L2: Mechanical Behaviour 1 Flashcards
What type of materials is Tg associated with?
Amorphous materials
What are polymer properties typically more sensitive to than for metals and ceramics?
Temperature change
What change occurs with increasing temperature in a polymer?
Change from rigid glassy state to viscous state - large drop in modulus
Define glass transition temperature
The characteristic temp at which a polymer’s behaviour changes between rigid glassy to rubbery
What type of molecular motion is enabled at glass transition temp?
Amorphous polymer materials can change their spatial arrangement of atoms by rotation about the chain (cooperative rotation)
Why must Tg be considered in structural design?
For load-bearing designs, stiffness can drop at increased temps, leading to dimensional instability and excessive deformation due to creep
List 5 key factors affecting Tg
- Chain stiffness
- Intermolecular interactions (hydrogen and covalent bonding, ionic interactions)
- Molar mass
- Additives (e.g. fillers)
- Moisture (swelling)
What is the fundamental reason for the viscoelastic response of a polymer?
They deform by 2 fundamentally different atomistic methods
- Elastic (distortion of lengths and angles of chemical bonds)
- Viscous (large-scale spatial rearrangements of atoms accompanied by decrease in their conformational entropy)
Why is the viscoelastic behaviour of polymers particularly evident around Tg?
They display both viscous and elastic behaviour simultaneously around Tg
Define creep
Time dependent strain response to constant stress
Which energy components does viscoelastic material have?
- Elastic/energic (stores energy)
- Viscous/entropic (dissipates energy)
Give the four stages pf a polymer’s strain-time curve, from stress applied to after stress removal
- Stress applied -> Almost instantaneous initial elastic response
- Creep - strain increases progressively with stress, slowing with time
- Viscous flow, signified by constant strain rate
- Stress removed -> Strain recovery (except for strain caused by viscous flow)
Define stress relaxation. How does it vary with time?
Time-dependent response to constant strain. It decreases with time
What do mathematical models for viscoelastic behaviours assume?
The behaviour can be represented in terms of combinations of springs (elastic) and dashpots (viscous) behaviour which act as independent elements
Describe the stress-strain relationship and loading cycle of perfectly elastic solids
Hooke’s law (stress = YM * strain)
Stress is proportional to strain and time independent
Net work is zero over a loading-unloading cycle
Describe the stress-strain relationship and loading cycle of linear viscous liquids
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
Describe the Maxwell model
Spring and dashpot in series. Stress is uniform, strain is additive (superimposed)
What equation describes the strain at the time when the load is applied for the Maxwell model?
instantaneous displacement = stress/E
Give the equation which gives strain at any time in the Maxwell model
Strain(t) = (stress/E) + (stress/eta)*t
What does tau represent? Give its equation
The relaxation time (a material constant)
tau = eta/E
Define relaxation time
Time taken for the stress to fall to 1/e of its initial value
What type of behaviour can the Maxwell model be used for?
Rubbery flow behaviour
What kind of stress relaxation does the Maxwell model predict?
Exponential
What recovery is predicted by the Maxwell model?
When stress is removed there is an instantaneous recovery of the elastic strain then no further recovery
Describe the Kelvin or Voigt model
Spring and dashpot in parallel. Strain is uniform, stress is additive/superimposed. Dashpot initially takes all of stress
Give the equation which gives time-dependent strain at any constant stress in the KV model
Strain(t) = (stress/E)( 1 - exp(-Et/eta) )
Describe the change in strain for the KV model
Exponential increase from zero up to stress/E (when stress in dashpot ‘relaxes’ away)
Why is the KV model not fit for describing stress relaxation?
No stress relaxation occurs, as when strain is held constant, stress = E*strain - the predicted response is that of linear elastic material
Give the KV equation for once stress is removed
strain(t) = strain at time of removal * exp(-E*t/eta)
What does the KV recovery equation represent? How does this compare to the Maxwell model?
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
What material model is used when a polymer’s temp is significantly above Tg?
Viscous flow
