4. mechanical properties of polymerspt.bme.hu/~vas/phd_polymer materials...

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Polymer Materials ScienceBMEGEPT9107, 2+0+0, 3 Credits

Lecturer: Prof. Dr. László Mihály Vas

Budapest University of Technology and EconomicsDepartment of Polymer Engineering

2016.11.24.

4. Mechanical Properties of Polymers

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Polymer Materials ScienceBooks, textbooks, lecture notes, guides

� G. Bodor: Structural investigation of polymers. Akadémai Kiadó, Budapest; Ellis Horwood, Chichester, 1991.

� I.M. Ward, D.W. Hadley: An introduction to the mechanical properties of solid polymers. J. Wiley & Sons, Chichester – New York, 1993.

� T.A. Osswald, G. Menges: Materials Science of polymers for engineers. Hanser Pub., New York, 1996.

� L.M. Vas: Lecture notes, ppt slides, http://pt.bme.hu/~vas

� G. Strobl: The Physics of Polymers. Concepts of Understanding theirStructures and Behaviour. Springer Verlag, Berlin. 1996.

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Polymer Materials ScienceRecapitulation

� Structure of Polymers (microscale levels)

• Atomic structure• Molecular structure• Morphological or fine structure

� Properties of Polymers (macroscale levels)

• Mechanical properties• Effect of temperature• Effect of humidity• Other properties

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Content of Polymer Materials ScienceRecapitulation

� Polymer materials, typical material classes, molecular and morphological structure of polymers, polymer blends and alloys

� Testing methods of polymer structures

� Mechanical behavior of polymer materials

� Behavior of polymers under changing temperature, humidity and other environmental factors

� Strength and fracture-mechanical properties of polymers

� Phenomenological modeling of the mechanical behaviors of solid polymers

� Statistical-mechanical modeling of polymers

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Classification of PolymersRecapitulation

� Classification in respect of structure

• Linear polymers (linear, chain molecular structure)

- Semi-crystalline polymers (e.g. PE, PP, PA, PAN, PET)

- Amorphous polymers (PVC, PS, PMMA, PC)

• Crosslinked polymers (network structure – amorphous polymers.)

- Elastomers (weakly cross-linked, e.g. rubbers: NR, BR, PUR)

- Duromers (strongly cross-linked; resins: e.g. UP, EP, VE)

� Classification in respect of thermal and mechanical behavior

• Thermoplastics (they can be molten reversibly ⇒ linear polymers; e.g. PE, PP, PA, PET, PVC, PS, PMMA, PC)

•Non-thermoplastics - thermosets- Linear polymers (Kevlar, PAN, cellulose, chitin, protein)- Crosslinked polymers (elastomers, duromers)- Semi-crosslinked & semi-crystalline polymers (wool fiber, XPE)

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Micro- and

macrostructural

levels of

polymersRecapitulation

Properties measurable on

macro-level are the resultant

of the microscale ones.

• Density

• Mechanical properties

• Thermal properties

• Moisture take up

• Others

Structural graph

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Mechanical properties 1.

� Micro- and macro-deformation components

Microdeformation components Macrodeformation components

• Energy elastic (εU) - reversible

• Entropy elastic (εS) - reversible

• Energy dissipating (εD) - irreversible

→→→→

→→→→

→→→→

• Elastic (εe)

(Mech: reversible)

(Tdyn: reversible)

• Delayed elastic (εd)

(Mech: reversible)

(Tdyn: irreversible)

• Remaining (εr)

(Mech: irrev.)

(Tdyn: irreversible)

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� General scheme of mechanical tests

A – sample, material-operator: Y(t)=A[X](t)

Stimulus Response

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Step function Ramp function Sinusoidal function

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� Time dependent mechanical properties - Creep

ATP WCE

LDPELDPE

Creep compliance:

Total strain of polymer:

ε(t)=εe+εd(t)+εr(t)

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� Time dependent mechanical properties – Stress relaxation

ATP WCERelaxation modulus:



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� Time dependent mechanical properties – Quasi-static

hysteresis

ATP WCEStimulus

XY-Record

RelaxationCreep



Sample: flexible foil, roving, fiber

A

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� Dynamic tests - periodic and impact loads

Dynamic test: Speed of stimulus is too large to neglect the inertial forces

Characterizing testing time [s]

Deformation speed [1/s]

Creep

Creep

tests

Impulse-like

tests

Impact

tests

Quasy-static

tests

Quasy-static

deformation

Wave propagation

of large speed

Tran-sition range

Elastic waves

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Effect of deformation-rate on the load-strain curve

Major Z.: Dinamikus mechanikai vizsgálatok … Anyagvizsgálók Lapja 1995/1. 21-24.

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� Time dependent mechanical properties - Dynamic tests

Deformation stimulus: step + sinusoidal

Stress response: relaxation + sinusoidal

Removing the relaxation response:

By high-pass filtering

(oscilloscope setting: AC mode)

A

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Strain stimulus: sinusoidal

Stress response: sinusoidal

Test condition: Linear viscoelastic (LVE) behavior

Performing: With small enough stimulus amplitude

δδδδ = delay in phase

Analysis of the filtered sinusoidal response

Energy loss/period:

Dynamic

hysteresis

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� Time dependent mechanical properties - Dynamic tests

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� Time dependent mechanical properties - Dynamic hysteresis

Dynamic material behaviors

Complex elastic modulus

Complex elastic modulus

and its components

Loss modulus

Loss factor

Dynamic or storage modulus

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Ideally elastic Viscoelastic Ideally viscous

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Mechanical properties 8a.

� Time dependent mechanical properties - Dynamic viscosity

Dynamic tensile flow –

under normal stress

Dynamic shearing flow –

under shear stress

Complex tensile viscosity Complex shear viscosity

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Components: Components:

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Mechanical properties 8b.

� Time dependent mechanical properties - Dynamic viscosity

Cox-Merz rule

The chord slope of the measured shear rate vs. shear stress curve (chord-viscosity) can be identified as the magnitude of the complex viscosity.

De Witt rule

Concerning the effect the angular frequency, ω, and the quasi-static shear rate are similar:

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� Quasi-static strength properties of polymers

Effect of drawing on the tensile test curve of fibers

Relationships between the structural and strength properties

Bobeth W.: Textile Faserstoffe. Springer-Verlag, Berlin 1993.2016.11.24.

BendingCompression

Tensile test

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Mechanical properties 9.a.

� Quasi-static strength properties of polymers

Effect of spherulitic structure and spherulite-size on the deformability of

polyolefins

Menges G.: Werkstoffkunde der Kunststoffe Hanser V. München, 1985.

2016.11.24.

Spherulite size

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� Toughness, impact strength of polymers

WRI – work up to starting crack/fracture

WRT – work of crack propagation

WT=WRI+WRT – total fracture work

Experience:

When modulus increases ⇒ impact

strength decreases

Pulse-like stimulus forms

Notched specimen form

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� Long-term strength properties of polymers

Basis of designing

polymer parts:

• Small deformability:σB,t – duration strength

σB,∞ - fatigue strength

• Large deformability:σε,t – duration stress

Creep curves

Stress-time curves

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Effect of temperature 3.

� Polymer material classes based on structure and thermal behavior

I. Amorphous (A) polymers

• Linear (L)>Thermoplastics (ATP)

Thermoplastic elastomer (ATPE)>Not thermoplastic

• Crosslinked (C)>Slightly crosslinked

Elastomers (SCE or R)

>Highly crosslinked (resins, HCR)

II. Semicristalline (S) polymers

• Linear (L)>Thermoplastics (STP)

Thermoplastic elastomer (STPE)>Not thermoplastic

• Post-crosslinked (e.g. PEX)

CelluloseProtein

Elastomer

PEX

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Polymers

L

A

S

C

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Amorphous polymer physical

states by chain heat motion:

• Glassy (G): mB, MB

• Rubbery (R): mB, MB

• Viscous (V): mB, MB

× ××

Heat motion types of chains:

• Micro-Brownian (mB): center of gravity

remains at place

• Macro-Brownian (MB): center of gravity

displaces

Transition temperatures:

• Tg : glassy

• Tm : crystal melting

• Tf : flow

• Td : decomposition (=Tb)

∆Gm=∆Hm-Tm ∆Sm=0 ⇒ Tm=∆Hm/∆Sm

232016.11.24.

≤≤≤≤

� Physical states of polymers

Physical condition

Solid Liquid Gas

Crystal-

line

phase

Amor-

phous

phase

Crystal +

Glassy

Amorph.

Crystal +

Rubbery

amorph.

Rubbery

amorph.

Viscous

liquid

Td

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� Measuring methods of thermomechanical curves

TMA

HCTT

11/24/2016

Y(T)=ε(to,T,σo), or

Y(T)=σ(to,T,εo)

DMA

Y1(T)=σB(T,v)

Y2(T)=εB(T,v)

Y1(T)=E’(T,ω),

Y2(T)=E”(T,ω) or

d(T, ω)

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� Thermomechanical curves of ATP

TMA curves

(Thermomechanical

analyzer)

HCTT curves

(Heat chamber tensile

tester)

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DMA/DTMA curves

(Dynamic

thermomechanical

analyzer)

Tb=Td

Glassy state

Rubbery state

Viscous flowstate


G

R V

εdom=εεεεe εdom=εεεεd εdom=εεεεr

Tr= rigidity temperature

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Single phase: amorphous

2016.11.24.

E.g.: PS, SB, ABS, PVC, PC, PVAL, PMMA

εdom=dominant strain


Viscous flow state

Glassy state

Rigidity

Tem

per

ature

Glassy state

Forced elasticity

Rubbery state

CLDCLD - Cross link density

Glassy state

Rubbery state

Viscous flow state

T

Transition temperatures vs. molecule mass

Effect of T, m, and CLD

Tb=Td

lg (msegm)

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Crosslinked

• Slightly crosslinked (SC)▬ Slightly crosslinked elastomers (SCE)

(Tg< 0oC; at Tg+20oC: > 100%

deformability)

• Medium crosslinked (MC)▬ Thermo-elastomers (MCE)

(Tg> 20oC; at Tg+20oC: > 100%

deformability)

• Highly crosslinked (HC) ▬ Resins/duromers (Tg> 50

oC)

RG

Single phase:

amorphous

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E.g.: NR, BR, CR, PUR

Tb=Td

CLD

Glassy state

Rubbery state

Rubbery

state

ELASTOMER

Glassy

state

THERMO-ELASTOMER

CLD – Cross-link density

Glassy state

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� Effect of mixture ratio (a) and softener (b) on the thermomechanicalcurves of ATP

Softener contentincreases

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As the effect of softener Tg (and/or Tm )

decreases by:

• Copolymerization (mainly: Tg),

• Softener (PVC: Tg),

• Moisture content (PA: mainly Tg)

Estimation of Tg :(short block copolymer)

Two phases detected ⇒ Non-miscible polymer blend

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E’

G

R

CC

R V

εdom=εεεεe εdom=εεεεd εdom=εεεεrεdom=εεεεe+ εεεεd

<

DMA

TMA

HCTT

Tm<Tf<Tb Two phases: amorphous + crystalline

Tm<Tf<Tb

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E.g.: PCTFE=PTFCETb=Td

� Semi-crystalline thermoplastic polymers (STP)

Crystal +Glassy amorphous

Crystal +Rubbery amorphous

Viscousliquid

Rubbery amorphous

Crystal

+

Glassy

Am.

Crystal

+

Rubbery

Am.

Rubbery

Am.Visc.

liqu.

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� Semi-crystalline thermoplastic polymers (STP)

Tf < Tm <Tbb

Effect of

crystallinity

<

G

C

R

V

C

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E.g.: PE, PP, POM, PA, PET, PBT

Tb=Td

Two phases: amorphous + crystalline

Crystallinity [%]

Crystal +Glassy amorphous

Crystal +

Rubbery

amorphous

Viscousliquid

CLD

Secundary dispersionregions G”

Crosslinked am.

Crosslinked am.

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� DMA curves of PE

• E’ monotonously decreases with T in general

• E’ may slightly increase in rubbery state.

• Otherwise increase in E’ refers to changes in structure (crystallization, crosslinking) during

measurement.

Kóczy L.: Szálasanyagok általános jellemzői. In: Textilipari Kézikönyv. Műszaki K. Bp. 1979.

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� Relationship between Tmand the structural properties

Thomson’s formula

Effect of the mean molecule mass (m): Effect of the crystallite size (h):

Ratio of Tm and Tg :(lamella of h-thickness and ∞-width;σe= surface stress∆Hcm=melting heat of crystal element)

(qm=specific melting heat)

ho=thickness of the basic element.

Tm is determined by

the thermodynamics:

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Fre

quen

cy

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Effect of temperature 10/1.

� Amorphous thermoplastic elastomer

(ATPE) – DMA curves

Copolymer (A,B)

The hard (B)

segment is

glassy amorphous

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Hard

Soft

Glassy

Rubbery AGlassy B

Rubber

yA

, B

Vis

cous

liquid

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Effect of temperature 10/2.

� Semicrystalline thermoplastic elastomer

(RTPE) – DMA curves

Copolymer (A,B)

The hard (B)

segment

is crystallized.

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Hard

Glassy

Cryst.

Rubbery ACryst. B

Vis

cous

liquid

Soft

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� DMA curves of drawn HDPE depending on the direction

HDPE

E’=E1

E”=E2

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Effect of temperature 9.� DMA curves of amorphous (APET) and crystalline (CPET) polyesters

2016.11.24.

Cold crystallization

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Polymermaterial

Tg[Co]

Tm[Co]

Tf[Co]

Tb[Co]

PE -LDPE-HDPE

-90...-25-120...-70

-124...138

PP - isotactic -35...-10 163...175 175 328...410

PVC – amorph. 60...105 - 150...180 185

PS 90...110 - 160...240

PAN 50...100 - - 300...330

PTFCE 45

PTFE -113, +127 325...330 - 425

PA6 40...60 215...220 310...380

PA6.6 45...65 250...260 310...380

PES -PETP 69...80 250...280 283...306

POM -85 178...198

PEEK 143 335

PC 130...180 255...267

PMMA 45...120

Polyisoprene(natural rubber)

-73

Aramid-Kevlar 300 550

� Heat expansion: larger by 8-10-times than that of metals

� Heat conductive factor: smaller by 1-3 magnitudes than that of metals

� Specific heat is larger, heat capacity is much smaller than those of metals

� Rigidity temperature(fragility, Tfr=Tr) measurement:

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Sample

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� Tensile test curves of ATP (a) and STP (b) polymers as a function of temperature

ATP (inclined to crystallization) STP

11/24/2016

Str

ess

Deformation

Str

ess

Deformation

Temperature

Load rate

High

||||Low

Low

||||High

Crosslinked

polymers

(duromer,

elastomer)

Linear

polymers

(thermopl.)

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� Effect of changing temperature rate

Tg increases with cooling rate ⇒ the glassy transition is of more

kinetic (heat motion related) than thermodynamic nature.

Javorszkíj – Detlaf: Fizikai zsebkönyv.

Műszaki K. Bp. 1974.

Hertzberg R.W.: Deformation and fracture

mechanics … J.Wiley, New York, 1989.

2016.11.24.

ATP STP

Crystal

Glass

LiquidOver-cooledliquid

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� Effect of excitation frequency (f) and temperature (T) on

thermomechanical curves of different types

•••• Phenomenon of mechanical glassing: shifting effect of frequency on Tg

•••• Temperature-time equivalence: by similar effects T~logto~log(1/f)

Increasing IncreasingIncreasing

log Frequency (f) Temperature (T) log Load time (to)

log

Modulu

s

Loss

fac

tor

log

Modulu

s

Loss

fac

tor

log

Modulu

s

Loss

fac

tor

2016.11.24.Ritchie – Critchley – Hill: Lágyítók, stabilizátorok, töltőanyagok. Műszaki K. Bp. 1976.

∼

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� Using temperature-time superposition for accelerating long term tests in case of ATP (a) and STP (b)

STP: Shifting by Arrhenius (Arrh)

equation (or a combination of WLF

and Arrh. formulae depending on

the temperature ranges)

ATP: Shifting by WLF equation

(determination is based on free-

volume theory

Time-shifting factor Modulus-shifting factor:

Thermo-rheologically simple material:

aT and bT depend on T only

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Effect of temperature 16.� Derivation of the shifting factor

STP: by Arrhenius equation

ATP: Derivation of the WLF equation based on the free-volume theory

Doolittle’s viscosity equation:

Free-volume fraction: Relaxation time:

Heat expansion coefficient:

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� Use of temperature-time equivalence for speeding the long-term tests – constructing master curve in case of ATP

Shift: with WLF equation

aT = shifting factor

Relaxation

measurements

Master curve at 25oC

E, R

ela

xati

on

mod

ulu

s [G

Pa]

Temperature, T[oC]

Time, t[hour]

2016.11.24.

c1= -17,44; c2=51,6 oC

Tg< T<Tg+100Castiff E.-Tobolsky T.S.: J. Colloid Sci. 1955.

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Effect of temperature 16.� Use of temperature-time equivalence for speeding the long-term tests – constructing master curve in case of ATP and STP

Creep shear relaxation modulus of PS (a) and tensile relaxation modulus of PE (b) as a function of the loading time at different temperatures and the constructed master curves

Thamm F.: Műanyagok szilárdságtana. TK.19722016.11.24.

Shea

r re

laxa

tion m

odulu

s, G

Load time, t [sec] Load time, t [sec]

Shea

r re

laxat

ion m

odulu

s, G

Ten

sile

rel

axat

ion m

odulu

s, E

Ten

sile

rel

axat

ion m

odulu

s, E

Load time, t [sec]

Load time, t [sec]

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� Use of other superposition principles for speeding up the long-term tests

Generalized shift factor:

Joint effect of the temperature (T) and water content (w) on the measured and calculated shear creep of UP; the calculation was performed with taking into account of the effect of T and w (record 1) as well as that of only T (record 2)

Resultant shift factor (thermo- and hydro-rheologicallysimple material):

Urzsumcev-Makszimov: MK.1982.2016.11.24.

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Effect of temperature 16.a.

� Influence of temperature on processing/application

� Basic properties of melt processing

Spencer-Gilmore state-equation

ATP: To=Tf

STP: To=max (Tm, Tf)

Arrhenius relation

Shear viscosity

Ef= activation

energy of flow

N= number of molecules

po= internal pressure (interaction of molecules)

Vo= own volume of molecules

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Effect of water content 1.

� Polymer states depending on the solvent concentration

Crystal+

Amorph.

Crystal+

Amorph.Amorph. Amorphous

LiquidSolid

PHYSICAL CONDITION

Polymer

Solvent

Dry Swollen Solution

2016.11.24.

Bobeth W.: Textile Faserstoffe. Springer-

Verlag, Berlin. 1993.Condition of dissolving: ∆GO=∆HO-T ∆SO<0

Dissolving of a semi-crystalline polymer

Solvent

Cross-bond

Polymer solution

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� Dissolving process – temperature dependent stages

(oldat)

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Polymer

Solvent

Gel layer

Liquid layer (solution)

Infiltration layer

Swollen solid polymer layer

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� Mechanism of water take up and its softening effect

Ways of water take up:

• Diffusive – direct (b)

– indirect (c)

• Capillary (d)

PAPolar molecule

Humidity = constantDrying

Moisturing

Humidity[%]Time

Humidity[%]

Drying

Moisturing

Wat

er c

onte

nt

Wat

er c

onte

nt

Wat

er c

onte

nt

Water content at equilibrium

Hyteresis

Macromolecule

Direct

Indirect

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Dry

Wet

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Effect of water content 4.� Time dependent process of liquid uptake

Water uptake of PET fiber bundle tested

by Krüss K12 micro-tensiometer

2016.11.24.

Czél G.: Nem kör keresztmetszetű kompozit csövek

viselkedésének elemzése. PhD, BME Bp. 2009.

An invertible explicit approximate solution of Lucas-

Washburn equation that is suitable for describing

both capillary and diffusive liquid uptake:

UP resin uptake of glass fiber mat

tested by Krüss K12 micro-tensiometer

UP resin uptake of glass fiber mat

in vacuum-injection tool

Vas L.M., Gombos Z., Nagy V.: Evaluation method of liquid uptake measurements

based on approximate invertible solution of the LW equation, (in press)

UP/üvegszál

Different approximate functions of water uptake

Measured

Function by Vas

Power function

Function by Ellyin

UP/glass fiber

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Polymers in the technoclimate 1.

� Environmental effects in the technoclimate

PP – polymer

part

Technoclimate

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Polymers in the technoclimate 2.

� Aging, decomposition processes

Gradual (a) and sudden (b) depolymerization

Degradation (a) and elimination (b)

Depolymerization:

PS, PMMA

Degradation: PA

Elimination: PVC (HCL pre-

cipitation)

Migration: PVC (colour, softener)

In addition a slight crosslinking can take place, as well.

2016.11.24.

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