Polymers- Linear Viscoelasticity

Question 1

Newton’s law for viscous liquid

Answer 1

σ=ηdε/dt

Question 2

Log(E) vs T graph with different regions named

Answer 2

Starts high and mainly constant in glassy. Curves down to very steep then starts to level off in leathery. Never reaches flat again and starts curving back down in rubbery. Continues curve back down in rubbery flow then viscous regions

Question 3

What does viscoelastic mean?

Answer 3

Display specs of both viscous and elastic types of behaviour

Question 4

Strain vs time for ideal, vulcanised and unvulcanised rubber (creep curve)

Answer 4

Ideal is a square.
Vulcanised almost square but too left rounded a bit, top right sharp but goes down like steep exponential decay very close to x axis.
Unvulcanised like vulcanised been pushed up from bottom right so more strain not recovered and first two sides never straight and more like same curve.

Question 5

Strain vs time for viscous state

Answer 5

Straight diagonal from x axis NkT origin. Then reaches some amount of strain when stress ended and stays there horizontal

Question 6

Different parts of a creep curve

Answer 6

Vertical distance from origin where it stays vertical is initial elastic response. Vertical distance between when first deviates from vertical and top left corner is region of creep. Vertical distance between top left and top right (stress removed) corners is irrecoverable viscous flow

Question 7

What is creep?

Answer 7

A progressive increase in strain, observed over an extended time period, in a polymer subjected to a constant stress

Question 8

Creep compliance formula

Answer 8

J(t)=γ(t)/σ
For strains below 0.005
After that graph becomes non-linear as it curves up

Question 9

Compliance vs log t

Answer 9

Starts at J sub U (unrelaxed compliance) then curves up and levels off at J sub R (relaxed compliance)

Question 10

Formula for shear stress in measurement of creep compliance

Answer 10

σ=Γ/(2πr^2s)
Where Γ is torque
r is initial/outer radius of cylinder
s is difference between inner/final radius and outer/initial radius

Question 11

Shear strain for measurement of creep compliance

Answer 11

lγ(t)=rθ(t)
Where l is length if cylinder
γ is shear strain (angle along length of cylinder up to side made by θ
r is outer/initial radius of cylinder
θ is angle any part of top face is moved around central axis

Question 12

Creep compliance in shear full formula

Answer 12

J(t)=((2πr^3s)/l)θ(t)/Γ

Question 13

Creep compliance in tension

Answer 13

D(t)=ε(t)/σ

Question 14

Stress relaxation

Answer 14

Apply a constant strain and observe that the stress required to keep it there decreases over time from the initial applied

Question 15

Stress relaxation modulus

Answer 15

G(t)=σ(t)/γ

Question 16

Stress relaxation modulus vs log t

Answer 16

Straits high a G sub U unrelaxed modulus (1 over J sub U). Curves down then levels off at G sub R relaxed modulus (1 over J sub R)

Question 17

Formula for stress relaxation modulus (lots of symbols)

Answer 17

Is the reciprocal of the long compliance modulus formula

Question 18

Oscillatory sinusoidal strain for linear viscoelastic material

Answer 18

γ=γ0sin(ωt)
σ=σ0sin(ωt+δ)
ω is angular frequency of strain
Stress lags strain by δ

Question 19

Storage modulus, loss modulus, loss tangent

Answer 19

Storage: G’=(σ0/γ0)Cosδ
Loss: G”=(σ0/γ0)Sinδ
Loss tangent: tanδ=J”/J’=G”/G’