1 / 21

DYNAMIC MODULI

DYNAMIC MODULI . Storage and Loss. Perfectly Elastic Materials. Mechanical properties described by elastic moduli. Viscoelastic Materials. have both an elastic and viscous component measurement of viscosity difficult by traditional methods.

vinny
Download Presentation

DYNAMIC MODULI

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. DYNAMIC MODULI Storage and Loss

  2. Perfectly Elastic Materials • Mechanical properties described by elastic moduli

  3. Viscoelastic Materials • have both an elastic and viscous component • measurement of viscosity difficult by traditional methods

  4. But how do you separate the viscous component from the solid component? solids liquid

  5. Complex Modulus • Define a “complex” modulus that covers both elastic and viscous components of the material • For example, Young’s modulus for a viscoelastic material takes the form E* = E’ + iE” • Similar definitions hold for G and K

  6. E’ is the storage modulus and measures the energy stored. It is like a spring. • E” is the loss modulus measures the mechanical energy converted to heat through viscous frictional forces. It is like the dashpot.

  7. When the girls jump on the trampoline, it deforms and “stores” the energy in the stretched molecules. The trampoline snaps back and returns the energy, causing them to fly upwards.

  8. When a diver hits the water, the kinetic energy of his fall is “lost” in the water. The water molecules slide past each other and result in heating.

  9. We often speak of the complex modulus E*=E’ + i E” i is an imaginary number ( ), E’ is the storage modulus and E” the loss modulus • This notation is easier to deal with mathematically. i indicates that the storage modulus is “out of phase” with the loss modulus

  10. Measuring Complex Moduli • Apply a sinusoidally varying force at frequency . • The strain will be out of phase with the stress by a phase angle . • One component is “in phase” with the strain (the elastic part); one component is out of phase (the viscous part)

  11. Mathematically Strain:  = o sin t Stress:  = o sin(t + ) Stress o Strain o 

  12. The stress can be decomposed into 2 components, one in phase with the strain (sint) and one out of phase by 90° (cost)  = ’ + ” = o’sint +  o”cost

  13. From this, two dynamic moduli can be defined

  14. Loss modulus Storage modulus • We can write the stress-strain relationship

  15. Dynamic Mechanical Analyzer (DMA) Sample is subject to oscillating stress under compression, tension, or bending Good for more solid-like materials

  16. Dynamic Rheometer Sample is subject to oscillating stress under shearing conditions Good for more liquid-like materials

  17. Thermal Analysis • Dynamic instruments are usually often capable of complex thermal analysis • Temperature can be held steady, stepped, or ramped from one temperature to another

More Related