L2: Mechanical Behaviour 1

Question 1

What type of materials is Tg associated with?

Answer 1

Amorphous materials

Question 2

What are polymer properties typically more sensitive to than for metals and ceramics?

Answer 2

Temperature change

Question 3

What change occurs with increasing temperature in a polymer?

Answer 3

Change from rigid glassy state to viscous state - large drop in modulus

Question 4

Define glass transition temperature

Answer 4

The characteristic temp at which a polymer’s behaviour changes between rigid glassy to rubbery

Question 5

What type of molecular motion is enabled at glass transition temp?

Answer 5

Amorphous polymer materials can change their spatial arrangement of atoms by rotation about the chain (cooperative rotation)

Question 6

Why must Tg be considered in structural design?

Answer 6

For load-bearing designs, stiffness can drop at increased temps, leading to dimensional instability and excessive deformation due to creep

Question 7

List 5 key factors affecting Tg

Answer 7

1. Chain stiffness
2. Intermolecular interactions (hydrogen and covalent bonding, ionic interactions)
3. Molar mass
4. Additives (e.g. fillers)
5. Moisture (swelling)

Question 8

What is the fundamental reason for the viscoelastic response of a polymer?

Answer 8

They deform by 2 fundamentally different atomistic methods

1. Elastic (distortion of lengths and angles of chemical bonds)
2. Viscous (large-scale spatial rearrangements of atoms accompanied by decrease in their conformational entropy)

Question 9

Why is the viscoelastic behaviour of polymers particularly evident around Tg?

Answer 9

They display both viscous and elastic behaviour simultaneously around Tg

Question 10

Define creep

Answer 10

Time dependent strain response to constant stress

Question 11

Which energy components does viscoelastic material have?

Answer 11

• Elastic/energic (stores energy)

- Viscous/entropic (dissipates energy)

Question 12

Give the four stages pf a polymer’s strain-time curve, from stress applied to after stress removal

Answer 12

1. Stress applied -> Almost instantaneous initial elastic response
2. Creep - strain increases progressively with stress, slowing with time
3. Viscous flow, signified by constant strain rate
4. Stress removed -> Strain recovery (except for strain caused by viscous flow)

Question 13

Define stress relaxation. How does it vary with time?

Answer 13

Time-dependent response to constant strain. It decreases with time

Question 14

What do mathematical models for viscoelastic behaviours assume?

Answer 14

The behaviour can be represented in terms of combinations of springs (elastic) and dashpots (viscous) behaviour which act as independent elements

Question 15

Describe the stress-strain relationship and loading cycle of perfectly elastic solids

Answer 15

Hooke’s law (stress = YM * strain)
Stress is proportional to strain and time independent
Net work is zero over a loading-unloading cycle

Question 16

Describe the stress-strain relationship and loading cycle of linear viscous liquids

Answer 16

At low strain rates, Newton’s law is obeyed (stress = coefficient of viscosity * rate of change of strain)
Stress is proportional to rate of deformation
Work is irreversibly converted to heat over loading-unloading cycle

Question 17

Describe the Maxwell model

Answer 17

Spring and dashpot in series. Stress is uniform, strain is additive (superimposed)

Question 18

What equation describes the strain at the time when the load is applied for the Maxwell model?

Answer 18

instantaneous displacement = stress/E

Question 19

Give the equation which gives strain at any time in the Maxwell model

Answer 19

Strain(t) = (stress/E) + (stress/eta)*t

Question 20

What does tau represent? Give its equation

Answer 20

The relaxation time (a material constant)

tau = eta/E

Question 21

Define relaxation time

Answer 21

Time taken for the stress to fall to 1/e of its initial value

Question 22

What type of behaviour can the Maxwell model be used for?

Answer 22

Rubbery flow behaviour

Question 23

What kind of stress relaxation does the Maxwell model predict?

Answer 23

Exponential

Question 24

What recovery is predicted by the Maxwell model?

Answer 24

When stress is removed there is an instantaneous recovery of the elastic strain then no further recovery

Question 25

Describe the Kelvin or Voigt model

Answer 25

Spring and dashpot in parallel. Strain is uniform, stress is additive/superimposed. Dashpot initially takes all of stress

Question 26

Give the equation which gives time-dependent strain at any constant stress in the KV model

Answer 26

Strain(t) = (stress/E)( 1 - exp(-Et/eta) )

Question 27

Describe the change in strain for the KV model

Answer 27

Exponential increase from zero up to stress/E (when stress in dashpot ‘relaxes’ away)

Question 28

Why is the KV model not fit for describing stress relaxation?

Answer 28

No stress relaxation occurs, as when strain is held constant, stress = E*strain - the predicted response is that of linear elastic material

Question 29

Give the KV equation for once stress is removed

Answer 29

strain(t) = strain at time of removal * exp(-E*t/eta)

Question 30

What does the KV recovery equation represent? How does this compare to the Maxwell model?

Answer 30

An exponential recovery of strain - this is the reversal of predicted creep. This is closer to what is typically observed in viscoelastic polymers than as predicted by the Maxwell model

Question 31

What material model is used when a polymer’s temp is significantly above Tg?

Answer 31

Viscous flow