outstanding problems in the physics of deformation of polymers dutch polymer institute (dpi)...
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outstanding problems in the physics of deformation of polymers
Dutch Polymer Institute (DPI)Materials Technology (MaTe)
Eindhoven University of Technology (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
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 to tension
+
intermolecular entanglement network
=
total
ageing
Mn
compression
e
from compression to tension
+
intermolecular entanglement network
=
total
ageing
Mn
compression
tension
e
eincreasing entanglement density
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
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 experimental/numerical method
indentation and scratchingresults: experimental: influence sliding velocity
visco-elastic visco-plastic Fn=300mNv =0.1µm/sr =50 µm
indentation and scratchingresults: numerical: deformation only
Fadh
Fdef
Ff = Fdef + Fadh
indentation and scratchingresults: experimental versus numerical deformation only
what about adhesion?
most basic dry-friction model:
Leonardo da Vinci (1452)Amonton (1699) - Coulomb (1781)
stick:
slip :
indentation and scratchingresults: numerical: influence interaction between indenter and polymer
indentation and scratchingresults: numerical: influence interaction between indenter and polymer
polymer
Fn
Ff
vx
A1
A2
Fsim
Ff = Fsim = Fdef Fadh = 0
indentation and scratchingresults: numerical: influence interaction between indenter and polymer
Ff = Fsim = Fdef + Fadh
polymer
Fn
Ff
vx
A1
A2
Fadh Fdef
Fsim
indentation and scratchingresults: numerical: influence interaction between indenter and polymer
Fadh Fdef
polymer
Fn
Ff
vx
A1
A2
Ff = Fsim = Fdef + Fadh
Fsim
indentation and scratchingresults: numerical: influence interaction between indenter and polymer
indentation and scratchingresults: numerical: influence interaction between indenter and polymer
visco-elastic visco-plastic Fn=150mNv =0.1µm/sr =10µm
indentation and scratchingresults: experimental versus numerical validation using different tip
indentation and scratchingresults: experimental versus numerical validation using different tip
indentation and scratchingresults: experimental versus numerical wear
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
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
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
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
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
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
PhD topic
marco van der sanden 1993 concept of ultimate toughnesstheo tervoort 1996 constitutive modellingpeter timmermans 1997 modelling of neckingrobert smit 1998 multi-level finite element methodbernd jansen 1998 microstructures for ultimate toughnessharold van melick 2002 quantitative modellingilse van casteren 2003 nanostructures for ultimate toughnessedwin klompen 2005 long-term prediction
jules kierkels 2006 toughness in thin filmsroel janssen 2006 creep rupture and fatiguetom engels 2008 coupling processing-propertieslambert van breemen 2009 3D modeling of micro-wear
financial support: TU/e, STW, DPI
acknowledgements
some thoughts…..some answers
question 1: how does molecular architecture determine deformation kinetics
and thus the long term behaviour as reflected in the time-to-failure
some thoughts…..some answers
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
some thoughts…..some answers
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
some thoughts…..some answers
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
some thoughts…..some answers
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
some thoughts…..some answers
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
some thoughts…..some answers
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)
some thoughts…..some answers
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
some thoughts…..some answers
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
some thoughts…..some answers
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
some thoughts…..some answers
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
some thoughts…..some answers
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
some thoughts…..some answers
and of course……semi-crystalline polymers
injection moulding of unfilled PE
orientation near skin
1 2 3oriented row structure
and of course……semi-crystalline polymers
Highimpact
injection moulding of unfilled PE
and of course……semi-crystalline polymers
0
10
20
30
40
50
60
70
80
0 5 10 15 20
Calcium Carbonate (Vol%)
Imp
ac
t Str
en
gth
(k
J/m
2 )
GATE
END
NO FLOW
injection moulding of CaCO3 filled PE
and of course……semi-crystalline polymers
flow-induced crystallization
leon govaert
acknowledgements
PhD topic
marco van der sanden 1993 concept of ultimate toughnesstheo tervoort 1996 constitutive modellingpeter timmermans 1997 modelling of neckingrobert smit 1998 multi-level finite element methodbernd jansen 1998 microstructures for ultimate toughnessharold van melick 2002 quantitative modellingilse van casteren 2003 nanostructures for ultimate toughnessedwin klompen 2005 long-term prediction
jules kierkels 2006 toughness in thin filmsroel janssen 2006 creep rupture and fatiguetom engels 2008 coupling processing-propertieslambert van breemen 2009 3D modeling of micro-wear
financial support: TU/e, STW, DPI
acknowledgements
and of course……semi-crystalline polymers
PhD topic
hans zuidema 2000 injection moulding, stress-induced crystallizationfrank swartjes 2001 crystallization in elongational flowsbernard schrauwen 2003 injection moulding, processing-property relationshans van dommelen 2003 multi-level analysis of propertiessachin jain 2005 PP-silica nanocompositesmaurice van der beek 2005 density after flow: PVT-Tdot-gammadotjan-willem housmans 2008 crystallization in multi-pass rheometer flows
barry koreman msc 3D modelling of injection moulding
juan vega pd rheology during crystallizationdenka hristova pd time-resolved X-ray (grenoble)wook ryol hwang pd particle-laden viscoelastic flow
university: gerrit peters, martien hulsen, han goossens, sanjay rastogi
financial support: TU/e, STW, DPI
acknowledgements