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Dynamic mechanical analysis
- 1. Dynamic Mechanical Analysis Mohammad Ansar SeniorProject Engineer SCTIMST 1
- 2. Contents • Visco-Elasticity • DMA •Temperature sweep • Strain sweep • Frequency sweep • Stress relaxation • Creep • Miscellenous calculations 2
- 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 3
- 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 4
- 5. Visco-Elasticity Viscous material Elasticmaterial Viscosity + Elasticity = Visco-elasticity Source https://www.machinerylubrication.com/Read/294/absolute-kinematic-viscosity https://www.sciencephoto.com/media/980971/view 5
- 6. Elasticity – Theability of the material to return its original shape after deformation 𝑺𝒕𝒓𝒆𝒔𝒔 ∞ 𝑺𝒕𝒓𝒂𝒊𝒏 𝑺𝒕𝒓𝒆𝒔𝒔 = 𝑴𝒐𝒅𝒖𝒍𝒂𝒔 𝒐𝒇 𝒆𝒍𝒂𝒔𝒕𝒊𝒄𝒕𝒚 × 𝐒𝐭𝐫𝐚𝐢𝐧 Instatanious Temperory 6
- 7. Viscous material- Stresscreate flow 𝑆𝑡𝑟𝑒𝑠𝑠 ∝ 𝑆𝑡𝑟𝑎𝑖𝑛 𝑟𝑎𝑡𝑒 𝑆𝑡𝑟𝑒𝑠𝑠 = 𝑣𝑖𝑠𝑐𝑜𝑠𝑖𝑡𝑦 × 𝑠𝑡𝑟𝑎𝑖𝑛 𝑟𝑎𝑡𝑒 Time dependent Permanent deformation 7
- 8. Elastic VS viscous Elasticmaterial • Instant • Temperory • Recoverable • Time independent Viscous material • Slow • Permanent • Irrecoverable • Time dependent 8
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- 10. Mechanical models Maxwell modelVoigt-kelvin model Source https://www.sciencedirect.com/topics/chemistry/viscoelasticity 10
- 11. Maxwell model 𝜀𝑡𝑜𝑡𝑎𝑙 = 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 11
- 12. Voigt kevin model Totalstrain same Total Stress = Stress of Dashpot + Stress of spring Source https://www.sciencedirect.com/topics/chemistry/viscoelasticity 12
- 13. Why Visco-Elasticity Without stress Withapplied stress Source https://www.doitpoms.ac.uk/tlplib/stiffness-of-rubber/rubber-conformation.php 13
- 14. Dynamic mechanical analyzer Elasticor 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” 14
- 15. Visco-elastic material undersinusoidal stress Elastic Viscous Visco-elastic or Polymer Source https://polymerdatabase.com/polymer%20physics/DMA.html 15
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- 19. Time Temperature super-positionPrinciple 𝜀 = 𝜎 𝐸 + 𝜎 𝑡/ 𝜇 WLF equation log10 𝑓 𝑓𝑛 = −17.44(T−Tg) 51.6+(T−Tg) 19
- 20. Strain Sweep &Payneeffect Payne effect = G’(1% strain) – G’(100% strain) 20
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- 23. Stress Relaxation Stress relaxationis a time-dependent decrease in stress under a constant strain Ϭ = Ϭ0 e-t/τ Time = t Relaxation time =τ 23
- 24. Creep Creep is thetendency of a material deform slowly under contant stress Source https://onlinelibrary.wiley.com/doi/epdf/10.1002/0471238961.koe00047 24
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- 26. Q. Choose highlyelastic material from the options a. Steel b. Rubber c. Fibre d. Plastic 26
- 27. Q. If a rubberball 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 27
- 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 28
- 29. Q. Arrange materialin order of increase in tan delta from given UTM graph https://www.smlease.com/entries/mechanical-design-basics/stress-strain-curve-diagram/ 29
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- 31. Imagine that youare 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 31
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- 34. a polymer havingrelaxation 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 34
- 35. Ϭ = Ϭ0e-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 35
- 36. Dynamic mechanical analysisof 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 36
- 37. ANS) 133.2℃ WLF equation 𝒍𝒐𝒈𝟏𝟎 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 ℃ 37
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