1. Viscoelastic materials
Alfrey (1957) listed 3 methods that use experimental curves to map out the viscoelastic character of a material:
Creep curve: function of time
Ralaxation curve: function of time
Dynamic modulus curve: dynamic modulus as a function of frequency of the sinusoidal strain
All of them should be independent of the magnitude of the imposed stress or strain. (linear viscoelastic materials)

2. Dynamic tests

3. Dynamic testing Rapid test with minimal chemical and physical changes.
There are 4 types (Morrow and Mohsenin, 1968):
Direct measurement of stress and strain
Resonance methods
Wave propagation methods
Transducer methods

4. Dynamic tests There are 3 criteria for dynamic tests
L/ < 1 : direct measurement of sinusoidally varying  and  (use in most foods)
L/ = 1 : resonance vibration
L/ > 1 : pulsed wave propagation (ultrasonic, sound wave: high frequency or low )
L = length of sample
 = wave length

5. direct measurement of sinusoidally varying  and 
Dynamic-Mechanical Analysis (DMA)
direct measurement of sinusoidally varying  and 

6. Dynamic or oscillatory tests
Dynamic or oscillatory tests are performed to study the viscoelastic properties of a sample. The tests are called microscale experiments compared to macroscale tests like rotational or viscometry tests.
Viscoelastic samples have both elastic (solid) and viscous (liquid) properties, the extreme described by Hooke’s law of elasticity and Newton’s law of viscosity.

7. Parallel-plate geometry for shearing of viscous materials (DSR instrument).
Rheometrics RFS II

9. Dynamic mechanical analysis (DMA), dynamic mechanical thermal analysis (DMTA) or dynamic thermomechanical analysis is a technique used to study and characterize materials.
It is most useful for observing the viscoelastic nature of polymers. An oscillating force is applied to a sample of material and the resulting displacement of the sample is measured.
From this the stiffness of the sample can be determined, and the sample modulus can be calculated. By measuring the time lag in the displacement compared to the applied force it is possible to determine the damping properties of the material.

10. Viscoelastic materials such as polymers typically exist in two distinct states. They exhibit the properties of a glass (high modulus) at low temperatures and those of a rubber (low modulus) at higher temperatures. By scanning the temperature during a DMA experiment this change of state, the glass transition or alpha relaxation, can be observed.

11. Dynamic Mechanical Testing
Deformation
An oscillatory (sinusoidal)
deformation (stress or strain)
is applied to a sample.
The material response
(strain or stress) is measured.
The phase angle , or phase
shift, between the deformation
and response is measured.
Response
Phase angle d

12. Dynamic Mechanical Testing: Response for Classical Extremes
Purely Viscous Response
(Newtonian Liquid)
Purely Elastic Response
(Hookean Solid)
 = 90°
 = 0°
Stress
Stress
Strain
Strain

13. Dynamic Mechanical Testing: Viscoelastic Material Response
Phase angle 0° < d < 90°
Strain
Stress

14. Dynamic (Oscillatory) Rheometry
The ideal elastic solid
A rigid solid incapable of viscous dissipation of energy follows Hooke’s Law, wherein stress and strain are proportional (s=Ee). Therefore, the imposed strain function:
e(w)=eo sin(wt)
generates the stress response
(w)=E eosin(wt) =  o sin(wt)
and the phase angle, d, equals zero.
Where eo = maximum amplitude
 = 2¶f = angular frequency
f = frequency in Hz or cycle/s

15. Dynamic (Oscillatory) Rheometry
B. The ideal viscous liquid
A viscous liquid is incapable of storing inputted energy, the result being that the stress is 90 degrees out of phase with the strain. An input of:
e(w)=eo sin(wt)
generates the stress response
(w)=  o sin(wt+p/2)
and the phase angle, d, p/2.
Where eo = maximum amplitude
 = 2¶f = angular frequency
f = frequency in Hz or cycle/s

16. DMA Viscoelastic Parameters: The Complex, Elastic, & Viscous Stress
The stress in a dynamic experiment is referred to as the complex stress *
The complex stress can be separated into two components:
1) An elastic stress in phase with the strain. ' = *cos
' is the degree to which material behaves like an elastic solid.
2) A viscous stress in phase with the strain rate. " = *sin
" is the degree to which material behaves like an ideal liquid.
Phase angle d
Complex Stress, *
* = ' + i"
Strain, 

17. Generally, measurements for visco
Generally, measurements for visco. materials are represented as a complex modulus E* to capture both viscous and elastic behavior:
E* = E’ + iE”
E*2 = E’ E”2

18. In dynamic mechanical analysis (DMA, aka oscillatory shear or viscometry), a sinusoidal  or  applied.
0 = peak stress
E’ = 0 cos/0 = E* cos
E” = 0 sin/0 = E* sin

19. Schematic of stress  as a function of t with dynamic (sinusoidal) loading (strain).

20. The “E”s (Young’s moduli) can all be replaced with “G”s (rigidity or shear moduli), when appropriate. Therefore:
G* = G’ + iG"
where the shearing stress is  and the deformation (strain) is  or . Theory SAME.

21. Complex modulus - G*
The complex modulus describes the total resistance of the sample to oscillatory shear,
s = G* g
Similar is he resistance to flow in rotational tests, .
s = h g
The complex modulus is determined in an oscillatory test at small angles of deformation. The viscosity is, on the other hand, calculated in rotational tests at varying shear rates (large deformation rates)

22. In analyzing polymeric materials:
G* = (0)/(0), ~ total stiffness.
In-phase component of IG*I = shear storage modulus G‘ ~ elastic portion of input energy
= G*cos

23. The out-of-phase component, G" represents the viscous component of G
The out-of-phase component, G" represents the viscous component of G*, the loss of useful mechanical energy as heat
= G*sin = loss modulus
The complex dynamic shear viscosity * is G*/, while the dynamic viscosity is
 = G"/ or  = G"/2f

24. For purely elastic materials, the phase angle  = 0, for purely viscous materials, 90.
The tan() is an important parameter for describing the viscoelastic properties; it is the ratio of the loss to storage moduli:
tan  = G"/ G',

25. G* = G’+iG’’= (G’2+G’’2)1/2
Complex modulus G*
G* = G’+iG’’= (G’2+G’’2)1/2
tan  = G” / G’
G’’ G*
G’ = elastic modulus or
storage modulus
G’’ = viscosity modulus or
loss modulus
tan  = phase angle or loss angle d G’

26. Tests Dynamic Oscillatory Shear Test
Plate oscillates at increasing frequencies
Strain and stress are measured to determine G’ and G’’
G’ represents the elastic (storage) modulus
G’’ represents the viscous (loss) modulus
When G’ > G’’ the fluid behaves more elastic
When G’ < G’’ the fluid behaves more viscous

27. Phase angle - tan d = damping factor
Phase angle tan d is associated with the degree of viscoelsticity of the sample. A low value in tan d or d indicates a higher degree of viscoelasticity (more solidlike). The phase angle d can be used to describe the properties of a sample.
d = 90  G*= G´´ and G´= 0  viscous sample
d = 0  G*= G´ and G´´= 0  elastic sample
0 < d < 90   viscoelastic sample
d > 45   G´´> G´  semi liquid sample
d < 45   G´> G´´  semi solid sample

28. Complex viscosity - h*
Complex viscosity describes the flow resistance of the sample in the structured state, originating as viscous or elastic flow resistance to the oscillating movement.
h* = G* / w
w = 2pf
A high value for the complex viscosity the greater is the resistance to flow in the structured state.

30. DMA Viscoelastic Parameters
The Modulus: Measure of materials overall resistance to deformation.
G = Stress/Strain
The Elastic (Storage) Modulus: Measure of elasticity of material. The ability of the material to store energy.
G' = (stress/strain)cos
The Viscous (loss) Modulus:
The ability of the material to dissipate energy. Energy lost as heat.
G" = (stress/strain)sin
Tan Delta:
Measure of material damping - such as vibration or sound damping.
Tan = G"/G'

31. of a Viscoelastic Material
Storage and Loss
of a Viscoelastic Material
SUPER BALL
LOSS
TENNIS
BALL X
STORAGE

32. DMA Viscoelastic Parameters: Damping, tan 
Dynamic measurement represented as a vector
G"
Phase angle  G'
The tangent of the phase angle is the ratio of the loss modulus to the storage modulus.
tan  = G"/G'
"TAN DELTA" (tan ) is a measure of the damping ability of the material (damping properties).

33. Viscoelasticity in Crosslinked, Amorphous Polymers
Plots of log G’, log G” and tan against log angular frequency (in radians per second) for a typical elastomer above its Tg;
Poly(styrene-co-butadiene) lightly vulcanized with a peroxide cure.
Note that at low frequencies the material has a low modulus and behaves elastically.
As frequency is increased, the material becomes stiffer, and less capable of storing inputted energy (generates heat upon deformation).
Storage modulus
Loss modulus
tan  = G” / G’

34. Other methods
L/ = 1

35. Resonance Vibration Method
In physics, resonance is the tendency of a system to oscillate at maximum amplitude at a certain frequency. This frequency is known as the system's natural frequency of vibration, resonant frequency, or eigenfrequency.

37. 1 0.5 w0.5 Wr = frequency at ratio equal to 1.0 Amplitude ratio

38. Free vibration method
Make an object vibrate freely. Vibration will stop with time.
Due to internal friction or viscosity, the dead of amplitude after time occurs.
Force acts here A1 A2

39. L/ > 1

40. The use of ultrasonic or sound wave for properties determination
Pulse Method:
Pulse = short duration wave (discontinuous)
Ultrasonic: high frequency
Transducer will produce ultrasonic wave. Input and output data can be obtained.
Time for sound travel through specimen can be calculate from length by time (L/T=velocity).

41. Determination of water content in crude oil

42. Instrument Test cell amplifier Pulse generator oscilloscope receiver
transducer