outstanding problems in the physics of deformation of polymers

outstanding problems in the physics of deformation of polymers

Dutch Polymer Institute (DPI)Materials Technology (MaTe)

Eindhoven Univ of Tech (TU/e)

APST ONE, Advances in Polymer Science and TechnologyJuly 8 – July 10, 2009, Johannes Kepler University Linz, Austria

Han E.H. Meijer and Leon E. Govaert

outline

1. introduction

2. predicting performance of present models

3. outstanding problems:

• first question: origin of deformation kinetics• second question: origin of ageing kinetics• third question: origin of strain hardening

4. summary

PC: necking• moderate localization• stable growth

PS: crazing• extreme localization• unstable growth

brittle tough

localization of strain

rheology:

branch of fluid mechanicscall themselves non-Newtonian but are Newton’s successors that are mathematically well educated and only deal withtransient homogeneous shear flowsit took them 50 years to arrive at a constitutive equation that is also valid intransient homogeneous extensional flows solid state rheology:

branch of solid mechanicsHooke’s successors that necessarily have to deal only withtransient inhomogeneous extensional flows

a comment on (solid state) rheology

rejuvenation

polystyrene PS

mechanicallyrejuvenated

moderateageing

severeageing

homogeneousdeformation

stable localisation

unstable localisation

ductile ductile brittle

ageing

ageing

from compression (intrinsic) to tension

+

intermolecular entanglement network

=

total

ageing

Mn

compression

tension

e

eincreasing entanglement density

outline

1. introduction

2. predicting performance of present models

3. outstanding problems:

• first question: origin of deformation kinetics• second question: origin of ageing kinetics• third question: origin of strain hardening

4. summary

from compression to tensioncompression

tension

from compression to tensioncompressionfit

tensionprediction

indentation and scratchingmesh

flat punch

round

Berkovich

a

a

b

b

c

c

indentation and scratchingindentor type

post-mortem visco-elastic visco-plastic

flat-ended cone angle: 60o diameter: 10.0 µm

indentation and scratching

visco-elastic visco-plastic

flat-ended cone angle: 60o diameter: 10.0 µm

indentation and scratchingline: experimentsymbol: prediction

post-mortem

ageing

ageing kinetics deformation kinetics

deformation rate

indentation and scratchingresults are quantitative lines: experiments

symbols: predictions

polymer

vFf

Fn

Fdef

Ff

Fadh= Ff - Fdef ?

T,v,scale effects

simulationsexperiments

strategyindentation and scratchinghybrid numerical/experimental method

indentation and scratchingresults: influence sliding velocity

visco-elastic visco-plastic Fn=300mNv =0.1µm/sr =50 µm

indentation and scratchingresults: deformation only

Fadh

Fdef

Ff = Fdef + Fadh

indentation and scratchingresults: deformation only

what about adhesion?

most basic dry-friction model:

Leonardo da Vinci (1452)Amonton (1699) - Coulomb (1781)

stick:

slip :

indentation and scratchingresults: influence interaction between indenter and polymer

indentation and scratchingresults: influence interaction between indenter and polymer

polymer

Fn

Ff

vx

A1

A2

Fsim

Ff = Fsim = Fdef Fadh = 0

indentation and scratchingresults: influence interaction between indenter and polymer

Ff = Fsim = Fdef + Fadh

polymer

Fn

Ff

vx

A1

A2

Fadh Fdef

Fsim

indentation and scratchingresults: influence interaction between indenter and polymer

Fadh Fdef

polymer

Fn

Ff

vx

A1

A2

Ff = Fsim = Fdef + Fadh

Fsim

indentation and scratchingresults: influence interaction between indenter and polymer

indentation and scratchingresults: influence interaction between indenter and polymer

visco-elastic visco-plastic Fn=150mNv =0.1µm/sr =10µm

indentation and scratchingresults: validation using different tip

indentation and scratchingresults: validation using different tip

indentation and scratchingresults: wear

outline

1. introduction

2. predicting performance of present models

3. outstanding problems:

• first question: origin of deformation kinetics• second question: origin of ageing kinetics• third question: origin of strain hardening

4. summary

rate dependence of PC

deformation kinetics

rate dependence of PC

deformation kinetics

constant stress

.

constant strain rate response rate-dependent yield

failure under constant strain rate and constant stress experiment governed by same kinetics

deformation kinetics

time-dependent accumulation of plastic strain: plastic flow

deformation kinetics

influence of thermal historyon intrinsic behavior

influence of thermal historyon rate dependence

deformation kinetics

influence of thermal historyon intrinsic behavior

influence of thermal historyon time-to-failure

PC

deformation kinetics and time to failure

strain rate dependence of yield stress stress dependence of time-to-failure

deformation kinetics and time to failure

deformation kinetics and time to failure

question 1: how does molecular architecture determine deformation kinetics

deformation kinetics and time to failure

question 1: how does molecular architecture determine deformation kinetics

and thus the long term behaviour as reflected in the time-to-failure

outline

1. introduction

2. predicting performance of present models

3. outstanding problems:

• first question: origin of deformation kinetics• second question: origin of ageing kinetics• third question: origin of strain hardening

4. summary

influence of thermal historyon intrinsic behaviour

influence of thermal historyon rate dependence

ageing and ageing kinetics

ageing

ageing

PS

PS: brittle fracture within hours PC: necking returns within months

ageing and ageing kinetics

ageing accelerated by temperature

Arrhenius temperature dependence; ΔH 205 kJ/mol

ageing and ageing kinetics

Isothermal creep loading master curve

ageing and ageing kinetics

ageing accelerated by stress

changes in thermal history captured by a single state parameter: Sa

behaviour independent of molecular weight distribution

rate dependence of yield stressaged loading curve

ageing and ageing kinetics

yield stress increases with time

ageing and ageing kinetics

ageing kinetics: two domains

temperature historyreceived

during processing

temperature historyreceived

during product life

• ~seconds

• high temperatures

• fast evolution

• ~years

• low temperatures

• slow evolution

evolution of yield stress in both domains governed by the same kinetics

ageing kinetics during processing

ageing kinetics during product life

both short-term and long-term deformation kinetics are captured !

rate dependent yield stress long-term failure

ageing and ageing kinetics

failure of polycarbonate products predicted accurately

without a single experiment !

rate dependent maximum load long-term failure

ageing and ageing kinetics

“yielding” is mechanicallypassing Tg by applyingstress

”melting’’ isthermallypassing Tg by additionof heat

Hodge and Berens, Macromol., 15, 762 (1982)

ageing and ageing kinetics

polystyrene PS

mechanical rejuvenation

ageing and ageing kinetics

question 1: how does molecular architecture determine deformation kinetics

and thus the long term behaviour as reflected in the time-to-failure

question 2: how does molecular architecture determine ageing kinetics

ageing and ageing kinetics

question 1: how does molecular architecture determine deformation kinetics

and thus the long term behaviour as reflected in the time-to-failure

question 2: how does molecular architecture determine ageing kinetics

and thus the polymer’s brittle or tough response but also the improved long term behaviour

outline

1. introduction

2. predicting performance of present models

3. outstanding problems:

• first question: origin of deformation kinetics• second question: origin of ageing kinetics• third question: origin of strain hardening

4. summary

reversibility of deformation

plastically deformed sample

heat aboveTg

thermally-inducedsegmentalmotion

returntooriginalgeometry

strain hardening

strain hardeningreversibility of deformation

intermolecular

network

intermolecular componentmodulus and yield stress determined by interaction on segmental scale

network componentrubber-elastic response of the entanglement network through chain orientation

total

network

inter-molecular

inspired Haward to decompose the stress

* 2 1N k T

N* : network densityk : Boltzmann’s constantT : absolute temperature

proportional to network density and temperature!

theoretical stress-stain response:

chain orientation entropy decrease

strain hardening

BPA-model:Boyce et al. (1988); Arruda & Boyce (1993)OGR-model: Buckley & Jones (1995), Buckley et al. (2004)EGP-model: Govaert et al. (2000), Klompen et al. (2005)

dr rG BNeo-Hookean hardening:

Gr

compression

tensiontorsion

2* 1N k T

strain hardening

true

str

ess

[MP

a]

true

str

ess

[Mpa

]

G’Sell & Jonas (1981), Haward (1993) Gaussian chain statistics

strain hardening

dr rG BNeo-Hookean hardening: 2* 1

N k T

strain hardeninginfluence of network density

2* 1N k T

• prevents extreme localization• stabilizes deformation in tension

strain hardeninginfluence of network density

• response proportional to network density

2* 1N k T

2 1

GN, Tg+30 oC

Gr , 25 oC

strain hardeninginfluence of network density

2* 1N k T

• response proportional to network density• two orders of magnitude difference

* 2 1kN

T

strain hardeninginfluence of temperature

• response proportional to network density• two orders of magnitude difference• contradicts entropic origin

PS/PPE20/80

40/60

60/40

80/20

100/0

PS/PPE20/8040/6060/4080/20100/0

* 2 1kN

T

strain hardeninginfluence of temperature

• response proportional to network density• two orders of magnitude difference• contradicts entropic origin•suggests viscous contribution

strain hardening

question 1: how does molecular architecture determine deformation kinetics

and thus the long term behaviour as reflected in the time-to-failure

question 2: how does molecular architecture determine ageing kinetics

and thus the polymer’s brittle or tough response but also the improved long term behaviour

question 3: how does molecular architecture determine strain hardening

strain hardening

question 1: how does molecular architecture determine deformation kinetics

and thus the long term behaviour as reflected in the time-to-failure

question 2: how does molecular architecture determine ageing kinetics

and thus the polymer’s brittle or tough response but also the improved long term behaviour

question 3: how does molecular architecture determine strain hardening

and thus the polymer’s response brittle or tough but also the anisotropic response after orientation

outline

1. introduction

2. predicting performance of present models

3. outstanding problems:

• first question: origin of deformation kinetics• second question: origin of ageing kinetics• third question: origin of strain hardening

4. summary

question 1:

summary

question 2:

question 3:

( )

( )t

,( )r r eG G T

deformation kinetics and time to failure

question 1: how does molecular architecture determine deformation kinetics

and thus the long term behaviour as reflected in the time-to-failure

deformation kinetics and time to failure

question 1: how does molecular architecture determine deformation kinetics

and thus the long term behaviour as reflected in the time-to-failure

at the yield stress main-chain segmental motion is initiated and parts of the chains can move along side each other

deformation kinetics and time to failure

question 1: how does molecular architecture determine deformation kinetics

and thus the long term behaviour as reflected in the time-to-failure

at the yield stress main-chain segmental motion is initiated and parts of the chains can move along side each other

this situation is comparable to the rubbery state the only difference being that now the mobility is stress-activated

deformation kinetics and time to failure

question 1: how does molecular architecture determine deformation kinetics

and thus the long term behaviour as reflected in the time-to-failure

at the yield stress main-chain segmental motion is initiated and parts of the chains can move along side each other

this situation is comparable to the rubbery state the only difference being that now the mobility is stress-activated

we are dealing with deformation rates at a stress-induced glass transition

deformation kinetics and time to failure

question 2: how does molecular architecture determine ageing kinetics

and thus the polymer’s brittle or tough response but also the improved long term behaviour

deformation kinetics and time to failure

question 2: how does molecular architecture determine ageing kinetics

and thus the polymer’s brittle or tough response but also the improved long term behaviour

at the yield stress main-chain segmental motion is initiated, parts of chains can flow

deformation kinetics and time to failure

question 2: how does molecular architecture determine ageing kinetics

and thus the polymer’s brittle or tough response but also the improved long term behaviour

at the yield stress main-chain segmental motion is initiated, parts of chains can flow

the force to achieve this increases with local densification (call it crystallization to know how to approach the problem and how to solve)

deformation kinetics and time to failure

question 2: how does molecular architecture determine ageing kinetics

and thus the polymer’s brittle or tough response but also the improved long term behaviour

at the yield stress main-chain segmental motion is initiated, parts of chains can flow

the force to achieve this increases with local densification (call it crystallization to know how to approach the problem and how to solve)

we are dealing with segmental densification kinetics on a order 10 monomer unit scale

deformation kinetics and time to failure

question 3: how does molecular architecture determine strain hardening

and thus the polymer’s response brittle or tough but also the anisotropic response after orientation

deformation kinetics and time to failure

question 3: how does molecular architecture determine strain hardening

and thus the polymer’s response brittle or tough but also the anisotropic response after orientation

after yield, main-chain large motion is initiated and entanglements become noticeable

deformation kinetics and time to failure

question 3: how does molecular architecture determine strain hardening

and thus the polymer’s response brittle or tough but also the anisotropic response after orientation

after yield, main-chain large motion is initiated and entanglements become noticeable

the force to achieve this increases with deformation and network density but decreases with temperature

deformation kinetics and time to failure

question 3: how does molecular architecture determine strain hardening

and thus the polymer’s response brittle or tough but also the anisotropic response after orientation

after yield, main-chain large motion is initiated and entanglements become noticeable

the force to achieve this increases with deformation and network density but decreases with temperature

below Tg the material is a fluid only via stress-induced breaking of secundary bonds