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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���

���

�

���

�����

���

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������

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�

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������������������������������������ �

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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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���

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���

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������

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�

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�

��

�No Solvent�

��

�Immersed in 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

The World Leader in Thermal Analysis, Rheology, and Microcalorimetry

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.