1. outstanding problems in the physics of deformation of polymers
Han E.H. Meijer and Leon E. Govaert
Dutch Polymer Institute (DPI)
Materials Technology (MaTe)
Eindhoven University of Technology (TU/e)
APST ONE, Advances in Polymer Science and Technology
July 8 – July 10, 2009, Johannes Kepler University Linz, Austria

2. introduction
predicting performance of present models
outstanding problems:
first question: origin of deformation kinetics
second question: origin of ageing kinetics
third question: origin of strain hardening
summary

3. localization of strain
tough
brittle
PC: necking
moderate localization
stable growth
PS: crazing
extreme localization
unstable growth
Falen: gradaties van reklokalisatie
Geen reklokalisatie: homogene deformatie
Matige reklokalisatie: insnoering / afschuifbanden : ductiel/taai falen, grote (zichtbare) plastische deformaties
Sterke reklokalisatie: crazing : bros falen, nauwelijks (zichtbare) plastische deformaties
Echter: op zeer lokale (microscopische) schaal, zeer grote deformaties, vaak groter dan voor macroscopisch taaie materialen!!

4. a comment on (solid state) rheology
branch of fluid mechanics
call themselves non-Newtonian but are
Newton’s successors that are mathematically well educated and only deal with
transient homogeneous shear flows
it took them 50 years to arrive at a constitutive equation that is also valid in
transient homogeneous extensional flows
solid state rheology:
branch of solid mechanics
Hooke’s successors that necessarily have to deal only with
transient inhomogeneous extensional flows
Falen: gradaties van reklokalisatie
Geen reklokalisatie: homogene deformatie
Matige reklokalisatie: insnoering / afschuifbanden : ductiel/taai falen, grote (zichtbare) plastische deformaties
Sterke reklokalisatie: crazing : bros falen, nauwelijks (zichtbare) plastische deformaties
Echter: op zeer lokale (microscopische) schaal, zeer grote deformaties, vaak groter dan voor macroscopisch taaie materialen!!

5. rejuvenation
polystyrene PS

6. ageing mechanically rejuvenated moderate ageing severe ageing unstable
localisation
homogeneous
deformation
stable
localisation
ductile
ductile
brittle

7. ageing

8. from compression to tension
intermolecular
entanglement network
total
ageing + = Mn

9. from compression to tension
intermolecular
entanglement network
total
ageing + = Mn
tension
increasing entanglement density

10. introduction
predicting performance of present models
outstanding problems:
first question: origin of deformation kinetics
second question: origin of ageing kinetics
third question: origin of strain hardening
summary

11. from compression to tension

12. from compression to tension

13. from compression to tension
fit
tension
prediction

14. indentation and scratching
mesh

15. indentation and scratching
indentor type
round a c a
Berkovich b b
flat punch c

16. indentation and scratching
flat-ended cone
angle: 60o
diameter: 10.0 µm
post-mortem
visco-elastic
visco-plastic

17. indentation and scratching
line: experiment
symbol: prediction
flat-ended cone
angle: 60o
diameter: 10.0 µm
post-mortem
visco-elastic
visco-plastic

18. indentation and scratching
results are quantitative
lines: experiments
symbols: predictions
ageing
deformation rate
ageing kinetics
deformation kinetics

19. indentation and scratching
strategy
hybrid experimental/numerical method
polymer v Ff Fn Ff
experiments
Fadh= Ff - Fdef ?
simulations
Fdef
interpretation of experiment by quantitative comparison with numerical simulation
T,v,scale effects

20. indentation and scratching
results: experimental: influence sliding velocity

21. indentation and scratching
results: numerical: deformation only
Fn=300mN
v =0.1µm/s
r =50 µm
visco-elastic
visco-plastic

22. indentation and scratching
results: experimental versus numerical deformation only
Fadh
Fdef
Ff = Fdef + Fadh

23. indentation and scratching
results: numerical: influence interaction between indenter and polymer
what about adhesion?
most basic dry-friction model:
Leonardo da Vinci (1452)
Amonton (1699) - Coulomb (1781)
stick:
slip :

24. indentation and scratching
results: numerical: influence interaction between indenter and polymer

25. indentation and scratching
results: numerical: influence interaction between indenter and polymer Fn vx Ff A2
Fsim
polymer A1
Ff = Fsim = Fdef
Fadh = 0

26. indentation and scratching
results: numerical: influence interaction between indenter and polymer Fn vx Ff A2
Fsim
polymer A1
Ff = Fsim = Fdef + Fadh
Fadh Fdef

27. indentation and scratching
results: numerical: influence interaction between indenter and polymer Fn vx Ff A2
Fsim
polymer A1
Ff = Fsim = Fdef + Fadh
Fadh Fdef

28. indentation and scratching
results: numerical: influence interaction between indenter and polymer

29. indentation and scratching
results: experimental versus numerical validation using different tip
Fn=150mN
v =0.1µm/s
r =10µm
visco-elastic
visco-plastic

30. indentation and scratching
results: experimental versus numerical validation using different tip

31. indentation and scratching
results: experimental versus numerical wear

32. introduction
predicting performance of present models
outstanding problems:
first question: origin of deformation kinetics
second question: origin of ageing kinetics
third question: origin of strain hardening
summary

33. introduction
predicting performance of present models
outstanding problems:
first question: origin of deformation kinetics
second question: origin of ageing kinetics
third question: origin of strain hardening
summary

34. deformation kinetics
rate dependence of PC

35. deformation kinetics rate dependence of PC
Plastische deformatieproces is sterk reksnelheidsafhankelijk, deze afhankelijkheid is gelijk
voor het het gehele gebied na het vloeipunt.
Afhankelijkheid kan worden geillustreerd d.m.v. een vloeikarakteristiek waarbij de vloeispanning
wordt uitgezet als functie van de reksnelheid. Deformeren met een constante reksnelheid leidt dan
tot een vloeispanning. Omgekeerd geldt echter ook dat het aanleggen van een spanning (zoals in een
kruipproef) leidt tot een (plastische) reksnelheid. Deze bepaalt vervolgens de tijdschaal van de plastische lokalisatie.
rate dependence of PC

36. deformation kinetics constant strain rate response
rate-dependent yield
constant stress  .
In deel 1 hebben we gezien dat de kinetiek van het faalgedrag in constante reksnelheidsproef en constante spanningsexperiment identiek aan elkaar zijn. In een trekproef is de vloeispanning gekoppeld aan de opgelegde reksnelheid, en in een kruipproef deformeert het materiaal met een constante reksnelheid gekoppeld aan de opgelegde spanning.
failure under constant strain rate and constant stress experiment governed by same kinetics

37. time-dependent accumulation of plastic strain: plastic flow
deformation kinetics
time-dependent accumulation of plastic strain: plastic flow

38. deformation kinetics influence of thermal history
Invloed van geschiedenis: verschillende toestanden
Vloeispanning verschillend, echter bij toenemende deformatie verdwijnt het verschil beide worden verjongd door plastische deformatie: verjongde toestand is hetzelfde voor beide materialen: deze toestand is dus onafhankelijk van geschiedenis?
Voor de vloeispanningskarateristiek : verschuiving naar links (lagere reksnelheden) : gevolgen voor door plastische reksnelheid : neemt af : tijd tot falen zal dus toenemen!
influence of thermal history
on intrinsic behavior
influence of thermal history
on rate dependence

39. deformation kinetics and time to failurePC
influence of thermal history
on intrinsic behavior
influence of thermal history
on time-to-failure

40. deformation kinetics and time to failure
strain rate dependence of yield stress
stress dependence of time-to-failure

41. deformation kinetics and time to failure
question 1: how does molecular architecture determine deformation kinetics

42. 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

43. introduction
predicting performance of present models
outstanding problems:
first question: origin of deformation kinetics
second question: origin of ageing kinetics
third question: origin of strain hardening
summary

44. ageing and ageing kinetics
influence of thermal history
on intrinsic behaviour
influence of thermal history
on rate dependence

45. ageing and ageing kineticsPS
PS: brittle fracture within hours
PC: necking returns within months

46. ageing and ageing kinetics
ageing accelerated by temperature
Arrhenius temperature dependence; ΔH 205 kJ/mol

47. ageing and ageing kinetics
ageing accelerated by stress

48. ageing and ageing kinetics
aged loading curve
rate dependence of yield stress
De invloed van geschiedenis wordt beschreven t.o.v. de verjongde referentietoestand door een enkele parameter
Sa, die dus de hoogte van de vloeispanning en de sterkte van de softening bepaalt. Vergelijkbaar met de verschillend
gekoelde materialen leidt dit tot een verschuiving naar lagere reksnelheden. Met verdere plastische deformatie wordt
deze verschuiving weer ongedaan gemaakt, het materiaal wordt weer verjongd, en bereikt weer de referentiecurve.
changes in thermal history captured by a single state parameter: Sa
behaviour independent of molecular weight distribution

49. ageing and ageing kinetics
In de vorige slide is te zien dat de thermische geschiedenis van invloed is op de hoogte van de
vloeispanning en dus ook van de hoeveelheid softening (=sterkere lokalisatie). Deze verandering
van de materiaaltoestand is echter een continue proces.
yield stress increases with time

50. ageing kinetics: two domains
temperature history
received
during processing
temperature history
received
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

51. ageing kinetics during processing

52. ageing kinetics during product life

53. ageing and ageing kinetics
rate dependent yield stress
long-term failure
both short-term and long-term deformation kinetics are captured !

54. ageing and ageing kinetics
rate dependent maximum load
long-term failure
failure of polycarbonate products
predicted accurately
without a single experiment !

55. ageing and ageing kinetics
“yielding” is
mechanically
passing Tg
by applying
stress
”melting’’ is
thermally
passing Tg
by addition
of heat
Hodge and Berens, Macromol.,
15, 762 (1982)

56. mechanical rejuvenation
polystyrene PS

57. 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

58. 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

59. introduction
predicting performance of present models
outstanding problems:
first question: origin of deformation kinetics
second question: origin of ageing kinetics
third question: origin of strain hardening
summary

60. strain hardening reversibility of deformation heat aboveTg return to
original
geometry
plastically
deformed
sample
thermally-
induced
segmental
motion

61. strain hardening
reversibility of deformation

62. inspired Haward to decompose the stress
intermolecular
network
total
inter-
molecular
network
intermolecular component
modulus and yield stress determined by interaction
on segmental scale
network component
rubber-elastic response of the entanglement network
through chain orientation

63. strain hardening chain orientation  entropy decrease
theoretical stress-stain response:
N* : network density
k : Boltzmann’s constant
T : absolute temperature
proportional to network density and temperature!

64. 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) Gr
compression
torsion
tension
This concept was adopted by many researches and extended to 3D constitutive equations
Neo-Hookean hardening:

65. strain hardening G’Sell & Jonas (1981),
Haward (1993) Gaussian chain statistics
true stress [Mpa]
true stress [MPa]
Neo-Hookean hardening:

66. strain hardening influence of network density
prevents extreme localization
stabilizes deformation in tension

67. strain hardening influence of network density
response proportional to network density

68. strain hardening influence of network density Gr , 25 oC GN, Tg+30 oC
response proportional to network density
two orders of magnitude difference

69. strain hardening influence of temperature
response proportional to network density
two orders of magnitude difference
contradicts entropic origin

70. strain hardening influence of temperature PS/PPE 20/80 40/60 60/40
80/20
100/0
response proportional to network density
two orders of magnitude difference
contradicts entropic origin
suggests viscous contribution

71. 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

72. 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

73. introduction
predicting performance of present models
outstanding problems:
first question: origin of deformation kinetics
second question: origin of ageing kinetics
third question: origin of strain hardening
summary

74. summary
question 1:
question 2:
question 3:

75. acknowledgements PhD topic
marco van der sanden 1993 concept of ultimate toughness
theo tervoort constitutive modelling
peter timmermans 1997 modelling of necking
robert smit multi-level finite element method
bernd jansen microstructures for ultimate toughness
harold van melick quantitative modelling
ilse van casteren nanostructures for ultimate toughness
edwin klompen long-term prediction
jules kierkels toughness in thin films
roel janssen creep rupture and fatigue
tom engels coupling processing-properties
lambert van breemen D modeling of micro-wear
financial support: TU/e, STW, DPI

77. some thoughts…..some answers

78. 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

79. 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

80. 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

81. 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

82. 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

83. 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

84. 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)

85. 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

86. 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

87. 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

88. 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

89. 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

91. and of course……semi-crystalline polymers

92. and of course……semi-crystalline polymers
injection moulding of unfilled PE
orientation near skin 1 2 3
oriented row structure

93. and of course……semi-crystalline polymers
High
impact
injection moulding of unfilled PE

94. and of course……semi-crystalline polymers
injection moulding of CaCO3 filled PE

95. flow-induced crystallization

96. acknowledgements
leon govaert

97. acknowledgements PhD topic
marco van der sanden 1993 concept of ultimate toughness
theo tervoort constitutive modelling
peter timmermans 1997 modelling of necking
robert smit multi-level finite element method
bernd jansen microstructures for ultimate toughness
harold van melick quantitative modelling
ilse van casteren nanostructures for ultimate toughness
edwin klompen long-term prediction
jules kierkels toughness in thin films
roel janssen creep rupture and fatigue
tom engels coupling processing-properties
lambert van breemen D modeling of micro-wear
financial support: TU/e, STW, DPI

98. and of course……semi-crystalline polymers

99. acknowledgements PhD topic
hans zuidema injection moulding, stress-induced crystallization
frank swartjes crystallization in elongational flows
bernard schrauwen 2003 injection moulding, processing-property relations
hans van dommelen 2003 multi-level analysis of properties
sachin jain PP-silica nanocomposites
maurice van der beek 2005 density after flow: PVT-Tdot-gammadot
jan-willem housmans 2008 crystallization in multi-pass rheometer flows
barry koreman msc 3D modelling of injection moulding
juan vega pd rheology during crystallization
denka 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