# Predicting Creep of Polycarbonate

## Introduction

Back in 2010 I gave a presentation on how to predict the creep response of thermoplastic materials. In that study I extracted stress-strain and creep data from a product brochure from Sabic for a Lexan resin. I thought it would be fun to redo that study using modern software and material models. The current version of MCalibration, for example, enables quick and accurate material model calibration. The first 2 pages from my original study are shown below.

The goal of this study is to compare the predictions from a few different material models to the following experimental data sets  consisting of monotonic tension and creep at different stress levels. All calibration results shown here were generated using MCalibration.

## Results: Linear Viscoelasticity

The following figure shows the results from an Abaqus Neo-Hookean hyperelastic model with a 6 term Prony series. The average error in the model predictions is 14.7% – which is not very good. The predicted monotonic stress-strain curve is almost linear, and the predicted creep rates do not scale correctly compared to the experimental data.

## Results: Ansys Linear Elastic with Creep

One material model choice in Ansys is linear elastic with a creep model. My favorite creep model is the strain hardening model:

$$\dot{\varepsilon}_{creep} = C1 \cdot \sigma^{C2} \cdot \varepsilon^{C3} \cdot \exp[-C4/T]$$.

The model predictions from this model are shown in the following figure. The average error of the predictions is 9.9%.

## Results: Ansys Elastic-Plastic with Creep

A more realistic Ansys material model is the MISO plasticity model with strain hardening creep. The average error of the predictions from this model is 6.5% – which is not too bad.

## Results: PolyUMod Bergstrom-Boyce Model

The Bergstrom-Boyce (BB) model is a non-linear viscoelastic material model developed for rubber-like polymers. Hence, it is not really a candidate for polycarbonate (PC), but since the BB-model is available in almost all FE codes, it is still interesting to see how well it can predict the response of the PC. The figure shown below show that the average error in the predictions is 12.2%. Which is clearly not very good.

## Results: PolyUMod TNV Model

The PolyUMod TNV model is my current favorite material model for all polymers. It is a modular model consists of 1-3 non-linear viscoplastic networks. In this case I used a Yeoh hyperelastic network in parallel with a 2 power-law flow networks with yield evoluation. The predictions from the TNV mode are  shown below. The average error in the predictions is 3.8% – which is excellent.

## Summary

The following figure compares the different models. As expected, the TNV model is the winner.

Here’s a short video of a PC hook being loaded to failure using Abaqus/Explicit and the TNV model.

### Calibrate a Material Model using DMA Data

Tutorial on how to calibrate a material model to both stress-strain and DMA data.

### Plot Viscoplastic Strain in PolyUMod and MCalibration

Description of how to plot the viscoplastic strain magnitude when using PolyUMod or MCalibration.

### Calibrate a PolyUMod Material Model with Failure

Tutorial showing how to calibrate a PolyUMod TNV stress-strain and failure model to experimental data.