The storage and loss modulus tell you about the stress response for a visco-elastic fluid in oscillatory shear. If you impose a shear strain-rate that is cosine; a viscous fluid will have stress proportional to the shear strain-rate (Newtonian) an elastic solid will have stress proportional to the shear strain (sine - integral of cosine). A visco-elastic response will be a mixture of the two. The storage modulus is the elastic solid like behavior (G') and the loss modulus is the viscous response (G''). These will cross-over when the frequency is equal to the reciprocal relaxation time.

Hope that helps,

Dave

Hi, in a different approach to your question, I would first ask why to carry out these kind of tests. In general, it is because you may suspect your material has a microstructure. Oscillatory sweeps are then used to infer on this microstructure, e.g. how strong it is.

A microstructure means that there are forces between the molecules or particles in the material. To break the microstructure you need to apply a force larger than the ones holding it. When the applied force is smaller than the molecular or inter particle forces, then G' is larger than G"; the material has some capacity to store energy and should be able to return, to some extent, to its initial configuration before a mechanical force was applied. The material behaves as an elastic solid, although not an ideal one because some of the mechanical energy is dissipated.

But when the applied force is higher, then the microstructure collapses and the mechanical energy given to the material is dissipated, meaning that the material flows. G" becomes larger than G'.

The crossover point where G" becomes largar than G' is the moment where the applied mechanical force overtakes the molecular or inter particles forces and the material starts to yield (or flow).

I wish to add that for the determination of the behaviour of the microstructure and for more accurate interpretation of the obtained data, amplitude is usually small to initially keep the response in the linear viscoelastic region before the yield point.

Please find the attached file of DMA book

Please, look here https://en.wikipedia.org/wiki/Dynamic_modulus

The storage and loss modulus in viscoelastic materials measure the stored energy, representing the elastic portion, and the energy dissipated as heat, representing the viscous portion

there is very simple and clear explanations:

http://www1.lsbu.ac.uk/water/rheology.html

They just are a decomposition of time dependent stress into real and imaginary parts of a complex number. In molecular terms, the real part G', is the motion of the polymer molecule which follows the macroscopic deformation, thus it is elastic and stores some of the deformation energy. The imaginary part G", is the rearrangements of deformed polymer segments to maximize entropy, thus it is a viscous response and dissipates some of the deformation energy. The moduli G' and G" are meaningful only in the linear viscoelastic case. In large deformations, the response to a sinusoidal deformation is not sinusoidal, so the decomposition will not have a molecular interpretation.

Hi all :

Generally

Storage modulus (E‘) is a measure of elastic response of a material. It measures the stored energy.

Loss modulus (E") is a measure of viscous response of a material. It measures the energy dissipated as heat.

Hello

Basically, At low temperatures which is replica of high frequency, the material is too stiff and behaves like a elastic material with phase angle tends to 0 degree leading to the storage of energy because at this stage the stress required to break the microstructure of material is less then its strength. Therefore the material stores the energy.

While at high temperatures which is the replica of low frequency, the material behaves like a viscous material with the ability of flow and the phase angle also tends to 90 degree leading to the dissipation of energy from the material in the form of heat because at this stage the stress required to break the microstructure of material is higher then the material strength. Therefore material energy dissipates.

At low frequency(high temperature), storage modulus is less then loss modulus whereas at high frequency(low temperature) loss modulus is less then storage modulus.

Thanks

In general, storage modulus is more sensitive to any changes in micro- or nano-structure of viscoelastic systems in frequency sweep test and information about rigidity of samples can be obtained by G’.

Hi, these kinds of tests are performed to understand the strength of the microstructure e.g. how strong is your material or material is showing viscoelastic property. The microstructure tells about the forces between the particles or molecules in the material. The storage modulus provides the energy storage capability in the material while the loss modulus offers energy dissipated within the material. In amplitude sweep test critical strain classified two characteristics region: linear viscoelastic (LVE) region and nonlinear viscoelastic region. When the applied strain will be less than critical strain material shows a linear viscoelastic behavior (elastic solid) and storage will be greater than loss modulus (material has the capacity to store energy). When the strain becomes larger than critical strain materials show a nonlinear viscoelastic behavior and dissipation of energy starts and materials will not return their original state and microstructure start to destroy. After that, at higher strain amplitude, the storage modulus and loss modulus intersect at a point where loss modulus will be greater than storage modulus. This point suggests the domination of loss modulus and microstructure are usually broken and material flow. When the storage modulus exhibited a stable plateau over the frequency test range means material indicates the sturdy solid-like behavior. Jayne Houghton

The viscoelastic characteristics of a sample can be determined as a function of timescale using a frequency sweep test.

Thanks for sharing

Hi Jayne,

Understanding viscoelastic response is very crucial for polymeric system as polymeric material has both amorphous and crystalline regions. The physical entanglement i.e. arrangement of microstructural composite domain greatly influence on net viscoelasticity.

Frequency is nothing but a strain rate only.

When the frequency is low, that means the relaxation time is large. The polymeric chains can relax at a greater extend, hence they will show elastic nature. This is called energy absorbing/storing capacity or storage modulus. As we increase frequency, the microstructure will gradually collapse to dissipate energy as a viscous response, hence loss modulus will increase. Moreover, the transition of solid like to liquid like responce with frequency is a subject of research. It may varry material to material based on their composition. The effect of if any secondery phase i.e. reinforcement effect on matrix material would alter their viscoelastic responces.

Loss tangent is also another one parameter which is storage modulus normalised loss modulus i.e. ratio of loss to storage modulus. This says more on net damping of the material. The loss tangent peak and the area under loss tangent will inform on the relaxation dynamics.