Visco-elasticity

1. Dynamic Mechanical
Analysis
Mohammad Ansar
Senior Project Engineer
SCTIMST
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2. Contents
• Visco-Elasticity
• DMA
• Temperature sweep
• Strain sweep
• Frequency sweep
• Stress relaxation
• Creep
• Miscellenous calculations
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3. Uninstalling Chain theory
• Polymers are complex chains
• Property of polymers depends on chemical
structure,molecular weight, side groups etc
• Prediction of final property is complex
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4. Installing visco-elastic theory
• Polymers are just combination of Viscous componant
and elastic componant
• Property of polymers depends on viscous componant,
elastc componant and composition of this componats
• Prediction of final property is simple
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5. Visco-Elasticity
Viscous material Elastic material
Viscosity + Elasticity = Visco-elasticity
Source https://www.machinerylubrication.com/Read/294/absolute-kinematic-viscosity
https://www.sciencephoto.com/media/980971/view 5

6. Elasticity – The ability of the material to return its original
shape after deformation
𝑺𝒕𝒓𝒆𝒔𝒔 ∞ 𝑺𝒕𝒓𝒂𝒊𝒏
𝑺𝒕𝒓𝒆𝒔𝒔 = 𝑴𝒐𝒅𝒖𝒍𝒂𝒔 𝒐𝒇 𝒆𝒍𝒂𝒔𝒕𝒊𝒄𝒕𝒚 × 𝐒𝐭𝐫𝐚𝐢𝐧
Instatanious
Temperory
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7. Viscous material- Stress create flow
𝑆𝑡𝑟𝑒𝑠𝑠 ∝ 𝑆𝑡𝑟𝑎𝑖𝑛 𝑟𝑎𝑡𝑒
𝑆𝑡𝑟𝑒𝑠𝑠 = 𝑣𝑖𝑠𝑐𝑜𝑠𝑖𝑡𝑦 × 𝑠𝑡𝑟𝑎𝑖𝑛 𝑟𝑎𝑡𝑒
Time dependent
Permanent deformation
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8. Elastic VS viscous
Elastic material
• Instant
• Temperory
• Recoverable
• Time independent
Viscous material
• Slow
• Permanent
• Irrecoverable
• Time dependent
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9. Visco-elastic material
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10. Mechanical models
Maxwell model Voigt-kelvin model
Source https://www.sciencedirect.com/topics/chemistry/viscoelasticity
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11. Maxwell model 𝜀 𝑡𝑜𝑡𝑎𝑙 = 𝜀 𝑆𝑝𝑟𝑖𝑛𝑔 + 𝜀 𝐷𝑎𝑠ℎ 𝑝𝑜𝑡
Total stress remain same
𝜎 = 𝐸 × 𝜀
𝜀 = 𝜎/ 𝐸
𝜎 = 𝜇 × 𝛾
𝛾 = 𝜎/ 𝜇
Upon integration
𝜀 = 𝜎 𝑡/ 𝜇
𝜀 =
𝜎
𝐸
+ 𝜎 𝑡/ 𝜇
𝛾 = 𝑑𝜀/𝑑𝑡
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12. Voigt kevin model
Total strain same
Total Stress = Stress of Dashpot + Stress of spring
Source https://www.sciencedirect.com/topics/chemistry/viscoelasticity
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13. Why Visco-Elasticity
Without stress
With applied stress
Source https://www.doitpoms.ac.uk/tlplib/stiffness-of-rubber/rubber-conformation.php
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14. Dynamic mechanical analyzer
Elastic or storage modulus is
E’ or G’
Viscous or loss modulus is
E” or G”
tan delta =
𝑳𝒐𝒔𝒔
𝑺𝒕𝒐𝒓𝒂𝒈𝒆
Source https://www.perkinelmer.com/category/dynamic-mechanical-analysis-dma
https://www.bccourier.com/global-dynamic-mechanical-analyzer-dma-market-2019-industry-dynamics-ta-instruments-netzsch-hitachi-high-technologies/
Complex modulus = G’+iG”
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15. Visco-elastic material under sinusoidal stress
Elastic
Viscous
Visco-elastic
or
Polymer
Source https://polymerdatabase.com/polymer%20physics/DMA.html
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16. Temperature Sweep
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17. Effect of crosslinking
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18. Cure charectaristics
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19. Time Temperature super-position Principle
𝜀 =
𝜎
𝐸
+ 𝜎 𝑡/ 𝜇
WLF equation
log10
𝑓
𝑓𝑛
=
−17.44(T−Tg)
51.6+(T−Tg)
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20. Strain Sweep &Payne effect
Payne effect = G’(1% strain) – G’(100% strain)
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21. Frequency Sweep
Source https://www.tainstruments.com/rpa-elite/
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22. Frequency Sweep-Relaxation time
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23. Stress Relaxation
Stress relaxation is a time-dependent
decrease in stress under a constant strain
Ϭ = Ϭ0 e-t/τ
Time = t
Relaxation time =τ
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24. Creep
Creep is the tendency of a material deform slowly under contant stress
Source https://onlinelibrary.wiley.com/doi/epdf/10.1002/0471238961.koe00047
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25. Question and Answers
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26. Q. Choose highly elastic material
from the options
a. Steel
b. Rubber
c. Fibre
d. Plastic
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27. Q.
If a rubber ball can rebouce back upto 80 cm
after droping height from 1 meter.
Then what will be the aproximate phase angle
between its storage modulas and loss
modulus
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28. Damping factor = 20/80
=0.25
tan delta = 0.25
tan−1
0.25 =
https://www.centropiaggio.unipi.it/sites/default/files/course/material/dma.pdf
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29. Q. Arrange material in order of increase in tan
delta from given UTM graph
https://www.smlease.com/entries/mechanical-design-basics/stress-strain-curve-diagram/ 29

30. https://openoregon.pressbooks.pub/bodyphysics/chapter/elasticity-and-hookes-law/
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31. Imagine that you are synthesising a material for
implantable dynamic load bearing application,
since it is implantable it should not or least generate
heat during its working condition,
Choose a sample among given which generate less
heat during its service
Sample Tan delta
A 0.5
B 0.25
C 1.25
D 6
E 10
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32. https://shodhganga.inflibnet.ac.in/bitstream/10603/235693/10/10_chapter%203.pdf
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33. https://shodhganga.inflibnet.ac.in/bitstream/10603/119900/1/thesis.pdf 33

34. a polymer having relaxation time (τ) is 60 days
then
If the sample is stressed to 2 MPa initially, then
the time required to relax the stress to
1 MPa will be
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35. Ϭ = Ϭ0 e-t/τ
1=2 e-t/60
0.5 = e-t/60
Take ln on both sides
-0.693 = -t/60
t = 51.58 days
Where Ϭ = stress after time t
Ϭ0= initial stress
t= time
τ= relaxation time
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36. Dynamic mechanical analysis of polystyrene (Tg = 100 ºC)
measured at a frequency of 1 Hz shows
the damping peak at 110 ºC. If the measurement is made at
10000 Hz, then the peak temperature (ºC)
will be
(A) 123.2 (B) 133.2 (C) 143.2 (D) 153.2
Tg = 100
At Fn
Tg = 110
At
1Hz
Tg = ?
At
10000 Hz
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37. ANS) 133.2℃
WLF equation
𝒍𝒐𝒈 𝟏𝟎
𝒇𝒏
𝒇
=
−17.44(T−Tg)
51.6+(T−Tg)
At 1 Hz T = 110, Tg = 100
10000Hz T= ?
Put first condition
T= 110, Tg =100, F = 1
𝒍𝒐𝒈 𝟏𝟎
𝒇𝒏
𝟏
=
−17.44(110−100)
51.6+(110−100)
=
−𝟏𝟕𝟒.𝟒
𝟔𝟏.𝟔
= -2.81, Fn=𝟏𝟎−𝟐.𝟖𝟏
=1.475× 𝟏𝟎−𝟑
Put Fn in second condition
Log (1.475x 10-3/10000) =
−17.44(T−100)
51.6+(T−100)
-6.83 =
−17.44(T−100)
51.6+(T−100)
=
17.44T−1744)
48.4−T
6.83T-330 = 17.44T-1744
T = 133.2 ℃
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38. Thank you
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