Stress/Strain – The Cause of Hysteresis

Urethane Rollers


You might remember your high school physics teacher saying “for every action, there is an equal and opposite reaction.” That’s a good way to think about stress/strain.

Stress is a measure of the internal reaction force. Strain is the measure of deformation.  These terms are used to define the intensity of internal reactive forces in a deformed body. They are associated with changes in dimension, shape, or volume caused by externally applied forces.

Hysteresis is the name used to describe failure of a urethane part under these conditions. Every time the urethane flexes, there is an increase in energy. That energy stored in the urethane wheel allows it to rebound, however it generates internal heat. When polyurethane elastomers undergo cyclic loading and unloading, mechanical energy is transformed into heat energy and the elastomer will heat up. If this heat buildup is too great, the results can be breaking loose from a bonded substrate or blowing a chuck of the urethane from the inside out.

As an example, imagine we have a cart with 4 urethane wheels. As we load the cart with heavy iron ore the urethane wheels compress and when we empty the cart the wheels return to the original size. Stress is a measure of the internal energy stored in the urethane wheel that allows it to return to its original size when the cart is emptied. Strain is a measurement of the deformation of the wheel.

Things you should consider to avoid Hysteresis:

Elastomer Hardness -With dynamic applications, the greater the cyclic deflection of the elastomer, the greater the heat buildup. Generally, an in-use deflection of 5-10% is acceptable, although a deflection of under 5% is desirable. If the deflection extends beyond 10%, then the part has a greater chance for blowout. Therefore, specifying a harder elastomer is usually recommended to minimize deflection. However, there are typically other performance attributes that also need to be considered, such as traction, where use of a softer formulation may be desired.

Part Loading – Even when the correct formulation has been used, the load on a wheel or roller can be uneven, leading to localized meltdown and blowout in the region of maximum load. This happens frequently with rollers when the ends are tightened down to increase the nip pressure. Proper installation of the part into service is critical. Loading across the face of the part should be as uniform as possible, and crowning of a wheel or roller may be required.

Load/Speed Considerations – Dynamics are a function of load and speed. If either is too great, then the part may not be able to dissipate the heat fast enough to avoid a blowout. This can happen even with a properly designed part. Sometimes it may be necessary to redesign the application. This can be accomplished by redesigning the roller to have a larger diameter, effectively reducing the speed. The part can also be made wider to distribute the load over a wider area.

How Dynamic Mechanical Analysis is Performed

Dynamic mechanical analysis (DMA) is an important technique used to measure the mechanical properties of elastomers, including hysteresis. It provides information on the ability of materials to store and dissipate mechanical energy upon deformation, which is used to determine which materials can be used in dynamic applications, such as rollers or wheels.

The basic properties obtained from a DMA test include storage modulus (E’ or G’), loss modulus (E” or G”) and tan delta (tan δ). (See definitions below.) Tan delta is particularly important for elastomers because it’s related to the material’s ability to dissipate energy in the form of heat. Glass transition temperature (Tg) and elastomer melting point can also be determined. The DMA data allow the development of structure-property-performance relationships for an elastomer; in other words, how do changes in chemistry, processing or composition impact performance.

How Dynamic Mechanical Testing Data is Obtained

Experiments are conducted by applying a small cyclic deformation to a sample over a wide temperature range. Elastomer samples are typically about an 1/8” thick, ½” wide by 2” long. They should be void-free and of uniform thickness to obtain accurate modulus values. Specimens can be machined from a larger cast polyurethane.

In the test, the sample is clamped inside an environmental chamber and cooled to -150°C. A small deformation is then applied, and the resulting force is measured. When the deformation is complete, the temperature is raised by 5-10°C, and the deformation is repeated. For elastomers, testing continues up to 250°C, at which time the elastomer starts to degrade or melt.

From the force response of the sample, it’s possible to calculate the modulus (stiffness) and dissipative (tan delta) characteristics of the elastomer. Typically, experiments are conducted by varying temperature at a constant deformation frequency (1 Hz); other frequencies can also be used to stimulate conditions more like field applications. Experiments can be conducted for shear (twisting) or tension (stretching). It’s also possible to perform experiments which monitor performance at an elevated temperature. From this data, an upper use temperature and durability can be estimated.

DMA Definitions
Storage Modulus: Measurement of energy stored during deformation and related to the solid-like or elastic portion of the elastomer. E’ is used for stretching deformations; G’ is used for twisting or torsional deformations.
Loss Modulus: Measurement of energy lost (usually lost as heat) during deformation and related to the liquid-like or viscous portion of the elastomer. E” is used for stretching deformations; G” is used for twisting or torsional deformations.
Tan Delta (tan δ): Indicative of the material’s ability to dissipate energy, where tan δ = E”/E’ = G”/G’
Glass Transition: Temperature region over which the material changes from a rigid, glassy solid to a more flexible, elastomeric solid. The glass transition region is denoted by Tg the glass transition temperature.