80262466 ebook engineering dynamic mechanical thermal analysis
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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
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