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1、2005 Training School DMA Basic Principle Is DMA Thermal Analysis or Rheology ?Definitions ?Thermal Analysis is the measurement of some characteristic of a substance as a function of temperature or time. ?Rheology is the science of flow and deformation of matter. ?DMA is the general name given to an
2、instrument that mechanically deforms a sample and measures the sample response. The deformation can be applied sinusoidally, in a constant (or step) fashion, or under a fixed rate. The response to the deformation can be monitored as a function of temperature or time. Rheology of Solids? ?Definition
3、of Rheology ?The Science of flow and deformation of matter. Importance of Solid Polymer Rheology ?Polymeric materials are used extensively ?desirable mechanical properties ?economical cost ?For most applications, mechanical properties are considered the most important of all physical and chemical pr
4、operties of polymers. ?Important facts when working with polymers ?Need to have some basic knowledge of the mechanical behavior ?Need to have an understanding of how the mechanical behavior can be modified by the numerous structural factors that can be varied Rheology Nielsen, Lawrence E., Mechanica
5、l Properties of Polymers and Composites, Marcel Dekker, Inc., New York, 1974, p. 1. Polymers Exhibit Wide Range of Mechanical Strength ?A single polymer can exhibit an extremely wide range of mechanical behavior ?Very hard and rigid solid ?Stiff to Soft rubber ?Viscoelastic liquids ?The Mechanical s
6、trength of a polymer is a consequence of ?Chemical Composition of the Polymer ?Dictates where changes in mechanical properties occur ?Physical Molecular Structure of the Polymer ?Dictates how changes in mechanical properties will occur Viscoelastic Spectrum for a Typical Amorphous Polymer Terminal R
7、egion Rubbery Plateau Region Transition Region Glassy Region Loss Modulus (E“ or G“) Storage Modulus (E or G) log E (G) and E“ (G“) Very hard and rigid solid Stiff to Soft rubber Viscoelastic liquid Temperature Deformation of Solids and the Modulus ?All materials change in shape, volume, or both und
8、er 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 material ?Youngs Modulus (Modulus of Elasticity) E ?Shear Modulus (Modulus of Rigidity) G ?B
9、ulk Modulus B The Three Moduli - Elastic Constants Bulk Modulus Youngs Modulus Shear Modulus E = G = hyd V/Vo B = WhereDashed lines indicate initial stressed state = uniaxial tensile or compressive stress = shear stress hyd= hydrostatic tensile or compressive stress = normal strain = shear strain V/
10、Vo= fractional volume expansion or contraction Poissons Ratio - The Fourth Elastic Constant ?Poisons ratio, , is the ratio of transverse to axial strain lz l0z z z l y y 2 ly- l0y 2 = z 2 lz- l0z 2 = = y z Poissons Ratio l0y Poissons Ratio ?If the volume of the specimen remains constant when deforme
11、d, = 0.5. ?Examples of constant volume materials are liquids and ideal rubbers. ?In general, there is an increase in volume given by V/Vo= (1 - 2) where V = increase in initial volume Vocaused by straining the sample. Comparison of Moduli and Poissons Ratio MaterialE(Gpa) G (Gpa) Steel2200.2885.9 Co
12、pper1200.3544.4 Glass600.2324.4 Granite300.3015.5 Polystyrene340.3312.8 Polyethylene240.388.7 Natural Rubber0.020.490.0067 Cowie, J.M.G., Polymers: Chemistry & Physics of Modern Materials, 2nd Edition, Blackie academic & Professional, and imprint of Chapman & HallBishopbriggs, Glasgow, 1991p. 275 IS
13、BN 0 7514 0134 X Basic Parameters and Units S.I. units = c.g.s. X 2 ?Stress = Force /Area Pa, or dyn/cm ? = tensile stress, = shear stress ?Strain = Geometric Shape Change no units ? = tensile strain, = shear strain ?Strain or Shear Rate = Velocity Gradient or d(strain)/dt 1/s ? = tensile strain rat
14、e, = shear strain rate ?Modulus = Stress / Strain Pa or dyn/cm ?E = Youngs or Tensile, G = Shear Modulus ?Compliance = Strain / Stress 1/Pa or cm /dyn ?Typically denoted by J ?Viscosity = Stress /Strain Rate Pa.s or Poise ?Denoted by 2 2 Viscoelasticity Defined Range of Material Behavior Solid Like
15、- Liquid Like Ideal Solid - Most Materials - Ideal Fluid Purely Elastic - Viscoelastic - Purely Viscous Viscoelasticity: Having both viscous and elastic properties Response for Classical Extremes Spring Dashpot Purely Viscous Response Newtonian Liquid = Purely Elastic Response Hookean Solid = E or =
16、 G In the case of the classical extremes, all that matters is the values of stress, strain, strain rate. The response is independent of the loading. Time-Dependent Viscoelastic Behavior: Solid and Liquid Properties of “Silly Putty“ T is long 24 hours T is short 0 is constant time 0 stress for t0 is
17、0 Stress Relaxation Experiment Response of 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, G(t) G(t) = (t)/ Stress decreases with time starting
18、at some high value and decreasing to zero. Stres s 0 time Stress Relaxation: Material Response Terminal Region Rubbery Plateau Region Transition Region Glassy Region log Stress Relaxation Modulus E(t) or G(t) log time Programming Stress Relaxation on the DMA Mode: DMA Stress Relaxation Method Equili
19、brate at _C Isothermal for _min Displace_min, Recover_min 0 Instrument Parameters Strain_% Stress Relaxation on PP Creep Recovery Experiment ?Stress is applied to sample instantaneously, t1, and held constant for a specific period of time. The strain is monitored as a function of time (t) or (t). ?T
20、he stress is reduced to zero, t2, and the strain is monitored as a function of time (t) or (t). Stress time t1t2 Creep Recovery Experiment time Stress t2t1 Response of Classical Extremes Strain time Stain rate for tt1 is constant Strain for tt1 increase with time Strain rate for t t2 is 0 t2t1 Stain
21、 for tt1 is constant Strain for t t2 is 0 Strain time t1t2 Creep Recovery Experiment Recovery ZoneCreep Zone Less Elastic More Elastic Creep 0Recovery = 0 (after steady state) / Strain t1 t2 time Creep Recovery Experiment: Creep and Recoverable Compliance 1/ Creep Zone Reference: Mark, J., et.al., P
22、hysical Properties of Polymers ,American Chemical Society, 1984, p. 102. J(t) time Jr(t) time Je Recovery Zone Creep Compliance J(t) = = (t)/ Recoverable Compliance Jr(t) = u- r(t)/ where u= Strain at unloading r(t) = time dependent recoverable strain Je = Equilibrium recoverable compliance 0 Creep:
23、 Material Response Terminal Region Rubbery Plateau Region Transition Region Glassy Region log Creep Compliance, Jc log time Programming Creep on the DMA Mode: DMA Creep Method Equilibrate at _C Isothermal for _min Displace_min, Recover_min Instrument Parameters Stress_MPa Dynamic Mechanical Testing
24、Deformation ?An oscillatory (sinusoidal) deformation (stress or strain) is applied to a sample. ?The material response (strain or stress) is measured. ?The phase angle , or phase shift, between the deformation and response is measured. Response Phase angle DMA Viscoelastic Parameters: The Complex, E
25、lastic, & Viscous Stress ?The stress in a dynamic experiment is referred to as the complex stress * ?The complex stress can be separated into two components: 1) An elastic stress in phase with the strain. = *cos is the degree to which material behaves like an elastic solid. 2) A viscous stressin pha
26、se with the strain rate. “ = *sin “ is the degree to which material behaves like an ideal liquid. Phase angle Complex Stress, * Strain, * = + i“ DMA Viscoelastic Parameters The Modulus: Measure of materials overall resistance to deformation.G = Stress/Strain The Elastic (Storage) Modulus: Measure of
27、 elasticity of material. The ability of the material to store energy. G = (stress/strain)cos The Viscous (loss) Modulus: The ability of the material to dissipate energy. Energy lost as heat. G“ = (stress/strain)sin Tan Delta: Measure of material damping - such as vibration or sound damping.Tan = G“/
28、G Storage and Loss of a Viscoelastic Material SUPER BALL TENNIS BALL X STORAGE LOSS DMA Viscoelastic Parameters: Damping, tan Phase angle G* G G“Dynamic measurement represented as a vector ?The tangent of the phase angle is the ratio of the loss modulus to the storage modulus. tan = G“/G ?“TAN DELTA
29、“ (tan ) is a measure of the damping ability of the material. Dynamic Time Sweep Strain Time Deformation?The material response is monitored at a constant frequency, amplitude and temperature. ?INSTRUMENT MODE Multi-Frequency ?METHOD Equilibrate at _C Isotherm for _ min. ?Frequency = single/multiple
30、?Amplitude = In Linear viscoelastic region ?USES ?Cure Studies ?Degradation Dynamic Strain Sweep ?The material response to increasing deformation amplitude is monitored at a constant frequency and temperature. Strain Time Deformation ?USES ?Identify Linear Viscoelastic Region ?Resilience ?INSTRUMENT
31、 MODE Multi-Strain ?METHOD Equilibrate at _C Isotherm for _ min. Strain Sweep ?Frequency = single only ?Amplitude = Program Table up to 28 values Dynamic Strain Sweep: Material Response Linear Region: Modulus independent of strain E or G Non-linear Region: Modulus is a function of strain Stres s c=
32、Critical Strain Constant Slope Strain (amplitude) Frequency Sweep ?The material response to increasing frequency (rate of deformation) is monitored at a constant amplitude and temperature. Strain Time Deformation ?INSTRUMENT MODE Multi-Frequency ?METHOD Equilibrate at _C Isotherm for _ min. Frequenc
33、y Sweep ?Frequency = Program Table up to 28 values ?Amplitude = single only In Linear viscoelastic region ?USES ?High and Low Rate (short and long time) modulus properties. ?Polymer melt processing (shear sandwich). ?Extend range with TTS Frequency Sweep: Material Response Terminal Region Rubbery Pl
34、ateau Region Transition Region Glassy Region 1 2 Storage Modulus (E or G) Loss Modulus (E“ or G“) log E (G) and E“ (G“) log Frequency (rad/s or Hz) The Viscoelastic Spectrum (E“ or G“) (E or G) log E (G) and E“ (G“) (E“ or G“) (E or G) log E (G) and E“ (G“) log Frequency Temperature log E (t) or G (
35、t) log Time log Jc log Time Creep Behavior in Each Viscoelastic Zone 250.0050.00100.0150.0200.0 time (s) 4.5000E-7 0 5.0000E-8 1.0000E-7 1.5000E-7 2.0000E-7 2.5000E-7 3.0000E-7 3.5000E-7 4.0000E-7 compliance (m2/N) TA Instruments 250.0050.00100.0150.0200.0 time (s) 1.0000E-5 0 2.0000E-6 4.0000E-6 6.
36、0000E-6 8.0000E-6 compliance (m2/N) TA Instruments 250.0050.00100.0150.0200.0 time (s) 1.5000E-3 0 2.5000E-4 5.0000E-4 7.5000E-4 1.0000E-3 1.2500E-3 compliance (m2/N) TA Instruments 250.0050.00100.0150.0200.0 time (s) 0.12000 0 0.020000 0.040000 0.060000 0.080000 0.10000 compliance (m2/N) TA Instrum
37、ents Flow 190C Plateau 150C Glassy 70CT 110C g 250.025.050.075.0100.0125.0150.0175.0200.0225.0 temperature (Deg C) 1.000E7 100.0 1000 10000 100000 1000000 10.00 0.01000 0.1000 1.000 tan(delta) 1.000E7 100.0 1000 10000 100000 1000000 G (Pa) DMA Force Ramp Test on Solids ?Force is applied to material
38、at a constant rate. Resultant strain is monitored with time. Force (N) time (min.) m = force rate (N/min) Deformation ?INSTRUMENT MODE DMA Controlled Force Mode ?METHOD Equilibrate at _C Isotherm for _ min. Ramp force _ N/min until _ N ?USES ?“Static“ modulus ?Determine linear region for clamps whic
39、h require static forces in dynamic mode (tension, compression, three point bending). DMA Force Ramp Test: Material Response Strain (amplitude) Linear Region Modulus independent of strain E or G Non-linear Region Modulus is a function of strain Stress c = Critical Strain Force Ramp Helps Establish Pa
40、rameters Stress Force Experimental Considerations ?The 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 Sample Considerations ?Deformat
41、ion Mode: ?E tension, compression and bending ?G shear ?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. ?Shape: Accurate/reproducible modulus depends on good sample shape consistent cr
42、oss-section throughout length. Sample size cannot exceed clamp restrictions Stiffness takes precedence. Sample Stiffness (K) ?The fundamental measurement of the DMA 2980 is sample stiffness (K) ?K = Force applied to sample/amplitude of deformation ?Range of Stiffness on the 2980 is 100 to 10,000,000
43、 N/m ?During an experiment, the raw signals measured are FORCE and AMPLITUDE. Instrument calibrations are applied to the raw signals. Stiffness is calculated directly from force and amplitude and modulus is calculated by multiplying by the appropriate geometry factor (GF). ?Modulus = Stiffness * Geo
44、metry factor = K * GF ?Stress and strain are calculated from force and amplitude respectively. SEE EQUATIONS IN CHAPTER 6 OF MANUAL. Sample Stiffness and Material Modulus Thick and Thin Samples That Have The Same Modulus Thick and Thin Samples Can Have The Same Stiffness High Modulus Material x = 10
45、 mm F = 1 N x = 10 mm F = 1 N Low Stiffness Sample F = 1 NF = 1 N x = 2 mm x = 10 mm Low Modulus Material High Stiffness Sample Changing Sample Stiffness Clamp Type To Increase Stiffness To Decrease Stiffness. Tension Film Decrease length or increase width. If possible increase thickness. Increase l
46、ength 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 decreas
47、e 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 d
48、ecrease diameter. Shear Sandwich Decrease thickness or Increase length and width. Increase thickness or decrease length and width. 71 Modulus Calculations in the DMA 2980 ?The instrument applies all calibrations and measures raw sample storage and loss stiffnesses (Ks). ?Modulus = Stiffness * Geometry Factor = Ks*GF GF = 1 F L 12I S(1+ ) L A 3 + 2 GF = L 48I S(1+ ) L 2A 3 + GF = 1 F L 192I S(1+ ) L 2A 3 + Dual Cantilever Single Cantilever 3-Point Bend L = Sample LengthI = Geometric Moment