## Introduction

It is often a good idea to run stress relaxation or creep experiments in order to get enough data for a material model calibration. One common question, however, is for how long time you should run these relaxation or creep tests. It is quite expensive to run experimental tests that take hours to run, short-term tests are nicer! In this article I will show that it is actually sufficient to run shorter-term stress-relaxation and creep tests in order to calibrate a suitable material model.

## Experimental Data and Method

I used the experimental data in Figure 1 to perform the study. This data is from a HDPE that was tested in uniaxial tension at three different strain rates, and in tensile stress relaxation at 3% and 7% strain for about 17 hours. The plan of the study was to first calibrate a material model to only the cyclic tension data, and then see if that material model can also predict the stress relaxation response. The results from that study will help determine the importance of using stress relaxation tests for the material model calibration. In a second study I calibrated a material model to the cyclic tension data and the first portion of the two stress relaxation tests. That material model can then be examined by comparison with the longer term stress relaxation data.

*Figure 1. Experimental data used for the study. (Click on image for high res).*

## Material Models

Since it is not clear if the results from this study will depend on the material model, I decided to analyze the results from two different material models: the PolyUMod TNV model and the PolyUMod TN model. Both of these models are usually good at predicting the stress-strain response of thermoplastics, and are therefore good candidates for the study.

## Results: PolyUMod TNV Model

Figure 2 shows a comparison between the experimental data and predictions form the TNV model calibrated to the uniaxial tension data only. The figure shows that the model captures the cyclic tension data with very high accuracy, but is a bit off for the stress relaxation predictions. Figure 3 through 6 show the results for cases where the material model was calibrated to different amounts of the stress relaxation data. The results indicate short-term relaxation data is sufficient for accurate material model calibration.

*Figure 2. Comparison between experimental data and predictions from the TNV model calibrated to cyclic tension data only.*

*Figure 3. Comparison between experimental data and predictions from the TNV model calibrated to the cyclic tension data and the first 1 minute of the stress relaxation data.*

*Figure 4. Comparison between experimental data and predictions from the TNV model calibrated to the cyclic tension data and the first 10 minutes of the stress relaxation data.*

*Figure 5. Comparison between experimental data and predictions from the TNV model calibrated to the cyclic tension data and the first 1 hour of the stress relaxation data.*

*Figure 6. Comparison between experimental data and predictions from the TNV model calibrated to all cyclic and 17 hours of stress relaxation data.*

Relaxation Time | Average Material Model Error |
---|---|

No relaxation | 4.5% |

1 min | 3.2% |

10 min | 3.5% |

1 hour | 4.0% |

17 hours | 2.8% |

## Results: PolyUMod TN Model

To examine if the results from the previous section depend on the material model, I repeated the study using the PolyUMod TN model. As is typically the case, the TN model slightly less accurate than the TNV model. The results show that also in this case theย short-term relaxation data is sufficient for accurate material model calibration.

*Figure 7. Comparison between experimental data and predictions from the TN model calibrated to cyclic tension data only.*

*Figure 8. Comparison between experimental data and predictions from the TN model calibrated to the cyclic tension data and the first 1 minute of the stress relaxation data.*

*Figure 9. Comparison between experimental data and predictions from the TN model calibrated to the cyclic tension data and the first 10 minutes of the stress relaxation data.*

*Figure 10. Comparison between experimental data and predictions from the TN model calibrated to the cyclic tension data and the first 1 hour of the stress relaxation data.*

*Figure 11. Comparison between experimental data and predictions from the TN model calibrated to all cyclic and 17 hours of stress relaxation data.*

Relaxation Time | Average Material Model Error |
---|---|

No Relaxation | 13.4% |

1 min | 12.2% |

10 min | 5.7% |

1 hour | 5.5% |

17 hours | 5.5% |

## Summary

- Having some relaxation data helps
- Short-term relaxation data is sufficient for material model calibration