Post on 07-Jul-2020
σσσσ = tensile stress, ττττ = shear stress
εεεε = tensile strain, γγγγ = shear strain
ηηηη ×
μ μ μ μ
ν
0zz
σz
σz
y
Poisson’s Ratio0y
Film/Fiber
Compression
3-Pt Bending
Cantilever
Shear Sandwich
Contact Lens
°
Modulus = Stiffness Geometry Factor
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 10 410 -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
(Pa)
Modulus = Stiffness Geometry Factor
Modulus = Stiffness Geometry Factor
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 10 410 -1
10 4
10 5
10 6
10 7
10 8
10 9
10 10
10 13
10 12
10 11
10 3
Modulus = Stiffness Geometry Factor
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
(Pa)
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
(Pa)
Modulus = Stiffness Geometry Factor
Stationary Clamp
Sample
Movable 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
(Pa)
1 mm thick40 mm diameter
2 mm thick20 mm diameter
6 mm thick10 mm diameter
Modulus = Stiffness Geometry Factor
MovableClamp Stationary
Clamp
Sample
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
(Pa)
Modulus = Stiffness Geometry Factor
≥ ≥
Parallel RazorBlade Cutter
Good for Films andSheets of rubber.
Cork Borer
Good for stiff foams andSheets of rubber.
ideal inclined
Force
If sample buckles duringOscillation. Modulus will be artificially low.
sagging variable thickness
Buckling during loading causes serious errors as buckled areas do not “feel” the force or deformationBuckling can be the result of non-uniform stretching, or crooked loading of a film. Observe film from edge while oscillating to verify goodness of load.If sample is buckling, reload a new sample.
Lightly finger-tightened + ¼ turn + ½ turn + 1 turn
Note: Details for calibrations are provided in the Appendix
Note: Details for calibrations are provided in the Appendix
≈ ≈ ≈
δ
δ ° °°
±
° °°
Thermocouple
= E*
= * d /dt
Str
ess
Strain Rate
= E* + (?)*d /dt
L1
L2
Started in 1927 by Thomas Parnell in Queensland, Australia
���τ ��Τ
(τΤ .
De = τ/Τ
Mark, J., et. al., Physical Properties of Polymers, American Chemical Society, 1984, p. 102.
γ
δ η
Deformation
Response
Phase angle δ
An oscillatory (sinusoidal) deformation (stress or strain)is applied to a sample.
The material response (strain or stress) is measured.
The phase angle δ, or phase shift, between the deformation and response is measured.
Strain
Stress
δ ° δ °
Purely Elastic Response(Hookean Solid)
Purely Viscous Response(Newtonian Liquid)
Strain
Stress
Phase angle 0°< δ < 90°
Stress
Strain
The stress in a dynamic experiment is referred to as the complex stress σ*
Phase angle δδδδ
Complex Stress, σσσσ*
Strain, εεεε
σσσσ* = σσσσ' + iσσσσ"
The complex stress can be separated into two components: 1) An elastic stress in phase with the strain. σσσσ' = σσσσ*cosδ δ δ δ σ' is the degree to which material behaves like an elastic solid.2) A viscous stress in phase with the strain rate. σσσσ" = σσσσ*sinδδδδσ" 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:
Phase angle δ
E*
E'
E"Dynamic measurement represented as a vector
A
A
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
γ
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δ
Clamp Amplitude (μm)
Tension Film or Fiber 15 to 25
Compression 10 to 20
3 Point Bend 25 to 40
Dual/Single Cantilever 20 to 30
Shear Sandwich 10 to 20
Specialty Fiber 15 to 25
γ ε
(γ( ) ε( )).
σ
1 2
σ/η
σ
1 2
σ
σ/η
σ σ
σ/η
η
γγ
Je = Equilibrium recoverable compliance
0.0
0.1
0.2
0.3
0.4
Str
ain
(%)
4 6 8 10 12 14 16 18 20 22
Time (min)
Sample: PET Film Creep at 75°CSize: 10.5490 x 6.2500 x 0.0700 mmMethod: CreepComment: Stress
DMAFile: C:\TA\Data\DMA\PetcreepOperator: Applications LaboratoryRun Date: 11-Sep-97 10:41
Universal V2.6B TA Instrum ents
0
20000
40000
60000
80000
100000
120000
Cre
ep C
ompl
ianc
e (μ
m^2
/N)
0 1 2 3 4 5 6 7 8 9 10
Time (min)
Poor Performance Good Performance Excellent Performance
Universal V2.1A TA Instruments
σ
σσσσ γγγγ
Stress
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0.0
0.2
0.4
0.6
0.8
1.0
Sta
tic F
orce
(N
)
20 40 60 80 100 120 140
Temperature (°C)
Sample: Iso strainSize: 13.5810 x 5.3000 x 0.0500 mmMethod: Isostrain
DMAFile: P:...\Q800 ISO STRAIN.002Operator: TerriRun Date: 2004-09-17 18:11Instrument: DMA Q800 V7.0 Build 113
Universal V4.1C TA Instruments
6.648657mm
0.0099
0.0100
0.0101
0.0102
Sta
tic F
orce
(N
)
2
4
6
8
10
12Le
ngth
(m
m)
20 40 60 80 100 120 140 160
Temperature (°C) Universal V4.7A TA Instruments
δ
δδδδ
δ
156.24°C(I)
150.86°C
160.83°C
158.35°C
159.85°C
Polycarbonate shavings3C/Min heating rate - clamped to 4 PSI Pressure30 um Amplitude
Expected Peak max in E" = 153C
0.02
0.04
0.06
0.08
[
]
Tan
Del
ta –
––––
–
0.1
0.2
0.3
0.4
0.5
0.6
[
] L
oss
Mod
ulus
(G
Pa)
– –
– –
4
6
8
10
12
14
Sto
rage
Mod
ulus
(G
Pa)
100 120 140 160 180
Temperature (°C)
δ
(LCR Meter) Frequency
Agilent 4285A
Agilent E4980A
° °
119.44°C
-55.49°C0.05
0.10
0.15
[ ]
Tan
Del
ta
10
100
1000
10000
[ ]
Los
s M
odul
us (
MP
a)
10
100
1000
10000
[ ]
Sto
rage
Mod
ulus
(M
Pa)
-150 -100 -50 0 50 100 150 200 250
Temperature (°C)
Sample: PET Film in Machine DirectionSize: 8.1880 x 5.5000 x 0.0200 mmMethod: 3°C/min rampComment: 1Hz; 3°C/min from -140° to 150°C, 15 microns,
DMAFile: A:\Petmd.001Operator: RRURun Date: 27-Jan-99 13:56
Universal V2.5D TA Instruments
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
20 40 60 80 100 120 140 160(°C)
20 40 60 80 100 120 140 160(°C)
E’
E’
δδ δδ
δδ δδ
0.025
0.050
0.075
0.100
0.125
0.150
Tan
Del
ta
10
100
1000
10000
Loss
Mod
ulus
(M
Pa)
100
1000
10000
Sto
rage
Mod
ulus
(M
Pa)
-150 -100 -50 0 50 100 150 200 250
Temperature (°C)
–––––– PET Film 1st Heat – – – PET Film 2nd Heat
Universal V2.5D TA Instruments
138.58°C129.01°C
1000
10000
1.0E5
1.0E6
1.0E7
Sto
rage
Mod
ulus
(P
a)
120 130 140 150 160 170 180
Temperature (°C)
sample5.003 Exxon Sample #5 sample9.001 Exxon Sample #9
Universal V2.6D TA Instruments
HDPELLDPE
LDPE
Property LDPE LLDPE HDPE
Melting Point (C) 110 120-130 >130
Density (g/cm3) 0.92 0.93 0.96
Tensile strength (Mpa) 24 37 43
Nielsen, Lawrence E., Mechanical Properties of Polymers and , Marcel Dekker, Inc., New York, 1974, p. 51-52.
19.51MPa
40
60
80
100
120
140
[ –––
–– ·
] Tem
pera
ture
(°C
)
0.001
0.01
0.1
1
10
100
[ – –
– –
] Lo
ss M
odul
us (
MP
a)
0.001
0.01
0.1
1
10
100
Sto
rage
Mod
ulus
(M
Pa)
0 10 20 30 40 50 60 70
Time (min)
Comment: 1 Hz, 20 microns
Universal V2.6D TA Instruments
Notes:Frequency = 1 HzAmplitude = 40 micronsForce Track = 150%Ramp Rate = 3°C/min.
10
100
1000
10000
1.0E5
Loss
Mod
ulus
(M
Pa)
10
100
1000
10000
1.0E5
Sto
rage
Mod
ulus
(M
Pa)
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
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
Tan
Del
ta
25 50 75 100 125 150 175 200
Temperature (°C)
––––––– Fibers Parallel to Length– – – – Fibers Perpindicular to Length
Universal V2.6D TA Instruments
Static Force is Held Constant
Sample Length Decreases
0.05
0.10
0.15
0.20
Tan
Del
ta
10
100
1000
10000
Loss
Mod
ulus
(M
Pa)
100
1000
10000
Sto
rage
Mod
ulus
(M
Pa)
-150 -100 -50 0 50 100 150 200
Temperature (°C)
–––––– PET Film in Transverse Direction – – – PET Film in Machine Direction
Universal V2.5D TA Instruments
Temperature (°C)
–––––– Polymer A– – – Polymer Blend: A + B–––– Polymer B
Ela
stic
Mod
ulus
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)
–––––– Polymer A – – – Polymer Blend: A + B–––– Polymer B
Universal V2.5D TA Instruments
20 40 60 80 100 120 140 160TEMP. (°C)
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
Del
ta
-100 -75 -50 -25 0 25 50
Temperature (°C)
PVC - Initial Condition PVC - Aged for 90 days PVC Aged for 150 days
Universal V2.4D TA Instruments
δ
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�No Solvent�
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(E" or G")(E' or G')
(E" or G")
(E' or G')
log Frequency Temperature
•
•
•
•
aT=140
aT=150
aT=160
°
Amplitude within the linear region
Quickstart e-Training Courses
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Appendix 1
≤
≤
≤
≤
≤
≤
≈ ≈ ≈
° °°
±
° °°
Thermocouple
AR
ES
-G2
Allows for alignment of upper and lower geometries.Requires alignment bar (3 pt bending, cantilever) or steel shim (tension)
DH
R
Axial mapping is used to relate the desired displacement with the control of the magnetic bearing. Better understand inertial effects with
the current geometry mass.