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

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

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!!

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!!

rejuvenation polystyrene PS

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

ageing

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

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

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

from compression to tension

from compression to tension

from compression to tension fit tension prediction

indentation and scratching mesh

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

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

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

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

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

indentation and scratching results: experimental: influence sliding velocity

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

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

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 :

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

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

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

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

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

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

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

indentation and scratching results: experimental versus numerical wear

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

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

deformation kinetics rate dependence of PC

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

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

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

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

deformation kinetics and time to failure PC influence of thermal history on intrinsic behavior influence of thermal history on time-to-failure

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

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

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

ageing and ageing kinetics 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 accelerated by stress

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

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

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

ageing kinetics during processing

ageing kinetics during product life

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

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

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)

mechanical rejuvenation polystyrene PS

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

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

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

strain hardening reversibility of deformation

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

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!

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:

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

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

strain hardening influence of network density response proportional to network density

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

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

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

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

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

summary question 1: question 2: question 3:

acknowledgements PhD topic marco van der sanden 1993 concept of ultimate toughness theo tervoort 1996 constitutive modelling peter timmermans 1997 modelling of necking robert smit 1998 multi-level finite element method bernd jansen 1998 microstructures for ultimate toughness harold van melick 2002 quantitative modelling ilse van casteren 2003 nanostructures for ultimate toughness edwin klompen 2005 long-term prediction jules kierkels 2006 toughness in thin films roel janssen 2006 creep rupture and fatigue tom engels 2008 coupling processing-properties lambert van breemen 2009 3D modeling of micro-wear financial support: TU/e, STW, DPI

some thoughts…..some answers

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

and of course……semi-crystalline polymers

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

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

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

flow-induced crystallization

acknowledgements leon govaert

acknowledgements PhD topic marco van der sanden 1993 concept of ultimate toughness theo tervoort 1996 constitutive modelling peter timmermans 1997 modelling of necking robert smit 1998 multi-level finite element method bernd jansen 1998 microstructures for ultimate toughness harold van melick 2002 quantitative modelling ilse van casteren 2003 nanostructures for ultimate toughness edwin klompen 2005 long-term prediction jules kierkels 2006 toughness in thin films roel janssen 2006 creep rupture and fatigue tom engels 2008 coupling processing-properties lambert van breemen 2009 3D modeling of micro-wear financial support: TU/e, STW, DPI

and of course……semi-crystalline polymers

acknowledgements PhD topic hans zuidema 2000 injection moulding, stress-induced crystallization frank swartjes 2001 crystallization in elongational flows bernard schrauwen 2003 injection moulding, processing-property relations hans van dommelen 2003 multi-level analysis of properties sachin jain 2005 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