Viscoelasticity: solid state strain and relaxation

Question 1

What is stress?

Answer 1

Measure of force applied to deform a material

Question 2

What is strain?

Answer 2

Measure of the deformation of a material (how much its moved)

Question 3

What is elastic deformation?

Answer 3

deformation that is reversible (material returns to its original state after removing load)

• caused by a permanent connection (ex. physical or chemical crosslinks or polymer scale)
• stress-strain is small

Question 4

What is Plastic Deformation?

Answer 4

permanent deformation even after load is removed

– causes non-reversible changes at the molecular layer (ex. breaking bonds/moving layers apart)

Question 5

What are Polymeric rubbers/elastomers?

Answer 5

polymers below Tg (below theta condition)
- at room temperature are at rubbery state

• reach an elastic limit when all the polymers are stretched (stretching is cooling but returning to original shape is heating in equilibrium reaction) (stretched is low entropy while unstretched is high entropy)

Question 6

What does the Deborah number tell us?

Answer 6

Gives the time dependence for chain relaxation (how much the polymer resists deformation forces)

• calculate as the characteristic relaxation time of polymer divided by the time scale of the stretching process
  **tells us that the slower the forces are applied, the more deformation we can get
• when Deborah number is 1, is more like a liquid

Question 7

How does hysteresis change the stress-strain curves?

Answer 7

repeat cycles show more less stress needed for the same strain

• get more permanent deformation (you give the chains more time to leave the crosslinks)

Question 8

What are the 3 situations we want to use to model deformation?

Answer 8

1. constant strain rate
2. creep (constant stress and look at time it takes for polymer to slowly stretch out - strain)
3. stress relaxation (constant strain and hold to evaluate stress evolution over time)

Question 9

What is the issue with the Maxwell model?

Answer 9

Doesn’t work well for creep (don’t get smooth logarithmic or exponential curves)

• elastic component and viscous component is series (constant stress for both units)

Question 10

What is the issue with the Kelvin-Void model?

Answer 10

Doesn’t work well for stress relaxation (calculates a constant max stress)

• elastic and viscous component in series (constant strain)

Question 11

What is the Zener model?

Answer 11

Combines the Maxwell and Kelvin-Void models to better predict both the creep and stress relaxation

• first elastic component in parallel with an in series elastic and viscous component

Question 12

Example:
For a Zener model that is 5 cm long and stretched to 6cm and held there for 90s, calculate the internal stress

E1 = 200 Pa
E2 = 500 Pa
n = 20 000 Pa.s

bonus: what is the internal stress if left for a very long time?

Answer 12

A: 50.5 Pa

bonus: 40 Pa