By Travis Parkman, DMA Product Manager (PhD)
Keywords: High Force DMA, Viscoelastic, Rigid Materials, Payne Effect, Prony Series
A dynamic mechanical analyzer (DMA) is a powerful tool for measuring a material’s viscoelastic properties, which includes but is not limited to its stiffness, damping, and compliance. As a quick refresher, viscoelastic material properties are time dependent material properties that are highly dependent on temperature, frequency, strain and stress [1]. If this is a relatively new topic for you, I recommend checking out a recent webinar we did with Akron Rubber Development Laboratory (ARDL), titled “DMA101: Dynamic Mechanical Analysis for Viscoelastic Properties”.
Figure 1: Electric vehicles (EVs) are an emerging application, experiencing new design challenges and the use of novel materials, making accurate viscoelastic characterization crucial for achieving ideal performance.
What makes DMA such a powerful tool for viscoelastic materials, is that you can directly control these conditions (temperature, time, strain, etc.) with a DMA. This is especially true for high-force DMAs, which have the added capabilities to deliver larger force amplitudes. This blog post will explore why using a high-force DMA is important for two common DMA tests.
CAPABILITY TO MEASURE MATERIAL BEHAVIOUR AT COLD TEMPERATURES
Temperature sweep tests are one of the most used DMA tests to understand the material’s performance as a function of temperature. This test is done by vibrating a material at a set amplitude and frequency, while controlling the rate of temperature change. This is also a great test to identify when the material will transition from a soft rubbery state to a hard glass-like state, or vis-versa, which is known as the glass transition temperature. However, when a material gets cold and enters its glassy state, a large amount of force will need to be applied to the material to maintain a constant strain [1].
This is something that is easier explained through an example using some experimental data. For the purpose of this exercise, a temperature test from -70°C to 20°C was run on a rubber sample using Metravib DMA+1000. The sample deformed at a constant frequency of 10 Hz at 0.2% strain. Figure 2 shows the measured shear modulus (red) and tan δ vs temperature from this experiment.
Figure 2: A classic DMA plot; the measured shear modulus (red) and tan δ (blue) vs temperature. Each data point is calculated from running a DMA test at that temperature point. This type of plot is used to measure the glass transition temperature is identified by the peak in tan δ curve. (Note: there are other DMA measurements to identify the glass transition temperature).
The shear modulus, shown in red, is denoted by a ‘G’ and quantifies the ability for a material to resist deformation. For example, a large shear modulus indicates a material is rigid and in this case indicates that this rubber sample is in its glass state, shown in Figure 2. Now, if you are wondering why this beautiful plot relates to the importance of a high force DMA, let’s plot the force that was required to achieve a constant strain of 0.2% for this experiment, which is shown in Figure 3.
Figure 3: Applied force to maintain 0.2% strain vs temperature.
For this experiment, the strain was controlled to 0.2%, meaning as the material gets stiffer, more force will be required to deform the material at this strain. If we read Figure 3 from right to left, we see that the required force greatly increases as we pass through the glass transition temperature (-29.19°C) and approach -70°C. The force is increasing because the modulus is increasing and peaks at 43.61N, which exceeds the force capabilities of common DMAs available.
UNDERSTAND HOW THE MATERIAL PERFORMS UNDER EXTREME LOADS
The previous example highlighted the importance of evaluating a sample at different temperatures with low strains, but what about when you want to test a material at high strains? Understanding the performance of materials as it is excessively strained is critical, for example let’s consider tires for electric vehicles (EV)s.
Figure 4: Did you know that the tires for EVs are designed differently compared to their fossil fuel counterparts? The large battery packs used in EVs make them heavier increasing the compressive strain on the tires. The instantaneous torques applied to the tires by the electric motor greatly increase the shear strain applied to the tires. These new loading conditions are causing tire companies to re-evaluate their rubber compounds to make sure these compounds can withstand these new loading conditions while maintaining fuel efficiency [2].
The concern how a material behaves under large strains is attributed to what is happening in the material on a microscale, which is the breakage of physical bonds in the material as it is strained (known as the Payne effect). These broken bonds will often form new bonds changing its shape and structural integrity (known as the Mullins effect) [1]. The data retrieved from a high force DMA can be used to compare blends or used in finite element models (FEM) through a Prony Series [3].
This effect is critical in understanding the structural integrity of a part (and should probably have a blog dedicated to itself in the future), however, the nice thing is that this can all be easily quantified through a strain sweep, which is a test that consists of vibrating a sample at a specific frequency and list of strain amplitudes.
To help explain these effects, let’s run a strain sweep from 0.01% to 20% strain on a filled rubber sample in tension. The temperature and frequency are kept constant at 25°C and 10 Hz, respectively. Figure 5 shows the results using a high-force Metravib DMA.
Figure 5: Elastic modulus (red) and tan δ (blue) vs. dynamic strain amplitude. The elastic modulus is greatly reduced at larger strains, meaning it will easily deform.
Figure 5 clearly shows how the material properties change with strain. The change in the Elastic modulus, denoted as ΔE, is caused by the Payne Effect , and shows a decrease in strength as the material is further elongated (strained) [1]. To achieve these high strains on a cured rubber sample, a large amount of force is required. The required force to get each data point is shown in Figure 6, which plots the applied force vs. dynamic strain.
Figure 6: Dynamic force amplitude (red) vs. dynamic strain amplitude.
This test shows that 42 N of force is required to strain a strip of cured rubber by 20%, which surpasses the maximum appliable force of a common DMA. The added benefit of running a high strain sweep is that it can quantify the Mullin’s effect and how a material recovers once the maximum strain is removed [1]. This is done by reversing the strain sweep, so the strains are applied from high to low. Figure 7 expands on Figure 5 by showing the measurements from the return sweep.
Figure 7: Dynamic force amplitude (red) vs. dynamic strain amplitude with a return sweep to demonstrate the Mullin’s effect. The direction of the sweep is indicated by the arrows.
The additional data from the return sweep in Figure 7 show that the material does not have the same material properties as before when it was strained at lower strains. This is because the bonds inside the material have broken and formed new bonds. These new bonds prevent the material from returning to its original shape and also effects the material properties [1].
FINAL NOTES
Developing an accurate understanding of your materials’ behaviour is critical and makes me think of the phrase about my modelling days, “garbage in, garbage out”, meaning a model is only as good as the data that is inputted into it. A high force DMA is a powerful tool for researchers to accurately measure the mechanical properties of materials under a wide range of conditions, improving their understanding of material behavior and helping to develop more accurate models.
Figure 8: Metravib DMA+300 has the capability to confidently apply large forces to a stiff sample while also having the control to apply small amplitudes to delicate samples. For more information, check out our new website. (https://ctherm.com/metravib)
If you would like to learn more about Metravib DMA+ series, contact us directly at sales@ctherm.com. Also if the topic of FEM interests you, I recommend a webinar we did in the past with ThermoAnalytics, titled “Importance of Thermal Conductivity in xEV Thermal Management Modeling”. This webinar focusses on EV and battery pack modeling.
WORK CITED
[1] K. P. Menard and N. Menard, Dynamic Mechanical Analysis. Boca Raton, FL: CRC Press, 2020.
[2] “Electric vehicle tires – everything you need to know,” Electric vehicle tires | Continental tires. [Online]. Available: https://www.continental-tires.com/car/tire-knowledge/tire-basics/electric-vehicle-tires. [Accessed: 11-Apr-2023].
[3] M. A. Tapia Romero, M. Dehonor Gomez, and L. E. Lugo Uribe, “Prony series calculation for viscoelastic behavior modeling of structural adhesives from DMA data.,” Ingeniería Investigación y Tecnología, vol. 21, no. 2, pp. 1–10, 2020.
About the Author
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Travis obtained his degree in Mechanical Engineering in 2015 from the University of New Brunswick. After graduation, he began his Masters, where he investigated a new method to measure cutting forces produced during machining. This research was later converted to a Ph.D. program, with a focus on identifying and adjusting for inertial effects present in force measurements used to monitor machining processes. Travis is the Metravib Product Specialist for C-Therm. |