Behavior that combines properties of an elastic solid and of a viscous fluid. In polymers it appears as stress relaxation and creep and depends on time and temperature.
Japanese name: 粘弾性
Viscoelasticity appears in 2 practice questions across 1 topic, including Polymers and composites.
Field: Polymers and composites
A viscoelastic material behaves like an elastic solid when loaded over a short time and like a liquid when loaded over a long time. Which it appears to be depends on the ratio of the material's relaxation time to the observation time. A familiar example is silicone toy putty, which snaps when pulled quickly, stretches when pulled slowly and flows flat when left alone. In polymers it appears as creep, in which strain increases under constant load; stress relaxation, in which stress falls at constant strain; and hysteresis, in which the loading and unloading curves do not coincide.
When a sinusoidal strain is applied, the stress in a viscoelastic material leads in phase by δ (0–90°). Splitting the stress into components in phase with the strain and 90° out of phase gives the storage modulus E′ (energy stored and returned) and the loss modulus E″ (energy lost as heat), and the ratio tan δ = E″/E′ is called the loss tangent. For a purely elastic solid δ = 0, and for a purely viscous liquid δ = 90°. In dynamic mechanical analysis (DMA) with varying temperature, E′ drops sharply near Tg and tan δ shows a maximum.
At small strains, Boltzmann's superposition principle holds, by which the effects of past stresses or strains can simply be added, and this is called linear viscoelasticity. Models of springs and dashpots describe behavior within this range; real polymers are approximated by generalized models with many Maxwell elements of different relaxation times in parallel, and this form is also used as input for finite element analysis. As strain increases, the response departs from linearity and superposition no longer holds.
In polymers, raising the temperature has the same effect as observing over a longer time. Near Tg the WLF equation log a_T = −C₁(T − Tr)/(C₂ + T − Tr) is widely used, and with Tg as the reference temperature, C₁ ≈ 17.44 and C₂ ≈ 51.6 K are the universal values. With these, relaxation proceeds about 700 times faster at 10 K above Tg. Damping materials are designed so that tan δ is large at the temperature and frequency of use, and for tire rubber, tan δ values on the low- and high-temperature sides serve as guides to grip and rolling resistance.
Answer: A. The Maxwell model, a spring and dashpot in series, can represent stress relaxation under constant strain
When a constant strain is applied to the Maxwell model (series), the spring stretches first and stress develops; then the dashpot slowly extends while the spring contracts, so the stress relaxes as σ = σ₀exp(−t/τ) (τ = η/E). In the Voigt (Kelvin–Voigt) model (parallel), the spring and dashpot always have the same strain, so the stress does not relax under constant strain. What the Voigt model represents is delayed elasticity (creep), in which strain approaches a constant value over time under constant stress. Under constant stress, the strain of the Maxwell model does not approach a constant value but keeps increasing in proportion to time. Real polymers are approximated by combinations such as the four-element model.
Answer: A. Raising the temperature has the same effect as measuring over longer times (lower frequencies)
Molecular motion in polymers is faster at higher temperatures, so relaxations that occur in a short time at high temperature take a long time at low temperature. Relaxation modulus curves measured at different temperatures can therefore be shifted along a logarithmic time axis to overlap into a single composite curve (the master curve). In other words, raising the temperature has the same effect as measuring at longer times (lower frequencies). The amount of shift (the shift factor) is described by the WLF equation near Tg and by an Arrhenius-type expression well below Tg. Using this principle, long-term creep and stress relaxation at room temperature can be predicted from short tests at high temperature.
Deformation by linear viscoelasticity includes a component that recovers with time and is proportional to the magnitude of stress. Plasticity is permanent deformation that occurs when the yield stress is exceeded and does not recover on unloading. In polymers both can occur at the same time.
It corresponds to the ratio of the energy lost as heat to the energy stored in one cycle of deformation, and equals the loss modulus divided by the storage modulus. The larger it is, the better the material absorbs vibration, and it is used to evaluate rubber and damping materials.
Yes. Even in metals at room temperature, jumps of interstitial carbon atoms and similar processes make strain lag slightly behind stress, which is measured as internal friction. The amount is much smaller than in polymers, but it is relevant to damping in precision springs and resonators and to creep at high temperature.
Creep Crystallinity Glass transition temperature Rule of mixtures Thermosetting resin