DuPont™ Hytrel® is a class of thermoplastic elastomers that has the flexibility of elastomers, and the strength and processability of thermoplastics. Hytrel is used in many different industrial appliations, including mechanical gears, consumer electronics, seals, cable insulation, etc. The mechanical response of Hytrel, and other thermoplastic elastomers, can be challenging to accurately represent in a material model for FE analysis. The reason for this is that the material behaves somewhere between an elastomer and a thermoplastic. Modeling the cyclic response and permanent set is often particularly challenging. Fortunately, there are modern non-linear viscoplastic material models that can capture all the experimental behaviors of this material class, including the strain-rate dependence, yielding evolution, strain hardening at large strains, and the recovery during unloading.
In this article I will show how different material models can predict the response of Hytrel 7246.
The figure below summarize experimental data that I have for the Hytrel. The data consists of uniaxial tension at three different engineering strain rates (0.0005/s, 0.05/s, and 100/s), and uniaxial compression at two engineering strain rates (-0.05/s, and -0.0005/s). This data set is not from an optimized smart test plan. The data set contains both tension and compression at different strain rates, and also loading followed by unloading. But since the experimental data did not contain the reloading response (after unloading), it is not possible to fit a Mullins damage model to the experimental data. Unfortunately, the data does not include information about the stress relaxation behavior at different stress levels, or information about the residual strain after unloading from different strain magnitudes. In this figure, and all figures below, I used MCalibration to convert the experimentally measured engineering strain and engineering stress to approximate true stress and true strain values.
For this material, DuPont reports the following datasheet values: 72D Shore hardness, tensile modulus: 550 MPa, yield stress: 27 MPa, yield strain: 23%, Poisson’s ratio: 0.47, stress at 5% strain: 14 MPa, stress at 10% strain: 23 MPa, stress at 50% strain: 24 MPa. The experimental data in the figure above appears to be in reasonable agreement with the datasheet values.
The usefulness of a the following material models was examined by calibrating the material models the complete dataset in the figure above:
The material models were calibrated to the data using MCalibration. In this case no experimental validation data was available, so the different models were only compared by how closely they could match the uniaxial tension and compression data.
Results: Abaqus Linear Viscoelasticity
Linear viscoelasticity is clearly unable to predict the large strain response of the material. This is not surprising, linear viscoelasticity should never by used to predict the response of a polymer after yielding!
The average error in the model predictions is 43%.
Results: Ansys MISO Plasticity
The Ansys MISO model is a multi-linear isotropic hardening plasticity model. In its basic form, which is used here, there is no strain-rate dependence. The model is excellent in that it can approximate the monotonic response (at one strain rate) very accurately. The main weakness in this case is that the predicted unloading response is underestimating the strain recovery. That is a well-known problem with isotropic hardening plasticity models in general.
The average error in the model predictions is 21%.
Results: Ansys MISO Plasticity with Strain Hardening Creep
In this case activating strain hardening creep with the MISO plasticity model does not improve the accuracy of the model predictions.
The average error in the model predictions is 22%.
Results: Abaqus Johnson-Cook Plasticity
The Johnson-Cook plasticity model is an isotropic hardening plasticity model, and will therefore significantly overpredict the permanent set after unloading. The strain-rate dependence of the Johnson-Cook model helps with the accuracy in the tension data, bringing the average error down to 18%.
Results: Abaqus Elastic-Plastic with Combined Hardening
The Abaqus elastic-plastic model with combined hardening consists of 5 backstress networks, and is similar to the Ansys Chaboche model. This model is based on kinematic hardening and is therefore much better at predicting the unloading response, but it is unfortunately strain-rate independent.
The average error in the model predictions is 17%.
Results: Abaqus PRF Model
The Parallel Rheological Framework (PRF) model in Abaqus is a modeling framework that is similar to some of the advanced models in the PolyUMod library. The most useful PRF model structure for most thermoplastic elastomers consists of 3 networks with Yeoh hyperelastic springs and power-law flow.
The average error in the model predictions is 10%.
Results: PolyUMod Three Network (TN) Model
The PolyUMod Three Network (TN) model is an advanced non-linear viscoplastic material model for thermoplastic materials. It does a good job at predicting all aspects of the experimental data for the Hytrel.
The average error in the model predictions is 6.9%.
Results: PolyUMod TNV Model
The PolyUMod TNV model is the most accurate material model in this study. This is not surprising, my experience is that the TNV model “wins” most studies of this type for all classes of polymers. The TNV model from the PolyUMod library is available for all major FE solvers: Abaqus, Ansys, LS-DYNA, COMSOL Multiphysics, MSC Marc, and Altair Radioss).
The average error in the model predictions is 5.7%.
MCalibration can also plot the probability that a given material model prediction has a certain error. The figure to the right shows that the calibrated TNV model has a 50% probability to predict an error that is 5.7% or smaller, and that the calibrated PRF model has a 50% probability to predict an error that is 10.3% or smaller.
Or alternatively, a TNV model prediction will with 80% probability have an error less than 12%. A PRF model prediction will with 80% probability have an error that is less than 26%. This clearly indicates how much more accurate the TNV model is over the PRF model for this Hytrel material.