the PolyUMod TNV model! This models matches all aspects of the experimental data well, and has an average error of 6.5%.

## Summary PEEK Material Model Study

Here is a summary comparison between the different material models. Three of the models clearly have very high average errors. I would not recommend using any of those models for PEEK. The Abaqus PRF, Ansys TNM, and PolyUMod models are better. As also was the case for thermoplastic-elastomers (see my study here), the TNV model is also the most accurate model for PEEK.

Another way to plot the results is to normalize the error with respect the the most accurate model (here the TNV model). That way it becomes easier to compare the errors between the different models. The following figure shows that the Ansys TNM and PolyUMod TN model predictions are about 65% less accurate than the TNV model. **The best Abaqus-native PRF model has an average error that is 75% larger than for the TNV model.**

If you have not tried the TNV model, then request a free trial license.