Rubber hysteresis loss determination quantifies the mechanical energy that a rubber material dissipates as heat during cyclic deformation, a property that governs heat build-up, rolling resistance, and damping performance. Accurate measurement of hysteresis loss through internationally recognized methods such as DMA and flexometer testing is essential for tire development, anti-vibration engineering, and compound quality control. This article explains the underlying principles, specimen requirements, test items, standardized methods, and typical applications of rubber hysteresis loss measurement.
Technical Overview
Rubber hysteresis loss refers to the mechanical energy dissipated by a rubber material when it is subjected to cyclic loading and unloading. Because rubber is a viscoelastic material, the stress-strain curve traced during loading does not coincide with the curve traced during unloading. The closed loop formed between the two curves is called the hysteresis loop, and the area enclosed by this loop represents the energy converted into heat per deformation cycle.
At the molecular level, hysteresis arises from internal friction: as polymer chain segments rearrange under stress, part of the strain energy is stored elastically while the remainder is dissipated through friction between polymer chains, between chains and filler particles, and within the filler network itself. The dissipated energy manifests as heat, which can accumulate inside thick rubber articles and accelerate thermal aging or even thermal failure.
Hysteresis loss is most commonly quantified through dynamic mechanical parameters. Under sinusoidal oscillation, the complex modulus (E* or G*) is resolved into a storage modulus (E' or G'), representing the elastic energy stored and recovered, and a loss modulus (E'' or G''), representing the viscous energy dissipated. The ratio of loss modulus to storage modulus is the loss factor, tan delta, which serves as the standard dimensionless indicator of hysteresis. Hysteresis behavior depends strongly on temperature, deformation frequency, strain amplitude, filler type and loading, and crosslink density, so all test results must be reported together with their exact test conditions.
In practical engineering, hysteresis has a dual character. Low hysteresis is desirable in tires, conveyor belts, and seals to minimize rolling resistance and heat generation, while controlled high hysteresis is deliberately designed into engine mounts, damping pads, and seismic isolation bearings to absorb vibration energy.
Testing Samples
Standard Vulcanized Cylindrical Specimens
For flexometer-based heat build-up testing, cylindrical buttons with a diameter of 17.8 mm and a height of 25 mm are the standard specimen geometry. Specimens are vulcanized to optimum cure, and both flat ends may be bonded to metal plates or tested unbonded with a constrained lateral expansion configuration. Surface defects, porosity, or non-parallel ends must be rejected because they distort the deformation mode and temperature rise.
DMA Specimens
Dynamic mechanical analysis accepts several geometries, including rectangular strips in tension or dual-cantilever bending, cylindrical or square blocks in compression, and dual-lap shear sandwiches in which rubber layers are vulcanization-bonded to metal plates. Strip specimens are typically 1 to 3 mm thick to ensure uniform temperature and strain distribution. Shear specimens are preferred at large strain amplitudes because shear deformation minimizes volume change effects.
Specimens from Finished Products
Cut or punched specimens taken from finished articles such as tire treads, bushings, belts, and damping elements can also be evaluated, provided their geometry satisfies the dimensional requirements of the selected method. For finished product evaluation, conditioning history, service exposure, and aging state must be documented because they significantly influence the measured hysteresis values.
Conditioning Requirements
All specimens should be vulcanized and then rested for at least 16 hours after curing before testing. Standard laboratory conditioning is 23 °C plus or minus 2 °C at 50 percent relative humidity for a minimum of 3 hours, or longer if thermal equilibration at the test temperature is required. Specimens must be free of mold release agents, oil contamination, and mechanical damage.
Testing Items
The core quantities determined in rubber hysteresis loss measurement include:
- Hysteresis loop area, expressed as energy dissipated per cycle in joules or as energy density dissipated per cycle per unit volume in J/m³
- Loss factor, tan delta, at specified temperature, frequency, and strain amplitude
- Storage modulus, E' or G', characterizing the elastic stiffness component
- Loss modulus, E'' or G'', characterizing the viscous dissipation component
- Dynamic heat build-up, reported as temperature rise in degrees Celsius above ambient at defined intervals
- Permanent set after cyclic deformation, expressed as a percentage of original height or deflection
- Fatigue life and static compression or hardness change associated with repeated cycling
- Rebound resilience, an inverse practical indicator of hysteresis energy loss
Testing Methods
Dynamic Mechanical Analysis (DMA)
DMA is the primary method for precise determination of hysteresis parameters and is covered by ISO 4664-1, ASTM D5992, and GB/T 9870. A specimen is excited with a sinusoidal force or displacement at controlled frequency, temperature, and strain amplitude, and the phase lag between stress and strain is measured. From the measured complex modulus and phase angle, the storage modulus, loss modulus, and tan delta are calculated. For linear viscoelastic behavior, the energy dissipated per unit volume per cycle equals pi multiplied by the loss modulus and the square of the strain amplitude, which directly links DMA results to the hysteresis loop area.
Typical test programs include temperature sweeps from -80 °C to 100 °C to map the glass transition region, frequency sweeps to assess rate dependence, and strain sweeps to reveal the Payne effect, which is the strain-amplitude dependence of the storage modulus in filled compounds. In tire laboratories, tan delta at 0 °C is used as a wet grip indicator, while tan delta at 60 °C and 10 Hz serves as a rolling resistance indicator.
Torsion Pendulum Free Vibration Method
Described in ISO 4663, this method subjects a strip specimen to free torsional oscillation and records the logarithmic decay of the oscillation amplitude. The damping and frequency-dependent moduli derived from the decay curve provide hysteresis information, particularly useful at low frequencies and around the glass transition.
Yerzley Oscillograph Method
ASTM D945 employs the Yerzley mechanical oscillograph, which records damped natural oscillations of a specimen in compression or shear. The ratio of energy loss to energy input per cycle, known as Yerzley hysteresis, together with Yerzley elastic modulus and set, characterizes the damping behavior of vulcanized rubber at low frequencies relevant to springs and mountings.
Flexometer Heat Build-Up Testing
Constant-stroke compression flexometer testing under ISO 4666 and ASTM D623, which corresponds to GB/T 1687 in the Chinese national standard system, subjects a cylindrical specimen to repeated compressive cycling while a small static load maintains contact. In the widely used Goodrich-type configuration, the specimen is cycled at 30 Hz with a stroke of 4.45 mm under a 250 N static load, and the temperature at the specimen base is monitored continuously, with the temperature rise at 25 minutes reported as the key result. Compression-shear flexometers described in the same standards apply combined deformation for evaluating compounds under more service-like loading. Permanent set after the test is measured as a supplementary result.
Rebound Resilience Testing
ISO 4662 defines a simple falling pendulum method in which the rebound height of a striker impacting a specimen is measured. Lower rebound resilience indicates higher hysteresis loss, providing a rapid quality control screening tool that correlates qualitatively with DMA loss factor results.
Rolling Resistance Correlation Testing
For finished tires, ISO 28580 defines the drum method for measuring rolling resistance, which is a system-level manifestation of hysteresis loss in the tire structure. Laboratory compound-level tan delta data are routinely correlated with drum results during tread compound development.
Applications
Rubber hysteresis loss determination supports material selection, product design, and regulatory compliance across many industries:
- Tire development: minimizing tread hysteresis at high temperature to reduce rolling resistance and fuel consumption while retaining high tan delta at low temperature for wet grip, in line with tire labeling requirements
- Anti-vibration engineering: selecting compounds with tailored hysteresis for engine mounts, suspension bushings, and cab mounts to attenuate vibration across target frequency ranges
- Seismic and structural products: designing high-damping rubber bearings for bridges and buildings that dissipate earthquake energy
- Power transmission and conveying: controlling heat generation in conveyor belts, V-belts, and synchronous belts to extend service life
- Footwear and sports surfaces: balancing shock absorption, energy return, and thermal comfort
- Research and development: evaluating filler-rubber interaction in silica and silane systems, studying the Payne effect, and validating finite element material models with measured dynamic moduli
- Quality control: benchmarking incoming compounds, monitoring cure and mixing consistency, and certifying conformance to customer specifications
Accredited third-party laboratories routinely perform these determinations and issue test reports that are accepted for international trade, regulatory submission, and product certification.
FAQ
What is rubber hysteresis loss?
Rubber hysteresis loss is the portion of mechanical deformation energy that is not recovered during unloading but is converted into heat. It is visualized as the area of the hysteresis loop between loading and unloading curves and is numerically characterized by the loss modulus and tan delta.
How are tan delta and heat build-up related?
Tan delta is the ratio of loss modulus to storage modulus and expresses the fraction of deformation energy dissipated per cycle. Under repeated cyclic loading, this dissipated energy accumulates as heat, so a higher tan delta at the service temperature and frequency generally produces a greater temperature rise in the finished article.
Which standards govern hysteresis loss determination?
Determination of dynamic hysteresis parameters is governed by ISO 4664-1, ASTM D5992, and GB/T 9870. Flexometer heat build-up testing follows ISO 4666 and ASTM D623, equivalent to GB/T 1687. Free vibration torsion pendulum testing follows ISO 4663, and Yerzley oscillograph testing follows ASTM D945. Tire rolling resistance is measured according to ISO 28580.
What are typical test conditions for DMA hysteresis measurement?
Common conditions include 10 Hz frequency and strain amplitudes of 0.1 to 10 percent depending on the application, with temperature sweeps covering the service range. For tire compound evaluation, specific data points at 0 °C and 60 °C are routinely compared because they correlate with wet grip and rolling resistance, respectively.
Why do different rubber polymers show different hysteresis?
Natural rubber, with its ability to strain crystallize and its regular chain structure, typically exhibits low hysteresis, while solution-polymerized styrene-butadiene rubber and compounds with high filler loading show higher hysteresis. Glass transition temperature, filler-polymer interaction, and crosslink density all shift the temperature and frequency dependence of the loss factor.
How can hysteresis loss be reduced in rubber compounds?
Effective strategies include selecting polymers with lower loss factor at service temperature, using reinforcing fillers with improved polymer interaction such as silica-silane systems, optimizing carbon black loading and structure, increasing crosslink efficiency, and adding processing or coupling agents that reduce filler network friction.