Using Dynamic Mechanical Analysis (DMA) to Describe Rubber Tire Performance

Written by Travis Parkman, Product Specialist Mechanical EIT

DMA is one of the most accurate methods to measure viscoelastic properties of rubber and polymer compounds as functions of temperature, frequency, time, stress, and/or strain [1]. A viscoelastic material exhibits both elastic and viscous properties. An ideal elastic material will store its energy as its deformed by an external load. When this load is removed, the material will return to its original shape (e.g. a rubber band). However, for viscoelastic materials a part of the energy used to deform the material will be dissipated typically into heat [2]. When we think of physics, energy loss is usually associated as an undesirable aspect but can also serve as a beneficial characteristic for numerous real life design applications, such as rubber tires or vibrational dampers [1,3].

HOW DOES DMA WORK?

A typical DMA test consists of applying a force to a material through a shaker while measuring this applied force and the sample’s deformation. Different test cells can be used to stimulate the material through compression, tension, or shear modes, depending on the application.

Figure 1. A typical force and deformation signal from a DMA test.

Figure 1 shows a typical waveform where the measured deformation and force are shown by orange and blue curves, respectively. The signal processing capabilities of DMA programs, such as Metravib’s DYNATEST, can accurately elucidate physical properties of a material, like the complex stiffness in real time. The complex stiffness, K*, is calculated through the following equation:

where F_o and D_o, are the amplitudes of the measured force and deformation, respectively. The complex stiffness is composed of two components, the storage, K’, and loss, K’’, component as is shown below.

K’ quantifies the elastic behaviour of the material that allows for it to return to its original shape while K’’ represents the loss of energy. If the material shown in Figure 1 was purely elastic, the deformation and force would be in phase; in other words, the peaks would be aligned. However, due to the viscous properties of a viscoelastic material there is resistance causing a difference between the two signals [3]. This phase shift between the deformation and force is represented by the Greek letter delta, δ. The relationship between δ and stiffness components is the following.

Tan(δ) is commonly referred to as the loss factor and conveniently describes the viscoelastic behaviour of the material as a ratio between the energy loss and stored during deformation. A low tan(δ) value means the material will return to its shape while a higher tan(δ) value means the material will lose some this energy in the form of heat. ACOEM© provides a video that further illustrates the DMA testing procedure along with the testing capabilities of their Metravib products and can be found at https://www.youtube.com/watch?v=CIb5yYkLl_M.

The true value in DMA is that it can calculate these properties in real time while controlling/changing conditions like temperature, frequency, and strain, which all affect the viscoelastic properties of a polymer. Figure 2 shows the typical results from a temperature sweep from 20 °C to 140 °C and the effect of temperature on tan(δ).

Figure 2. A plot of temperature vs tan(δ).

Why is this important? Where do I start? How do I even start?!

DMA’s large choice of testing capabilities can be intimidating since it opens the door to several different testing combinations. Deciding what the appropriate testing procedure relies on a comprehensive understanding of DMA along with the application it is being applied for.

Let’s start off with an industry that DMA has established itself as a pillar in quality insurance, TIRES.

THE IMPORTANCE OF DMA IN THE TIRE INDUSTRY?

In a world where we are conscious about our environmental footprint, now more than ever, tire companies are developing new blends with natural materials [5] and reducing rolling resistance [1] to meet our expectations for greener solutions. This is all done while also ensuring a high level of safety for you and your passengers, by maximizing tire traction for different road conditions.

During typical operation, tires are subjected to cyclic loads, varying road conditions, temperatures and if you live in Canada, large impacts from potholes. DMA is a preferred testing method in the tire industry since it can evaluate different materials while simulating these conditions.

One of the most useful material properties measured during a DMA test is the loss factor, tan(δ). A low tan(δ) is correlated a low rolling resistance since none of the energy transmitted from the wheel to the road are lost while a high tan(δ) is related to good traction characteristics [4]. The temperatures used to evaluate the loss factor are shown in Table 1.

Table 1. Tire characteristics associated with tan(δ).

For an example, let’s say a tire company wants to test a new rubber blend, labelled as Blend B, for a set of summer tires. The desired aspects for a summer tire are to have good wet traction when it is raining while also having a minimum rolling resistance in dry conditions. This ensures a high level of safety for all the passengers in the vehicle while maintaining good fuel economy. Table 1 shows that these are both functions of tan(δ) at specific temperatures. Therefore, the recommended methodology would be to conduct a temperature sweep while maintaining the frequency and strain to a controlled level.

Figure 3. Temperature vs tan(δ) for two arbitrary tire blends.

Figure 3 shows the resulting temperature vs. tan(δ) plot for the two tire blends with arbitrary values. We can see that Blend B is a more suitable material to use for a summer tire. It has a relatively higher tan(δ) at 0°C compared to the original Blend A, suggesting it has better wet traction.  Tire Blend B also has a lower tan(δ) at 30°C, suggesting that it will have a lower rolling resistance, therefore better fuel mileage.

This is just one of the ways DMA is used in the tire industry. DMA testing can also provide useful insights into several applications. For more information into this subject or other applications and whether Metravib DMA can help you, contact us directly at info@cthermanalysislabs.com.

Works Referenced