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)
42
Embed
Viscoelastic materials Alfrey (1957) listed 3 methods that use experimental curves to map out the viscoelastic character of a material: –Creep curve: function.
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Viscoelastic materialsViscoelastic 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)
• 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)
Dynamic testsDynamic tests
Dynamic testingDynamic 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
• 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
Dynamic testsDynamic tests
• There are 3 criteria for dynamic tests– L/ < 1 : direct measurement of
Dynamic or oscillatory testsDynamic 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.
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.
Parallel-plate geometry for shearing of viscous materials (DSR instrument).
Parallel-plate geometry for shearing of viscous materials (DSR instrument).
Rheometrics RFS II
AnglePhase
)('
)(''tan
G
G
L o s s T a n g e n t
LiquidViscous
MaterialicViscoelast
SolidElasticHookean
o
o
90
900
0
V i s c o e l a s t i c M e a s u r e m e n t sT o r q u e b a r
S a m p l e
C u p
B o b
S t r a i n S t r e s s
o
o
O s c i l l a t o r
P h a s e A n g l e
0
cos)('
oG
S t o r a g e M o d u l u s
0
sin)(''
oG
L o s s M o d u l u s
• 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.
• 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.
• 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.
• 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.
Deformation
Response
Phase angle
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.
A rigid solid incapable of viscous dissipation of energy follows Hooke’s Law, wherein stress and strain are proportional (=E. Therefore, the imposed strain function:
sint)
generates the stress response sint)
sint)and the phase angle, , equals zero.
A.The ideal elastic solid
A rigid solid incapable of viscous dissipation of energy follows Hooke’s Law, wherein stress and strain are proportional (=E. Therefore, the imposed strain function:
The stress in a dynamic experiment is referred to as the complex stress *
Phase angle
Complex Stress*
Strain,
* = ' + i"
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.
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’2 + E”2
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’2 + E”2
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
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
Schematic of stress as a function of t with dynamic (sinusoidal) loading (strain).Schematic of stress as a function of t with dynamic (sinusoidal) loading (strain).
COMPLEX MODULUS:
I E' I = I E* I cos I E" I = I E* I sin
LOSS MODULUSSTORAGE ( Elastic) MODULUS
I E* I = Peak Stress / Peak Strain
E*=E’ + iE”
t
0
o
o
2 /
/
STRESS STRAIN
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.
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.
Complex modulus - G*
The complex modulus describes the total resistance of the sample to oscillatory shear,
G
Similar is he resistance to flow in rotational tests,.
=
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)
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
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
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"/2f
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"/2f
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',
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',
Complex modulus G*Complex modulus G*
G* = G’+iG’’= (G’2+G’’2)1/2
tan = G” / G’
G’ = elastic modulus or storage modulusG’’ = viscosity modulus orloss modulustan = phase angle or loss angle
G’’
G’
G*
TestsTests
• 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
• 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
Dynamic Oscillatory Shear TestDynamic Oscillatory Shear Test
Phase angle - tan damping factorPhase angle - tan damping factor
Phase angle tan is associated with the degree of viscoelsticity of the sample. A low value in tan or indicates a higher degree of viscoelasticity (more solidlike). The phase angle can be used to describe the properties of a sample.
= 90 G*= G´´ and G´= 0 viscous sample
= 0 G*= G´ and G´´= 0 elastic sample
0 < < 90 viscoelastic sample
> 45 G´´> G´ semi liquid sample
< 45 G´> G´´ semi solid sample
Phase angle tan is associated with the degree of viscoelsticity of the sample. A low value in tan or indicates a higher degree of viscoelasticity (more solidlike). The phase angle can be used to describe the properties of a sample.
= 90 G*= G´´ and G´= 0 viscous sample
= 0 G*= G´ and G´´= 0 elastic sample
0 < < 90 viscoelastic sample
> 45 G´´> G´ semi liquid sample
< 45 G´> G´´ semi solid sample
Complex viscosity - *Complex viscosity - *
Complex viscosity describes the flow resistance of the sample in the structured state, originating as viscous or elastic flow resistance to the oscillating movement.
* = G* /
= 2f
A high value for the complex viscosity the greater is the resistance to flow in the structured state.
Complex viscosity describes the flow resistance of the sample in the structured state, originating as viscous or elastic flow resistance to the oscillating movement.
* = G* /
= 2f
A high value for the complex viscosity the greater is the resistance to flow in the structured state.
AnglePhase
)('
)(''tan
G
G
L o s s T a n g e n t
LiquidViscous
MaterialicViscoelast
SolidElasticHookean
o
o
90
900
0
V i s c o e l a s t i c M e a s u r e m e n t sT o r q u e b a r