DMA Training 2018-August - TA...
Transcript of DMA Training 2018-August - TA...
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Dynamic Mechanical AnalysisBasic Theory & Applications Training
TA Instruments – Waters LLC
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Course Outline
• Basic Theories of Dynamic Mechanical Analysis
• DMA Instrumentation and Clamps
• Introduction to DMA Experiments
Dynamic tests
Transient tests
• DMA Applications and Data Interpretation
• Troubleshooting Experimental Issues
• Time-Temperature Superposition (TTS)
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Basic Theories of
Dynamic Mechanical Analysis
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DMA Definitions
• What is a DMA? Dynamic Mechanical Analyzer/ Dynamic Mechanical Analysis
• What does a DMA do? A DMA measures the mechanical/rheological properties of a material as a function of time, frequency, temperature, stress and strain
• What are the typical samples a DMA can handle? Thermal plastic and thermosets Elastomers/ rubbers Gels Foams More….
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How Does a DMA Work?
• Apply a force or a deformation to a sample, then measure sample’s response, which will be a deformation or a force.
• All mechanical parameters (stress, strain, modulus, stiffness et al) are calculated from these 2 raw signals
Length
Area
Force
Deformation
Stress (Pa) = Force(N)Area(m2)
Strain = Deformation (m)
Length (m)
Modulus (Pa) = Stress (Pa)
Strain
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What Does a DMA Measure?
• DMA measures the viscoelastic properties (stiffness and damping) of a material as a function of time and temperature. These are reported as
Modulus (E and G) / Compliance (J)
Damping factor (tan d)
Transition temperatures (e.g. Tg)
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Newton’s Law of Viscosity
• For a purely Viscous Liquid, Stress is proportional to Strain Rate dε/dt
•The slope of stress over strain rate is the viscosity of the material
σ = η* dε/dt
Str
ess
Strain Rate
η
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Hooke’s Law of Elasticity
• For a purely Elastic Solid, Stress and Strain have a constant proportionality
• The slope of stress over strain is the Young’s modulus of the material
σ = E*ε
Str
ess
Strain
E
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Viscoelasticity Defined
Range of Material Behavior
Ideal Liquid ----- Most Materials ----- Ideal SolidPurely Viscous ----- Viscoelastic ----- Purely Elastic
Viscoelasticity: Having both viscous and elastic properties
• Most of the materials in the world have both elastic and viscous behavior. Therefore, they are viscoelastic
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How to Describe Viscoelastic Behavior?
σ = E*ε + η*dε/dt
Kelvin-Voigt Model (Creep) Maxwell Model (Stress Relaxation)
Viscoelastic Materials: Force depends on both deformation and rate of deformation and vice versa.
L1
L2
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Mechanical Property Becomes Time Dependent
•In tensile testing of viscoelastic materials, the rate of extension will give different results
the stress depends on both the strain, and the strain rate
σ = E*ε + η*dε/dt
Stre
ss, σ
Strain, ε
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Time-Dependent Viscoelastic Behavior
http://www.theatlantic.com/technology/archive/2013/07/the-3-most-exciting-words-in-science-right-now-the-pitch-dropped/277919/
Started in 1927 by Thomas Parnell in Queensland, Australia
Long deformation time: pitch behaves like a highly viscous liquid
9th drop fell July 2013
Short deformation time: pitch behaves like a solid
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Time-Dependent Viscoelastic Behavior
T is short [< 1 sec] T is long [>2 hours]
Deborah Number [De] = /
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Viscoelasticity, Deborah Number
•Old Testament Prophetess who said (Judges 5:5):"The Mountains ‘Flowed’ before the Lord"
•Everything Flows if you wait long enough!
•Deborah Number, De - The ratio of a characteristic relaxation time of a material () to a characteristic time of the relevant deformation process ().
De =
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Deborah Number
• Hookean elastic solid - τ is infinite• Newtonian Viscous Liquid - τ is zero• Polymer melts processing - τ may be a few seconds
High De Solid-like behaviorLow De Liquid-like behavior
IMPLICATION: Material can appear solid-like because1) it has a very long characteristic relaxation time or2) the relevant deformation process is very fast
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Dynamic Mechanical Testing
Deformation
Response
Phase angle d
An oscillatory (sinusoidal) deformation (stress or strain)is applied to a sample.
The material response (strain or stress) is measured.
The phase angle d, or phase shift, between the deformation and response is measured.
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Phase Angles
Purely Elastic Response(Hookean Solid)
Purely Viscous Response(Newtonian Liquid)
Viscoelastic Response(Most materials)
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The stress in a dynamic experiment is referred to as the complex stress *
Phase angle d
Complex Stress, *
Strain,
* = ' + i"
The complex stress can be separated into two components: 1) An elastic stress in phase with the strain. ' = *cosd' is the degree to which material behaves like an elastic solid.2) A viscous stress in phase with the strain rate. " = *sind" is the degree to which material behaves like an ideal liquid.
The material functions can be described in terms of complex variables having both real and imaginary parts. Thus, using the relationship:
Complex number: 𝑥 + 𝑖𝑦 = 𝑥 + 𝑦
Dynamic Stress: Complex, Elastic, & Viscous Stress
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DMA Viscoelastic Parameters
The Elastic (Storage) Modulus:Measure of elasticity of material. The ability of the material to store energy.
The Viscous (loss) Modulus:The ability of the material to dissipate energy. Energy lost as heat.
The Modulus: Measure of materials overall resistance to deformation.
Tan Delta:Measure of material damping - such as vibration or sound damping.
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Storage and Loss of a Viscoelastic Material
Rubber Ball
Tennis Ball X
STORAGE
LOSSX
Phase angle d
E*
E'
E"Dynamic measurement represented as a vector
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Viscoelastic Spectrum for a Typical Amorphous Polymer
Terminal Region
Rubbery PlateauRegion
TransitionRegion
Glassy Region
Loss Modulus (E" or G")Storage Modulus (E' or G')
Very hard and rigid solid
Stiff to Soft rubber
Viscoelastic liquid
Temperature
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DMA Results Can Correlate To…..
Stress
Strain
Stiffness
Damping factor
Transition temperatures
Modulus (E, G) / Compliance (J)
Stress
Strain
Stiffness
Damping factor
Transition temperatures
Modulus (E, G) / Compliance (J)
Processing ConditionsProcessing Conditions
Stress
Strain
Stiffness
Damping factor
Transition temperatures
Modulus (E, G) / Compliance (J)
Processing Conditions
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DMA Instrumentationand Clamps
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DMAs from TA Instruments
RSA G2 Discovery DMA850 Q800
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DMAs from TA Instruments
Motor Applies Force (Stress)
Displacement SensorMeasures
deformation (Strain)
SampleForce Rebalance Transducer (FRT)
Measures Force (Stress)
Actuator Applies deformation
(Strain)
Sample
Fixed
Combined Motor & TransducerSeparate Motor & Transducer
RSA G2 DMA850 and Q800
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RSA G2: Schematic Dual Head Design
Transducer
Motor
Upper Geometry MountLower Geometry Mount
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DMA850: Schematic
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DMA850 and Q800: Humidity Option
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DMA Specifications
RSA G2 DMA850 Q800
Max Force 35 N 18 N 18 N
Min Force 0.0005 N 0.0001 N 0.0001 N
Displacement Resolution
1 nm 0.1 nm 1 nm
Frequency Range 2 x 10-6 to 100 Hz 1 x 10-4 to 200 Hz 1 x 10-2 to 200 Hz
Dynamic Deformation Range
± 5 x 10-5 to 1.5 mm ± 5 x 10-6 to 10 mm ± 5 x 10-4 to 10 mm
Temperature range -150 to 600°C -150 to 600°C -150 to 600°C
Isothermal Stability ± 0.1 ± 0.1 ± 0.1
Heating Rate 0.1oC to 60oC/min 0.1oC to 20oC/min 0.1oC to 20oC/min
Cooling Rate 0.1oC to 60oC/min 0.1oC to 10oC/min 0.1oC to 10oC/min
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DMA Mode on DHR and ARES-G2
Force Rebalance Transducer (FRT)
(Measures Stress)
For the ARES-G2, the bottom Actuator remains
locked during DMA function
Sample
Servo control on Null position
(Strain)
Strain control & dynamic test only
ARES G2 and DHR DMA Mode
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Specifications of the DHR-DMA and the ARES-G2 DMA
DHR – DMA mode
ARES-G2 DMA mode
Motor Control FRT FRT
Minimum Force (N) Oscillation 0.1 0.001
Maximum Axial Force (N) 50 20
Minimum Displacement (m) Oscillation 1.0 0.5
Maximum Displacement (m) Oscillation 100 50
Displacement Resolution (nm) 10 10
Axial Frequency Range (Hz) 1 x 10-5 to 16 1 x 10-5 to 16
• Dynamic test only
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Clamps for DMA850 and Q800
S/D Cantilever Film/Fiber Tension 3-Point Bending Compression
Shear Sandwich Submersible Tension Submersible Bending Submersible Compression
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Clamps for RSA G2
Film/Fiber Tension
Compression
3-Point Bending
S/D Cantilever
Shear Sandwich
Contact Lens
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RSA G2 Immersion Clamps
• Immersion clamp kit offers 3 geometries with temperature control from -10 to 200 C in the FCO.
Tension Compression 3 Point Bending
Tension: Up to 25 mm long, 12.5 mm wide and 1.5 mm thick.Compression: 15 mm in diameter; maximum sample thickness is 10 mm.Three Point Bending: includes interchangeable spans for lengths of 10, 15, and 20 mm. Maximum sample width is 12.5 mm and maximum thickness is 5 mm.
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What Samples Can DMA Measure?
• By changing the clamp, we can test a range of different materials: solid bars, elastomers, soft foams, thin films and fibers
Solid Polymers
Elastomers
Films
Foams Composites
Fibers
Polymer Melts
Gels
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Deformation of Solids and the Modulus
•All materials change in shape, volume, or both under the influence of an applied stress.
•The Modulus measures the resistance to deformation of a material when an external force is applied.Modulus = Stress/Strain
•We can define three kinds of Moduli for a materialYoung’s Modulus (Modulus of Elasticity) EShear Modulus (Modulus of Rigidity) GBulk Modulus B
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The Three Deformation Modes and Moduli
ShearModulus
BulkModulus
Young’s Modulus
E =
gG = hyd
DV/VoB =
Where Dashed lines indicate initial stressed state = uniaxial tensile or compressive stress = shear stresshyd = hydrostatic tensile or compressive stress = normal straing = shear strainDV/Vo = fractional volume expansion or contraction
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Relationship Between Moduli and Poisson’s Ratio for Elastic Isotropic Materials
• Elastic Isotropic materials are materials in which properties at a point are the same in all directions. Some examples of isotropic materials are unorientedamorphous polymers and annealed glasses [1].
• If any of the two elastic constants of a homogenous (in which properties do not vary from point to point) isotropic material, the other two may be calculated [2].
1. Nielsen, Lawrence E., Mechanical Properties of Polymers and Composites, Marcel Dekker, Inc., New York, 1974, p. 1.
2. Hayden, H. W., Moffatt, W.G., and Wulff, J., The structure and Properties of Materials, Volume III, Mechanical Behavior,John Wiley & Sons, Inc, New York, 1965, p.26.
E = 2G(1 + n) = 3B(1 + 2n)
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Poisson's Ratio - The Fourth Elastic Constant
• Poison's ratio, n, is the ratio of transverse to axial strain
l0zlz
z
z
ly
-y
2ly - l0y
2 =
z
2lz - l0z
2 =
n = - y
z
Poisson’s Ratiol0y
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Poisson’s Ratio
•If the volume of the specimen remains constant when deformed, n = 0.5.
•Examples of constant volume materials are liquids and ideal rubbers.
•In general, there is an increase in volume given by DV/Vo = (1 - 2n)where DV = increase in initial volume Vo caused by straining the sample.
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Comparison of Moduli and Poisson’s Ratio
Cowie, J.M.G., Polymers: Chemistry & Physics of Modern Materials, 2nd Edition, Blackie academic & Professional, and imprint of Chapman & HallBishopbriggs, Glasgow, 1991p. 275ISBN 0 7514 0134 X
Material E (GPa) n G (GPa)
Steel 220 0.28 85.9
Copper 120 0.35 44.4
Glass 60 0.23 24.4
Granite 30 0.30 15.5
Polystyrene 34 0.33 12.8
Polyethylene 24 0.38 8.7
Natural Rubber 0.02 0.49 0.0067
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Testing Solids on a Rheometer
Torsion (rotational) and DMA (axial) geometries allow solid samples to be characterized in a temperature controlled environment.
Rectangular and cylindrical torsion
3-point bending Cantilever Tension
Shear Modulus: G’, G”, G* Young’s Modulus: E’, E”, E*
E = 2G(1 + ν) ν : Poisson’s ratio
Parallel plate
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How DMA Calculate Modulus?
DMA850 and Q800 RSA G2
Stiffness (K) = Force / Displacement
Modulus (E) = Stress / Strain
GF: Geometry factor. Clamp dependentCan be found in online help manual
Stress = Force x K
Strain = Displacement x KnModulus (E) = K x GF
K:Stress constantKn :Strain constantClamp dependentCan be found in online help manual
GF = KKn
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Choose the Correct Clamp for Testing
Sample Dimension Films and fibers: tension clamps Bars and cylinders: bending clamps O-rings and tablets: compression and/or shear
Deformation Mode: E [tension, compression and bending] G [shear]
Sample Stiffness: Machine range fixed: 100 - 10, 000,000 N/m. Stiffness of
sample related to its dimensions [L, w, t]. Stiffness may limit sample size to below clamp maximum.
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DMA: Dual Cantilever Clamp
Highly damped materials can be measured Best mode for evaluating the cure of supported materials
Sample
Stationary Clamp
Movable clamp
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Geometry Factor - Dual Cantilever Clamp
Modulus = Stiffness × Geometry Factor
If length/thickness > 10, Poisson’s Ratio term is dropped
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Operating Range of the Dual Cantilever Clamp
16 mm long10 mm wide4 mm thick
35 mm long12.5 mm wide3.2 mm thick
35 mm long12.5 mm wide1.75 mm thick
8 mm long12.5 mm wide0.1 mm thick
10 510 210 110 0
Geometry Factor (1/mm)10 3 10 4
10 -1
10 4
10 5
10 6
10 7
10 8
10 9
10 10
10 13
10 12
10 11
10 3
Mo
du
lus
(P
a)
Modulus = Stiffness × Geometry Factor
DC
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DMA: Single Cantilever Clamp
Best general purpose mode (thermoplastics) Preferred mode over dual cantilever for most neat
thermoplastics (unreinforced), except elastomers Clamping torque is important
Sample
Stationary Clamp
Movable clamp
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Geometry Factor - Single Cantilever Clamp
Modulus = Stiffness × Geometry Factor
If length/thickness > 10, Poisson’s Ratio term is dropped
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Operating Range of the Single Cantilever Clamp
17.5 mm long12.5 mm wide3.2 mm thick
17.5 mm long12.5 mm wide1.75 mm thick
17.5 mm long12.5 mm wide0.5 mm thick
10 510 210 110 0
Geometry Factor (1/mm)10 3 10 4
10 -1
10 4
10 5
10 6
10 7
10 8
10 9
10 10
10 13
10 12
10 11
10 3
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DMA: 3 Point Bend Clamp
Best mode for measuring medium to high modulus materials Conforms with ASTM standard test method for bending Purest deformation mode since clamping effects are eliminated
Moveable Clamp Force
Sample
Stationary Fulcrum
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Geometry Factor - 3 Point Bending Clamp
Modulus = Stiffness × Geometry Factor
If length/thickness > 10, Poisson’s Ratio term is dropped
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Operating Range of the 3 Point Bending Clamp
20 mm long12.5 mm wide2.5 mm thick
50 mm long12.5 mm wide3.2 mm thick
50 mm long12.5 mm wide
1 mm thick
10 510 210 110 0
Geometry Factor (1/mm)10 3 10 4
10 4
10 5
10 6
10 7
10 8
10 9
10 10
10 13
10 12
10 11
Mo
du
lus
(P
a)
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DMA: Film and Fiber Tension Clamp
Best mode for evaluation of thin films and fibers bundle or single filaments
Small samples of high modulus materials can be measured TMA-like constant force and force ramp measurements
aka. mini-tensile tester Force track and constant force control
Movable clamp
Sample(film, fiber, or thin sheet)
StationaryClamp
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Operating Range of the Film/Fiber Tension Clamp
Geometry Factor (1/mm)
10 mm long5 mm long
0.2 mm long
20 mm long4 mm wide
0.1 mm thick20 mm long0.1 mm diameter
10 -1 10 010 1 10 2 10 4
10 310 5
10 4
10 5
10 6
10 7
10 8
10 9
10 10
10 11
10 12
10 13
Mo
du
lus
(P
a)
Modulus = Stiffness × Geometry Factor
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DMA: Compression Clamp
Good mode for low to medium modulus materials(gels,elastomers)
Materials must provide restoring force(support necessary static load)
Options for expansion & penetration measurements Typically shear component is significant
Stationary Clamp
Sample
Movable Clamp
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Operating Range of the Compression Clamp
10 -110 010 -210 -310 -4
10 4
10 5
10 6
10 7
10 8
10 9
10 10
10 3
10 2
10 1
Geometry Factor (1/mm)
Mo
du
lus
(P
a)
1 mm thick40 mm diameter
2 mm thick20 mm diameter
6 mm thick10 mm diameter
Modulus = Stiffness × Geometry Factor
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DMA: Shear Sandwich Clamp
Square sample configuration provides pure shear deformation Provides Shear Moduli: G*, G', G" & G(t) Good for evaluating highly damped soft solids such as gels and
adhesives & elastomers > Tg Can be used for high viscosity melts and resins
MovableClamp
StationaryClamp
Sample
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Operating Range of the Shear Sandwich Clamp
each piece2 mm thick
10 mm square
each piece4 mm thick
5 mm square
10 -110 010 -210 -3
10 4
10 5
10 6
10 7
10 8
10 9
10 10
10 3
10 2
10 1
Geometry Factor (1/mm)
Mo
du
lus
(P
a)
Modulus = Stiffness × Geometry Factor
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Changing Sample Stiffness
Clamp Type To Increase Stiffness… To Decrease Stiffness… Tension Film Decrease length or increase
width. If possible increase thickness.
Increase length or decrease width. If possible decrease thickness.
Tension Fiber Decrease length or increase diameter if possible.
Increase length or decrease diameter if possible.
Dual/Single Cantilever Decrease length or increase width. If possible increase thickness. Note: L/T 10
Increase length or decrease width,, If possible decrease thickness. Note: L/T 10
Three Point Bending Decrease length or increase width. If possible increase thickness.
Increase length or decrease width. If possible decrease thickness.
Compression – circular sample
Decrease thickness or Increase diameter.
Increase thickness or decrease diameter.
Shear Sandwich Decrease thickness or Increase length and width.
Increase thickness or decrease length and width.
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DMA Clamping Guide
Sample Clamp Sample Dimensions
High modulus metals or composites
3-point BendDual Cantilever
Single CantileverL/T> 10 if possible
Unreinforced thermoplastics or thermosets
Single Cantilever L/T >10 if possible
Brittle solid (ceramics) 3-point BendDual Cantilever
L/T>10 if possible
Elastomers Dual CantileverSingle CantileverShear SandwichTension
L/T>20 for T<TgL/T>10 for T<Tg(only for T> Tg)T<2 mm W<5 mm
Films/Fibers Tension L 10-20 mmT<2 mm
Supported Systems 8 mm Dual Cantilever minimize sample, put foil on clamps
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Available DMA Experiments
(1) Dynamic Tests
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Dynamic (Oscillatory) Testing
Available oscillatory test modes
•Strain (stress) Sweep
•Time Sweep
•Frequency Sweep
•Temperature Ramp
•Temperature Step (Sweep) (TTS)
•Others
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Some Clamps Require Offset (static) Force!
Clamps with offset force:Tension FilmTension: Fiber3-Point BendCompressionPenetration
Force/Time Curves
OFA
0A
A = Oscillatory force amplitudeOF = Offset force (static force)
Clamps without offset force:Single CantileverDual CantileverShear Sandwich
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Offset (Static) Force
Static force [General] Used in tensioning clamps to prevent sample buckling [tension], or loss of
contact with the probe [compression] during the test. Static force must exceed dynamic force at all times during experiment
Applied before dynamic oscillation to automatically measure sample lengthConstant Force
Applies same static force throughout experiment Can be used with highly crystalline or cross-linked materials
to measure displacement at constant force for quant. expansionForce Track
Applies Static Force in Proportion to Sample Modulus. Used in "Tensioning" Clamps to reduce stretching as specimen weakens
Ratio of static to dynamic force: Static Force = (Force Track %/100) x (Stiffness x Amplitude) where stiffness = Force applied to sample/amplitude of deformation
Values from 125-150% work well for most samples
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Offset Force on DMA850
Constant static force Force track
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Offset Force on Q800
Constant static force Force track
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Offset Force on RSA G2
Constant static force Force track
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Temperature Ramp with Force Track
•Static Force tracks Dynamic Force throughout Temperature Ramp
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Choosing Force Track Parameters
Clamp Type Static Force Force Track Tension Film 0.01 N 120 to 150% Tension Fiber 0.001 N 120% Compression 0.001 to 0.01 N 125%
Three Point Bending Thermoplastic Sample
1 N 125 to 150%
Three Point Bending Stiff Thermoset Sample
1 N 150 to 200% Can use constant static
force
Initial static force before testing
Note: Constant (or static) force can be used as long as static force > dynamic force through out the entire experiment.
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Dynamic Strain (Stress) Sweep
• The material response to increasing deformation amplitude is monitored at a constant frequency and temperature. Time
Deformation
USES• Identify Linear Viscoelastic Region• Resilience/elasticity
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Dynamic Strain Sweep: Material Response
gc = Critical Strain
ConstantSlope
Results depend on strainLinear viscoelastic regionResults independent of strain
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Programming Strain Sweep on DMA850
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Programming Strain Sweep on Q800
Mode: DMA Multi-Strain
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Programming Strain Sweep on RSA G2
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Dynamic Time Sweep
Time
Deformation • The material response is monitored at a constant frequency, amplitude and temperature.
USES• Curing studies• Fatigue tests• Stability against thermal degradation
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Epoxy Curing on Glass Braid
Instrument: DMA850Clamp: Dual cantileverSample: Epoxy coated on glass braidDynamic time sweepTemperature: 35°CFrequency: 1 HzAmplitude: 10 m
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Programming Time Sweep or Fatigue on DMA850
• Time sweep example • Fatigue example
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Programming Time Sweep on Q800
Mode: DMA Multi-Frequency-Strain
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Programming Time Sweep or Fatigue on RSA G2
• Time sweep example • Fatigue example
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Frequency Sweep
• The material response to increasing frequency (rate of deformation) is monitored at a constant amplitude and temperature.
Time
Deformation
USES• Quick comparison on modulus and elasticity on
solids• Study polymer melt processing (shear sandwich).• Estimate long term properties with extended
frequency (time) range using TTS
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Happy & Unhappy Balls
10-1 100 101102
105
106
107
108
10-2
10-1
100
Freq [rad/s]
E
' ()
[d
yn/c
m²]
tan
_de
lta (
) [ ]
Unhappy ball
Happy ball
Modulus is the sametan d is very different
Happy & Unhappy Balls
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Frequency Sweep: Material Response
Terminal Region
Rubbery PlateauRegion
TransitionRegion
Glassy Region
12
Storage Modulus (E' or G')Loss Modulus (E" or G")
log Frequency (rad/s or Hz)
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Programming Frequency Sweep on DMA850
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Programming Frequency Sweep on Q800
Mode: DMA Multi-Frequency-Strain
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Programming Frequency Sweep on RSA G2
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Dynamic Temperature Ramp
• A linear heating rate is applied. The material response is monitored at a constant frequency and constant amplitude of deformation. Data is taken at user defined time intervals. Time
Data Acquisition Interval
m = ramp rate
Recommend ramp rate for polymer testing: 1-5˚C/min.
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Temperature Step & Hold- Single /Multi-Frequency
• A step and hold temperature profile is applied. The material response is monitored at one, or over a range of frequencies, at constant amplitude of deformation
Time
Soak Time
Step Size
OscillatoryMeasurement
Time
Step Size OscillatoryMeasurement
Soak Time
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Temperature Profile on Amorphous Polymers
Temperature
Terminal Region
Rubbery PlateauRegion
TransitionRegion
Glassy Region
Loss Modulus (E" or G")
Storage Modulus (E' or G')
DMA Applications Range
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Temp Ramp on Polycarbonate
Clamp: single cantileverTemperature:ambient to 180°CHeating rate: 3°C/minFrequency: 1 HzAmplitude: 20 m
PC sample
p/n: 982165.903
• Available from TA for Instrument verification
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Programming Temp Ramp/Sweep on DMA850
• Temp Ramp Example • Temp Sweep Example
Note: Measurement can be done with single or multiple frequencies
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Programming Temp Ramp/Step on Q800
Mode: DMA Multi-Frequency-Strain• Temp Ramp Example • Temp Sweep Example
Note: Measurement can be done with single or multiple frequencies
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Programming Temp Ramp/Sweep on RSA G2
• Temp Ramp Example • Temp Sweep Example
Note: Measurement can be done with single or multiple frequencies
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Experimental Considerations
• Sample Deformation Mode Stiffness (sample size and shape) Clamp Type (sample size and shape)
• Static Force/Force Track
• Amplitude (single/multiple)
• Frequency (Single/multiple)
• Heating Rate/Temperature Program
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Selecting Appropriate Amplitude and Force
• Strain considerationMust be within the linear region
• Force considerationMaximum - 18 N on Q800, DMA850Maximum - 35 N on RSA G2
• Yielding /Creep If the force is too high the specimen may deform irreversiblyMust consider behavior at all temperatures and frequencies
• NoiseHigher amplitude = lower noise (generally) Trade off against yielding/creep behavior
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Frequencies
• Single Frequency In a temperature ramp the most commonly used frequency is
between 1 to 10 Hz (6.28 or 63 rad/sec)• Multiple Frequencies For an ambient test the commonly used frequency range is
from 0.1 – 10Hz. Frequency sweeps at multiple temperatures for Time-
Temperature Superpositioning (TTS) Run from high to low frequencies for faster initial data
acquisition (for DMA850 and Q800 users)• Data Collection Rate Lower frequencies take longer time - control experimentMore frequencies = longer experiment
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Temperature Program
• Temp ramp Commonly used heating rate: 1-5°C/min
Larger samples have more thermal lag
Use slower ramp rates for lower frequencies and frequency sweeps because these take more time
• Temp sweep No thermal lag but time consuming
Commonly used for TTS testing, typical temp step: 5-10°C
• Multiple temp steps Commonly used to mimic certain application temperature profile
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Available DMA Experiments
(2) Transient Tests
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Transient Testing
Available transient test modes
•Creep-Recovery
•Stress Relaxation
•Iso-strain Temperature Ramp
•Iso-force Temperature Ramp
•Stress-Strain Rate Tests
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Creep Recovery Experiment
• A stress is applied to sample instantaneously at t1 and held constant for a specific period of time. The strain is monitored as a function of time (g(t) or (t)).
• The stress is reduced to zero at t2 and the strain is monitored as a function of time(g(tor(t
Stre
ss
timet1 t2
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Creep Recovery Experiment
Response of Classical Extremes
Stain for t>t1 is constant Strain for t >t2 is 0
time
time time
Stain rate for t>t1 is constant Strain for t>t1 increase with time Strain rate for t >t2 is 0
t2t1
t1 t2t2t1
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Creep Recovery: Response of Viscoelastic Material
Creep > 0
timet 1
t2
/
Strain rate decreases with time in the creep
zone, until finally reaching a steady state.
Mark, J., et. al., Physical Properties of Polymers, American Chemical Society, 1984, p. 102.
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Creep > 0
timet 1
t2
RecoverableStrain
Recovery = 0 (after steady state)
/
Strain rate decreases with time in the creep
zone, until finally reaching a steady state.
In the recovery zone, the viscoelastic fluid recoils, eventually reaching a equilibrium at some small total strain relative to the strain at unloading.
Mark, J., et. al., Physical Properties of Polymers, American Chemical Society, 1984, p. 102.
UnrecoverableStrain
Creep Recovery: Response of Viscoelastic Material
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Creep Recovery Experiment
time
Recovery ZoneCreep Zone
Less Elastic
More Elastic
Creep > 0 Recovery = 0 (after steady state)
/
t1 t2
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Creep Recovery : Creep and Recoverable Compliance
Mark, J., et. al., Physical Properties of Polymers, American Chemical Society, 1984, p. 102.
J(t)
1/
time
Creep Zone
J r(t)
time
Recovery Zone
Creep Compliance Recoverable Compliance
Where gu = Strain at unloadingg(t) = time dependent
recoverable strain
Je = Equilibrium recoverable compliance
more elastic
Je
Creep experiments report the material property Compliance which is in a sense the inverse of Modulus
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Creep-Recovery Test on PET Film
Stress: 5MPa
Instrument: Q800Clamp: TensionTemperature: 75°CStress: 5MPa
p/n: 984309.901
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Creep: Material Response
Terminal Region
Rubbery PlateauRegion
TransitionRegion
Glassy Region
log time
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Programming Creep Recovery on a DMA850
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Programming Creep Recovery on a Q800
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Programming Creep Recovery on a RSA-G2
• A pre-test is required to obtain sample information for the feedback loop• Stress Control Pre-test: frequency sweep within LVR
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Programming Creep Recovery on a RSA-G2
Creep Recovery
• Stress: needs to be in the linear region• Creep time: until it reaches steady state• Recovery time: until the compliance and strain reach plateau
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Stress Relaxation Experiment
Strain is applied to sample instantaneously (in principle) and held constant with time.
Stress is monitored as a function of time (t).St
rain
0time
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Stress Relaxation Experiment
Response of Classical Extremestime0
time0
stress for t>0is constant
time0
stress for t>0 is 0
Hookean Solid Newtonian Fluid
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Stress Relaxation Experiment
Response of ViscoElastic Material
For small deformations (strains within the linear region) the ratio of stress to strain is a function of time only.
This function is a material property known as the STRESS RELAXATION MODULUS, E(t)
E(t) = (t)/g
Stress decreases with timestarting at some high value and decreasing to zero.
time0
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Stress Relaxation: Material Response
Terminal Region
Rubbery PlateauRegion
TransitionRegion
Glassy Region
log time
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Stress Relaxation Happy and Unhappy Balls
Happy ball has an infinite relaxation time
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Programming Stress Relaxation on a DMA850
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Programming Stress Relaxation on a Q800
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Programming Stress Relaxation on a RSA-G2
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Iso-strain/Iso-stress Temperature Ramp
Temperature
Time
Data Acquisition Interval
m = ramp rate
• The strain or stress is held at a constant value and a linear heating rate is applied.
• Valuable for assessing mechanical behavior under conditions of confined or fixed load (stress) or deformation (strain).
• Example: Measure sample shrinkage (length shrinkage or shrinking force)
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Iso-Strain Temp Ramp: Measure Shrinking Force
Strain = 0.05%
Sample is held at a constant length; shrinkage force is measured
X
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Iso-Force Temp Ramp: Measure Length Shrinkage
Hold force at 0.05NTemperature : ambient to 120˚CRamp rate: 3˚C/min
X
Sample is held at a constant force; shrinkage is measured
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Iso-Strain/Iso-Stress on a DMA850
• DMA Iso-strain• Hold strain constant and
measure sample shrinking force
• DMA Iso-stress• Hold stress constant and measure
sample dimension change
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Iso-Strain/Iso-Stress on a Q800
• DMA Iso-strain• Hold strain constant and
measure sample shrinking force
• DMA Control force• Hold force constant and measure
sample dimension change
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Iso-Strain/Iso-Stress on a RSA G2
• DMA Iso-strain• Hold strain constant and
measure sample shrinking force
• DMA Iso-force• Hold stress constant and measure
sample dimension change
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Stress-Strain Testing
time
Linear rate
HenckyRate
Axial Test: Strain Rate Controlled• Sample is deformed under a
constant linear strain rate,
Hencky strain rate, force, or
stress for generating more
traditional stress-strain curves.
• Measure sample’s Young’s
modulus, yield stress, strain
hardening effect and sample
fracture
time
Linear rate
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Polysaccharide Film Stress-Strain Test
time
Linear rate
Geometry: TensionTemperature: 37°CRate: 10 m/s
Strain hardening
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Strain/Stress Ramp on a DMA850
Stress RampStrain Ramp
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Strain/Stress Ramp on a Q800
• DMA strain rate mode• Strain ramp• Displacement ramp
• DMA control force mode• Force ramp
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Strain Ramp on a RSA G2
• Linear strain rate • Hencky strain rate
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DMA Applications and Data Interpretation
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The DMA Results Can Correlate To…
DMA Results:
E, G, JTan d
Tg, Tb, Tg
Molecular structures• MW and MWD• Branching• Crystallinity• Crosslinking• Phase• Relaxation
Product properties• Transition
temperatures (Tg, Tb, Tg)
• Environmental resistance
• Impact strength• Long term
behavior, aging• Adhesion
Processing:• Heat history• Residual stress• Shear or orientation• Temperature• Fillers
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Most Common DMA Test – Temp Ramp
• The most Common DMA measurement is a dynamic temperature ramp
• The test results report modulus (E*, E’, E”), damping factor (Tan d) and transition temperatures (Tg)
• Provide information to polymer’s structure-property relationship
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What is Glass Transition (Tg)?
•A transition over a range of temperature from a glassy state to a rubber state in an amorphous material
•Mechanical: Below the Glass Transition, the material is in a brittle, glassy state, with a modulus of 109 PaAbove the Glass Transition, the material becomes soft and flexible, and the modulus decreases two to three decades
•Molecular: Below the Glass Transition, polymer chains are locked in place, without sufficient energy to overcome the barrier for rotational or translational motion. At temperatures above the Glass Transition, there is molecular mobility, and chains can slide past each other
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How to Define Tg in DMA?
Onset of E’ Peak of E” Peak of Tan d
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Secondary Transitions
Turi,Edith, A, Thermal Characterization of Polymeric Materials, Second Edition, Volume I., Academic Press, Brooklyn, New York, P. 487.
Glass Transition (Tg) Cooperative motion among a large number of chain segments,
including those from neighboring polymer chains
Secondary Transitions (Tb, Tg) Local Main-Chain Motion – intra-molecular rotational motion of
main chain segments four to six atoms in length Side group motion with some cooperative motion from the main
chain Internal motion within a side group without interference from side
group. Motion of, or within, a small molecule or diluent dissolved in the
polymer (eg. plasticizer.)
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Primary and Secondary Transitions in PC
Instrument: DMA850Temperature:-150°C to 180°CHeating rate: 3°C/minFrequency: 1HzAmplitude: 15 m
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Primary and Secondary Transitions in PET
Instrument: RSA G2Temperature:-150°C to 110°CHeating rate: 5°C/minFrequency: 1HzStrain: 0.1%
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What Will Affect Tg and Modulus?
• Heating rate Thermal lag
• Test frequency
• Polymer structures Rigid polymer chain shows higher Tg (e.g. PS)
Flexible polymer chain shows lower Tg (e.g. PE)
Crystallization
Degree of crosslinking
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The Effect of Test Frequency on Tg
• The glass transition is a kinetic transition. It is therefore influenced strongly by the frequency of the test. The Tg is a molecular relaxation that involves cooperative segmental motion.
• Because the RATE of segmental motion depends on temperature, as the frequency increases, the relaxations associated with the Tg can only happen at higher temperatures.
• In general, increasing the frequency will Increase the Tg
Decrease the intensity of tan d or loss modulus Broaden the peak Decrease the slope of the storage modulus curve in the region of
the transition.
Turi, Edith, A, Thermal Characterization of Polymeric Materials, Second Edition, Volume I., Academic Press, Brooklyn, New York, P. 529.
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PET Film: Effect of Frequency on Tg
• PET film tested at 0.1 Hz, 1Hz and 10 Hz
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Chemical Composition of Polymers
•Polymers are long chains of repeating units (monomers)
•The chemical composition determines mechanical properties, and the temperature where transitions occur
Polyethylene Tg : -128° C Polypropylene Tg: -20° C
Polystyrene Tg: 100 ° C
“Introduction to Polymer Viscoelasticity,” 2nd Edition. Aklonis, John J; MacKnight, William J. Wiley-Interscience
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Effect of Crystallinity in Polymer
“The major effect of the crystallite in a sample is to act as a crosslink in the polymer matrix. This makes the polymer behave as though it was a crosslinked network, but as the crystallite anchoring points are thermally labile, they disintegrate as the temperature approaches the melting temperature, and the material undergoes a progressive change in structure until beyond Tm, when it is molten”
Cowie, J.M.G., Polymers: Chemistry & Physics of Modern Materials, 2nd Edition, Blackie academic & Professional, and imprint of Chapman & HallBishopbriggs, Glasgow, 1991p. 330-332. ISBN 0 7514 0134 X
Random Chain100% Amorphous
Fringed MicellCrystalline
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Effect of Crystallinity on Tg
• Crystalline Polymers - multiphase systems - can be thought of as being made up of an amorphous phase containing dispersed crystalline units.
• Simple Picture of Two Phase System - crystalline phase acts to restrain mobility of neighboring amorphous regions
• General Case for Semi-crystalline PolymersIncreasing Crystallinity will: increase the glass transition temperature decrease the intensity of the glass transition peak broaden the transition temperature range
Turi, Edith, A, Thermal Characterization of Polymeric Materials, Second Edition, Volume I., Academic Press, Brooklyn, New York, P. 518.
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Effect of Crystallinity on Modulus
0% Crystallinity (100% Amorphous)
25%
40%
65%
M.P.
Temperature
Cowie, J.M.G., Polymers: Chemistry & Physics of Modern Materials, 2nd Edition, Blackie academic & Professional, and imprint of Chapman & HallBishopbriggs, Glasgow, 1991p. 330-332. ISBN 0 7514 0134 X
• Crystallinity mostly affects the sample at Tg <T < Tm,
• Below Tg the effect on the modulus is small
• The modulus at T > Tg of a semi-crystalline polymer is directly proportional to the degree of crystallinity
• Remains independent of temperature if the amount of crystalline order remains unchanged
Increase Tg
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Polymer Crosslinking
• Linear polymers can be chemically or physically joined at points to other chains along their length to create a crosslinkedstructure
• Chemically crosslinked systems are typically known as thermosetting polymers because the crosslinking agent is heat activated.
• Thermosetting polymers never molten
Ward, I.M., Hadley, D.W., An Introduction to the Mechanical Properties of Solid Polymers, John Wiley & Sons Ltd., New York, 1993
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Effect of Crosslinking on Tg
Increasing Crosslinking
Higher Density
Less Free Volume
Restricted molecular motion
More Energy needed
Higher Glass Transition Temperature
Cowie, J.M.G., Polymers: Chemistry & Physics of Modern Materials, 2nd Edition, Blackie academic & Professional, and imprint of Chapman & HallBishopbriggs, Glasgow, 1991 p.262 ISBN 0 7514 0134 X
For low values of crosslink density, Tg can be found to increase linearly with the
number of crosslinks.
For high crosslink density, the Tg is broad and not well
defined.
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Effect of Crosslinking
120
160
300
1500
9000
30,000
M = MW betweencrosslinks
c
Temperature
Increase Tg
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Amorphous, Crystalline and Crosslinked Polymers
Amorphous
Crystalline
Crosslinked
increasecrystallinity
increasecrosslinkingM
odu
lus
(E o
r G
)
Temperature
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Polymer Cold Crystallization (PET)
• Modulus (E’) increase due to cold crystallization
What happened here?
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PET: Heat-Cool-Heat Test
In second heat: • Tg shifted to higher temperature • Transition becomes much broader and weaker• Rubbery plateau modulus increased more than one decade
Before test
After test
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Anisotropic Materials
• Anisotropic materials have different properties in different directions. fibers, wood, fiber-filled composites oriented amorphous polymers, injection molded
specimens crystalline polymers in which the crystalline phase is not
randomly oriented
• Show different moduli at different measurement direction
Nielsen, Lawrence E., Mechanical Properties of Polymers and Composites, Marcel Dekker, Inc., New York, 1974, pp. 39-40.
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Anisotropic Material
Notes:Frequency = 1 HzAmplitude = 40 micronsForce Track = 150%Ramp Rate = 3°C/min.
10
100
1000
10000
1.0E5
Los
s M
od
ulu
s (M
Pa
)
10
100
1000
10000
1.0E5
Sto
rag
e M
odu
lus
(MP
a)
20 40 60 80 100 120 140 160 180 200
Temperature (°C)
––––––– Fibers Parallel to Length– – – – Fibers Perpindicular to length
Universal V2.6D TA Instruments
Storage Modulus
Loss Modulus
A B
length
A
BA
B
• Polyester/Glass Fiber Reinforced Composite
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Anisotropic Material
104.55°C
96.82°C
Notes:Frequency = 1 HzAmplitude = 40 micronsForce Track = 150%Ramp Rate = 3°C/min.
0.02
0.04
0.06
0.08
0.10
0.12
Ta
n D
elta
25 50 75 100 125 150 175 200
Temperature (°C)
––––––– Fibers Parallel to Length– – – – Fibers Perpindicular to Length
Universal V2.6D TA Instruments
A B
length
A
B
• Polyester/Glass Fiber Reinforced Composite
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Oriented Polymer: Shrink Wrap
•“Shrink Wrap” is widely used in packaging to conveniently label irregularly shaped containers
•When this kind of biaxially oriented film is heated, it turns to shrink and returns to lower energy random-coil state.
•PET-based LabelZ-direction
X-direction
•RSA G2: 5˚ C per minute, 1 HzZ
X
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PET Film Measured at X and Z Direction
Z
X
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Len
gth
(m
m)
Iso-force Temp Ramp: measure shrinkage
Hold force at 0.05NTemperature : ambient to 120˚CRamp rate: 3˚C/min
Z
X
z
x
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Str
ess
(
kPa
) Iso-strain Temp Ramp: measure shrinking force
Strain = 0.05%Temperature : ambient to 120˚CRamp rate: 3˚C/min
Z
X
z
x
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Blending of Amorphous Polymers
• Blending polymers with different glass transition temperatures and modulus will create new materials that may show better physical properties
• If the polymers blended are completely compatible then the blend behaves like an ordinary amorphous polymer with a single transition region and an intermediate glass transition temperature.
• If the polymers are incompatible, then the blend will show separate glass transitions
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Polymer Blend – Miscible Case
Temperature (°C)
l–––––– Polymer Ap – – – Polymer Blend: A + B–––– Polymer B
Ela
stic
Mod
ulu
s
100%Polymer B
Polymer BlendA + B
100 % Polymer A
Aerospace Coating
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l l l l l l l l l ll
l
l
l
l
l
l
lp p p p p p p
p
p
p
pp
p
p
p
p
89.77°C
76.19°C
46.46°C
-0.5
0.0
0.5
1.0
1.5
Tan
Del
ta
-25 0 25 50 75 100 125
Temperature (°C)
l–––––– Polymer Ap – – – Polymer Blend: A + B–––– ∙ Polymer B
Universal V2.5D TA Instruments
100 % Polymer A
100%Polymer B
Polymer BlendA + B
Polymer Blend – Miscible Case
Aerospace Coating
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Polymer Blend - Immiscible Case
• Acrylonitrile-Butadiene-Styrene (ABS) is a polymer blend
Tg of “B”
Tg of “S”
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Using Glass Transition to Evaluate Blending
• Investigating manufacturing blend uniformity
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Effect of Filler on Modulus
20
60% mica
40% mica
60% asbestos
40% asbestos
20% mica
20% asbestos
20% calcium carbonate
polystyrene control
Nielson, L. E., Wall, R. A., and Richmond, P. G., Soc. Plastics Eng. J., 11, 22 (1966)
40 60 80 100 120 140 160
Temperature (°C)
Sto
rag
e M
od
ulu
s (E
’)
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Effect of Aging on Elastomer O Rings
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Effect of Aging on Tg of PVC Roofing Membrane
l l ll
l
l
l
l
l
l
l
ll
l
l
l
l
l
l
p p pp
p
p
p
p
p
p
p
p
p
p
p
p
p
p
10.44°C
Initial 90 days
12.82°C
150 days
14.91°C
0.0
0.1
0.2
0.3
0.4
Tan
Delta
-100 -75 -50 -25 0 25 50
Temperature (°C)
l PVC - Initial Conditionp PVC - Aged for 90 days PVC Aged for 150 days
Universal V2.4D TA Instruments
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Effect of Plasticizer
• Plasticizers are generally low molecular weight organic additives which are used to soften rigid polymers
• Typically added to a polymer for two reasons:1. To lower the Tg to make a rigid polymer become soft 2. To make the polymer easier to process
• Plasticizers act as lubricant in polymer chains
• Therefore plasticizers will have the effect of:1. Lowering the Tg and broadening tan d peak2. Lowering the moduli (E’ and E”)
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Effect of Plasticizer on Vinyl Flooring
Higher % Plasticizer
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Humidity Influence: Nylon Film
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O-rings: Stress Relaxation
• Squeeze the O-ring to a certain strain. Hold it constant, then measure how long it takes for the force to relax
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Creep Tests on Packaging Bags
l
l
l l l l l l l l
p
p
p p p p p p p p
0
20000
40000
60000
80000
100000
120000
Cre
ep
Co
mp
lianc
e (
µm
^2/N
)
0 1 2 3 4 5 6 7 8 9 10
Time (min)
l Poor Performancep Good Performance Excellent Performance
Universal V2.1A TA Instruments
• Apply a load force, then measure how much the bag is stretched
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Memory Foam: Multi-Step Creep RecoveryS
tra
in
(%
)
Stre
ss
(Pa
)
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Troubleshooting
Experimental Issues
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Factors That Influence Measurement Results
Geometry• Clamp• Sample size• Sample loading• Sample integrity
Check list• Clamp calibrations• Proper loading
torque/force• Sample uniformity
and thermal stability• Bad contact or
sample bending and twisting
Test Parameters
Check list• Loading force• Proper force track• Equilibration time• Heating rates• Amplitude• Frequency
Primary measurements• Force• Displacement• Temperature
Check list• Instrument
calibrations• Thermocouple
position
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Instrument and Clamp
• Periodically calibrate the instrument following the online help manual
• Perform clamp calibration every time when attaching a new clamp on the instrument
http://www.youtube.com/user/TATechTips
• Perform confidence verification check using polycarbonate provided by TA Instruments
p/n: 982165.903
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DMA850 Flow Chart of Calibration Procedures
• Follow the online help manual
• The stability verification is performed at installation
• Instrument calibration includes 2 steps: force and phase
• Clamp calibration: perform when newly attached.
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Q800 Flow Chart of Calibration Procedures
Clamp
Position
Instrument
MassZero Compliance
ElectronicsForceDynamic
BalanceWeight
Select ClampClamp MassCompliance
0.005 steel0.010 steel0.020 steel0.030 steelThick steel
Analyze data
• Instrument calibration includes 3 steps: Electronics, Force, and Dynamic
• Position calibration: calibrate the absolute position of the drive shaft. Perform this calibration when DMA is moved, reset, or powered down.
• Clamp calibration: perform when newly attached.
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RSA G2 Flow Chart of Calibration Procedures
• Follow the online help manual
• Instrument calibration: force and phase angle check
• Clamp calibration: mass (perform when newly attached)
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DMA Confidence Check - Polycarbonate
• Load Polycarbonate (L 17.5, w 12.85, t 1.6mm)• Use Single Cantilever Clamp 20-30 micrometer amplitude 1 Hz frequency
• Storage Modulus at Room TemperatureE' = 2.35 GPa (2350 MPa) +/- 5%
• Tan Delta at Room TemperatureTan d < 0.01
• Transition TemperatureTan d peak between 155-160°C @ 1Hz, 3-5°C/minE" peak will be about 5°C lower
p/n: 982165.903
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Sample Preparation
•DMA measurement results are highly depending on the quality of sample preparation
• Sample flatness and uniformity have big influence to the accuracy of the test results
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E’ Increase in a Strain Sweep
l ll
l ll
ll
ll l l ll
p
p
p
p
p
p
p
p
p
p
p
p
pp
0.01
0.1
1
10
[
] D
ynam
ic F
orc
e (
N)
p
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
[
] S
tora
ge
Mo
dulu
s (M
Pa
)l
0.1 1 10 100 1000
Amplitude (µm)
Instrument: DMA Q800 V21.3 Build 96
Universal V4.5A TA Instruments
Why does E’ increase with increasing amplitude?How to verify linear viscoelastic region?
Instrument: Q800Clamp: 3-p bendingTemperature: ambientAmplitude: 1-500 mFrequency: 1Hz
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E’ Increase in a Strain Sweep
l ll
l ll
ll
ll l l ll
p
p
p
p
p
p
p
p
p
p
p
p
pp
0.01
0.1
1
10
[
] D
ynam
ic F
orc
e (
N)
p
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6000
7000
8000
9000
10000
[
] Sto
rag
e M
odu
lus
(MP
a)
l
0.1 1 10 100 1000
Amplitude (µm) Universal V4.5A TA Instruments
The sample is not flat and not in full contact with the clamp face.Solutions: (1) Prepare a flat sample
(2) Increase force track or increase static force
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E’ Increase in a Temp Ramp
• The E’ of a material should not increase with temperature unless it is crystalized or crosslinked
Instrument: DMA850Clamp: tensionTemperature:0°C to 180°CHeating rate: 3°C/minFrequency: 1HzAmplitude: 10 m
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Noisy Modulus After Tg
0.0001
0.001
0.01
0.1
1
10
100
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10000
Lo
ss M
od
ulu
s (M
Pa
)
0.0001
0.001
0.01
0.1
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10000
Sto
rage
Mo
dul
us (
MP
a)
-100 -50 0 50 100 150
Temperature (°C) Universal V4.5A TA Instruments
What is the problem with this data collected after Tg?
What’s wrong here?
Instrument: Q800Clamp: tensionTemperature:-100°C to 150°CHeating rate: 3°C/minFrequency: 1HzAmplitude: 10 m
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Noisy Modulus After Tg
Sample stiffness is below the instrument spec. (100N/m)Solution: Increase the sample stiffness (wider, thicker, shorter)
78.71°C39.76N/m
0.1
1
10
100
1000
10000
1.0E5
Stif
fne
ss (
N/m
)
0.0001
0.001
0.01
0.1
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10000
Lo
ss M
od
ulu
s (M
Pa)
0.0001
0.001
0.01
0.1
1
10
100
1000
10000
Sto
rag
e M
odu
lus
(MP
a)
-100 -50 0 50 100 150
Temperature (°C)
Instrument: DMA Q800 V21.2 Build 88
Universal V4.5A TA Instruments
Instrument: Q800Clamp: tensionTemperature:-100°C to 150°CHeating rate: 3°C/minFrequency: 1HzAmplitude: 10 m
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Sample Sagging
• Sample sagging after Tg
• Solution: use cantilever clamp instead of 3-p bending
Instrument: RSA G2Clamp: 3-p bendingTemperature:50°C to 180°CHeating rate: 3°C/minFrequency: 1HzAmplitude: 10 m
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Compression Testing on Foam/Rubber
Question: How to measure correct modulus?Answer: (1) Prepare regular sample
(2) Apply appropriate static force
(1) Poor contact
(2) Appropriate
(3) Over squeezed
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Time-Temperature Superposition (TTS)
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Time and Temperature Relationship
(E" or G")(E' or G')
(E" or G")
(E' or G')
log Frequency Temperature
• Linear viscoelastic properties are both time and temperature dependent
• Some materials show a time dependence that is proportional to the temperature dependence Decreasing temperature has the same effect on viscoelastic
properties as increasing the frequency, and vice versa• For such materials, changes in temperature can be used to “re-scale”
time, and predict behavior over time scales not easily measured
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Time Temperature Superpositioning Benefits
• TTS applies to materials that are thermo-rheological simple. When all relaxation times have the same temperature dependence
•TTS can be used to extend the frequency beyond the instrument’s range. Frequency is correlate to time and shear
• Creep or Stress Relaxation TTS can predict behavior over longer times that cannot be practically measured
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TTS Limitations
• TTS works with polymers that are thermo-rheological simple
• TTS does not work if:
Sample is partially crystalized, crosslinked, or highly filled
Sample change properties (e.g. crystalize, melt, cure, decompose) within temperature of interest
Polymer contains multiple phases: composite or blends
Liquid samples with multiple components
• TTS has been used as empirical rules to predict sample properties over long time scales
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Guidelines for TTS
• Decide first on the Reference Temperature: T0. What is the use temperature?
• If you want to obtain information at higher frequencies or shorter times, you will need to conduct frequency (stress relaxation or creep) scans at temperatures lower than T0.
• If you want to obtain information at lower frequencies or longer times, you will need to test at temperatures higher than T0.
• Good idea to scan material over temperature range at single frequency to get an idea of modulus-temperature and transition behavior.
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Sto
rag
e m
od
ulu
s
(P
a)
Reference T
TTS Shifting
• Generating frequency sweep data at different temperature steps• Select your reference temperature (e.g. 155°C)
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Sto
rag
e m
od
ulu
s
(P
a)
TTS Shifting
aT=150
• Low temperature data shift to higher frequencies
Reference T
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Sto
rag
e m
od
ulu
s
(P
a)
TTS Shifting
aT=145
Reference T
• Low temperature data shift to higher frequencies
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Sto
rag
e m
od
ulu
s
(P
a)
TTS Shifting
aT=140
Reference T
• Low temperature data shift to higher frequencies
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Sto
rag
e m
od
ulu
s
(P
a)
TTS Shifting
aT=160
Reference T
• High temperature data shift to lower frequencies
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Sto
rag
e m
od
ulu
s
(P
a)
TTS Shifting
aT=165
Reference T
• High temperature data shift to lower frequencies
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Sto
rag
e m
od
ulu
s
(P
a)
TTS Shifting
aT=170
Reference T
• High temperature data shift to lower frequencies
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Sto
rag
e m
od
ulu
s
(P
a)
TTS Shifting
aT=175
Reference T
• High temperature data shift to lower frequencies
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Master Curve from TTS ShiftingS
tora
ge
mo
dul
us
(
Pa
)
• TTS Master Curve using 155°C as reference
Each frequency sweep test
range
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WLF and Arrhenius Equations
• Master Curves can be generated using shift factors derived from the Williams, Landel, Ferry (WLF) model
log aT= -c1(T-T0)/(c2+(T-T0))
aT = temperature shift factor T0 = reference temperaturec1 & c2 = constants from curve fitting
Generally, c1=17.44 & c2=51.6 when T0 = Tg
• The Arrhenius model works better if T > Tg+100°C; or T < Tg and polymer is not elastomeric temperature range is small, then c1 & c2 cannot be calculated precisely
ln aT = (Ea/R)(1/T-1/T0)
aT = temperature shift factor Ea = Apparent activation energyT0 = reference temperature R = gas constant
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Shift Factors aT vs. Temperature
WLF model
• Shift factors fitted with WLF model
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Lo
ss m
odu
lus
(
Pa
)
Cole-Cole Plot to Validate TTS
• The Cole-Cole plot and van Gurp-Palmen plot are commonly used to validate the application of Time-Temperature Superposition (TTS).
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Pha
se a
ngle
(
°)
van Gurp-Palmen Plot to Validate TTS
• The Cole-Cole plot and van Gurp-Palmen plot are commonly used to validate the application of Time-Temperature Superposition (TTS).
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References for TTS
1) Ward, I.M. and Hadley, D.W., "Mechanical Properties of Solid Polymers", Wiley, 1993, Chapter 6.
2) Ferry, J.D., "Viscoelastic Properties of Polymers", Wiley, 1970, Chapter 11.
3) Plazek, D.J., "Oh, Thermorheological Simplicity, wherefore art thou?" Journal of Rheology, vol 40, 1996, p987.
4) Lesueur, D., Gerard, J-F., Claudy, P., Letoffe, J-M. and Planche, D., "A structure related model to describe asphalt linear viscoelasticity", Journal of Rheology, vol 40, 1996, p813.
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Setting up TTS procedure on DMA850
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Setting up TTS procedure on Q800
Amplitude within the linear region
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Setting up TTS procedure on RSA G2
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Getting Started Manuals
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Trios Online Help Manual
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