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Dynamic Mechanical Thermal AnalysisDMTA V

Users Training CourseRheometric ScientificOne Possumtown Rd.Piscataway NJ 08854

Dynamic Mechanical Thermal Analysis

• Rheology - the study of flow of materials• DMTA is Rheology on solids• Also called Dynamic Mechanical

Spectroscopy - it gives a spectrum of behavior of materials which are subjected to a dynamic or steady deformation.

Dynamic Mechanical Thermal Analysis

• DMTA looks at how materials respond to an imposed stress.

• The stress deforms the materials.• The DMTA measures the strain - how

far the material moves, and calculates how much energy is stored or dissipated during the process.

Mechanical Testing• Dynamic (Oscillatory) - Deformation

is applied as a sinusoidal function.

• Steady - Deformation is applied as a constant over a time period.

Review of terms

• Stress- Force deforming the sample perunit area τ (or) σ = F/A

• Strain- the distance sample moves in response relative to the sample length

in shear: γ= ∆ X/ ∆ Y • in tensile ε = ∆ L/Lo

Hooke’s Law

• Describes the behavior of an ideal elastic solid.

• Relates the applied strain to the resultant stress (or visa versa).

• The proportionality factor is called the modulus of the material. Denoted as E or G

Review of terms• Young’s Modulus is the ratio of

dynamic stress to strain, E* (measured in tensile or bending mode)

• E= σ/ε • Shear Modulus is the ratio of

dynamic shear stress to strain, G*• G= τ/γ• for most rubbery polymers: E=3G

assuming a Poisson ratio of 1/2 (Poisson’s ratio is the linear contraction relative to the extension in tensile)

Review of terms

• Viscosity - the resistance of a material to flow. High viscosity materials need more force to make them flow than low viscosity materials.

• Shear thinning - materials that become thinner, lower viscosity, as you increase the stress deforming them.

Newton’s Law

• Describes the behavior of ideal fluids according to the stress and shear

• Proportionality factor is viscosity, η .• Ideal viscous fluids are linear with shear

rate, no shear thinning• τ = η dγ/dt = η γ•

Newtonian And Non-NewtonianBehavior Of Viscous Fluids

Material Response To A Sinusoidal Deformation

(Dynamic Mechanical Testing)

Strain Strain Rate+ γo

+ γo

+ γo

+ γo

Material Response To A Sinusoidal Deformation

(Dynamic Testing)

τ*(t)

ElasticResponse

Time Time

τ*(t)γ (t)

γ (t)

ViscousResponse

Material Response To A Sinusoidal Deformation

(Dynamic Mechanical Testing)

δ

γ (t)

τ (t) τ (t)τ'

τ''

Review of terms• Storage Modulus, E’ - component in

phase with the applied sinusoidal deformation; relates to stiffness of materials

• This is the elastic behavior of a material-the solid-like properties it displays

• The storage modulus is a measure of how a material stores the energy of deformation, and allows material to regain shape after deformation

Review of terms

• Loss Modulus, E”- component out of phase with the applied sinusoidal deformation; relates to damping ability of material

• This is the viscous nature of the material -its liquid-like behavior

• The loss modulus is an indication of how the material dissipates the energy used to deform it.

Modulus relationships

Complex Modulus

Loss (viscous) Modulus = E” Liquid like behavior

Phase angletan δ = E”/E’

Storage (Elastic) Modulus = E’solid like behavior

Review of terms

• tangent delta- E”/E’ dimensionless, related to the damping characteristic.

• This is also called the loss tangent.

• A high tan delta means a greater ability to dissipates stress and behave more like a liquid.

Material Properties Dynamic Testing: shear or bendingComplex Modulus

Storage Modulus

Loss Modulus

Complex Viscosity

G∗=∗τ00γ

G' G= = ∗τγ0

δ' cos

G" G= = ∗τγ0

δ" sin

η ω∗=

∗ G

Or E* = σ∗/ ε

Or E’ = σ’/ε = (σ∗/ε)cos δ

Or E” = σ”/ε = (σ∗/ε)sin δ

Loss tangent tan δ = G”/G’ or E”/E’

Material Properties (Steady Testing)

Viscosity

S tressR elaxationM odulus

C om pliance

η τγ= &

G t t( ) ( )= τγ

J(t) t= γτ( )

How does DMTA operate?DMTA is a Controlled Stress Instrument

• It generates data via a feedback loop: Strain is asked for in the method for stress is applied to the sample.

• Actual strain is measured, as is the applied stress to allow rheological data (E’,E”, tan delta) to be calculated.

Position sensor/ drive shaft movement

• A current to the motor moves the drive shaft.• Motion of the drive shaft is detected by a

position sensor consisting of a static probe and a target attatched tot he drive shaft.

• Change in magnitude of gap between probe and target produces a current in the position sensor, which is converted into a distance measurement.

• All are thermally isolated from the furnace.

How a data point is calculated• The User defines the geometry; accurate

measurements of the sample are CRUCIAL!• Strain is multiplied by a geometrical constant to give

an actual displacement that the DMTA will try to achieve.

• At the first data point 5% of the full scale allowable dynamic force is applied to the sample.

• Displacement is measured and the feed back loop takes over to control the force needed for the next data point.

• Note: this initial 5% dynamic force can be changed in software with version 6.4.1 and higher via the measurement options section.

Achieving the strain desired...

• Chosen strain is divided by actual strain and if ratio is between 0.85 and 1.15 (+/-15% window,user selectable defaults) the measurement can be taken. If this ration is outside the window, the applied force is multiplied by this ration and again applied to the sample.

Achieving strain levels….• Once strain falls within the window the standard

measurement process begins:• 2048 points are taken for strain and force from

1 to >64 cycles depending on frequency.• Strain and force are cross correlated to models

of a Sine and Cosine representing a perfect solid and fluid. This yields two phasors representing normalized strain and force amplitudes and their respective phase angles.

• Effects of mass of drive shaft and tools are taken into account to give correct applied force.

Controlling the needed force...

• For the next data point the previous force is applied and if necessary modified to achieve the chosen displacement.

• Movement of the drive shaft due to sample “growth” does not affect the measurement of displacement in dynamic motion.

Controlling temperature• Temp. is measured by a PRT in the

radiant oven. PID loops adjust the line voltage to power the furnace to heat.

• If using LN2, a solenoid (with 3 user selectable control features in ver. 6.4.1 and higher) allows LN2 into a cooling container surround the furnace, no LN2 ever touches the sample!

• Oven and LN2 can only operate if oven lid is fully closed- for safety reasons.

Review of terms

• Viscoelastic- Polymers display the behavior of both elastic solids and viscous liquids.

• Linear Viscoelasticity- Region where the modulus is independent of the applied deformation

Linear and Nonlinear Stress–Strain Behavior Of

Elastic SolidsNonl inear

Reg ionL inearReg ion

10-2 10-1 100 101105

106

107

0.0

0.1

0.2

0.3

0.4

0.5

strain [%]

E' (

bA

)

[Pa]

tan_delta (bA

)

[ ]

4 Sequence of Dynamic Strain Sweep Tests

b A Test 1 of 3b B Test 2 of 3b C Test 3 of 3

Rheometric Scientific, Inc.

E'

tan delta

Length = 5.0 mmWidth = 10.42 mmThickness = 2.45 mmFrequency = 1 Hz

Linear Viscoelastic region determination

Important material behavior:• Materials that are stiff have a high

storage modulus, E’

• Soft materials have a high E”

• tan delta gives the ratio of the two: E”/E’

• Materials change properties at the glass transition, stiffness (E’),and ability to dissipate stress (E”) change rapidly, thus the ratio (tan delta) gives a peak.

E’ = Storage Modulus = Elastic response

E” = loss Modulus =Viscous Response

tan δ = E”/E’

DMTA Modulus vs. Temp.

Temperature

log

Mod

ulus

Test Set up

Testing Options

DMTA testing modes• Dynamic

– Single point - to set parameters– Time sweep at constant freq.– Dynamic strain sweep– Frequency dependence– Temperature dependence– Combinations of freq./temp. dependence

DMTA testing modes• Transient

– Static load - creep and TMA mode– Constant strain - stress relaxation– Strain rate testing- Stress vs. Strain Curves

Testing Conditions • Variables

– Deformation % strain – Rate/Frequency in Hz or Rad/s– Temperature ramp or step isothermal– Time

Deformation Dependence (Dynamic Strain Sweep Testing)

or E’

Frequency Dependence (Dynamic Testing)

Thermoplastic showing dramatic frequency dependance of E’

10-2 10-1 100 10120.0

0.0

1x108

2x108

3x108

4x108

5x108

6x108

7x108

8x108

9x108

0.06

0.08

0.1

0.12

0.14

0.16

Freq [Hz]

E' (

bI

)

[Pa]

E" (

bJ

)

[Pa]

tan_delta (bK

)

[ ]

Hidden Information

E’ Storage Modulusincrease with frequency.Material will be stiffer athigher frequency.

10-1 100 101 102102

103

104

105

103

104

105

PDMS frequency dependance

Frequency, rad/s

Mod

ulus

, G',

G" [

Pa]

Eta* [Pa.s]

Rheometric Scientific

Loss Modulus, G"

Storage Modulus, G'Eta* [Pa.s]

Temperature Dependence (Dynamic Testing)

or E’

or E”

Step testing

Ramp

Frequency/Temperature testing

• Frequency Temperature Ramp:Temperature ramps while frequencies are swept, two variables changing.

• Long frequencies or fast ramp rates will cause temperature to change before frequency sweep is complete

• Used only as a screening tool

Frequency/Temperature testing• Frequency Temperature Sweep:

Isothermal Temperature steps at which frequencies are swept only one variable changes at a time

• Soak time used to allow thermal equilibration

• These are long runs, but clearly better data

• Used for Time Temperature Superpositioning (TTS)

Relationship – Time And Temperature

• Short Time / High Frequency(Rate) / Low Temperature

• Long Time / Low Frequency(Rate) / High Temperature

Relationship – Time And Temperature

Relationship – Frequency And Temperature

Time Temperature Superpositioning• Data taken at higher temperatures represents

data taken at lower frequencies (long times)

• Data taken at lower temperatures represents the behavior at high frequencies (short times)

• Data can be shifted horizontally to create a Master Curve

• TTS Software package uses WLF, (Williams Landel Ferry) equations

10-1 100 101102

101

102

103

104

105

106

107

Overlay of Frequency Temperature Sweep Data

Frequency [Hz]

G' S

tora

ge M

odul

us

G'b J 280 cb E 260 cb F 240 cb G 220 cb H 200 cb I 170 cb D 160 c

10-3 10-2 10-1 100 101 102 103 104101

102

103

104

105

106

107

10-1

100

101

102

Master Curve Data

Frequency [Hz]

tan

delta

G' or G

" [Pa] tan delta G"/G'

G" Loss Modulus

G' Storage Modulus

Material Response To A Step Change In Stress Deformation

(Creep Testing)

t1 Time

τ

ElasticResponse

t2 Time

Stress

γ

t1 t2

Material Response To A Step Change In Stress Deformation

(Creep Testing)Viscous

Response

Time

τ

t1 Time

γ

t2

Stress

t1

t2

Material Response To A Change In Stress Deformation

(Creep test)

0.0 60.0 120.0 180.0 240.00.0

2.0

4.0

6.0

8.0

time [s]

Stra

in(t)

(bQ

)

[

%]

Figure 1: Creep and Recovery Test

DMTA IV

Rheometric Scientific, Inc.

Zone 1 Zone 2Constant Strain: 4.26%

Recoverable Strain: 3.39%

Equilibrium Strain: 0.87%

TMA mode• Tensile or compression geometry• Sample of a measured length is

subjected to a temperature ramp• A load may be placed on the sample,

either in tension or compression• Change in length of the specimen is

measured• Coefficient of thermal expansion can be

calculated

0.0 50.0 100.0 150.0 200.0 250.0 300.0-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

Temp [ ]癈

Dis

plac

emen

t (A

)

[m

m]

Sample in Compression

Linear Expansion

Blowing agent "puffs" and collapses

encapsulated blowing agent

Material Response To A Step Change In Strain Deformation

(Stress relaxation Testing)

Material Response To A Step Change In Strain Deformation

(Stress relaxation Testing)Elastic

Response

t1 Time

τ

Time

τ

ViscousResponse

t1

Material Response To A Step Change In Strain Deformation

(Stress relaxation Testing)

Material Response To A Step Change In Strain Rate

Deformation (Steady Testing)

St ra inRate

Stra in

Timet1 Timet2 t1 t2

Material Response To A Step Change In Strain Rate

Deformation (Steady Testing)

ViscousResponse

Timet1 Timet2 t1 t2

ElasticResponse

Material Response To A Step Change In Strain Rate

Deformation (Steady Testing)

Timet1 t2

ViscoelasticResponse

Stress/Strain curveslooking for linear regions

0.0 0.5 1.0 1.5 2.0 2.5 3.00.0

1x105

2x105

3x105

4x105

5x105

6x105

strain(t) [%]

stre

ss(t)

(bA

)

[dyn

/cm

2 ]Strain Rate Test at -125癈

Geometriesand

Testing considerations.

DMTA IV has six pure modes of deformation

• Dual cantilever bending• Single cantilever bending• Three point bending• Tensile• Compression• Shear sandwich

How the deformation is made in bending

• Bending modes pull samples downward by a chosen amplitude then push up past zero to the same amplitude:

ClampNegative Strain amplitude

Positive Strainamplitude

Sample moves X microns in negative direction, then X microns in the positive direction

Zero position

Zero position

Clamp

Dual/Single Cantilever Bending

• Adjustable lengths• Three frame sizes• For solid bars• Coatings on substrates• Layered materials• For specimens >1 mm

in thickness

Three Point Bending

• Three frame sizes• For solid samples• Best geometry for

very high modulus(rigid) samples

• Eliminates edgeeffects from clamping

• For samples that“grow” with temp.

How deformation is made in tensile geometry

– In a dynamic run tensile force pulls downward then returns towards the starting position but not past the zero point

Mobile clamp

Stationary clamp

Strain Amplitude

Zero position

Lo

∆L

Stress = σ = F/A

Strain= ε = ∆L/Lo

Area = w * t

Tensile Geometry

• Films and Fibers• Elastomers• TMA mode• Auto-gap sets sample

length reproducibly• Pretension and

autotension keepssample taut duringtesting

Compression Geometry

• Foams• Gels• Determines the

resilience of foamstructures

• Auto gap setsthickness

How deformation is made in shear sandwich geometry

Stress: Force per unit areaStrain: Magnitude of deformation relative to sample geometry

A: Area

y

Shear Sandwich

• Pastes and gels• Elastomers• Best in horizontal

orientation• Useful for melts and

viscous fluids

Sample types

• Thermoplastic - can melt and reform into a solid without significant change

• Thermoset - heating will not melt it, material will cure/cross link and harden

• Elastomer - lightly cross linked, pliable, will not melt

• Polymer blend, Copolymer or “Alloy”

Sample’s physical states

• Material may be a solid rectangular bar• A solid film• A fiber or bundles of fibers• A polymer coating on a substrate• Thick melts or viscous liquids• Foams, wet or dry, soft or rigid• Pastes or gels

Sample loading techniques

• Clamping torque is important!• Too much torque on the sample will

create stresses radiating into the sample and distorting the data

• Too light clamping torque can cause sample to slip

• Re-clamping at lower temp. after contraction may be necessary

How to avoid clamping effects

• Keep clamp tension reproducible --even if stress patterns affect absolute results, the run to run variations will be minimal

• Thicker specimens fare better• Use of rubber “grips” between steel

clamps and films improve results– sections of rubber bands can be used,

without introducing creep effect

Sample measuring errors• When measurements on samples are

inexact, the moduli values are affected.• Specimens with uneven surfaces or

geometries will not give consistent moduli.• Bear in mind that moduli are usually

plotted in log form, a slight change visually on the graph is a large change in data.

• Transition temperatures will not be affected.

Effect of incorrectly measured diameter on E’ of steel wire

Effect of incorrectly measured length on E’ of steel wire

How films and fibers differ from other sample types

• Films and fibers are often more fragile requiring a gentle treatment in loading and testing

• Production often involves tremendous stresses on the material: drawing, orienting, annealing, extruding

• Internal stress causes rapid changes during and after Tg, measuring system must compensate rapidly

How films and fibers differ from other sample types

• Uneven thickness are more problematic since aspect ratio is extreme

• Measuring the thickness of films and fibers can be imprecise

• Because of difficulty in loading, good lighting is important over work area

How films and fibers differ from other sample types

• Deformation is in tensile, bending and compression generally not practical

• Sample length is more variable than bending modes: clamp geometry doesn’t interfere with size. Autogap keeps sample length constant.

Using Multiple Fibers

• In many cases, the testing needs to use bundled fibers to represent real life

• Evenly distribute or wind the bundles• Avoid kinking that would make some

fibers longer than others• Approximate sample dimensions and do

not use absolute modulus values: run to run variations may be large

Sample Loading considerationsfor films

• Curling of films– Electrostatic effects on thin films can cause

static attractions that make loading frustrating

– Small residual stresses in the film from processing can cause curling

– Thin brittle films are subject to cracking while trying to flatten for loading

Sample Loading considerations- buckling

• Buckling during loading causes serious errors– Effective sample length is the shortest line

of contact by clamps, so by measuring the whole width you will have large errors, the buckled areas will not “feel” the force or deformation

– Difficult to evenly smooth sample as you load

– You can stretch the sample while doing so, causing stresses in the material

Sample buckling

Even sample width

ClampsSmooth sample distributes stress evenly across sample width

Buckled sample has an effective width narrowed to only the region that is taut between the clamps, modulus values depend on correctly measured geometry

Sample width is taut region only

How to avoid buckling• Wider samples are harder to load- buckling is

more of a problem• Thin film samples are more difficult to keep

smooth• Load the stationary grips first- this will give

you a “third hand” as you align and smooth the sample, in case the mobile grips move during loading.

• Glance across the sample at an angle when loaded- do you see ripples?

Auto-tension during a run• The force needed to keep a specimen taut

during a dynamic run can change• Dimensional changes

– as load remains on the sample it can creep– as a sample softens during heating it will

elongate, or shrinkage can occur as stress relaxation takes place

• Stiffness changes– modulus values change dramatically at Tg

Avoiding Buckling during the run• This additional tensile force is additive

to the dynamic force, one must take care not to exceed linear viscoelastic regions

Stress

Dynamic Force alone

Dynamic + Pre-tension

Linear region exceeded

Strain

Auto-tension during a run• a static pre-tension will not keep specimen

taut, buckling will occur if sample elongates• static pretension alone can exceed plastic

deformation if sample shrinks• static pre-tension can exceed linear region as

sample softens• need to have tracking with autotension which

can change the force with changing sample modulus

Tensile sample length

• In tensile geometry where a sample is long:– care must be taken to avoid temperature

gradients: heat rises run DMTA in horizontal orientation…. Or you will see:

– these temperature gradients can cause a broadening or doublet in Tg

– Failure can occur at the top edge, necking

Residual Solvent content• Many materials contain residual solvent• This acts as a plasticizer, lowering

modulus and Tg• Measuring systems must avoid

changing the sample:– forced air convection furnaces “dry-out’

specimens– slow heating rates can also dry out and

embrittle the sample

What happens on sample drying

• Loss of moisture or residual solvent can raise the modulus of the material

• Without the plasticizer (or solvent) Tg is raised

• Embrittlement• Draw ratio decreases• Lower elongation at break

DMTA study of solvent or fluid effects on material behavior

• Elastomer solvent swell

• Medical applications• Leaching of

plasticizers• Destructive fluid

interactions• Fluid effects on

creep