ENME307: Thermomechanical properties of polymers

Viscoelasticity

domain of amorphous phase

Loading polymer

molecular rearrangement in amorphous phase (back stress)

Unloading polymer

polymer wants to recover and recoil (dependant on time and temperature)

Viso

flow of polymer chain

Elasticity

back stress

Creep strain

fully recoverable due to back stress

Creep test

constant load, measure resulting in strain

Unrelaxed creep compliance

not enough time for motion

Relaxed creep compliance

all mechanisms already occurred

J-value

underestimate, constant for given load (not dependant on stress)

Linear viscoelastic creep

as temp increases relaxation increases at shorter time scales

Dissipation

caused by internal friction, low temp, low free volume, no dissipation

Temp and modulus

shift curves left and right

Stress relaxation molecules

constant stress loading and constant strain. No change in dimension/volume change internal stresses holding molecules together change over time

Higher strains

larger stress decay (non linear)

Relaxation modulus

over time (Accelerated with temp) less stiff, more mobile, less stress

Loading rate

increased shear rate, increased mechanical behaviour,

Long term polymer loading

not much initial creep strain, jump at start due to Eleatic response or rapid creep

Stress relaxation

given strain applied to polymer and the resulting decrease in stress (load) I measured as the sample relates over time

Creep behaviour

set stress applied to the polymer and the resulting changes in strain are measures as a function of time

Isometric

constant strain

Isochronous

constant time

Amorphous behaviour

very stress, vary strain, strain partially reservable

Creep behaviour

instant elastic response -> rapid creep (fully recoverable) -> reptation, creep slows (irreversible flow)

Relaxation time

time polymer redistributed internal stresses through molecular motion under constant strain

Retardation time

time polymer redistributed internal strain through molecular notion under constant stress (creep)

Viscoelasticity depends on

material composition, structure, deformation rate, loading time temperature

Relaxation curve - viscoelasticity

characteristic retardation time – max change in gradient

Relaxation curve – rubber

plateaus, mobility mechanisms used up

Relaxation curve – flow

non reversable reptation

Increasing relaxation time

increases material viscosity

Theory of linear viscoelasticity

phenomenological, does not show molecular motion

Time constant – represents how long it takes for stress to relax (spectrum)

Maxwell model

good for relaxation, bad for creep

Kelvin/Voigt model

bad for relaxation, good for creep (no initial elastic jump)

Standard linear/Zenner model

spring in series with parallel spring and dashpot

Burgers model

spring and dashpot in series with parallel spring and dashpot

TTS requirements

thermorheologically simple (no shape change), no more than 1 molecular motion type, if multiple transitions, same shift factor.

Physical aging

occurs in amorphous phase, isothermal contractions below Tg, stiffens polymers as less free volume. Modulus increases

WLF equation

assumes free volume only cause of relaxation, limited to rubebry range

Properties over time

compliance increases, stiffness decreases

Long term loading

Arrhenius all temps, WLF in GT

Master curves

allow properties without doing long term experiments, use to get parameters for equations

Dynamic properties

frequency effects damping

Damping

conversion of energy heat via friction

Elastic properties

in phase with strain/stress

Viscous properties

out of phase with strain/stress. No energy stored so max stress and change in strain

Polymer properties

some shift between phase and stress

Tan delta

how much material behaves as a viscous and how much behaves as an elastic.

Tan delta close to zero

elastic material

Free vibration data collection

measure at natural frequency, no frequency control

Forced vibration data collection

control frequency so greater delta accuracy

Relaxation mechanism

initial due to side group beta transitions. Then Tg due to main chain alpha reptation

Past Tg

no internal friction, so flows easily, low damping

DMA relaxations

picks up modulus and changes it to tan delta

Temp increases

as frequency increases

Branching increases

tan delta, goes for lower Temp

High loading rate

shifts tan delta right (higher temp)

Strength and modulus dependencies

depends on tsep speed and temp

Close to Tg

rate of testing largest effect

Well below Tg

polymers behave elastically v=0.3

Above Tg

v =0.5

Tensile test

not simple as rate of deformation influences mechanical properties

Mechanical properties

higher strain rate, higher modulus, higher strengths

Hight temp/low strain rate

stress relaxation occurs during test (chains have enough time to rearange)

Low temp/high strain

stress relaxation does not occur (no time for chains to unravel)

Short term behaviour

tensile test lower than DMA, tacticity, basic stress strain

Design stress

Brittle use UTS, Tough yield use yield, Tough no yield use 0.5% offset yield