Technical Article: Racquetball bounce represents viscoelastic response

By Jeffrey A. Jansen, Laboratory Operations Manager, Stork Technimet, Inc.

While we were playing racquetball the other day, my friend observed the unique elastic properties exhibited by the ball. Anyone who has hit a racquetball knows how effectively and sharply the ball bounces, with very little apparent loss of energy. Without knowing it, my friend had just observed the viscoelastic properties of the ball in response to stress; in this case the exertion of force from the racquet and subsequently, the wall. The rubber material used to produce the racquetball was obviously selected to elicit the desirable property of high elasticity.

Viscoelastic Principles
At this point, most discussions of the viscoelastic properties of thermoset elastomers, commonly referred to as rubber; turn to Maxwell’s spring and dashpot model combining Hooke’s Law and Newton’s Law. However, my friend, an accountant by profession, was not up for that discussion, and to be perfectly honest such dissertations often leave me scratching my head. A simpler way to explain the properties of the racquetball had to be found.

While the concept of viscoelasticity is extremely complex, it is the key to the behavior of all polymeric materials, and in this instance the rubber racquetball. All polymeric materials simultaneously exhibit varying amounts of elastic and viscous behavior.ⁱ Because of this, a basic understanding of these two phenomena is essential. Elasticity, simply expressed, is a reversible response to stress, whereby the material exhibits recovery and resilience. Alternatively, viscous deformation represents the permanent deformation that occurs through the exertion of stress. The combination of elastic recovery and viscous deformation is often complex and is unique to individual polymeric materials based upon their structure and formulation. While all polymeric materials display a significant level of elasticity, rubber in particular is known to have a relatively highly elastic response to stress.

Elasticity is the term commonly used to quantify a material’s elastic and viscous behavior. A recent proposal by A. Schob, which is particularly appropriate in the case of the racquetball, evaluates the "elastic efficiency" as:

Formula 1

Various vulcanized elastomers exhibit a wide range of ratios, with some materials producing values as high as 75% and greater. Such rebound elasticity has been shown to be highly temperature dependent.ⁱⁱ

Glass Transition
The properties of polymeric materials—and elastomers in particular—are greatly affected by temperature. In the case of elastomeric materials, a fundamental temperature-related characteristic is the glass transition temperature (Tg). From a materials engineering standpoint, the glass transition defines the temperature at which large-scale segmental molecular motion begins.ⁱⁱⁱ

The implications of the glass transition temperature vary depending on the material type. For semi-crystalline thermoplastics, the glass transition temperature represents the point at which the material changes from being stiff and brittle to ductile. For amorphous thermoplastics, which do not exhibit a true melting point, the glass transition temperature represents the point at which the material softens and loses all load-bearing capability. For thermoset materials, the glass transition temperature also has significance.

Thermoset elastomers have glass transitions that occur below ambient temperature. Because of this, rubber products by definition exhibit elastic behavior at room temperature, as readily observed on the racquetball court. However, at temperatures below the glass transition this and other properties are considerably different.

Many physical properties undergo a dramatic change as the material passes through the glass transition. Because of its widespread effect on performance, the glass transition temperature is a very important fundamental material characteristic. The most obvious changes are those that can be directly measured analytically. This is particularly true for analytical techniques such as thermal analysis. Differential scanning calorimetry (DSC) measures the change in heat capacity, in which the glass transition is apparent as a step transition in the thermogram. Thermomechanical analysis (TMA) assesses the change in the expansion / contraction properties of the material above and below the glass transition. Finally, dynamic mechanical analysis (DMA) evaluates the material’s viscoelastic properties, specifically the modulus. Above the glass transition elastomers are soft and ductile and demonstrate a high degree of elasticity, while below this point they are relatively hard, stiff and brittle. DMA is generally accepted as the superior method for measuring the glass transition temperature, and is perhaps the most intuitive as it directly assesses the mechanical properties of the material, as modulus, over a temperature range.

Racquetball Material Analysis
The glass transition temperature of a rubber material is dependent on both the molecular structure, based upon the identity of the polymer, as well as the entirety of the composition. As such and testing of the racquetball material was conducted in order to characterize the composition of the material and gain insight into its properties. The rubber was initially analyzed using micro-Fourier transform infrared, spectroscopy (FTIR). The analysis produced results consistent with a polyisoprene rubber compound, as shown in Figure 1.

The material was further characterized via differential scanning calorimetry (DSC) and thermo-mechanical analysis (TMA). Both tests produced results consistent with an elastomeric material. The DSC and TMA results showed glass transition temperatures of -80 °C and –85 °C, respectively. This is in agreement with the accepted glass transition for a polyisoprene rubber. The DSC and TMA thermograms are presented in Figure 2.

DMA testing was also performed on the racquetball material and the resulting thermogram is presented in Figure 3. The results clearly show that the material undergoes a drastic reduction in modulus as the temperature is increased past the glass transition. The DMA testing clearly indicates the effect of temperature and specifically passing through the glass transition on the mechanical properties of the rubber.

In order to further illustrate the dramatic effect of temperature on the properties of rubber, compressive mechanical testing was performed on several racquetballs using a universal mechanical tester. One set of balls was compressed at ambient temperature, while a second set was tested after cooling in liquid nitrogen to -125 °C. The balls tested at ambient temperature reached the limits of the test fixture, 5000 lbs(f) without rupture. The balls, having an original diameter of 2.25 inches, compressed to 0.50 inches, demonstrating significant ductility. Upon removal from the test fixture, the balls fully recovered, without apparent loss of mechanical properties or permanent deformation.

Conversely, the balls tested at -125 °C exhibited extremely brittle properties. The testing produced catastrophic rupture after the application of a load of 500 lbs(f). This corresponded to a deformation of only 0.02 in. This massive change in apparent compressive strength, based upon temperature, is illustrated in the mechanical test data shown in Figure 3.

The obvious brittle properties exhibited by the elastomer below the glass transition temperature were confirmed through an examination of the fracture surface via scanning electron microscopy (SEM). The fracture surface exhibited classic brittle crack features, including a generally smooth morphology with hackle marks. The fracture surface contained features normally observed on amorphous thermoplastic materials. Amorphous thermoplastics are used at temperatures below their glass transition temperature, and as such the similarity in fracture surface morphology between such materials and the subambient rubber represents the glassy, brittle state of the material, and not the composition of the material.

Given the outcome of the mechanical testing, the dramatic effects of temperature, and in particular the application of stress to a material which is being above or below the glass transition temperature of a material, were apparent. At ambient temperature on the racquetball court, approximately 100 °C above its glass transition temperature, the racquetball behaved in a truly elastic manner. However the same ball literally shattered when exposed to minimal stress below the glass transition. The implications of this example are significant. The temperature at which a polymeric material is used while in service will have a significant impact on the performance of the part. Imagine the ramifications of using a seal or a hose below the glass transition temperature, with the part displaying brittle, glassy properties. However, the experiment also raises an interesting question, could a pool cue ball be used for playing racquetball at extremely elevated temperatures?

ⁱNicholas P. Cheremisinoff, Elastomer Technology Handbook, CRC Press, Boca Raton, 1993, Michael P. Sepe
ⁱⁱ Werner Hofmann, Rubber Technology Handbook, Hanser Publishers, Munich, 1989
ⁱⁱⁱ John Schiers, Compositional and Failure Analysis in Polymers, John Wiley & Sons, LTD, Chichester, 2000