Introduction
In some situations you need a material model but you only have very limited experimental data, and it may not be possible to generate more experimental data. In my example I only have a single tensile stress-strain curve for Hytrel 8724 that was available online.
In this article I will discuss what to do in a situation like this. Specifically, I will try to demonstrate that it can be possible to do better than a simple elastic-plastic material model.
Elastic-Plastic Material Model
The image of the stress-strain curve can quickly be converted to stress-strain data using MCalibration. It is then very easy to fit a linear elastic model with isotropic hardening plasticity to the stress-strain curve. The figure below shows that the predicted stress is basically identical to the experimental data.
This similarity, however, does not prove that the elastic-plastic material model is an accurate model. This material model, will not predict the unloading response well, and the model will predict no strain-rate dependence at all. The question is: how can we do better than this since so little information is available.
PolyUMod TN Model
If we had more data it would be easy to calibrate a more advanced (and accurate) viscoplastic material model. Some times, however, it is possible to overcome that limitation by using experimental data for a similar material. In this case I already have excellent experimental data for a similar Hytrel (7246), and I also already have a calibrated PolyUMod TN model for that Hytrel. See this study for the details. To use the results from that study for our current problem I can simply perform the following steps:
1. Copy the already calibrate TN material model for Hytrel 7246 to the MCalibration file for this material. The following figure shows the predictions of that material model before doing any calibrations.
2. Set both mm parameters to not be optimized. Also set both p0 parameters to not be optimized. The mm parameters control the strain-rate dependence, and the p0 parameters control how the yield stress in compression is different than in tension. In this case we have not information about that, so the best we can do is to assume the same value as for the similar Hytrel that we have data for (7246).
3. Scale all material parameters with units of stress by a factor of 0.5 in order to better match the experimental data. This can be achieved by clicking the “X0” button in the material model toolbar.
4. Run the material model calibration using the Simplex method. The Simplex method is good at preserving material parameters values, which can be useful when limited experimental data is available.
The figure below shows the results after a few minutes of calibration. Note that you should not let the calibration run for a long time when only limited experimental data is available (since this can cause parameters to float away). This material model does not match the tension data as accurately as the elastic-plastic model, but it will predict the unloading and strain-rate response significantly better!
The images below show the predicted load-unload response and the strain-rate dependence of the calibrated TN model.
Summary
In this article I showed how you can calibrate a non-linear viscoplastic material model to a single monotonic tension stress-strain curve if you already have a calibrated material model for a similar material. In this case using a viscoplastic material model can be significantly more accurate than using a basic elastic-plastic material model.
