# Viscoelasticity

As viscoelasticity refers to a partially elastic , partially viscous material behavior. Viscoelastic materials combine the characteristics of solids and liquids . The effect is time , temperature and frequency dependent and occurs with polymer melts and solids such as B. plastics , but also with other materials.

## Material behavior

Kelvin body
Maxwell body
• The elastic component basically causes a spontaneous, limited, reversible deformation ,
• while the viscous part basically causes a time-dependent, unlimited, irreversible deformation.

The viscous and elastic components are differently pronounced in different viscoelastic materials, and the type of interaction also differs.

In rheology , elastic behavior is represented by a spring , the Hooke element, and viscous behavior by a damping cylinder, the Newton element. Viscoelastic behavior can be modeled by combining two or more of these elements.

The simplest viscoelastic models are:

• the Kelvin body. The spring and the damping cylinder are connected in parallel . When loaded , e.g. B. by stretching , the deformation is braked by the damping cylinder and limited by the spring in its extent. After relief, the body goes back to its starting position due to the Hooke element. The Kelvin body is thus deformed over time like a liquid, but limited and reversible like a solid.
• the Maxwell body. It results from the series connection of Hooke and Newton elements. When loaded, the spring deforms immediately, after which time-dependent and unlimited viscous deformation begins. After releasing the load, only the spring moves back, the viscous part remains. There is therefore a time-dependent, unlimited, irreversible deformation as with a liquid, but there is also a time-independent and reversible spontaneously elastic component as with a solid.

More complex models of viscoelastic behavior are the Zener m , Zener k , Lethersich , Jeffreys , and Burgers models.

The complex shear modulus and the complex elasticity module are also used for quantitative description .

## Transition between viscous and solid substance behavior

All liquids and solids can be viewed as viscoelastic materials by specifying their storage and loss modulus , and / or their loss factor . ${\ displaystyle G '}$${\ displaystyle G ''}$ ${\ displaystyle \ tan \ delta = G '' / G '}$

With ideally viscous liquids ( Newtonian fluid ) the storage modulus is very small compared to the loss modulus, with ideally elastic solids, on the other hand, which obey Hooke's law , the loss modulus is very small compared to the storage modulus.

Viscoelastic materials have both a measurable storage modulus and a measurable loss modulus. If the storage modulus is greater than the loss modulus, one speaks of solids, otherwise of liquids.

liquids Sol-gel transition Solids
Material behavior ideally viscous viscoelastic ideal elastic
Storage and loss module ${\ displaystyle G '' \ gg G '}$ ${\ displaystyle G ''> G '}$ ${\ displaystyle G '' = G '}$ ${\ displaystyle G '' ${\ displaystyle G '' \ ll G '}$
Loss factor ${\ displaystyle \ tan \ delta \ gg 1}$ ${\ displaystyle \ tan \ delta> 1}$ ${\ displaystyle \ tan \ delta = 1}$ ${\ displaystyle \ tan \ delta <1}$ ${\ displaystyle \ tan \ delta \ ll 1}$
Substance law ${\ displaystyle \ tau = \ eta \ cdot {\ dot {\ gamma}}}$ ${\ displaystyle \ tau = f (G ', G' ', \ gamma, {\ dot {\ gamma}})}$ ${\ displaystyle \ tau = G \ cdot \ gamma}$

In the last line the shear stress, the shear and its change over time mean (see sketch under complex shear modulus ). The viscosity is related to the imaginary part and the modulus of elasticity is related to the real part of the complex shear modulus. ${\ displaystyle \ tau}$${\ displaystyle \ gamma}$${\ displaystyle {\ dot {\ gamma}}}$${\ displaystyle \ eta}$${\ displaystyle G ''}$${\ displaystyle E}$${\ displaystyle G '}$

## causes

### With polymers

The viscoelasticity of polymers is based on the delayed establishment of equilibrium between the macromolecules during or after mechanical stress. The proportion of the respective expansion components in the total expansion is determined by secondary bonds ( dipole bond , hydrogen bond , Van der Waals bond ) and molecular entanglements. The time-dependent stretching component is determined by stretching, untangling and untangling processes.

The reversible elastic behavior is caused by the entropy elasticity . Depending on the temperature, stress duration and speed leads to irreversible viscous Molekülabgleitungen.

### With metals and ceramics

In crystalline solids such as metals or ceramics , defects such as interstitial atoms or dislocations are predominantly responsible for delayed elongation and thus for viscoelastic behavior. In most cases, the deviations from the ideal elasticity are significantly smaller here than with plastics.