Mechanical Properties: Stress-Strain ExperimentsStatic (Quasi-Static) Testing

•

• Example: Tensile test, compression test, shear test, torsion test

y

TS

necking

tensile

Mechanical Properties: Stress-Strain ExperimentsStatic (Quasi-Static) Testing

Source: Ebewele/Fried

Mechanical Properties: Stress-Strain ExperimentsStatic (Quasi-Static) Testing

Source: Ebewele

Mechanical Properties: Stress-Strain ExperimentsStatic (Quasi-Static) Testing

Stiffnesss:• Ability to carry stress without changing dimensions•

Strength:• Ability to sustain dead load• Tensile strength:• Fracture strength:

Elasticity:• Ability to undergo reversible deformation or carry stress without permanent deformation•

Mechanical Properties: Stress-Strain ExperimentsStatic (Quasi-Static) Testing

Ductility:• Ability to undergo plastic deformation before fracture• % Elongation (EL) [at yield or at break]• %EL [at break] = (Lf – Lo)/Lo x 100• Magnitude of %EL depends on Lo

Resilience:• Ability to absorb energy without permanent deformation•

Toughness:• Ability to absorb energy without fracture•

Er(t): “time-dependent elastic modulus” or “relaxation modulus”:

Er(t) = (t) / o = time-dep. / instantaneous

- magnitude dependent on time and temperature

Er(10) = / o = @ 10 sec / instantaneous

Mechanical Properties:Dynamic Testing

Relaxation modulus - Er(t) - of same 5 samples of poly(-methylstyrene) in the molten state (186 C):

• Highest Mw (A-5): longest relaxation time

log time

log

Er(t

) (d

yne/

cm2 )

(P

)

Mw

1 GPa = 109 Pa = 1010 dyne/cm2

High modulus (short time); modulus independent of Mw

intermediate modulus (1-100 s); modulus independent of Mw

lower modulus (> 100 s); modulus dependent on Mw

Modulus = 0 eventually

Relaxation Modulus: Time and Temp Dependence

• Decrease Er (t) with increase T• Large decrease of Er (t) at T = and > Tg

• Decrease Er (t) with increase time: decrease is greater with increasing temp.

Log timetempTg

Highest TT > Tg

Lowest TT << Tg

Glassy

LeatheryRubbery plateau

Rubbery flow

Viscous Flow (liquid)

Tm

“Stress Relaxation”

tempTg

Glassy

LeatheryRubbery plateau

Rubbery flow

Viscous Flow (liquid)

Tm

Molecular Level?Glassy: T << Tg

Er(t) ≈ E (elastic modulus)

Leathery/Glass transition region:

-“viscoelastic solid” (viscoelastic) – deformation is time-dependent

Rubbery plateauEr(t) plateaus, low-“Rubbery liquid” (viscoelastic)-

Rubbery flow region-“Very viscous liquid” (viscoelastic)-

Viscous flow region-“viscous liquid”-no elastic behavior, only viscous flow-

PS

Stress Relaxation• If held at some constant, instantaneous stain () the resulting stress () exerted by polymer will decrease with time (“acts weaker”)

Stress-relaxation test:

Creep

• If held at some constant, instantaneous stress () the resulting strain () exerted by polymer will increase with time (elongates)

Creep test:

Why does stress relaxation (and creep) occur?

Exact molecular causes can vary, five general categories:

1. Chain scission: - Via oxidative degradation and hydrolysis- For instance: 3 chains bearing load one is cut less stress exerted (stress relaxation) [or increased strain (elongation) (creep)].

2/3

Chain scission

This mechanism is important in biodegradable polymers

Why does stress relaxation (and creep) occur? (cont.)

2. Bond interchange - MW is not decreased (i.e. no degradation)- Chain portions change partners and cause a release of stress

Why does stress relaxation (and creep) occur? (cont.)

3. Viscous Flow (i.e. Molecular Relaxation)

- Caused by linear chains slipping past one another

- E.g. viscous flow of Silly Putty

Why does stress relaxation (and creep) occur? (cont.)

4. Thirion relaxation- Reversible relaxation of the trapped entanglements in elastomeric networks- When stress is applied, entropic forces return the chains to their near original

positions- Elastomeric networks will relax by ~5% via this mechanism (in a few seconds)

Under stress

DYNAMIC MECHANICAL ANALYSIS (DMA)

- Measure response of material to periodic stress -

- Can apply stress (strain) in tension, compression, shear, bend (see next slide)

- Also measure the phase difference or “lag” () between two sine waves

material responseapplied stress

phase angle ()

amplitude

Temperature

Fdynamic

Fstatic

For

ce

time

DYNAMIC MECHANICAL ANALYSIS (DMA)

() phase difference, phase lag or “dissipation factor”

DMA Modes of Deformation

DYNAMIC MECHANICAL ANALYSIS (DMA)

time

Dynamic Mechanical Moduli

An advantage DMA over stress-strain curves is that the elastic and viscous components of the modulus can be separated

DYNAMIC MECHANICAL ANALYSIS (DMA)

Dynamic Mechanical ModuliE* = E’ + iE”

E* = complex modulusE’ = storage modulus

E” = loss modulus

tan = E”/E’

Tan = loss tangent or “damping”

E’

E”

E*

As decreases E* approaches E’

DYNAMIC MECHANICAL THERMAL ANALYSIS (DMTA)

If concurrently heated at a set rate: can detect thermal transitions

Tg determined as:

DYNAMIC MECHANICAL THERMAL ANALYSIS (DMTA)

If concurrently heated at a set rate: can detect thermal transitions

Tg determined as:

DYNAMIC MECHANICAL THERMAL ANALYSIS (DMTA)

Can detect weaker thermal transitions: