Model Verification
Using finite element analysis and known experimental data to verify the accuracy of material models for PET, POM, PP, and HDPE
A group project completed during 4th year of University.
Teammates: Fang Te Fong, Afdhal Zofran bin Mohd Amin, Nur Amanda binti Mustapha Kamal
Industrial Partner: Crux Product Design
Purpose
Finite element analysis was used to verify the validity of the material models. The low error values discussed in the 'Material Model' section reflect how well the calibration software matched the prediction to the set of experimental data it was given. They do not necessarily reflect accuracy when comparing the material model to real-world materials. To verify this, the material models must be used in FEA and the behaviour compared to a physical recreation of that scenario. Rather than carry out new tests, FEA simulations were created for each of the experiments described in the 'Practical Testing' section. To prevent circular verification, where the model's validity is tested using the same data used to create it, separate data that was not accessed during the material model calibration process was used.
Unfortunately, due to software licensing issues regarding PolyUMod, the Three-Network Viscoplastic (TNV) material models could not be tested in the FEA simulations. This meant only the linear viscoelastic model could be verified.
Finite Element Analysis
Simulated Uniaxial Tensile Test
Simulated Uniaxial Tensile Test Using the PET LVE material model
The simulation shows the specimen extended at a rate of 5mm/min with a displacement of 2mm. The scale deformation factor is 1 and the rainbow contours represent the relative stress distribution throughout the specimen. Convergence testing conducted using the same model showed that a 0.5mm-sized mesh is sufficient. The output data from this simulation was the force required to maintain displacement equal to the physical tests.
Simulated Drop Tower Test
Simulated Drop Tower Test Using the HDPE LVE material model
The simulated drop tower test shown is 3ms after impact. The scale deformation factor is 1 and the rainbow contours represent the relative stress distribution throughout the specimen. Convergence testing conducted using the same model showed that a 1mm-sized mesh is sufficient. Two planes of symmetry were used to speed up calculation. The output data from this simulation was the vertical contact force between the impactor and the top surface of the specimen.
Simulated DMA
Simulated Dynamic Mechanical Analysis Using the POM LVE material model
The specimen shown is oscillated at a frequency of 1Hz and an amplitude of 0.015mm. The scale deformation factor is 100 and the rainbow contours represent the relative stress distribution throughout the specimen. Convergence testing conducted using the same model showed that a 1mm-sized mesh is sufficient. The output data from this simulation was the force required to provide oscillation at the designated frequency.
Material Model Evaluation
As mentioned earlier, only the linear viscoelastic (LVE) material models could be tested in the FEA simulations. One limitation of LVE-based material models is that they don't model the viscoplastic behaviour of the polymers so have very limited accuracy outside of low-stress-and-strain regions. This causes an increasingly large divergence between the modelled and experimental results as the strain and therefore the unaccounted-for viscoplastic unrecoverable deformation increases. This can most clearly be seen in the simulated results from the drop tower test.
Example comparison between simulated and actual drop tower test data for PET
Across all four materials, the model was initially accurate then diverged as stress increased. In the case of PET, it diverged 1.2 seconds after impact and fit the experimental data very well when within the linear viscoelastic region. This is as expected given the LVE model's limitations.
Example comparison between simulated and actual uniaxial tensile test data for HDPE
Across all four materials, the model accurately captured the initial gradient of the experimental data for both extension rates. Then, as damage accumulation is not considered, the predicted required force continues increasing as the real specimen begins to viscoplastically deform.
The difference between the model's predictions for extension rates of 5mm/min and 500mm/min shows that it is capturing the effect of strain rate.
Example comparison between simulated and actual DMA data for PET
Looking at the DMA data more clearly shows the model's ability to capture a material's strain-rate dependence. As DMA only involves oscillation with a small amplitude (0.015mm), it only causes small strains, making the LVE model suitable across the entire testing range.
It can be seen that the model predicts behaviour accurately until the forcing frequency exceeds 10^5 rad/s. At this point, the required drive force increases sharply. Since the exact pattern is shared across all the materials, it is unlikely to be an error in the material models and instead is due to the inertial effects within the simulation not being calibrated for as they are in a physical DMA test.
The simulated practical tests show that the four linear viscoelastic material models are effective at characterizing their respective material's behaviour within the small region they were intended for. The simulated DMA tests and the simulated uniaxial tensile tests show that this is true for a range of strain rates. However, the models become very inaccurate when the material is subjected to high strains, and since they vastly overestimate their respective material's strength and stiffness, are not yet suitable for general design use.
For access to the full design report, get in touch at Michaelsvanidze0@gmail.com.