In this tutorial series I will describe in detail how one can select and calibrate an accurate material model for polyether ether ketone (PEEK). PEEK is a high stiffness (E=3.6 GPa) and high strength (UTS=100 MPa, strain to failure about 50%) semicrystalline thermoplastic with a glass transition temperature of about 143°C and a melting temperature of about 343°C. It is used in many applications requiring high strength, such as high temperature seals; and in biomedical devices like fusion cages, ligament anchors, and dental implants. Some of the big manufacturers of PEEK is Victrex, Solvay, and PolyOne.
This tutorial will discuss both a suitable experimental test program for PEEK, and how to select, calibrate, and compare the predictions from different material models (also called constitutive models). I have divided this tutorial series into different parts, since it is so much material to cover.
Note that the information presented here is applicable also to other thermoplastics!
We tested a generic PEEK material in uniaxial tension and uniaxial compression at different strain rates. The figure below summarizes the experimental data.
In tension, we characterized the material response using two engineering strain rates (0.001/s and 0.1/s). In compression, we used three different engineering strain rates (-0004/s, -0.1/s, and -1000/s). The slow and intermediate strain rate test were performed on a traditional electromechanical test machine, and the high rate compressive tests were performed on a custom-built drop tower. As is typically seen for thermoplastic, the Young’s modulus does not change with strain rate, but the yield stress increases significantly with strain rate.
There are two common responses of thermoplastics when plotting the yield stress as a function of the logarithmic strain rate. The first type of response is a linear dependence between the (log) strain rate and the yield stress. This is the case for PEEK. The other response is a bi-linear response, where the slope of the yield stress vs. (log) strain rate undergoes a transition at some intermediate strain rate. If you know that a thermoplastic material has a linear dependence between yield stress and (log) strain rate, then it is not necessary to test the material over all orders of strain rate of interest. In this case it is possible to accurately extrapolate the yield stress response to outside the range of strain rates tested. The problem is that it may not be known if a specific thermoplastic material has a linear of bi-linear response when plotted this way. So my general recommendation is to perform the experiments over as wide range of strain rates as needed for the indented application. After all, the ultimate goal of this work is to determine a material model that can accurately predict the response of the material for all strains, strain rates, and temperatures, that are needed.
The figure above also shows that the yield stress in compression is about 20% higher than the yield stress in tension. This difference between the yield stress in tension and compression is typical for thermoplastics, but the magnitude of the effect is different between different polymers. This is an important effect that need to be experimentally determined. In the figure I also plotted trend lines for the tension and compression data. We only have data at two strain rates in tension, so the tensile trend line is less reliable. The data, however, is in agreement with the typical observation that the slope of the yield stress vs. (log) strain rate curve is independent on the loading mode.
Note that we only performed uniaxial tension and uniaxial compression tests on the PEEK. We did not perform any shear tests, biaxial tests, plane strain tests. The choice of only using uniaxial tests was motivated by the material modeling approach that we will use. In other words, in this case it is not necessary to test the material in different loading modes. This is very convenient since it reduces the number of experiments that are required.
Also note that we performed more experiments in compression than in tension. As mentioned above, the reason to test the material at multiple strain rates is to extract the viscoplastic response of the material. There is no need to perform these tests in both tension and compression, one is enough! The reason we need to test the material in both tension and compression is to determine how the yield stress, or as I prefer to call it, the flow resistance changes with hydrostatic pressure. The easiest way to obtain this information is to perform the tests in uniaxial tension and in uniaxial compression.
One more comment, the reason we performed the highest strain rate tests in uniaxial compression is that the gauge section of a tension specimen is typically longer than the height of a compression specimen. We can therefore reach higher strain rates in compression than in tension (assuming that the max applied loading rate is the same in tension as it is in compression, which it is for our drop towers).
PEEK is a viscoplastic material with a stress-strain response that is highly non-linear. Fortunately, as will be shown in this tutorial series, the material response (deformation, stress-strain, and failure) can be accurately modeled is we use an appropriate material model. And there are multiple options that are good.
In the next part of this series, we will setup the material model calibration using the MCalibration software.