Polymer Melt Rheology: A Guide for Industrial Practice

Polymer Melt Rheology A Guide for Industrial "'''''''1"'#.'''''''

Polymer Melt Rheology A Guide for Industrial Practice

F. N. Cogswell

Godwin Limited

ISBN 1 85573 198 3

2003FN British CaltaJc,gu:mg in Publication Data A ,-alACllVJ~Uv record for this book is available from the British All stored in a retrieval the Printed

PU[)Uc,atIcm may be reproduced, or transmitted in any form or any means~ Ath"""UftC"" without cQ[)vng:m owner.

ext.enem:e of of leI art of ~Y"£'C"'A;"_ pra,Ctlt:tODlers of that technology, and a o,eve:lot)eO academic contributors to this field. stimulation, this book is respe(~tttlllV lAn'!:l1"trnA."tCl

ba'~k:Q"rOlmd SCl~en(:e

PUBLISHER'S NOTE While the pnlrlCll)leS of careful sUl1tabtllty of caJI~uJ~itl(J.n not be form or contents person tnc;~re4::m.

in this book are the nr".l'tn.f'f' pulblis,heJrs cannot in the solutions to inl"llultill'!:lJ problems and any kind in of or out or any error reliance any

Contents

xi xiii

Notation Introduction

1

1 Fundamental concepts

5

1.1 2e('me~trv

of deformation rlleolof21cal response of materials

1.2 Thermal and tlle:rmtodymlmJic response

1.3

"'h\'
and chemical

15

Cat,aDle of measurement response of melts to deformation shear flow in a cone and rheometer J::,1(Jn~:atlon;al flow rheometers Vi~iCOjelal)tic

2.2

9 10

1 Rheometry for polymer melts 2.1

5 6 7

17 17 19 23

Measurement of aplJarlent rlle:olctgical ......" ....,."'jr.A" 2.2.1 API)are.nt 2.2.2 and exit effects 2.2.3 Inference of elastic respoillse 2.2.4 Observation of extrudlate am:.eal'an«:;e 2.2.5 for app,arelot rl1leOl4oglcaI DI~ODlertijes 2.2.6 to rheometers 2.2.7 The Melt Flow as rheometer 2.2.8 Miniaturisation

24 25 30 30

2.3

Process simulators

34

2.4

Priorities and costs for

upa

31 31 32 33

33

35

3 Physical features and Dow 3.1

'emtl)eJratl11re and

39

rtu:~01()2V

39

3.2 Pressure effects

44

3.3 DepeIldence of rhe~01()2Y on time

46

3.4 Stress 3.4.1 behaviour 3.4.2 Elastic response as a function of stress 3.4.3 Viscous response as a function of stress 3.4.4 Modification of mechanical

49 49 51 52 53

3.5

Deformation 2e()mc:~trv and 3.5.1 Bulk deflormlatl<m 3.5.2 hlongatloIlLal flow 3.5.3 flow

rh(~01()2V

54 54 54 56

3.6 Flows flows 3.6.1 3.6.2 Pressure-driven flows in channels of other than circular cross-section flows 3.6.3 3.6.4 sections of thickness 3.6.5 Biaxial extensional flows 3.6.6 The interface

4 Rheology and structure 4.1

71

Chain stiffness and conformation 4.1.1 Chain 4.1.2 Chain diameter 4.1.3 Molecular aspect ratio

4.2 Chain

57 57 58 60 63 64 65

71 73 73 73

distribution

77

4.3 Chain branctlmg

81

4.4

83

M(uptloJl02Jical structure in melts

4.5

plasti(~sers

and lubricants

5 Adventitious Dow phenomena 5.1

91

Plasticisation

92

5.2 Chemical 5.3 Instabilities associated with a

84

92

in

vis,~ositv

93

ix 5.4 Instabilities in

93

5.5 Melt

94

5.6 Melt memory

95

5.7

97

in structured materia1s

5.8 5.9 5.10

97

effects

99

induced instabilities Non~laminar

100

flow

5.11 Die exit instabilities

101

5.12 Coextrusion instabilities

102

5.13

104

flow instabilities

106

5.14 Phenomena associated with solidification

111

in polymer

6

6.1 Introduction

111

6.2 Low flow processes 6.2.1 6.2.2 Deformation of an extrudate under 6.2.3 Processes associated with relaxation of 6.2.4 of a surface a melt

115 115 116 118 118

after flow

119 119 120 120 120

6.3 6.3.1 6.3.2 Distributive 6.3.3 6.3.4 Work 6.4 Constrained flows 6.4.1 Screw extruders 6.4.2 Wire 6.4.3 Pressure-driven flows in dies and moulds 6.4.4 Constrained flows defined pressure

121 121 123 123 124

6.5 Free surface flows 6.5.1 6.5.2 Film 6.5.3 Vacuum

125 126 127 127

and blow

6.6 Bulk deformations

128

6.7 Select

129

x 7 Future developments in polymer rheology

133

Appendix I: Additional sources of error in l"llr'\lIl~~rv visc;;onletlry 1 in the die 2 at die wall 3 Pressure and effects 4 Shear modification effects 5 Non-laminar flow

135 135

Appendix 2:

Int,,,.rn,r,,.tl:ltl(,\n

of extensional

vi"{~n"jtv

136 137 139

139

from flow through an orifice

141

die Appendix 3: The inference of elastic modulus from

Dosit~extnlsicm

143

s\lVellin2

145

Appendix 4: RUlptUJre behaviour Appendix 5: Data sheet for

l"llflHI!::.rv

Appendix 6: COlnp(llris<)O

146

flow

rhe:ololgic,al proJJtert:ies of two

of low-

148 Appendix 7:

152 Appendix 8:

154 Appendix 9:

prc.celisiIllg nrnr)eT1tv data for a

geJler,al-I'urpol~e

156 Appendix 10: Appendix 11:

prc)Celiislrlg property data for an nylon at 285°C

In Ilectlion

prC)Celisirlg property data for an

In.l lectllon

of

158 of

160 Appendix 12:

pr()Ce:sslrlg property data for a

of

and a

162 Appendix 13: Emlpirlcal observations of flow in channels of cOIlnplc,x cross-section Appendix 14: Flow a of extrusion with

slot or annular die to thickness

165

uniform

170

Author index

173

index

176

Preface

and tnc:~rD110a'v",amlC which form the meaSlJlnl1tll the flow of

sciences

InS>UJflYU

1981

rne:OI()IlV and the assoc].ate:d DJIlVS]lCal and chemical methods of on the

rc:~srx)nSie.

F.N.C.

Notation

R L

R' L' Q p

y n 11

recoverable elong,lU(Jtnal

Introduction

raw efficieltlcy in the de~U2rled nolvn1er to suit a move towards interaction ae\relCtn new or na."m()flU)US raw material.

literature both in trade and m()flO'2fC1PtIS:.l-· I :.l have been tne:or~v-ess,en1tlal t"n~efi()m~en()IOjglCl(l1

as a basis from which we can progress and discuss effects

2

The OOlectlvc:!s of the res:eaJrcn from which this book ext,erien(:e of a material in a response of the ort~all;:t

the

l1p.lrn.l~"C

are:

t'"'ru'ulp.:I""irln nlrnl","'Cc'

between ...n.j'",nr'",1 new or

lrrU"rn11!",11

ohlecfl've~ has led to SImlpllltlcattOJilS who are in the of arise. Those who are not so sinlplilficaticlns are mtJ~oauce:a where COJllPleXltlt~s and where the circumstances future research will dernOllstr'ate that are sut.stantullJy c(}r:'~.. c,~... but my tion in this is to be rather than de1timtlv4e.

eXJ)en,em~e

nOlvn1er rnf~OI()OV

cur'rerltlv

into a cOJllplex

to be in the final

~nr,p~rc

and the first clalntl(~atton.

3 more in a strletcnec[J. F.nrtnnl::ttl"lv nature lead f'1"~Ul1l"l(f of thin film. Our UllICOIISCllOUS, of the unusual 0011eCltlVe is to assist in to in the of irntlrO'IIl"fl £1&>"'11"''.11'\1""

then~

theoretitun.dalnelltal des.cnlPU()ll of what would be pnlctltlolllers, who are tneoreUCl;ans the SU!l[lltlCal1lce. To nUI"rl"l.rtp(! all other Each is concerned with his own truth, which both to be same when the two are married we have a cornpJete unl:lerstandJlng. To that to be consummated much has construction of between those and several books been laid on have aUempt(~d to build such a framework. The dit1tlC\llltv that the first is a secure base on both foundation on bank so I shall not to build bnc[Jge:s. ohllecl]ve of this work to chart the nature of the river demonstrate even if it is not DOs.Sltlle river is not so after alL

4 REFERENCES

1.

2. IVI L;I'\LI:: I VI:: V 3. Nlel!iSen, 4. R"'lirl'h11".n

5. 6. MiddleJ1nan, 7, HOJm€~S- 'IV alKer 8. pp.~lr~ln 1966. 9. 10. 11.

12.

.... t"."f""" mlouJdinll.

Plastics and Rubber

\OiUltlVIl. '\JVIUWIU.

1981.

Fundamental Concepts

the~rmloplas1tlcs

during prc,cel,SlllI2 we are con-

are necessary to the are necessary to achieve which may be del.lbe:rat:ely

1.1 RHEOLOGY Kn~eOI4[)e:y is the of deformation and flow: of all the reS1OOl1lSeS it is the one which is most felt. We have all SQtlee:rea toc,thl)as1te kneaded from our of descnttlD2 readlDJg, but nt't"'Il1rlp

the

is to materials eQtlatllon of state. The ..... .,.£'\11" . ."'"

geJleral1~;ea

this is deformation history once the eqllatJIOn eX):lenmeJots. At the other of the "....".""4<.."' ..... cOlnplex materials and cOlnplex course is to amllv~.e which are Qual11:aUVeJlY discover such ex):)en.ments This text takes this a01:lroacll-the quanltItu;;atlon Three material states are relevant to nolu""Pt' pr()CeSSiloe:: form in which materials are fed to the process -the form in which are nC!11!:llllu Sllat:.e<1 -the form of the final one in which some Sbalpll1lg may

llratnular-1the

melt solid

6 de:formtiltictn occurs. in iUfJlstI'ati:ne: solid response are mc:lucled dej'me:d as

cn~:mSl'e

1.1.1 Tbe Geometry of Deformation are three simple cleJtormaltlOifiS. In

the stress is aOIC)lie:d

t~m2entialJ

1

stress strain

y

1

rate

1.1

Ii

shear: area A and distance h remain constant

(b) In simple extension

deformation

stress is a01)l1e~a normal to the surface of the material

stress

UE:=

strain (unity)

E:=

rate of strain

e

7

I both vary

extension: cross-sectional area A and

In bulk deformation the stress is aDl)Ue:eJ normal to all faces. The stress is the apl)l1e:a pressure, and the strain the in per unit vollunlle.

a stress normal stress. The nr£lNll"'!:l1 aeltorm(lltlcms clomple:x flows COInO~OUIlaea SOlll1tlcm to this double cor:npliex11ty slnllplifu~atllon of tensor notation which is the sta.rtl]nQ··DOlmt For the of this work it is sufficient to reC'02Illse those exist: with siRlpljtfic,ati()ns in the response of lUH1'3111"U

1.1.2 Tbe Rbeological Response of Materials There are three of response to an stress: viscous eJetorrnatlon and rUDiture. In viscous flow a material continues to deform as and the in to flow is (llss1pateeJ defined as of stress to rate of strain in The of some common materials are Table 1.1 Viscosities of some Common Materials

Air Water Olive oil

10-5 10-3 10- 1

loo

1()2

1(lLl 06 1()9 Glass

1()21

stiff

8

Strain

Stress Time

1.3 Newtonian behaviour

response of a material is to flow with a stress the is said to hellla,re low stress level many melts aDI)ro,!:lch ms,tarltJv under stress and the is material possesses an ratio of stress to recoverable If all the deformation is reversible and is aDlc>l1e~d stress the material is to a Hookean response 1.4). At deformations approach Hookean and many nnlvn~pr melts have a lower mc,oulus than riA·............... '"

Stress Time

1.4 Hookean behaviour 11..... 1"...... melts delIDons1tra1te well model in Hookean elastic <:tn'"lnc:,O illustrated in £0 ..

elastic:o-~rjsc~()US

reSDO]tlSe to stress. The Maxin a

m(jltel~ial will as a Matx\\reH aOl)arlent "'""ro......:""'" an modulus which tel1[)Dc~ra1tune. pressure, stress, of deformanrl'\np,rtll'"'<:t which we record and use are thus the nnJrlnf"pnt anl')arent Maxwell modulus. more viscous than most

very

Fundamental

9

Lo,nce'DlS

Dashpot

a

Strain

Spring

Raversible deformation

Stress Time

b

1.5 a Maxwell model b Its response to stress

role in deterl1mnmg the maximum rate at which a deformation ....rr.I".,.'~e carried out: it is the initiation process for that important ....... h,"'''''.,. prc)Ce!,SlIllj! it is frequently

interactions rupture phenomena which determine the

elastu;ity

1.2 THERMAL AND THERMODYNAMIC RESPONSE cOlnpres,sio'ilit:y of materials we have ~lr''''~£1I'll and in viscous flow, rI"" •.,."d'" and SPt'~Clt:lC

is as pressure. For a aplueC:lation of tOIl~etller with the nowned as msulClltlJ1lj! handled by the for COlllvelltl(Jlnal ma1tenals. APpeniOloes include typical data for several polymers. The rate of during is determined by thermal

which is readily aPI'lle:o

the corlcel,t of Fourier number:

Fourier number eX(:haJflgeo from both sides of the sectlolll, transfer on the square of

thl(:kmess, a sec1tlOn

aDllro.ach thermal minutes. cOlnplexltv due to surface heat transfer . ....nl'l1.....,.,... melt and dlfter,ent still air = 10 air at 10 mls 50 metal surface = 400 water 2000 While it is POS,SIDIe to measure the thermal and the:rmlodVfiiilmlC .............."" ..lh""c techmQU(~S which have been de~ileh)ne~d eSI.aOJIlSrleO technique for cr .. nu" .... n ngl-2'I£'nl!l:rlll ..........1""..... "" .. melts-the ......,...... ,,""....., ~erlenitlCm as as heat streamlines of a QUiescent: state and must in .....c ...""'r"r stable. only be lost It is also '.....,'...."1"2'<:>11'12' solid to an !ltnnnr'ln{'Uul. values of APIPenOlCles 7-12.

tnClU(Jlea in

1.3 PHYSICAL AND CHEMICAL CHANGE The ..... ".t: .....,. One iSPf()cesse~o been demonstrated to have a flow That ....""1"'...",. .. plaStl(!lse:o and lubricated to achieve easier flow and may further mOlol1led whose method of their desired effects is near one extreme of PJastJ(~s include some additional co]np'on(~nt pr()Ce:)Sll1l~ or to their service pe]:-tOJrm~tnce. &.I.nhJ1rn"... nolvtnpr" are now Dec;oI1nmtg mlcrc;~asllngJly used. tnc;~nrlOJ;llasitlc melts derive from resins and thermal of process may allow some of that order to be retained. we have seen the of

11 a distinctive mc$ODnliSe of a with its pr()ce~ssttl!~ clllar'acl:enStl4:!S between that pr()Ce::iSlrl~ an(~--OI the en(i-Dlfoauct

are

m(]~le(:UUlr ",""'''''_HL.

in a meltll1l2 omnI-local hot "~a.~~£~~ nrnt\lplm when RUlnnmg the extruder cold any material prone to

and so hot ooltimum machine tel1npc~rature. are least severe in constrained IDllectlon mCml(lme:. where the are nC!tloll!u of discoloration

12

Rheology

or mechanical weakness of the The of pla.stl(~S as much as a factor of two injection moulding but products, although care in handling. The problems are more severe in extrusion processes where thickness or of meJUIlUl instabilities in variations as a result of the screw. are at their most severe in which the extrudate or to stretch and blow where to be of local variations in result in amounts of stretch. The plastics in this field less than 20 per cent If ae2raaaucm

DJ~021'eSSjes

only ~I"'htllv rf~dUiced a 10V\'-mlOle~CUJlar··we:l1!l1tt. volatile, tail may be "'V. "n.., ...... plas'ticlsin1! the flow and IP!l"'t1~O' ......"'....""'JU,, brittle, low-molecular-weight or voids as mechanical weak11esses product. A laudable desire to exposure to heat as low as DO~iSlble lead to too little consideration to hOlmolgelflls;atU)n: in a degradable polymer, it is easy to extrude a of unmolten material. While the undegraded polymer in a matrix of overall molecular of such a product the molecular of and so the "'t ...".... n1~h much attlectled. molecular to a value Mw/MN of about (Molecular weight distribution is ext:Hallled

and del:onne4l. work is nr."rtl1l~';:' structural to obtain a full nrr\nprhl"'
Fundamental Concepts

13

RBFBRENCBS

5. 6. 7.

8....."',.....". prc)CelSSlrlg aids I::"repar,atl(Jln and Pn/vm4rJr

Science

"-".U'"""""",, Two

Rheometry for Polymer Melts

Kl1leometry is the art of maKlnlg useful measurements of the deformation flow Df()Dertl(~S of measurement which is may fall one nrr\nA.rtu of the material. 1'AI •.,.1''''A oror.er1:tes of a series of materials. mvestllgalte its and its DOltentIal Demonstration of a pn~en('m(~n(Jln effect. of new which into novel The mtleraCt14cms between a material and its en'virlonJlllent. The different categ()nc~s of measurement may different ~nl·'\t·r1.~rl"'pc rne:olTletl'yand on any measurement it is necessary to what that measurement is to acJrneve. The two critical must be asked of method of measureis the only one ment are 'Is it and 'Is it sufficient?'. If a which the information about the then it is necessary, and if the which it is to resolve the QUlestllon under then the sufficient. Thus if we wish to the linear behaviour of a melt we methods of measurement from those which would to Tnr,hl1rp behaviour of melts in film that for much more far less so~)hil)tic:ate~d rtleometrv which would be unsuitable to the first task. this review of rheometers is to define those areas in teC:hnlqtle is most The review is biased eXl)entenc;e and limited of a that my for a more review of rtu~onl1eters undelrlyiin,g their use several texts are available ,1-4 PV1,.....,."·.A .... I"'A

Melt

16 Table 2.1 Classes of Rheometer for Melts in Common Use Classllkation ROTATIONAL METHODS

Method

Variables

Eccentric disc and 'balance' rheometer

Limitations

Strain and

shear and

Near to linear Strain

PRECISE DATA

Strain Strain rate Strain recovery Stress Stress Stress relaxation Time

Normal stress PRECISE DATA

As above

Torsion SQUEEZING

Penetrometer Parallel

EXTRUSION

Melt flow rate

flow

flow

Flow rate Pressure Swell ratio Extrudate appearance

APPARENT PROPERTIES COMPARATIVE ENGINEERING DATA

TORQUE

Instrument extruder 'Brabender'type

COMPARATIVE force volume

Resistance to flow Extensional and

fREE SURFACE FLOWS

PRECISE DATA

Strain rate <1 s-1

force

Extrudate Drawing

CoMPARATIVE Sheet inflation Bubble inflation

PRECISE DATA Biaxial extension COMPARATIVE

difficulties

17

2.1 RHEOMETERS CAPABLE OF PRECISE MEASUREMENT 2.1.1 Viscoelastic Response of Melts to SmaU.amplitude Deformation The

and measurement of of oDtalllllDl2 nrpr'IClP

mOlduJusarerreQuen4~-IOel)erldent.

rate in are rare,

amlpJlltu4je-.aepeJ()d4~nt because sut:t1C1~entjly small

maximum strain that from

"U""'"F'.,U

c

.

'e

y•

fl·

"0 C

•• ••...

-

f /)

, where

is the strain amlPlltlllde and

Such

data CllCllra(:tel"lSlJ12 the rnC:!0l()2V are ways of data. The differen~ces int en:.re1tatjion rest on whether stress or strain assumed to be the co]tltr oUiin2 meCll~lm!)m. Most under strain but response would be if stress were the mechanism. Most COlmDilOlllv strain is assumed to be the the dVlrmrmc 1

1

11' =

sin 0

and the modulus: Of

=-""T"jr:ns

0

ampWtudes, 0 is the

and (J) is 1Ddlepc~ndent

of element

18

G'

b

2.2 a model b Maxwell model

aeJ)en.
the material is reS'P.on
J.UUi...,...,,", at sul11Clenttlv t.o a Maxwell m.odel. use the Maxwell noilvnler melts share the that the Maxwell mtcerpretcitlOJn the an easier

.oSc:illaltOl"Y shear rhe.ometers9,1O,H in the lirrlitaLtioln is .one .of time-scale of measurement frDm the inertial effects.12 the behaviour of liquids at dVlnarmc measurements with strain amlpUlu(leS pnnclpal aa'vallltaJ~es of dVlnarmc measurements for the of melts are:

of the

.. h",.file,,,,,·.,

tecnmQuces have received and may be used to .obtain in the linear over a very wide range of treQU4enc:y a direct measurement of elastic as well as viscous Dr()Oertu:~s--anld

on~Cls:e

(ii)

19 ~~b~~~~

~~~

~~

COltllP'aflin2 elastic response. between and information relevant to the very short time·scale response of POsslltlle to obtain a strain as all the data are nr£"'I,.,-t",C! a solutiong£'Tln
have been )ls~ld,ranta~~es

which must be borne in

of measurement

are:

(i) The

the nOII1·nne;:lT

response al>1)arlent SPt~CIJtllen

pJrepfanlUOfn and accurate eC1tllpJtllel!1t can be

2.1.2 Steady Shear Flow in a Cone and Plate Rheometer

The of the cone and every element of the is to an loenncal are described in standard texts),2.3 There are two oel)en.01I112 on whether the is to under constant stress or constant rate The constant-stress is the is apl)Ue:d direct and deformation measured from a scale. probably the rheometer which can be made and is eSt)eCIalllV useful as a since the can be felt and the deflection seen, rather than measured with transducers. The constant-rate in which one face is rotated at a series of rates and the is measured on the nr~"f"'rr... rI in most commercial instruments. If the instrument is has an
a

b rbeometers

a COllstalnt-lstress b Constant-rate type Wc~iss,enlbel-g!O

notes when an elastic as the shear stress there is a rheometer that pull the across the face of the instrument and a normal faces measured instruments in which the That thrust is most accounts the common for that class strain rate is of instrument. own use of normal stress measurements has been limited for I have never been able to of their and evidence-the normal force "",vf"."u,'1"'T"ll can be related to TU·".,....,.'"I nu,.rlr,,,, ..,,, take a different and the ht"" ..",t'lU-.,. "'I.o,un,.,. Whatever the fundamental int,en::.reltatllon mal stress measurements unlclOl11bted,lv elastic response of melts. The measurement of the stress transients and cessation of shear flow also offer for de(Jucln}! the elastic Such tranSlenlts can be of absolute measurements demand an effect as the 'stress OV4erSJIlO()t Jlhell0I1t1el110n stalrI-UlD of flow at a constant rate, the stress realCbJlng its condition and some WCtrkiers deduce :se(:onaal'V flows can also be that it some a close lnspe<;Uctn Since the contribution to total instrument face on the cube

an individual annulus of the a small loss of adhesion near

21

Rheometry for Polymer Melts

Strain rate

a

b

Time

As set up and running with no 'overshoot'

'Overshoot' evident

2.4 a The stress overshoot phcenOfme:no:n: stress passes thr,ou,!h a maximum and

b

~eciondlarv

cone and

rheometer

the of the ""'.1"1"''''' and so on the stress in a double cone measured. ins,trtJlm~ent to be used at much rheometer higher stress argument «~«lU"" the of the for eX~imlple stress OVcerSJno(lt for tbe £>"O'I"T_"'_ exist. My is that, were very should be seen-but they are not. The mterr.reltatJOn of apparent stress overshoot phenomena as an lnC1trl1tTt1~"'nt effect is able to raise in the heart of eXJ)er]lm~mt:al rheologist alike. While the resolution of that arJ~Ul1ne)1t remains doubt such observations must be treated with caution. The nh~O::l"'rlHitlnn of adhesion failure may be of considerable in palrm;::uUlf a40vEmt::Ule of the constant-stress cone and is the ease with which the stress may removed the observer to record strain recovery as a function of time for stress histories. The ratio of shear stress to recovered shear a simple comment on the elastic respolnse which may be related to observations of frozen-in strain in mOlul(lmJ~S and in that all a desire of the Tt1!l'''~1'1!:l1 to revert to an earlier state. use of recoverable shear as the has the additional while it is measure of elastic meastJlreci, it is the thing which is nallJPCmlJng. ae~;tgJ)ea to measure strain recovery after constant-rate aeJtormaltlOin

22

Yn.I\IJt1"1Pl'

Melt K/1;eo,tolJ.'V

Measured c

.~ (/)

Time

Time Applied

Time CONSTANT STRESS

Time CONSTANT RATE OF STRAIN

2.5 Deformation of Maxwell model: under constant stress

flow is attained

A further of the use of constant stress COJllpare:o with an .'''<'V.'''.... ment at constant rate is that it time to reach equlllorlUln response. This difference in demonstrated for a Maxwell model under constant is attained instanwhile under constant strain rate the to condislow oPleraltlOifl is that most T' • •

at constant shear stress are more Ois.criimj,natoJ~y shear rate in non-Newtonian svs;telns. rhc~OInetrv are: The of cone nrf~Clselv defined flow at low shear stress. aDd on both

in a

of

sensitive to the As a measure of under low stress it is which structure may break down structural characteristics of the under stress. The limitation of this class of rnc~orneltrv for melts is associated with the very

23

Shear stress

shear flow data for melts at different temperatures or of different

molectllar weil2hts: ratio of viscosities at constant stress is

than that at constant

rate

surtac:e area to volume of the which limit its usefulness to relatrvelv low stress measurements. OOSSllDle to overcome the associated with the nnnln'lPT:'the rate of heat would still OI)eraltIOtn of the instrument at

2.1.3 Elongational }i'low Rbeometers No than

of

has advanced more t"!u'\U11Iv flows. This progress measurement are now COlrnntler'CUllUy

The slmtph~cltv how it
24

Stress 2.7 blongatlOnlal strain rate, E

The and of constant stress or constant rate as the controlling mode of deformation apply to extension as wen as shear. The reduction of the time transient available when making measurements at constant stress is of in flow when making measurements on melts whose decreases In such f"Xl'f"r
2.2 MEASUREMENT OF APPARENT RHEOLOGICAL PROPERTIES BY CAPILLARY FLOW The that we can only determine the nrf"{'n~p polymer melts under a limited range of limited interest leads to a quest for other The criteria which these methods should meet are:

rJle()lOI~IC;al

of are of of measurement.

should cover the strain rate range of interest in PfilCtl.caJ measured should reCluurea so that it may be The should be {,{,U'1VP'ntf"ntllv (better than 5 It should be pm'SIO.le of less than 100 g and as 1 g. Capillary flow meets many of these reQluir·em,en1ts.

f t .......-.""' ..1· .... '"

prc.ce~)sml~

(up

property

Drc:~feI'abllv

as little

2.2.1 Apparent Shear Viscosity from Capillary Flow CapIUaJry flow will be

in most

wall shear wall shear rate,

y

By the of onrlrnr'U'tota eC~Ullpment shear stresses in

POSSlltJle cOllVe~nl~~ntlv to measure 0-001 to

operaLtlctn have been used: cOlltn)lIe~cl nrac-C'nl-'" r"",,",ur'lrHT a measurement of re(~Ulnng a measurement of

nr~~C:C:lllrp

Barrel

'~..,.',lIn ....

extrusion rheometer

reilat1()QshlP between flow rate and associated tnc:t10nal losses l1a40ltr!:ih'.,. to make the above the die rather than reCIUllrecl to drive the

(eS1Dec:talllv when the (iii)

enf;!~lDeernlg tOllen:mce~s.

26

Melt Rheology

20 mm diameter barrel will take apl:UOXlIl£1ately 15 minutes to reach thermal of size to accommodate equilibrium, will take a a melt pressure transducer near to Intlerpretl!ltlC'll of Cal)lll:ary rne:Ofiletlry the PoiseuiUe eOllatlon a true measure of uu:r....nc"f"u at the op,eraltlnl2 f"'.rn ..""'... aPI)ar,ent rather of corrections is the true 'ittl;! ....nc:l ..u ..'V" .. """"' ...."u. is recommended:

:l_

aPtlarlent wall shear aPJ)arlent wall shear stress, as leaOlIll2 to where is the pressure thl'OU,2h an orifice die rate. It is further recommended that the die used in such measurement should have a ratio of between and and 32. calnU,ary flow "'f.l~~"'l1nl" and friction losses Ends pressure

at the die wall of pressure on viscm~ltv Influence of on volume Influence of IntJIUel£1ce of on tenloeratlure Modification of the material due to work in the Inlluc~nc:e

27

2.9 The Darrel··nel~nt effect die radius Barrel radius R',

L

POI,st[,le. measurements when the measured

.,.,.,....... ,,~~

that a wall shear rate shear stress

nh~~p."'llP.<1

Pressure

L/R correction col're(~tlv

gn:ullcent may be of several but this extensive poL "',_,,"' _ _ , the choice of two dies The colmlJ-im,ne; a die an orifice

where

as

is the pressure Some eX]:>erlm1ent:ers

Error band in pressure

L/R

a

L/R b

2.11 Determination of pressure gra!Dle]lt a flreferJred b Dies of too similar LIR

Finally, the measurement of as a function of corrected Han,35 pressure situated in the has dellDo,ns1:ra1ted that the ends correction is a of an entrance and smaller exit pressure drop where is attached to the exit pressure drop as a measurement of This is in conjunction with a screw rather tbe needed in the die to the transducer necessitates rates whicb are mos.t conveniently acbieved in such an apl)aratus.

Presentation of Capillary Vl$lconrret,"y For the measurement of apparent ",i."".,.....,·.+" flow tbe ends COITe(:tl(Jln should be made and tbe metbod of sbould be noted witb the data. An method is the two-die method one die witb LIR = 32 and an orifice of tbe same Some of tbe additional sources of error will be found in 1. Tbe data be of versus log wall versus sbear stress are of flow

t

Pressure

Die exit pressure drop Die land

2.12 The ends correction is a

COfnOC)Ullld

10"

of entrance and exit pressure

105

Stress (N/m2)

2.13 A,ma,rellt .",.,,,,...,.1',, versus wall shear stress: IOVi/-oemmv DoJlve1tllvieilie at

30 2.2.2 Entrance and Exit Effects

exit nT*,"CC11T*," tool and and pressure drop and OO:st-f~xt]ruslon SWlelllnil. measurement cannot, at rt""lr.o.'I".rn'T,,,,,rt dmectJlv pOJateo from a series of several measurements 2.2.3 Inference of Elastic Response from Capillary Flow The most obvious during capillary extrusion sWielJtnil. The in SlDlpJest appears to be a reverSIon towards an earlier state and as such is as evidence of recoverable strain. Post-extrusion increases as flow rate and decreases ratio increases To make a measurement of swell be taken into account For praLCUcal. n 'lIrnnc*,"c measurement which most and an ao€~au.ate obtained the extrudate flush with the length the diameter of the solidified extrudate 5 mm of the The two measurements of swell ratio from an orifice die (Bo) and from a die of ratio 32 (Bd to the maximum and minimum values of swell ratio. Appendix how the elastic modulus of the melt may be deduced from such measurements.

Shear rate (,-1)

'i

J fI)

•

1000

•

100

•

10

2.14 Effect of die lentnD-to··ra
230/2

Melts

Vr..h'"'Ior

31

2.2.4 Observation of Extrudate Appearance ",,'rn'U,.rt.,. useful extrudate from ........""cu."".. non-laminar flow occurs the non-laminar flow or sUlta(;e nnDer1:ec'tlons. nr£,\n.,.rf'u"'C! no hold and data for f'r"'!:lf'",.rt with The extrudate to deduce of the DrC)Ce!,SlIlli and also to obtain evidence of Cletauc;:CI dllSCU,ssi()fl of the of lrre:gui,ar

2.2.5 Equations for Apparent Rheological Properties the eqllLauons

recommenClc;~d

a u.;}lri.,.1'u of measurements on Clltterlent DO,lvnler Table 2.2 Equations for Apparent Rheological Properties Shear now shear rate shear stress recoverable shear YR' from shear

U1Q£'£'\Ql'h,

shear modulus pSt:~udopJtastici1:V

index n from

Extensional now extensional stress extensional ViSC05.itv recoverable extension modulus in extension rupture stress

onset of non-laminar

* This eqllation, while complex in Where capillary

app~arance,

.", are the index, shear viscosity at the same volume flow rate.

32

Polymer Melt Rheology

2.2.6 Accessories to CapllJary Rheometers

Stretching Flow An obvious access~orv to an extruder is an instrumented haul-off. Measurements of in-line tension, and rate can of value in comparing to carry the stretchability of polymers. out such the use which has been in many demonstrated that clipping a weight on a method of comparing sample and allowing it to draw it solidifies is a of measurement highly viscous in stretching flows, and no could possibly be less that an extruder exists. The main the flows, drawback of all such measurements is the difficulty of with velocity and complex history and temperature to yield fundamental The only which are easy to draw ratio and maximum stress to the material has been SUI)lectea ftnrr'p./~rp.::l in thinnest The measurement is thus most for studying phenomena like rupture where maximum stress is the most important factor, or for comparative of the extensibility of mattelials. Preshearing The melt from a capillary rheometer the material is subjected to a well ael:lDe~a section may be used for preparing melts of different so that the parameter may be evalu· influence of that important, though often ated in Iilpl"!:lr!!:atp eXl)erim~ents.

2.15

Pl'p~hp~riI'Hr

The Measurement of Velocity Flow tJl1'etrtnllem:eand Streamlines As well as mechanical measurements of stress it is to make during flow. direct measurement of the streamlines and of stress The measurement of stress has been Wales: 50 such measurements 1'1"£111111'1" S()pl1llstllcaltea eql1Jp.ment, eXI)erllmc:mtlitiC)fl and interpretation but the lDltOrnlatllon which they Improvements in tracer have reclentllv measurement of velocity distribution in COlnpllex

Rheometry

33

Polymer Melts

aWlntjitative measurements on the flow 'in vivo'. The introduca qUlCllltatl"e IllldgJrnelrlt to be made of the strl~anrulJ'le pa1:tern and authors how such can illuminate differences between materials and the of various flow detectls.:J-," "''''' .. "........ of all leaks the

rheometer a study it is correction for is VdPldV where

cornpJ·es~.jbi.lity of melts. In cb~lrec~s different volume to allow

tantgellt bulk modulus,

2.. 2.7 The Melt Flow Indexer as Rheometer

The Melt Flow Index is a control test used to assess the of a melt flow rate is extremely standard conditions. a sensitive in between of the same polymerisation fami .. IV--lllnm~r ideal conditions it can to within 3 per ....... '''' ......Ju'"'' of 1 cent in molecular polymers whose is of the This not ne(~e~,ariily which have been made by different routes nnl'vtnprliO: having the same melt flow rate may vary by more than an maeDJttU(le under other conditions of capiUalry

after prolceS,SIDJi. e~.pe4:1allv eSt)eClalJIV useful indication of cnalng4~s Flow Indexer invites the eXJ)eliime:ntE~r eO(X)uraging him to the nT't'~nJ:>,T'tu

2.2.8 MiDiaturisatioD

The leaKa,~e

can be miniaturised to allow measurements to be made In a small the of as 0·1 g of become severe if a ram-driven is used: gas pressure is more A of miniaturised and

Because a COlnpanlUv'e test.

wOlrKl11l2 with very small sa110pl,es, abf;Ol1ltely necessary and then as

34 Conclusion I have dwelt on rheometer as a tool for obtamme: eflj~m4eermg data and for the assessment of materials. The Ilm,ltaltlOllS of the data in fundamental terms must be rec:ogms1ed. caJ,aOle of .......L",.,rh..,in are ne~cessal~V favour of Avir ...n,rt~jr ... on which a pnlctlcal flow in mOlulcts su[nec:n\ire assessment of

2.3 PROCESS SIMULATORS a the shortest time time-scales often so that the melt may

shc)rtc:omlmjl~s:

mlrlUte$. These Sh(utlcolmrl2S mean may aUow a true response of the in out rheometric measurements at a best is at best an "'".............." nr~("..Il·A we can do with The second alternative is to use a screw melter a material at a on which rheometric measurements can mc'tI1100:S.;):;! This is a solution'thr'u.n,n measurement can be as versatile in terms of rate there is the the flow rate also chalngc~s A screw melter also a of mattelrlal conventional ram extruder since it will take time for the eq'Ula:;_mcent eqluiliibrliul1rt. The use of screw extruders to rheometers is unlctolJbted,lv ae~ilfaOle ....... "'.("f'1I"... when material cm:ml!:e tec:hnlqlles are at their when rh ...,,,"L'f';!,, 4i:tllnr\nrtPfl The use of such as film and ...... <>10"" control tests when eV~llmltjrlg .,,,,o.l'''I~-UU of ext:)enefl(~e

value in establlshmg two materials. The of such teC:hnlqlles which may of itself ob~;CUlre which may be prc~mlnerlt pr()OllctltOn eql.npment, and versa. rt ........... "'...

as

Rheometry for Polymer Melts of all polymer prclceS.Slng. to make qualitative and co[np~lral1ve measurenrr'I"AC~C The provides information on to gerlenltiotn and time-scale to fusion sometimes to under COIl(1I1tlOI1S which may approximate to under which melts pr()Ce:SSlng. As with other instruments, and tolerances to 'run in' the surface and it is often is attained. Although it the instruments they are commonly used for rate of gelation is a critical feature to the process. The geJilitlOtn

AV~IUAnle

2.4 PRIORITIES AND COSTS FOR SETTING UP A PLASTICS PROCESSING RHEOLOGY LABORATORY

laboratory with all the equipment which would be p]rocc.:~SSU12 could cost £250000 (1980 ctectllca1tea eXl0er'lmen1taUsts to make effective use of much the A much more modest sum-£8500-will serve to equip a laboratory which will be able to meet most of the to it. nnl'urn,ar

r13£1'I1U-13

Essential. A Melt Flow Index tester for measurements and OUiuu:ative assessment of behaviour. Such equipment is obtainable for about Very highly desirable. A .. c~lPi1llarv rne:O[[lett~r ducer located in the barrel above including a will allow the measurement of enJnn4eerm2 orifice die _ This erties according to Standard recommendation and is currently AV~ulAnle at a cost of about <3 ...... _ , , ,. ..,."';• . ,

Highly desirable. Constant-stress cone stress behaviour and direct measurement of V1S1£':OI1S equipment is available at a cost of about

of low orc.oelrtles. Such

These instruments will nrrnl1rt"" an excellent basic eQ1Lupme:nt. are recommenae:a in part for electrical and mechanical SlDlpliclt:y allows them to maintained and with a minimum of eXI)erien,ce. From such a basis it may be to develop to more and techniques, the of which will depend much on the nature of the work to be """.·... ""'n out. established that it is POS.SlDle to have an effective rnt~014[)glcal laboratory for a modest a second becomes 'Can we afford not to have such a labOratto['vT

36 RBFBRBNCBS

1. 2.

U/t1, ..... I ",n,

J(n~wl'~Klcal

1975. 1 j~chj~iql.teS, Ellis Horwood

(di~.trit)Ute~d

dyrlamic response of

6.

7. 8.

and

9. 10. 11. 12.

13. 14. HenDOw 15. 16. 17.

IS9,

Plastics

J::.,n,~lneer'InK

18. 19.

20. 21. MaJrcwell. 22. Coi!'sweIL

23.

Research Notes in Mathematics No. 1979. Rheometries, Frankfurt and 24. 'Munstedt hl()ntl;atl0nlll Flow Rheometer' built New Extensional flow of nnllvlO:1'vrf'np 25. R. 1965. rhc:~ol()gy of ool'vmc~r melts under Plastics and 26. .....V11I."""'U.

37 27.

Rheometer zur schaften von Kunststoffschmelzen unter 8 1969.

der deformationsmechanischen

28. bl()n~:atlon.al

29.

behaviour of a low elong~ltiofnal

flow and failure of 1978. "",.."",lVILI. Godwin, 1981. 34,

30. 31. 32. 1961.

Doilve'thv'lel1te melt

33.

l"h"..... II',..nr

34. 35. 36.

39.

t"vtl"l1".""n

sWleUiln2.

Journal

8

""-Vj","""",u,

40. 41. 42. phcenc~m(m(J~n

of draw resonance in 1966. SpiJlnillg of molten oolvetJllvl4enes. 1972. spInning, Transactions

43.

44.

'"TJ.r".J.l.Lh

45.

Dolvethvliene melts in and Rubber 47.

HJLQ
48. :swcerclJ[ow

The realities of Plastics and ""-Vil:.i:ln,""u. F. N. and Krul, biaxial extensional

Pn/vlH...,.

l
49. 50. 51. nolvtl1lene.

in The J(fl,eoliO"RV

38 53.

l,;Ofl:sweU.

55.

1975. 60. 'Brabender 61.

made Saddle pJ\lnrn Garden

PJ~COltnar~nh7, W

Rheo~

Physical Features and Flow

The 'What is the of a nnll'l.11"r''''' ... ·,' aP1,ropriate answer lie within four orders pn~rslc:al environment. easy prC)Cel)SIl1Ill; rotational one need is for a two is quite different so environment of that which is easier to mould is not nelc:essaIlly ,",u"a.J,.I",,-,.t 6 return to the Qu~estJlon influence of the environment on relevant to such processes.

3.1 TEMPERATURE AND RHEOLOGY As heat is SUI)pll!ed

nnll'l.1"'l""'"

the molecules vibrate more ... ~:n"'11'111"

""",",£"',,,,,, curves for a

of at low tenlPerature very much less seIlsltlve ll;re:att:~r

39

40

\

\

\ \ \ \

,

\

Shear stress

terno.~ratll1·e

is the of close theoretical de'velooiine: master curves have also

been oul:>lis,heci. from one OO.lvnler molecular of tenloeratlure which Because the of VIS'C05!ltv Table 3.1 compares that del:>endel!lce the different are cOlnmlonllv orocesse
P,,"u"'I"'rll

Features and Flow

41

, " " ...... Modulus ......

- -Temperature (OC)

TeIIDPIeratuf!e-deJ)Emd.en<;e of elastic modulus and

VUU'0f;11'h.l

at low shear:

(-

energy to raise a to a time necessary to cool a material to a form-stable are also to be avoided where these may lead to ae'COInpoSltlon Thus, in we seek to process at the lowest po:ssllJJe tel1rlpc:,ra1tufC:!. but the lowest often be o01talIleCl heat The the dis:sip~ltio.n of heat if the material can be softened heat in process, excessive heat can sometimes be avoided at a later

Melt Table 3.1 Relative Fluidity Index of 10°C

for an Increase in Test

Polymer

RFI*

Branched

150 250

1·35 1·3 1·25

200

1·2

200

1·2

200 Linear

6:6

200

1·7

200 250

2·5 1·9

250

1·5

350

1·5

275

1·35

275

1·35

200

1·2

200

3·0t

RFI --,-.!!!l~~~~~ at constant stress. pol'vvirlylchlolride the 'melt' known to be

n:: 1

, ,Rate'" I constant Str~ss constant

: n =0.2

3.3 Deperlde:l1ce of vlSC:OSi'tv on terrlPelrat1.ire: polvethvllene

ten~phthallate

Table 3.2 EX)Jerlmellltai Methods to Tec:hnique

the InOuence of Pressure on Viscosity Problems

Operator

Rotational Pressurised concentric

measurement lDClep'eneJellt of pressUlrisirlg

Extrusion Pressurised

MaxweU9 Westover10

Double-die method

Choi 11

Non-linear plot

Porter12

Direct descendent of rheometer

l"1U'llll!"TV

modification of rheometer

l"Q1'\ .. II,:.ru

Friction losses. measurement derived small difference between two pressures Pressure delpelldt~nt on flow rate and die J?;eCJm.etr'y

44 3.2 PRESSURE EFFECTS pressure both free volume and leaClullg to an in VISiCOS~ltv of pressure on 1"Arlln"",..,·

measurement results 3.2 and Since the influence of pressure on is aua1l1tatlveJlv ""' ........ 1.,. .. in to that of a suitable way Clel)enlClelnce is

Table 3.3 Increase of at Fixed Shear Stress by Hydrostatic Pressure of 1000 atm

Maxwell' Westover and Itow Porter12

1000

270 250 200

50

4·8

40

3·9-5·3 4·0

30

nr~~c!c!ln"p may be corlSldlere:Cl ore:SStlLre. increases the Vl!O:lr-nC:ltv' necessary to bring the melt back to its on:gm.aJ turlctllon as

4-0

'''IQr'r''QY,..'1T

This function has the appearance of a function and it is oaJrtlculatrlv intc~re:stiIlU~ to compare it with the Isoen1troDlC function

which is the instantaneous tenlperature rise resulting from the aplPlu;atJlon of pre:sstltre. That function may be cOllVe:nic:mtlly rrleaSUl'eCl in a cat>U1::uv rheometer 3.4 and Table that if no direct close these functions measure of the influence of is then the thermoClVlrlarmC function be as a The correlation also SUf~ge:sts unreasonable between and entro[,v which would seem to merit theoretical consideration.

Pln1.Q;p.,,1

Features and

Table 3.4 Ratio of VIQ4PNlttv Polymer

5·3

X

10-1

4·2 8·6 4·0 3·3

1·6 X 10- 7 1·5

1-5 1·2 1·1 1·2 1·9 1·4

3·3 2·8 4·0 2·7 2·8 2·8 2-7 3·5 3·6

1·4 SO 0-4

3·1 SO 0-5

2·2

3·1

3·2 6·7 5·1

5·7 3·6 6·7 5·0 SO 1·7

Pressure transducer

Thermocouple

3.4 Measurement of temperature rise

It is easy to recoa:flise on ternDleratUl~e I"n."' ....,,,.1 within one or two de'!rec~s theoretical texts asume that excuSle for the

ccent:12r~l(te

inc:olIlpr!essiblle,

nrn1.rU1'lnn

cOlmb.imlticm of high pressure and low temperature cn'st,llllliatJlon of some so that in some cases will the material flow

46

VA,h,,,.,,.:>.-

Melt J(11:eO,lOIl'V

Strain

Stress

Time

3.5 Evaluation of creep under constant stress

3.3 DEPENDENCE OF RHEOLOGY ON TIME Maxwell is achieved. time-scale of real be filled order of

have a cornplete aPlueC:latlon how that rh""r.lr"nu mt'eralcts essential to gn'nr~>"l~::t1'~ and Evaluation of creep eXlpel"lm,ents under constant stress before

......

0.11'

l'

Time

3.6

Im~e-aepfmC.1ent

flow is

apparent Maxwell parameters

101'

Ph\J(,I,f'nl

Features

47

109 10· 107

/

/

106

/

/

105

G

/ 10·

/

/ 10- 2

Cvclic loading ~ (s/rad)

3.7 compan!mn of

established Maxwell pal~alTlet~~rs:

Creep loading (s)

and osc:lllaltOl:y shear flow:

at 20ne

allows the mtC:!fPret,ltlo,n of tllTle-cler)endelflt alDoBlrellt

otc.Ue:d as a function of time these cornmonlly have the form shown in

llelrWf~en

where stress and strain are n r.."nr\rt1nn!:l1 evaluation of as a first ani~UUU I1'eQUellCV and time texts, for eXclm1ple 1-<1"'11*"11,)

a series measureat constant maximum tlnle-1C1el)erldent, response in the non-linear CH}SS'-DI10IS

t1vln~rnlr

aplprC)ache:s, and from are consistent time-scale response is truncated.

48 Modulus (N/m2) Stress (N/m2)

......

-- ...... ......

10

Time (s'

Time (s'

3.8 0-3 at

DVflamjc

-10

response data in the non-linear

ratio the vU::,f"nc:tth, time-scale of a mattet"tal Deborah number, mountains melted from

retllectlna the of the timeDf()Derti~~s is the memory which the nmle-~iCaJLe for which a material has a the natural time of the the flow. the 11""1'"'1'1\, ..,11 the

process

> 1 the process is dominantly such that if < 1 the In use of this COflceltn orC)CelSS a)lal~(SIS it essent:lalllv since the material of the characteristic material. If we COI1SI(ler of a low stress deformation round a comer fol:loVl,ed we must consider two Df()cesses:

= 10

(b) Flow in the die time-scale of nr£',..p.lOt~ high shear stress,

I

100 s

0-01 s

In this case the remote small disturbance in the streamlines as the melt flows round the bend will be remembered at the die the extrudate to even the melt has dominantly viscous flow in the die with which we are concerned when collsi(lerling

P"'''~'rnl

Features

a low stress deformation is remembered after a

3.4 STRESS is stress, which may vary

3.4.1 Rupture Behaviour cOlnp.an~,on

the stress levels which liquid ~v~tenl~ with useful solids. water will cavltalte"U even when all contamnnants, the

Tnr'I"P/~rf"~ at often an indication of telltsiotn tliinnilltg and a transition to SU),ertlclalJly lDcrealS1I112 the rate at

a

t)ien2IVI()Ur

b

3.10 a b

~UI>erJtJClciUy

brittle failure failure

50 Table 3.5 Results of RIIIBhlll"ec Stress Tests: Braucbed PoJyetbyl'eue MFI 0·3 Experiment

Constant-force extension 24 Orifice flow die

150 190 150 190

nnll"C'f'''r~''np

::::=10 atm ::::=100 atm

bmefrilnglenc;e at the entrance COJTef>Do'nome: to a maximum IO\:4/-c1I~ns;ltv nnlh.lp·th'lI'lp."p the

Shear Shear modified There is also some indication a small of crj"staJIlS'atJOn. presence of toreuz:n V-V\.IJ,,,,.,, to assoclate:o with such contaminants.

0-3 0-7 slgmtlca.ntJy increased by increases the

51

Physical Features and

0' '';;

.,...

.,~...

"c:

3.0

2.0

••en...c:...

PVC at 170"C

o 1

3 5 10

OOSSll[)!e 2eller,al

e~J(pl,amltlCJ~n

of rupture behaviour is that it is associated on a scale of about 100 nm. Provided the tensile stress enOUJlln. surface tension suffices to such faults stable. Ho,mC.2elmSlilIn'u'U'n1lTPri gel:atlCm in PVC achieved use of orC)Ce!iSllll2 nVIClrc.st::ttlc pressure all to reduce Whether characteristic of tun:Clalnelltal to material or an artefact remains to be estaOJIISJ"lteCS theOff:tic.al work . ... , ....'V~'... L.., is the ultimate method of failure both in thin sections such as and fibres due to rlr!UXT1ln('r thick sections in both those where the solidification stresses cause extremes normal is most cornmonlty an intermittent is most ....:><::.£UII" effect with stress and achieved notches both in the material and in the is also the critical in the initiation of 10c:llmln2. n""i~u1l'..... 1r

3.4.2 Elastic Response as a Function of Stress

When an elastic band is at low stress the deformation is ...."£, ....., ..1-....... ,,,1 to stress and at stress the a nnl"n,,,,,,r melts. The same qualitative reSPOI!1se For nn,l"rr.,,,,,,.. melts the bulk mc.csuJUS some five orders of t1'''''''.'.:lt-.,.... than the shear mCJtCSutus for purposes,

ratio may be taken as 1/2. The bulk modulus accord!1D2 to:

""rulc!c!L'l.n'C!

with hvclrm.tatic

+9P When is the bulk modulus at pressure P above bulk at atmlosptherlC pl'eSS111re. The shear and

In

atnlosphc~nc

and

is the

may

,",-"U.'U..,"''''''

a critical role in process is elastlc:JtV is also manifested in the have a

6), and the faster a

3.4.3 Viscous Response as a Fundion of Stress The non-Newtonian behaviour of polymer under both shear and extenrec:enred detailed treatment in the and models of sotlhl~itlc~atl()fi have been to the del:>enidelllce At the um.opJI11S1:Icated level it is worth nhCtPT'lI'lna that the model des'cnll)es the qualitative of melts to both and extensional stress.

Viscosity

~

Viscosity

linear

wide molecular _ _ _ _ _ _ _.........;;w=eight distribution Stretch

Shear

3.12

~

branched

shear and extension: the distinction between rotational and

irrotational flows "c!1.~111"

of course, to real rather than the cl1()Pt:)ed lubricated with tomato sauce. If a bowlful real dj~:211112 in a fork and move it from

h,P'!:I'lftiU

,..I-ntc-'p,,.,1

53

Features and

3.4.4 Modification of Rheology by Mechanical History rl4>l'!~T'int1,.... n~

of nT'~'~Tl~~1 pr{)Ce~;su1Ig

assume an state as the sItuattlO>DS, material response at any nT'~.'t1U'Ul~ thermo-mechanical reductIon in

eql1ilibri1um will reflect the eql1ilibrium nr...,.n""rt.,,,,~ may be Slgll1ltlcarltly imt>ro'ved me~cn,am,cal urr,.rv,"nn may be the most effectIve

eOl1ililbrilum

Table 3.6 Modification by Mechanical History: Branched Polyethylene MFI 190°C/1'16 Thermomechanical

Melt Dow rate

Swell ratio

Shear modified After solution and

0·28 0-66 0-27

1·47 1·14 1·47

54 3.5 DEFORMATION GEOMETRY AND RHEOLOGY There are three distinctive 1!e()metrJes of deformation:

shear and

3.5.1 Bulk Deformation When are to hvclrotstaltlc in volume. If the stress is a hV41rotstalttC mClenenl(1eIlt of such factors as cnj:ln,~e in

solidifies lead to most cornm,onllV ~t'\n!l,rpl'lt frozen-in stress or cavitation. An class of pr(.ce~~sU1lg olperatl(m 50 per cent eXt),anS:lOn of gas reJ~~ase~a

3.5.2 Elongational Flow material is drawn from one cross-sectional area to

3.13 Elclnglltlonal flow

Such flows dominate the and vacuum torJmlIlg nroices,ses and indeed the whole class of be termed 'free surface rn~·nlrul''!.1 in flow is QuaU1:atlveJtv different from that under

55

Physical Features

Cross·sectional area A v

Draw distance s

Force F

Vo

3.14 Stress variation in volume flow rate at die

ara.wU12 of an extrudate

v U.,.I,~t"ljr"

at haul-off

stress of a

sut)lej~t

close approximation to that the stress (JE

has its maximum at the The total

nalLU·IOII

FIA

where

in the process,

e the time-scale of the process,

slv aDllar,ent extensional vlscmntv t

Comt)InJtn9; these we obtain

This derivation assumes that all the response is viscous flow, an aSSUlTlptlon which be if the melt is inelastic or if the whole nrr~",.,..~c the elastic is saturated rellatl()flShlP will be

obvious siglnifilcallt tensile deformations can constrained flows whenl~Vf~r the streamlines converge or dl\l'en:ze--t()r e;"arnplte in the and exit of in calenders and in 3.

,

,

I

,

a

b

c

3.15 Tensile deformation in constrained flow section of extrusion die

' . 'n ....................

c InJection

mOruldim~

3.S.3 Simple Shearing Flow a deformation but also a to the rneolo1fOc;al

a

b

3.16 a Flow between reilltlv'eiv b Pressure-driven flow lrnlnrn·t~t1t

surfaces

between such flows. First is the qUl~stllon rel=:ttivelv mO'Vl1l12 surfaces there is the adJlesilon lJet'wee~n the melt and the nvclm,staktlc pressure COJnponc:!nt

t1lttl"·t'Plnt"I"·"::

nomc,genec)us so that is exl:ra<;tecl. that heat must first traverse the rpl~tivpliv mlOVlng surfaces ClOmlJna1:e cornmonlly found in dies are ImlDOJ1aIlt tensile contributions

practical cc)nstailled flows

O/n,,,'''''''/

Features and

a sQuleez:m2 flow

3.17 Shear effect

aDI)earS to

3.6 FLOWS HAVING COMPLEX GEOMETRY of UI",,,,"OIl"hi

the fact that pr{)celssil1l2 we find many flows

i(len'tifit~d

....,..1'11...... .,...

3.6.1 Superposed Shearing Flows We have noted two that between rel'lltiv'elv

m(JIVU1Iil

3.18 Pressure-driven flow

thriOull~h

an annulus where the mandrel is rotated

how such flows may be treated we consider a an annulus the mandrel is .." .. ,.. .. "",rl4,,* is the volume flow rate and !J is the rate of rotatilon. tnrlOlUlrn

extrusion shear rotational shear rate,

=2n:RDIH

normal addition pr()celc:tur'es. total shear rate,

=

+

pn~sslJre-dr'ive:n

58

Polymer Melt Khleol47flV

The

eftiectlve VISI~O!il:ttv

the p=

aplJarem

Vl(:t"n'~lhl COI~re!)Po.nd1D2

to the total shear rate in the

Table 3.7 Calculated aud Observed Pressure Drops io Helical Flow for a MC1IUJdliog of PoIy(methyl at 230°C an annulus of 30 mm, H of radius 9·75 mm at an extrusion Pressure drop, P Rotatiooal

Total shear

22 11 3·1

and

and to mU'0(11uclllg

3.6.2 Pressure-driven Flows in Channels of other than Circular Cross-section

ideal cross·section. The fol.lm~ll1l~ For the of flow an:::tIV!i:l!i: cOll1lplex

3. L of the channel land A cross-sectional area

20 2b

2c

of the minor axis of the included of the axis of the included chord the axis of the die

of of

area area

rate

PI"I'lHcir,nl

Features and Flow

3,19 Flow anatlVSIIS: parameters descritting

From these

pal~anlet~ers

we may define the dinlensio:nle:ss a X=b~l

y=

1

WOlrklf:l2

re~latjion:)hiI~fur

can cOlnolex cl1,mnels can estjibli.she~d

Shear rate Stress Ull"..... tr ....u..

shear y=

+

shear Pressure

=

Swell ratios for YR >

dies

(

1-0

formulae:

60 Swell ratio for Dies of zero

zero

."",.,,~ ..... ,

(vii)

( B.,Bb : (exponential

3.6..3 Converging Flows

In rnl'V""rOllno

of a an extensional flows are much more Jde~alJ:secl flows in the as to 1) that when two ","".ar'ln ... mtc~ra':tlOln and umloubtedlv ~hl'''~rllno and an extensional dallnting cornplex11tv if the full were made. a Quanltitaltive the strain rate histories shows that at the wall of the ,,""llnL"U"l1 is zero, the shear strain rate has its maximum and the extensional strain rate zero, while maximum strain rate occurs where the is at its maximum and the shear strain flow is sUJ)el1po~,ed

PfC12nlatic view thus aIJows us to COlDP'ute the flow as determined

One

the interaction between the flows addition of the shear and extensional

ilie

fur

cyfmdlrtcal flow: pressure where is the COfltrilt>utton due to to ex1:en:SlOlnal flow and

+ Sh€~arl!Dg

flow and

is the contribution due tan 8

where ro is rl is 8 is OSI is

n OBI

the the the the

die radius die exit radius half of convergence ,shear stress to the shear rate at die wall at the Yt = the volume flow is power in the relation:ship is the extensional stress average extensional tan strain rate, £1 =

1.1£.. , ..."",,1

Features and Flow

61

3.20 Extensional flow and sbearu12 flow in a .. "' ....""...,.1"1 die

shear is the dominant flow rel:atl()nSblp between flow rate COlnp()llelnt At about If

rate rupture, the At the becomes we

stn~tcl1liD1:t

mm

130 S-1

for streamline therefore whence

the half

tan (J = 2 x 7/130 = 0-1 of convergence 6 rI"' ....."',"'.,

62

Melt Rheology

were used to effect the whole of the reduction from 20 mm to the length of the would be such that 91L = tan 90 mm. For most purposes such a would be ex(;ee,om2lv long and would to Thus we a sut)SlCllaJ":V at what diameter is this "'ctor~"',..o.rlf·1 A taper would be 45° and so, since the 7 we have

i.e.

tan

r=

i.e.

7

we may dele1u(;e 14 = (4 x nr~,.tprrp,rI

m and ro=2·2mm die for this extrusion is one that reduces the overall Further optimisation may in be

by by

"'"..",""."' ... '1 ....... flow, swell ratio is taken as oOltential "'""..... ,...h........, ..." from """""'''1"''''''

and from extension; exp

ERI

COJrre:soCtndine to the stress at the die exit COlrre!mcfndine to the extensional stress at .... """,11""'''''

and dies with contraction from 0-01 to 1·57 for flow

U!:ll"'!t1'1i'"

value Pressure Swell ratio

deviation 16% taD.en:~C1

annular radial In any of I"'n1"''''''I" ...ii1'1O' flows it is necessary to bear in mind fact that the ex1:en:sioJnal vi!itl~os:jtv may be several orders of "'''''''!:li'.", .. than the shear thus, no matter how to the extensional should never be since it is which are likely to the stresses the material and so determine the quality

Phll<'lr'fll

Features

63

Flow

3.22 Die

that allows reduction of

L

3.6.4 Extrusion of Sections of Varying Thickness In such as extrusion blow it be desirable to extrude a tube wan thickness so when tube inflated into the .......,......... , the final wall thickness can have a desired variation. A case is the of a tube into a where a uniform wall This can, of thickness is the die to the non-uniform jntlatllon

b

8

3.23 a Uniform parisoJ!l: thin-cornered mouldm2 b uniform thickness of mouldmg

one section of the the melt will flow more r~l'\u11Iu may cause the paJ1SOin to 'banana' or the end to To overcome this cannot be an additional to flow is thick-section passage. Most extrusion dies need to be well with a acceleration towards the die In one the around the is so that ..... '.f'' '........ 'I.1""I,nr'11tu and variable and can be calculated

relatlOn:Sblp shear stress to of SeCtlOllS <>,..",." ... the die we see a Qua1i1tatiive £'1

64

Melt KnleOlc:»gv

I'rtl\1"",(1'"

Pressure equa'

~

1 "

.. -'-"

1

Thin section at low velocitv

Thick section at velocity

Uniform velocity

c

-+ HN +b

a

~tt"~lt,,"{nr

pal~ISOln tJlllCKness~

has been used to obtain a variation of 50 per cent in in it has to be to maCfilDllllg has to be means of a

3.6.5 Biaxial Extensional Flows makUllg direct measurement of extension aplpre~claLtI()ln of such these are small in encountered the of biaxial extension. Measurements made on indicate that at low stress the modulus are and shear response Modulus G 3G

shear extension Pure shear or Uniform

4G 6G

much less

I.U'-''''""U

(JeICluc!eO from studies on

Ilm.lUrlg elastic response in

some indication of the solids

extension is the

in this may be more

+

PhUC.Pfll

Features

---.,.",.,. 10.

10'

Tensile stress (N/m2)

3.25 Biaxial (- - -) and uniaxial

extension: toy balloon rubber at 200C

where D is the draw ratio in the direction of and B is the draw ratio in the of the sheet normal to the direction of .....,"'nujlO,. This should be used as a ull1.rlriinn since th"~nr"O" SUj~J!:e:sts any nel:essaI"lly be tension and nV1Doltne:SlS which is of response mono1tllalmelflt rllr~uJ'in{1' and film we may rnt:~OI()2V of biaxial flows. a dominant role in film DlOWlrU!

3.6.6 The Viscosity Interface dltter,ent

If a melt flows one of two the

uu:!,f'nc:!.tu

Slt1Jatlofls can occur. before whereas through If we cOllsuier the of the central of the interface then we of the interface is define an acceleration factor N such that of the in uniform VISICOS,ltv tube. where Vis the of viscosities of new and old studies if M is the mdlca1te values for N as shown in Table 3.8-a may be

High vis1coslitv

Low viscosity

3.26 Interface behaviour of melts of different

uuu'nc1tv

Table 3.8 Effect of 'H£'........rih' Ratio on Centreline Velocity Ratio ratio, M 1()4 1()2 10 1 0·1 0-01 0·0001

Centreline 0·55 0-65 0-80 1·00 1·20 1·32 1·40

Stable

Skin too viscous

Skin too fluid

b

8

3.27 Sandwich

mould!m~

Phuc;ronl

Features

of nr.I""",,,r if is of lower a the new on the wall of the machine from which it viSicm.ltv of melts is sensitive to teIlt1oe~ra1turc~, own source of nonpffiPrtlvP

The above

this COlnoletle. it indicates that that oot:imi~ationandex~.loi1tation,

REFERENCES

L

N. and 37,

Bulk

"tel'ne.t"

of

Dolvmc~ric

':)1'':)I',",U',:).

Journal

tJ(..lir;;;ru,;.r;;;.

2.

J, D., Viscoelastic

3.

5. Johnson. 6. Malrkm,ritz.

9.

Ma~"weIL

Prl'linprtiPfl

Pn#Vn1prfl

2nd "''''''''U,II.

,",uat.Jt,",l

68

Polymer Melt Rheology

to.

11.

Determination of melt VIs(~OSlty

an extrusion 12. R.

Journal

R. S.

13. 14.

pb~rsic()·ctlemlical

pro,perties of

Lm~SWE~1I

15. 16. MelLssnler extension of pOIvmc~r 1972. 17. Macdonald, I. the

extensional rheometer for uniaxial 16 Transactions

Small deformations

Khlf!0IC1R'V

International

on

H. Influence of non-Newtonian

J. J., '-'Vi~W""U. viscoelastic 19. Deborah and Barak in H. K. 1960. 20. D. C. F. and

dVlllamlc response of

18.

LJetorP1Ultiol't. Fracture and

21.

22.

23. 24. Swcerdltow

Rip'pfr;no"pn/~p

27. 28.

to

Studies

communication, 1979. me:tl:Ulcr:vla1te C4Do()lvlnelrs as aids ShtJrrk.f,kin.

nolvmcer melts, Plastics and

29.

Comparllion of the elongcltio:nal constant strain colnp;ari!son between

31. YnIVPn,r:-r

bnJllrneC:!rtfllJl and Science.

PnlvmpY
Physical Features and Flow 32. 33.

(with 382 pOI,vm,ers in uni· 11

35. 36. rhe:olo~e;lcal

ec::tuatl011S of state,

rr()Cec~all'tgS

mtc~e;nlttea

strain 1966.

39. 40. Middleorlan, AJ ...." ......"'.

41.

cornp()uI1ldlIle; and rheolo>e;lc;al M tJ'tpriwl,fi:

and Ap,pUc'atllms.

Applicatic)O No.

44. 45. 46. 47.

48.

52.

elone;,ltIOtnal flow of nnlvml,,:r

Plastics

70 53.

"'--'VI~"WI;;U.

54. 55.

56.

·nn\/.,.,.'lYln,n

flow and flow: a cOl1npilabon. Journal 4, 23--38, 1978. of melts in extrusion

'-AJ1i/:;:)WCU.

lDI1ectJIOn mould

Plastics

57. 58.

59.

R., Biaxial extension of an elastic

60. 61. 62.

of non-Newtonian fluids-a 1971. conlmutnic,abon, 1974. Plastics and Pn,fllnlfPY!.C 39, Sandwich "T.J.J--.....u.

63.

64.

Rheology and Structure

Easy

Difficult

Service properties Poor

4.1

- - - - - 1___- -

Excellent

,h.,." and ease of prClcesismg: a common

.....n /....,. ..

4.1 CHAIN STIFFNESS AND CONFORMATION ,," ........·h .... "'1

alPP1reCIatlion of how chemical structure influences chain tleXJtJ.tll1:y be obtained of molecules from this means the molecule of is fle,[ibl,e, with full freedom to rotate each of nalrahvdroJrv benzoic acid has little freedom of ... "".rttl'" of the aromatic and intractable as a

72

H

\ /

H

H

\ /

H

H

\ /

H

/C,/C,/C, c

H

/

C

\

H

H

/

\

H

/

C/ Polyethylene

H

Poly parahydroxy benzoic acid

4.2 bXclml)leS of Dolvmc~r chemical structure

To determine the influence of chain stiffness and conformation on rne~0l()2V we must first seek some of molecular size2 and draw a cOlnp.an~;on between and a of the of the melt.

73 4.1.1 Chain Length

For a from

is oDltaule
the

nn·lun""" ..

L=

where

is the

and

of the

is the molecular

unit.

4.1.3 Molecular Aspect Ratio

Returning to the we may an1ticioalte to a first aPlprctxiJnaltiolll, ratio of molecular

of molecular and diameter COllsi(ierine; a constant we may deduce

In the

which follows we consider molecules of of molecules useful ","'L"~ ""r"t.", ... on narrow mOtlec:uUlr obtained in the polynlerlsatlon ....

Table 4.1 Rheology Parameters related to Molecular Aspect Ratio for Common Polymers Aspect ratio tOOO At Tg + 200"C

Polymer 9·1 x 10- 12 -20 10 6·0 50 4-1 100 2·4 60 4-0 -10 8-1 60 7·6 70 5·6 40 5·3 110 2-6 220 4·5 -120 3·2

180 210 250 300 260 190 260 270 240 310 420 80

770 770 730 950t BOOt 1190 1010 1210 1086 1020 1060 950

Estimated accuracy a factor of two_ uncertainty because of either temperature or molecular t Indicates

D (m)

M

5·5xl0- 10 6·7 8·4 9·6 6·4 4·7 5·3 5-6 6-1 8-5 6·7 8·3

60000 110000 200000 400000 160000 58000 69000 100000 120000 330000 150000 260000

1-2x 1()3 2-0x 1()4 0-8 1·0 0-5 0·4 0-3t 0-5t 0-3t 10-0 3·0 2-0 10-0 5-0 10-0 10-0 2·0t 3·0t 2·0 4-0 8-0 1-0 1-0

6·0x 1()4 4·0 2-0 2-0t 20·0 10-0 30-0 30-0 8-0 30·0 2-0

3 4 4 4

0-06 0-08 0·08 0-06

2 1 4 3 4 4 2

0-03 0-02 0-06 0-02 0-15 0-05

Structure

a sinlplifie:d view of

For the sake of this cOlnp:aru;on we in the form of three pal'amlet{;~rs: the at a shear stress of the at a shear stress of at, the shear stress at which

1()3

is a of non-Newtonian behaviour, From these three terms we may derive the palranlet1ers fO

and

The former is a characteristic or natural time function. strain or Melt rne~olol!V
the latter an elastic shear makInlg as necessary to make any The choice

mc'le(:ult!S may the calculation of can metnet
Intl"\t"tlun~ltpll,\l

Table 4.1 magmtueJle for rioT"''''''',,,,,,,,,,,, nnihln'&>r~' we of the structure. attribute the chain stiffness to the t1e'~ibilitv

ratio at 200°C above but variation so that the ratio From this we can deduce on the stiffness of the chain. the non-Newtonian of the as defined the shear the has decreased to one-half its low shear also varies with chain a correlation between non-Newtonian flow and orientation, is one The which seems least consistent with the H.lVUU.JlU.".

Polymer Melt Rheology Table 4.2

related to Molecular Weight: PoIy(metbyl methacrylate) at 210°C

Weigbt ... .,..,.n"...., molecular 34000 75000 160000 360000

2x1()4

600 16000 400000 8000000

30 x 1()4 8 x 1()4

3xl()4 2xl()4

tleJnlJlle comonomer in tenlJ)erature and so the ",,,,£,,,,,£,"tu and so is by flexibility of the lJac:klJ4one by the use of the comonomer, or by lDCre(llSllll.2 effective cross-sectional area of the molecule the of pla,stic:Js~'r the to an enhancement of nonNewtonian behaviour and so a further reduction in under any high shear condition. Thus, as a aplprc.xnnalt1011l, we can observe a common n~t't"U"n determined their cnt!ml[Cal ture. may in two ways: as a which to Drc~dic:t the of a melt from its chemical structure, and a of dependent on chemical and as a framework within more detailed to another. is not a rule consistent with an intuitive a01Pre:ci3ltloln eXlstelnce of such an empirlical to such a 'rule' and the~exc~pltlolns. and One such exception calculated that rodlike predlc1:lOn has

77

Xhleol<,R'Y and Structure

low 'H'c:!,f"'nC!1t'l state is only seen once the material is sheared rest there to be evidence that it is not results the 'H1c:!,f"'n,~1tv which

4.2 CHAIN LENGTH AND LENGTH DISTRIBUTION det.ermliniJlg the

Molecular

eXI)rel)sictn as That rell:lltIOlrlSnllJ)

true for a narrow range of molecular wp:tottt~· a sug,ges,ted aJ)l)earS more aJ)1:)r01Pn,lte:

+ that the 01"P'!:lt&> .. the orCIOalJlllltv down under Molecular and number average

del:me:Cl in many ways, of which are the most common:

average

Mw== == one which may different m,ole,CUHlf weiolhtliL For to

104

105

Shear stress (N/m2) ble~ndin~

s8nllplces of different molecular COlnoc)ul1ld blended conrtoound blended

Oft

Number molecules

.....

",,

a

b

4.4 a Molecular - - broad b Narrow c Broad MWD,

en1tan2lements per chain

79

Rheology and Structure

Molecular Distribution A major variant on molecular is molecular distribution (MWD), poJlydlspiennty index as the ratio of to number usually aVf~ra"e molecular sarnplle has a narrow molecular of so that a similar stressed flow. In a of broad molecular chain molecules appear to form a nriltp4"tnrp netvllork hrA'thr~.. n 4.4). assurrlptJlon that it is the which resist del:onna1tlOll, nnlh,",,,,,," of broad molecular amount of the total stress. is causes elastic response in those which retarded by viscous resistance as the smaller molecules conform. in a
>

-

Q.)

__L -____________________

-...

.~

( /)

j

Q.)

8

~~

Time ~

4.5 Effect of MWD on strain recovery after - broad MWD, narrow MWD

flow

If we assume that it is stress which orients the so reduces a second consequence of the uneven stress is that the at a lower average stress tail is in on of of low molecular the flow curve shows two distim:t a transl1tloIlS of non-Newtonian response: the first occurs at a low ~vp'r~('J"" stress is the few long molecules, pla.ClIllg stress; and at the same stress ummodllJled low molecular The more response for of tion shows a more .... r<:>£111·"'1 Note that while two nnl'Vn1f""rlO: Ill\JlstI'atf~d VllO:f'n
enltangle~mc~nts,

Polymer Melt Rheology

-

", ,

, "

-

104

103

10'

Shear stress (N/m2)

a

,,

,,

, \ \

\ \

\

\

\ I• \'

I I

,

•1\ •

104

b

106

Shear stress (N/m 2 •

4.6 a

- -. 185000

15000

81

J(/i:eo,toR.'V and Structure

4.3 CHAIN BRANCHING

Linear molecule

Branched molecule

a

b

--------- -+ .c

4.7 a Branched and linear molecules b Shear flow c flow

N 106

E 'fii

~

~

8

.!! 10 6

>

10 6

104

a

Stress (N/m2)

---'""1.""",---Stress concentration

/ b

~

Tension thinning

Tension stiffening

Necking

Uniform draw

strc;~tchin2 flow behaviour of linear (- - -) and branched MFI 0·3 at Istre b Effects of stress concentrations on flows

Thus similar in other tests may be a to stress extensional of to flows. The for the in increase with stress means that local stress concentrations are less

H.1l~eolof}.~v

and Structure

83

flow br
ch~m2Ie.

"'.C,"'''U:'1t"U on ternplera,tU]"e twice as sensitive to ternp~era.tUJ~e clear that it is not the short l"U·"''''f't''oAC since the t"Al'nn,"'1"Q,tUI"A cs=>nCl'iti'l,rlhl

We may also note that the sensitive to mechanical There is also evidence are rather more shear thinniln2 These ....++.....'An.,..""..

4.4 MORPHOLOGICAL STRUCTURE IN MELTS

find a basis either in continuum or in substantial evidence that the molten " ...... n1"..... h,"'> .. " but contain other levels of which that is cornmonJly plroc~~sst~d content and for there is " ... ,... "",,,, of scales from cluster flow mC~lec:ulf~S are to accrete and flow assurrlptiion for such flows. The size and between" the clusters are assumed to be ,,1"1"£...... ""1'11 aepel[)aC~nt for it is a feature of all where a that the is very sensitive to such nnl11I'1'1''''''

,..,..,'"+'',110 ....'''

84

cry'staJltIle polymers often in the same tures several tens of above nnl!vrnIPr.;: is accentuated rec~ry!itajllisling

po!)se~)s

a remarkable memory of that to tenrtpe:ra-

to In we noted three ditteren~t::es in extensional flow in the of the rhe:ol()gy history. features SUJ1~ge:)t determined h"",t'Hnl'I011r

me~ch:amsm is identified. While all these responses are highly spe:CltllC be considered an sensitivity to exception rather than a rule, there is nOltnlJ!1f.l. rlle(JllO'~Y of such "'v~tp",,,, thermomechanical which distmgUlSh(~s from that of 'normal' It presunrled which can be djscolmt~ed: dramatic effects onl~mlatll1lg structural effects may essential to note that a prC)Cel)Sll1lg opelratltOn that the of a material

4.5 BLENDS, FILLERS, PLASTICISERS AND LUBRICANTS with be noticed that nnl'l1rnp.n:z pla,stl(~S but combination with ad(llti'ves serioulslv deficient. It

85

,, \

103

"

,,\ \

,\

'\\,

102

\\ \

\

104

Shear stress higll1-visco:sitv incl[)mlpatjlble

nnhilrnprc

at

275°C

staOUlsers, mould release aimed at COfltiD:nilllg refineS()Ptllstlc3ltion in the nnllvrntprc

O'TP'!:ltl'"r

and apt>ears pr(,l)al)lv aSSOCJ,atc;~Cl with very CllSpeJ:SlOin at a 1 ~m level. The flow be deformed to an empS()lo. lDCre(]lStrl2 the surface area . That work to be but such work is recoverable on removal of the stress as the reverts to its it is desirable that the continuous so that work is more done to j:lrtuP"'p it is to construct a blend of a amount of 10vv~v]iscc)sl1:v with a small amount of this most

"'n ... "'t ...nrot ..... n vu.,uu,.:t.

u.", .....-u,d-"

86

.:...... .. ~

... "...~ ". ....

"

Shear stress (N/m2)

4.10 Blend of 66

InUJr_v1'i:t"n.~ihl

... "Irtn" ........

lOW'-Vl!,CO!mv

-

DOI,,,mers at 285°C

blend

cornp!Jnfmt. The

--

of blends is the concentration of the A review of the

-

,

"

\ \

10"

Shear stress (N/m2)

4.11 Effect of low Base 0·29 volume cone.

ratio filler MFI 20 at 130 C aspect ratio filler Q

f(hlf!OIC1.2'V

87

and Structure

mc)Ortlccltl()n, tend to increase the U1Co;,f"flC!ltU prc~po:seo to describe MalrOll·Ylerc:!e n~latl0nsllllf), that I have found eSP'ecI:aUv

"

",

---~-~ ...............

",

...

"

\ Stress

4.12 Effect of filler concentrations Base pol'ymc~r Low aspect ratio fiUer Agglome]ratc~d low aspect ratio filler aspect ratio fiUer

88 resistance to COIIIUloction with

Molecular

----~r;::;. lUb'ica1.1 Plasticiser Temperature

Log shear stress

4.13 SUlnmarv of factors afft:,ctiIlg the

Vl!i:(~ositv

of

pol~rmers

SpatC1l1lg out the molecules. Their most obvious effect is to tend to reduce the elastic modulus of the stress. The effectiveness of a platstitcisc~r cOIlcentI'ation, cOlnp:atit)ili1ty and "1C.(,l'\C~tf''I.1

or extenlau The effects of fillers the other factors mtluenC]lng

1'">-.,._.....,"', the mtJlueloce microstructure of the ......".£'1.. "'1factor, The pr(.ce~)sil1lg ht",t", ....,

gellerau~,eCl 'liQ,('ru~thl

with

89

structural is sometimes the shortest route to i"1~rit"l1tni(Y a situation. To this a simple measurement such as Melt Flow Index on base polymer and the end-product should be included in all studies.

REFERENCES

1. Courtauld Atomic

IYIUUta:s.

2. 3.

4. 5. 6. Morgan,

7..HU"I\.~U.

8. 9.

11,

10. Uraesslc!v

12.

14.

J

a\.uv li\..

15 .......... '.h'VU.

on the Structure

Journal

Pn/u.,...." ..

Science

90 19. C02:swell.

On the Formation oresented at the 1980.

Inrin"t,r'u

Molecule C:on:ferienc:e on

20.

22.

25. 26.

27. 28. 29.

30. sUS,peJIlSliOns from unimodal

31.

32. on fibre orientation in Journal Materials Science, 13,

"l(:f'n<:lhr

of the effect of mIlectJlon fibre filled nolvnl'onv-

,-,"UIULI""'J.

Five

Adventitious Flow Phenomena

The success of a a desired the

plaS{I(~S pro(~eSSm2

opelratl!On

not the aclue'vln,(1 of energy, but also The most obvious ex[)re~;sJ()'n is the occurrence of in the CO]npleX is the of order in the dlt:ter~ent directions .,.""run',-",£!

92

Polymer Melt Rheology

5.1 PLASTICISATION incidence of a All machines have a limited cal,at'1111tv slightly surface flaws) above a critical output rate, largely mClep,enlaellt of such factors as nominal melt tenlPeratlure nnlun"tpr grade and die is most commonly ascribable to are continually pushed to this limit. The fact makes this a common form of defect but one which is ex1:relrne.lv positively to ti1pntt1hr S.2 CHEMICAL CHANGE cn,lnll~e

alters the structure and so nec:ess,anJlv time of a melt prclce~.smig oner'abon--t1vnil~alllv

~ueo'r~CJP

average dwell broad time distribution which is eX~l22terated scrap material. Further, the history is elements pass a mechanical proportion may be shear (for eX(llml)le, the flight and wall). In a well streamlined flow small spaces where material may remain static for very but from which it may disturbed to enter the flow. In a normally stable melt it is with such extreme elements of material (maybe less than 1 per that we must treat, and with their three products: cent of the total crosslinked gel particles, low-molecular-weight polymer and volatiles. If crosslinked particles are formed in the they will <::In,....,.<'.:.r as ne1ter!()2Eme:It1C~s in the final product. Because the are rubbery, can deformed and attenuated and so with a remarkproduct quality, may act as As well as strless,-concc~ntrating features nucleate other such as rupture in film or fibre pro~ce~isin2. By serves to lubricate the flow. held up in a dead space, may to do no harm, but any continuous process has some instability which serves to expel such material at random the main stream. of the flow is lubricated and eases the When this a local flow in that rise to a thicker with a long fading tail like a comet. on the of and the with which that enters the flow, defect may appear or mild and continuous. In the latter case it is sometimes problem by the deliberate addition of a lubricating well through the polymer. Because the low-molecular-weight polymer is as a lubricant it may be difficult to make a positive of this nomenon, though it may be to construct lubricated situations for comparison. Extremes of may lead to volatile formation producing bubbles in

Adventitious

5.3 INSTABILITIES ASSOCIATED WITH A CHANGE IN VISCOSITY "-'_ .. ,"'.....'.., .. 3 we noted that a melt of lower while a one of In the former case process is the latter may to come to equilibrium, elements of the hlah_\J'1~1'.n~11rv melt the flow for a prolonged period. In the flow of one n~il""""A" another it may then appear that the flow of the lower UtQ,(>nCl'lhl inferior-the meek often blamed for the ...1t"."'r""lo ..'1'f'u~" extrusion to select an op1:imum material,

5.4 INSTABILITIES IN

E.tA~L.lUJl::..l 'U:!.tUI..JCI

SYSTEMS

or ntg~n-lrnelt1[lg of similar magmtu(jle as in film or fibre exalgg~erated in appearance and may act as nQ,rl'tr'iA'"

94

5.1 Flow in a disc Maximum orientation - - Orientation in final mouldliml :5n,laU12 denotes orientation frozen

5.5 MELT ELASTICITY

U.I'''''''~,.V''

lDllectlon uV,c"L.J..",. The mae:ni.tucle m",

mouldine: by means of a that it is That nr(1.C11](~e both skin of the ""..."""'+"" ... + in the central

95

Adventitious Flow Phenomena

Weld line

5.2

~el)afl:lttclD

and reVl1eldlin2 of flow past an obstacle

to millimjsiflg onenteo, but that OnC;!ntiCltlcm SllOSC~Quentlv Because the relaxation of order is a low the relaxation time of the materml--ttle A indication of the relative rel,aXattlofn to be of materials and under different conditions is to COlnp,are the characteristic time of the material with the time scale of the of Deborah Number low ratio indicative effective relaxation. 5.6 MELT MEMORY

The fact that melts possess a memory, rise to such effects as orientation and allows to remember non-uniform ctetects. of which and lumpy tre,QU(!ntJIV encountered. pa~;Slfllg an obstacle and rewelds downstream of that in the of the weld be

96 time for the relaxation of those local stresses. We may note that mcrealSll1Ul the of the reduces the rate of rel,aXfJltJO,n sec.anltIOfn occurs in the shear teJ111pt~ralturc~, nor pressure will ehInin.ate dlsltnbute weld such PflltlCl[)leS

i round ~ across

~ round

i across aU across

5.3 Weld distribution

means of a

mandrel

considerations The t>eJldlnf! of the streamlines under such if at die may cause the extrudate to bend or 'banana' an effect which may sometimes be nA ... " ...... "" the ...,&:•..." ....." of laminar flow fields. the case at the of oDmple:x and ""l"l1it'.1I'1'I;1

mtJrodluCltnf! a relax,ltio'n zone in the material's In all these cases the relmjrernell1t It matters not at all if that peJrturb,ttictn is small in to strain histories: some memory of it will as as the characteristic time of the material nPf'tnl't(! Features such as 'choke' ... o.,~."£""'''' and so in the process, and can IffiIOr()Ve wiJI do to relieve a heltero,g4em~OltS cannot be de!il,grled •...,.,,,....,. •.*<:"',* tool.

97

Adven:tittc,us Flow Phenomena 5.7 MEMORY IN STRUCTURED MATERIALS ma1terials~ of structured melts whose orJltartiSCllti(Jln thermomechanical tellll[)C~ra'tur!e.

oro(jtucces a easier tlo~Nmi!. _'-"""'r",,,,,A each deformation tenl0e:rature than the oreCe
•• ' .... .,

5.8 CRYSTALLISATION EFFECTS ..... QJt

"",,",u.,,;u ... J

high stress combined with most below the nominal structures which Such and

......"',rh".."'"

appear as and indicated that controlled stress may lead to with enhanced cnrst(lUll,atllon rate under stress is an In'1nr\lrt!:lI'lt OJ),eraltll1l2 conditions of free surface flows such as

98

Polymer Melt J(nleot472V

Shear stress

5.4 'Forbidden' shear rates

material the While most cOInmlonly nl!'\~fI'rvf'·rt also been detected in pojlytc~tf(lthJIOrlethyle:ne, molecu1ar in

nnlll.1nrnrn/ll"nfl'

the discOlltiIlU11ty associated extrusion from an orifice die defined shear stress in suggests that it is indeed a pncenc.mt~nOln

BRII.lld-uO

of

Low swell Slow output

5.5 Flow in unstable

swell output

the effect has of

99 of notes that the COilstl]ctlon on the die land near to the die sufficiientlythenhC!tTn~tU\n

5.9 THERMALLY INDUCED INSTABILITIES 'lnc,£"oc' •• "

cnj:m,~e

can lead to unstable flow. VISiCOS:ltV COCJtnR;ie. and viscous "wnnof'"r-",... t source of

V"""!:l'f'cnn3": notes the which can occur "'1,',",""",I""U m()UI~clmll! or extrusion when a hot melt flows a cooled Cmml1lel. section flows slower than its section cools more ..", ..... £111" becomes more while cools less .. .,.r'urlll.., f'ln'irlit,,,· an unstable which can

Hot wan

--+ Coo, melt

--+ 5.6 Effect of a constriction sublse()IUell1t to flow of cool melt tllr'ou~~ a hot section

While the flow of a hot melt Tn ..,,..,,,,,,,,,, a cooled sec:u(Jln ~1"np'~TC mlJlen~ntlv um;tat)le. the flow of a cold melt a hot section can also a constriction Here the VISiCOS:ltv ... 'f''''rI ••~n .. flow is tolloYveCl eXl~O~leCl to the intense flow at the break up the The flow flow is slow the whole a ternp1eraltulre ... > 1, where a is coefficient of thermal dltfus;i0I1. x is the half or if it is fast en<)u~:n 'rgrUPlr'lY

100

5.10 NON-LAMINAR FLOW More has probably written on the sut)Je~ct of 'melt fracture' than any other or notoriety, which might be rheological phenomenon of disputed by normal stresses. As oligirlally 11.,,"Ci"'lMn,:,11

origil1latf~s

pany COllstJ~airled

i"'r\1",u~•.,.ftill'\c"

Recircullting or'dead

with the very tensile stresses which accomflow at the entrance to extrusion dies

.~I~ ~~~y ~ltJ ~(6 ~:;-Iamln.r ~~ (,\> 1'"\

I

\

Rupture at entry

\ .l Triggered in die

Chaotic (tension-stiffening melts'

Regular (tension-thinning melts)

J

5.7 Non-laminar flow

Phenomena

101

Pn~:AihIA site of initiation of non-laminar flow

5.8 Restricted 'choke' section

may accumlUl~lte, reduce the and so rate of extem,lOll, not exceeded. While the should be sulJllected other common sites are or bars to mc:re~ise nrl"4:!~llrA in the of the relative flow rate in rt.t'·F"" ...,"' ...... the die Non-laminar flow defects at such flow. remote from die the As a result of many prc'ce~;Slllt~ Oloerat14:>ns laminar flow at extrusion rates two in would cause 5.11 DIE EXIT INSTABILITIES

tensile stresses may also exist at the die where the surface accelerates from zero inside the die to the extrusion 'l1AI.nL'>.1~" If the surface stress the then

surface breaks. The crack so formed into the I'>vl~ ..... rto1rl'> surface from a loss to the texture of -"hal'''''''''',," be from a micro metre to several millimetres and of cmnp.araDle ampli1tude. The is if the able to ela.sti4:;allly so that skin can stretch and the stress SU[)SeICluc~ntJly relax wltholLit ex<:eedilll2 the critical materials of low elastic are thus less

also assists

stress relaxation. Surface filled or otherwise cornmonJly observed in less elastic.

aelDol>lts may not, when corltarmnate the extrudate so pf()CeSSlm~,

Somewhat to this class of defect is an mstat)ll11ty front of an Here the front is Clllt'UPl"tp,t1 deformation 5.10) should the front rU[Jtture. tnrou:g:n. The burst is transmitted to the surface as a confer a decorative and the process of stress ......."'.I"A."'t1~ in a

5.12 COEXTRUSION INSTABILITIES

The search after desirable combinations of n ... np,rt" err"''''"11'n in coextrusion This tec:nnol(~2Y £ ...

have led to with it a new range

tenaeltlcy for a maltenal makes it erA ..' ...... ':1'II1.1

same

'l11<>,('>n<>,.i"u4L.

A

I

3

""

Shear rate

5.11 Inters,ecttnJ?;

vis,:ositv/~,he(u

rate curves of two oo)vmiers

Adventitious Flow

103

t'n4~nOtmt:~na

Shear rate profile

As combined

After extrusion (rod)

After extrusion (sheet)

5.12 Shear rate

may cause distorted interface

or lower than the main stream. If the two .....nl"I....,,"'".,." families such that their flow curves intersect difficult to obtain a SatlSnlct4Jry in a 'black box' and sut>sel(luc~ntlY StlblC~ctt:~(l driven flows nelcessal'UY A match elasticities interface may stress effects at the interface.

different

Secondary

Primary

5.13 """"JIJ""," formation where a

stream meets a 'weak' stream

104

Polymer Melt Rheology

'normal' stresses at the 'I1AI .....",,,h, dllSC()ntmullty for two streams of equal vi <:t.l"nc:!l hI the other. Problems pressure fluctuations in the thickness of COCltlIll2 A further form of coextrusion defect is a ... "",t."'l1ltl,,,lu observed in thin of a melt on one ViSI~OSlltVJlS,44 (such are when the die tnrlous~n melt flows is This class been attributed to 'draw resonance' associated with the flow of the surface of critical thickness sheet extrusion: mSl:alJllIty if H is the of the sheet and N is the where h is the ratio of the of the to that of the main stream. An alternative or a similar has been in terms of a critical shear While as an event, as that it a defect sometimes described as 'runny paint' other observers have can a effect for decorative finishes'.

5.13 STRETCHING FLOW INSTABILITIES processes blow and vacuum TrU'rn"nn achieve a thin, and sometimes onentea, sectlolll. If the stress in such a process exceeds the 1"lIl",tllt'P catastroJ)hic:allly lr,t""'~1"1I'nt""ti or a hole is torlmelCl. its own in pra,ctl(;e "'1nt'I1""" OC(;aSlIOnal pJllerlonleIllon associated with stress raisers locally mc:re,lSlfU! above the rupture threshold or that tlmeshold

to

Less which a continuous rl1"~l'\J.l1lnn nrc)Cp.l~~ becomes between thick and thin sections-a sometimes as resonance' In processes such as blow m(ml~ClUlIe: and vacuum thin may be observed. The effect is most in where resistance to ex1:enSlonal flow decreases as the stress level increases and is to 'neClune:' Resistance to deformation of '"~t"rU:!tt'l1 while in some may as int"rp!:I~pc at modest stress levels elastic modulus increases mc:re~lSIfU! stress so that at stress the deformation may In both ends of this n."·1'...·'" observed if the process COc,tUlle: is observed to

Adventitious Flow

rh4~n(;~mEma

tralllsition to a more favQuJrabJle

~OS,SiblUtv

of

break bV

c:

.~

\

';: tU

\

>

::

Viscosity dominated

~

,

Elasticity dominated ......

-

.¥

u

:.c

Rupture

~ ',~---=~----------------------~~~~LHaul-off/extrusion rate

5.14 Thickness variation as a function of haul-off rate

local variations in Vlscm.ltv'-lthe the more vis:cous--l eaclID2 local variations in Vlcf'nc:dv relJtresent real dltitercmcles but may reflect diflrercmctes ture or variations in structure from the thermomechanical the process The conlblflatU)n from a thin or narrow may lead to a "'11.,·t-tu~T' form of annular die and a SUl)seawent dralWIlUZ If the melt of the die or the .,.'V...........,u·

more to

£1T'!:tUTllno

i

I

I

I

bead

Curtaining

5.15 cirlculnfe~re)lCe

bead and ·cnrtaj.ninlJ;f

is unsu[)o(>rt(~d may cause it to fold inwards or 'curtain' The eXistence phten()mc~na may a close control of in certain critical processes. The material from the middle of a flat film or sheet die is under a constrained extensional flow to pure shear. That at the of such a die is Thus a three element ap1pr()xilmation

106 ...

/

\

I

\

I

\ I

\ I

1

extension

5.16 Schematic

nj~a"~1m

",. -

of 'neck-in' and

Long draw

......

,

Rupture I

.......

I I I

-;

Haul-off/extrusion rate

5.17 'Neck-in' related to extension rate

5.14 PHENOMENA ASSOCIATED WITH SOLIDIFICATION As a polymer solidifies its "u"·t"" .....",, the difference between the

nplrU;lH'v

melt can be as much as 25 per cent. :rYistaUls,atlion is a nucleated cOlnp()Sitlonorofpn)ce!~Slf;lg

be

nlcrtnrtpn

at room ternpleraltUlre nu~cle;atlC)n, as a result either of nom(]lgenec)us then the surface of the Such can sut,)e1cteo to a deformation as it

Adventitious

107

Phenomena

cr\l'sta,ll1s:es, since the alr~ea(JIV CJrYSlraume deltormaltloln more than their ~1'n,nr1r'\h .. sUl~roun~dilllgS. of the section and thick secltIOlltS. 'nlC

atllrlOS'llll,erelS. a is es]:)ecIallIV PlnrrIUr!:.opi1 if there

elliptical section

Void

of thick sections

5.18 Defects

Conclusion The

and the from the more IIlst(;~ad phl.lOS,optlV of

that of 'melt fracture' and rp£1I11U'P more elusive del:ects, such as 'lulmptm~~ss' delicate definition and SUl)DI·es~nOll1. still of 'melt fracture' used that there is still a sur'nr~ess1ion and eXJ)IOI.tatlon aSSOCJlat~~a with ....r.llu ..... "" ...

REFERENCES

1. 2.

Structural foam mouldm~ with 1979. Note PP TD leI

1972. 3. Borocz, L and Kubat, J., Phase seV1anltiotn Plastics and Rubber 4

surface J..-IUIUI;#'U.

4.

flow of

19

5. :SChmldlt.

6.

and

7. 8. 9.

10.

Modern Plastics

Dollvolefitn films

11.

IntllUelrlCe of formulation on the cornD<)unidiI112 cornp()unds. Plastics and Rubber M(4~terjrats

12. 13 . ...:"'... " .......

15. 16. .,,,...,....."' ...

17.

MaCklc~v

18. :southern. 19.

D. behaviour of stress crvstailltsc;:d

1977.

20.

21.

22. Meltzger. 1964. 23.

Unstable flow of amorplbOl11S

l!,n.gmeermg and

11

n.nlv:me'rll:

tttrmlgb caa:.. n~tnes,

4,

Adve1i~titijC1US

Flow

t'hj~nO'mE~na polvm~ers:

a second site of melt

frt}lr-tnlrp

1963. discolltirluil~intheflowcu~esofool.vet:hvllene.

Transac27.

"t:lIIUlcUU,

28. 29.

30. Plastics

3L 32. 33.

34.

Transactions and Plastics 37. HulilmBLnn,

Journal

38.

Transactions and

1975. 43.

110

Melt

44.

Interfacial flow 35th Annual

45.

46. 47. 48. 49. 50. 51. 52.

in molten

8 Science and

53.

1967. effects on

54. 55. 56. 57.

in

MSc

Rheology in Polymer Processing

6.1 INTRODUCTION

The orecedltn2 cJla.pters have eXI)loJred response in nnll"....""... melts. The response may with """"I"'i-1I"'
&l>vf· .... ,-i
mould pressure tec:hnolc)2V Dn~c11.1de

the

112 A

, 0 "'I,;

" ,---':IIp---A

Q!)

o u

c Number of mouldings MOluldllD~

costs related to ofclducticm rate

economics of the OfClce:ss. available. While there is a wide range

sulJ'lectea to a Four distinct

Material transfer-the tec~nnOl('2V to that at aplplu;atllon of deformation processes to achieve not but also a orientation. -lllStlalllv ro,,.rnru·.c",,,c the of removal of heat to achieve a form-stable but can also involve such CO
concentrate on it in more a problem, for the obsession that extrudate on.gmate in the die may lead to a fruitless detail in quite the wrong Personal eXt)efllen(!e to the admission this is a easy thing to The can be avoided is to the .......,,. ... 1&1> ...... While it is true to say that some may have SOI)hi!)tic:att:~d SC1Jutlons. Freeze line

6.2 Pollvethvlene film blo,wiIUl process

JO{lI!CUUl in the right the solution is usually consider the occurrence of a

reliance on heat l'f""""'1"<:at""rI a DOlrri(h!e-lil~e in ex~cessiv'e

or uneven because of local shear regIons, may as

of the feedstock may uneven flow of the material into hopper or the adventitious incorporation of amounts of or other volatile materiaL The screw chosen .....,.Iu..... "'.. tives as lubricants and DUtmc:!nts. A worn screw which oel~mits

114 the flow tnriom;~n tc::m[)en:itUlre glraUlents of the memory of a turbulent screw-may all account for a extrudate.

to a U01"'",,~hfT UraWtflQ' nrocess will to eX(llggc~ralte and may itself

~ry:stajlhs,atj4[)n,

which may vary with

a

or

may be uneven. CO()llDr2 rate interactor result from

CO()JlDISt air may cause a mspec;tlCtn of the ......r,rln,,..t and of the pr('ce~)s the source of the or to eliminate Imme:(fUlteJIV obvious then eXlpet'lm,ents pf()CelSsll1lg rate and tenlperature COJ1CllJSU)nS can be checked All the of proceS~>lnSt and .rI""nt.lh"

1'h.,>",lr'..,."

of the

115

B

A---__'_, Shear stress Knieol~()~u~s

alPPJ'oprialte to different processes

ln1,pl'''u~n mCluHltn:l!:. while C is most aPI)ropn:ate to blow mClul(ltnll!:. "-'"......."....,.. 4 identified how these different may be attained. To out different are we may l"1<1C'C'liru flow processes five groups:

Low flow prc1ces,ses J,".UAJ,1llJ::. flows Constrained flows Free surface flows Bulk deformations viscous or

Each class of flow may include response.

elastic

6.2 LOW FLOW PROCESSES This class of is determined material under low stress includes most of the prc)Ce~SSt~S teIISl()n. gr~lvit.aUom:l1 forces and stress relaxation are isms.

JiioJ

u u .. ,,""' .......

process, which determines the rate at which a rotational ""-~''''''''JiioJ of are sucked into a of

2Jtrs where s is the surface terISl()n. and v the Each paI'tlcJle of melt x is formed in a t

116 Powder resistance

Melt

tension

t t t , t t

t t t t t t Heat

Heat

6.4 The smt:emlg process

is not heat transfer eX3.mple is in Table 6. L

This reJfltlOJDSh.ip be if the n'2l1....1t"·I#'OC! are too

nrt"V"A,t:'C!

as it may

Table 6.1 Slnlerinl of Low-density Polyethylene MFI 20

Thickness

3 X 10-3

Temperature

130

170 210 250

Viscosity at zero shear

Surface tension

31 X 10-3 25 20 16

Time to form a glossy surface (s) Calculated

Observed

1400 780

0-6

1600 640 270

0-2

120

5·4 x 103 1·8

390 300

6.2.2 Deformation of an Extrudate under Gravity Deformation of an extrudate is a low stress process. bX.amlplc:!s flotation of a thick cable Co(ltlDt2 nn'l.lll'2lrt"lC! over a centra) core t>ec:aU!>e the melt in a The shear stress level Pf()celiS is of the stress = (R-

6.5 Buoyancy causes

For a

IU!cnnlinll' medium -

of a central core to float UmJlar4:is in a

bath

melt 30 mm diameter t't"u,I#'Orino: a central core 10 mm the stress level is of the 50 N/m2 that the nrl'"\nI"lrlinn'!l1 to the thickness of The time for del)end on the b"n1npr~tlln'p f,tnlldlc:!nt and the square of the

117

I

Cross-sectional area A

6.6

thickness of

coattm:~.

of an extruded tube under

Thus

total deformation = shear rate

x time shear stress x tmle/'V1SI~m.1tv

and is The sag an ~vt ...nrl~rI eX,lmlPJe of deformation under ,.,. . ".ud'u In such a process

blow m()UIIQlIl12 is another extensional

stress where I is the A is e is the g is the l'vrnr;;.Uv

paJ'lSCJ1n

rlPlrt
constant.

this stress is in the order taLPe1reo so that a

t)ec(J,mc:~s

smanc:~r Clross·sc~ct]lon

stress Strain rate Total strain Total deformation eX~lml)le,

=i =i

=!

=!

total deformation of 0-1 m would be obltalIleO l

must

c ............n ......

118

6.2.3 Processes Associated with Relaxation of Orientation after Flow Df{)ce!,S the stress levels and aetorlloatlon

QUlillt,atn'e rltleC)tol!!IC,al

n~St"Omie

and

sJ1t~aflln2 cJ1~lrajctelnstlc

in

Modulus / (N/m 2;"

Characteristic 'time (s)

103

,

\T

\ 10"

Shear stress

6.7 Relaxation of orientation after flow:

104

105

Shear stress (N/m 2 J IO'W'-l1enSJltv ru:llv~~th"lef1te

MFI 2·0 at

AJtJ1(m~.J1 the characteristic time is very short at stress relaxes that relaxation is acc:OlrlPamed the orientation molecules. The final of the molecules is a when relaxation zones to allow a material to or to form a uniform or when sel1ectm2 Dolvrniers m()Uj OlIlL2 applltC:iltl<mS where a lack of orientation is ..""'e......""rf rJ1(~Oll()glcal response which must I

6.2.4 Wetting of a Surface by a Melt The wettlllll!

Conclusion Low flow and as a result have received attention the literature. In such processes we tend to be ae~lllllig with stresses which are either internal to the material or external to the process

119 outside our control: it is thus difficult to find oel,lRller can manoeuvre. The need to locate if low flow processes have a very

n¥~. . . ftrl

6.3 MIXING PROCESSES The of flows unclerstalllOlnR. Almost every plasttC:IS1I1R lflaCJiUuery element so there is a COlfl1PoundjlnJl: machines based on varied prInCIples. discern four "~¥nAtC'·

manujfac1tun~r

apJ)llc:atl()Q of energy

6.3.1 Dispersion

He:SlO«es the method of actlllevlDll OlSlperSlOlll. at which it is attiempte:d h@l~~Vllrv worked is also critical. If the lDs:reclleJllts aJl:J~10me:ra1:e or suffer "'f'f' ..·.f'.r.'" the matrix is moUeJIl. p:artJculate malteJ~lal and extended chain t"¥'l'C't~lC' nnllvlTl@lr11f' substances which are sut)seIQuc~ntlv difficult to melt. plasti(;isaltio,n and more difficult to In . . .,o.,,:>Illu ideal to add fillers to the melt rather than to solid feeds.

120

Polymer Melt Rheology

dlsIPer:,e a small amount of low-viscosity material in a easy to thin down porridge by adding milk drc.ppine: lumps of into a bowl of milk and stirring n1"£'I,rhu''''' appetising result-the skills of are, indeed, c1e'.relc"lnf'~c1 in the kitchen. U1(!j"'n~:ihl__, t

6.3.2 Distributive Mixing Distributive mixing, aimed at is achieved by rows of the interruption of streamlines. on a screw or by the use of static flow. Distributive is of importance when the flow streams of different u.,,('One,.f'u and, more when those different viscosities are the result of 6.3.3 Homogeneity onllect:1Ve of all is homogeneity but nOlmogeIleI1:y is not mixing. A notable ex(;epltio1n lOtlrO(1uctlon of the which the solid separa'te from the melt the barrier flight, elements of the bed UlrlOUfl~n the extruder without melting. The barrier may break be nrt:~vent~ this and allows COJIS14deI'able increases in output rate to achieved. In the flow of ma'tenals, hOInO~tenc~ltv det,emls also on f'",,",n"'1"af'II11"'" the final flow to tp",np1"tltII1I'P to increase in the same way. the die This nalrf'f~.lhl tenlPeratlure build-up due to heat n ... r''''1''~:lht'.n and prOlmOttes which is more stable. n1"{"t1n,('f'

6.3.4 Work Input work input. Excessive work input is it All kinds of If the work input may also lead to heat generation and to is uneven it may indeed be a source of in the wrong it may defeat the of the or unwanted attrition. There are many the work input during UUJ'nUI"', but the in the final analysis, on the lOQ~re'llents to be mixed.

121 6.4 CONSTRAINED FLOWS

ConstlralIleCl flows are of two mOIV1Jlli! surfaces and pressure of r.Ollvp:vn1UJ 6.4.1 Screw Extruders

In the barrel of a screw extruder the flow is a COlnplex In the power reomr,em,ent ovi'..... , ...,.,.. the flow between the reilltiv'eiv t'n('1,Vll1,O' where shear rate = where D is the screw diameter H is between screw root and barrel wall N is the screw in revolutions per minute. The shear rate extruders is of the order 10-100 elements of the those which pass between the screw flight and at very rates. The resJICleJIlCe time of melts in the a screw extruder is of the order of 100 a total average of the order of 3000 units of very considerable flow purposes.

6.9 One unit of shear

In

dies and the nozzles of 10 I,ectlon moulCl1Oe; machines the flow is rates at much The shear rates in such flows have described in an kn<)wleClil~e of flow rate

pn~SS1ilre·ClI]V€m and the shear SOlllletlmc~s e'tcec~atrle; 100 000

shear rate = where M D T N

is is is is

the the the time the number of u .. " ........

"lIVU

122

a

b

c 6.10 Selection of die diameter for wire a too restricted b Die too c Die correct size

cm/eT'in~

.... """"' .... >

--6.11

of convergence of die, 28

123 While such formulae are no substitute for accurate cal,cullaticm a of the of strain rate involved in a as a check that more have not gone

nrc'i"'p,~.:!C!

6.4.2 Wire Covering i"'cnJP,r,na nrr,i"'P,c~C!

the choice of

I'h'~'Ult1lnU1n

diameter

Iml)OSC~S

a need to

shear at the i.,.+,.,.ri""'''A of the melt .......... 1'"1 . . "''''..,

With the correct die dll1neIlsl<)fi--u:suatUy about 10 per cent coated wire-the at the with the conductor and the outside surface of the material is rel~~tl\l'elv easy to release such surface stresses

6.4.3 Pressure-driven Flows in Dies and Moulds We have noted

Dr€~SS1lfe-drwe:n flows in dies and moulds contain COllnp(melots. If 2(J is the of of a die then the tan (J for

tlHr"'!:lt"'r than 900 the melt will tend to a 'dead' space in the comer of the die and Pf()dUlCU1tg a 90° convergence, so that for such dies the stretch rate is aplpro~xirnat:ely most constrained flows the extensional is less than the shear strain. because the resistance to eJong~ltional flow be very much due to shear the stresses ty""."tAr~t""rI extensional than those assoclate:d with the to maintain the I10W---Hle Q1uarltitl:lthre the shear flow cniuactens1tlc, presence of flow or onentatllDn, reSlPOl'1lse. No matter how small the stn:~tcllling it never be Ig(]lOrled: flow, the first QUlestllon be re(luce~(l

124

Polymer Melt Rheology

...... ...

6.12

Strc~tcl1lina

flows in

inie~cti()D mIOu,IQUlf!;

warping or ..... Ir'..... n of the moulding. At the front of flow, the stretching flow may lead to instability features in the ~nl,\p,!l,r~''' ...... of the of the product. While it is too to say that aU prcJblen:lS of product in constrained flows are associated with strletchll1UZ they should placed at the top of the list of causes for elimination.
6.4.4 Constrained Flows Dermed by Pressure Gradients A final dass of constrained flows occurs when relatively moving surfaces 2el1erate which in turn the This dass is ,,,...... '1'."'.£1 cal'efl(lerllD2 nrc)ce!;;s where the flow is constrained between r01:atlD2 Again there is a flow component r'nn,~ ... rI nrf~!il!ililre 2ra:(J1e~nts

(ll1l''\ ...

#

Drag I

I

Pressure I

I

,pumPing I

I I I

I

I

Shear stress r

Tensil!t I

I

Pressure profile

Shearing field

Stretching flow

Figure 6.13 Constrained extensional flow in caumoienlllg

125 to a dominant

sn~~ar]tng

flow 7

as a first aplprc.xlIna ltlolll,

y stretch rate, t

2VIH

=

where R is the calender bowl radius H is the calender V is the linear ,,""I,"....1h:r Note the of the in rto.f'""rrntr\u'"y from which we may

6, 14

Sq1Jlee~~ing

flow

models for their in this class include sallee:ZII1If! Knc~adm2 flows found in COlnmlen:lal

6.5 FREE SURFACE FLOWS

Free flows are also of two kinds: those where the bulk of the material is worked and those in which it is the surface which is affected. Free surface flows are dominated In we noted at the exit the extrusion die there is a sm:gulan1:y the surface of the melt accelerates from zero to a finite "o.l,n","1t" resulting in an intense strletchil112 flow of the surface leading to pm.SlOle defects. In the streamlines of the surface near to exit 6. we observe a pattern which, even without is qualitativec!ln"1l1~" bubble blowing process in polythene film. Film blowing reaumes

a

b

6.15 Surface flow exit of extrusion die b At front of moulding

a

a pressure inside the bubble and so, in a re(Jluu~ed to induce the of the surface .~u,,,,,,,,,__·,, reOIUlrem!ent to a die exit pressure studied by the flow situation at the front of a mOUlO.lnf! nrc)ce!..s where the melt conditions we can the stretch rate at the front as E = where v is the of the front and h is the QPt"'l!:l1"~lf'ti'.n between the surfaces. Should stretch rate that at the rUJ:,tm:es, a defect will be observed in the surface of the moulding In more obvious free surface flows of fibre spinnilng whole of material is to a strletchlI1lg of such processes is described in

nlnWlrlO

the the

maximum stress total strain

u""l.nl"'.1tu

at the freeze line and va is the

s is the draw distance.

be eStlmalteo. are not lnClepenlCiellt vj:ln~lbt(~s sec:uonal area of the and the die. For most film or processes, is of the order 10 so that an estimate of the strain rates in such a process is strain rate = ariiWoortruiCe 1"Pl'llH1","'1O:t a very detailed of tenlPerature profile the line is the most

6.5.1 Foaming eX(im1ple of free surface extensional flow which is of "",,,'u'-'II,, As with aU the critical the defonnation aplpr<J1xunalte stress in the tmlmltng nrC\{",l'>'i1(! one in ISOllatlon. is where P is the pressure a bubble of radius r and wall thickness h. The volume of to the volume of the remains constant:

where 2R is the distance between the c\1"lcnn~1 nucleation sites. And so we as an aplpr<J,xnna1tlolll, stress

"23

n""'CCII ..':> remains constant, the stress bubble size increases. characteristic allows which is eSt)eClaJJIV e:"ag;gel'ate~d than smaller ones-a deformation decreases with stress. In we observed that branched materials have a resistance to deformation which increases with stress a more uniform cell that such materials should resistance to also tends to increase with stress if carried out more when the material response is more

6.5.2 Film Blowing and Casting, and Blow Moulding

more terlslcm-stlJttell1lnig the more elastic is In the extrusion Co(ltnlig nrnl"':>cc sus;celDtlltJle to 'neck-in'. In blow mouldme

process deformation is dOlmUlaI1ltly elastic. Both these courses lead inevitstress and so to the of balance to are a delicate one. The ODltlOllS !t111!tIII!thilp to stabilise a of may not available. in the defer to the advice of the However the context, we must Bard: .. , 'twere well it were done '1'" 1'1 ...........

6.5.3 Vacuum Forming

One process which is almost ",nt', .. where a sheet is sucked into a the most extreme tlnlwllnf! are at their minimum thickness and strain

process, of the

",hl

6.16 Vacuum

IOflrnl11lg

Polymer Melt Rheology

the sheet. In this process the stress is limited to about one atrnO!)pJ1lerc~, (rlh) x for processes, rlh::::::: stress for the nl"r\l"p,~" level of 1()6 The ideal response for a material in such a process would allow extension to strain and rapid after that. The aVf~ra~fe in the much less than the maximum strain reached in the average draw in a vacuum maximum draw in the corners material would tend to m(mJlriUJIl! into the corners, leading to more even

I

6.17 Deformation response in vacuum

toflmlllig

Ideal Conclusion Free surface strletcDJI1l2 to achieve thin sections: an to achieve enhancement important sec:onoalry oblf~ctllve may orientation, on the response of the melt. 6.6 BULK DEFORMATIONS

but cnCllngC;!S of COInOlres~)ed per

is al"~111111~1_ such an optias PY{"P"':IVP the quality usually better than that of nl"l"""11rp

in building up or relteasin2 dlsplacernellt from an accumulator

in

6.18 Observed

nmlla-tln

to

predeternlJnc~d

flow rate

aettencls on the volume of the acc;unlul,atofr--a the accumulator will ..",... relaxation will be more prc:deterllDiIled flow rate. Bulk cornPl'ess,ibillity :>Ilt",

Heat from the surface a moulded or so first. As the molten interior shrinks it exerts a force that an outer shell onto the solid skin, That force may the surface to buckle or or, if a be the the skin is melt. If that tension the melt may cavitate.

, ..7 SELECT BIBLIOGRAPHY In this Ch,lptc~r between and pr()CeSSJ10e:, nre:seIlt across a wide

t'rul1cIJ)les of roti:ttl(J'nal mOuIOIne: 1972.

Extrusion ~xt'·UJll,(Jn.

Van

H.F. Fiber and Yam

Polymer Melt Rheology

130

Film Blowing P. L. and Huck, N. D., Effect of .,.n...1"....l1c1nn variables on the IUDiOalnel'ltaJ orooerties of tubular 26 114-120 and 26 1961.

moulctme: SYll!1p()S1l1m,

Transactions

the ." .....

1975. C;alen(JrraR.~e,

. . . '.. "' ........"" Francais . .

PL....... ,,.,"',,

et

1 '• •;

131 REFERENCES

lDl lect:lon

1.

2.

m()tul(llDJ~.

Plastics and Rubber

Effect of extrusion variables on the fundamental Dollve'thv'lel1le film, 26,

3.

4. 5. 6. 7.

in Journee Apph<=aUons des

8. 9. 1966.

Future Developments in Polymer Rheology

of the interaction between

rnC;~OJ()1!V

decades

in

134 The last have seen a mitigalte the major flow defects

nrn,u" ... ",

such as their train a new f(erlenltlCln gnt,\pgrg"i"'p will COIltulUe

REFERENCE

1.

,V ....... cfv'ev

J.

Wiley, 1962.

APpeJ:1!OlX 1

Additional Sources of Error in Capillary Viscometry

1 The Velocity Profile in tbe Die A correction is freQuc~nt.lv made to take into account the fact that the melt means that the aSSUITlea pa)~aJ:)jOl1c 'Us:>lnl"'l'hl psc:::uaopJ.astlc nature of DIUIl-lIKe. This ,..,..·..0''''.......... the die is is form: true waH shear rate, rel.atl()nshlP shear stress ....................t ......... <31 to

............

......

......

......

......

.....

.....

""

0.1

shear rate

A1.l Effect of the Rabinowitsch correction on a uncorrected data corrected data

flow curve

The of the correction term + tnt-tnl1t11 as n goes from to 0, but in the error in VlSCOS,ltV nrt"'\nr1rt1nnlll to at shear rate, that the COJrrec::;ticm a maximum value of per cent when n

Before to

whether it is aOilroonate to make this correction it is desirable the use to which are to be put.

(i) Where data are to be used for COlnOfilra1:tve n",~nn,Q"'
2 Slip at the Die Wall A

rate is that COlnm,OnJlY preS,URleO to occur with svstenlS pal'Uc1ula1te rather than mC,le<;ulIU "AI.n~'lh, n.en~lVl()Ur near the die wall is is the treatment of die Chamgc~S in the flow behaviour with to obtained dies of different radii aOl,arient shear rate at a pressure volume flow

+

ap)Jarlent shear rate, where v := From this be oJOltteCl indication of v from the the indication on the assulIlotiion true shear rate at die and must be treated with caution. Several authors3.4.5 have an association between wall and flow defects. For geller;al OIUl1JiOS€~S it is sufficient to assume no at the die wall. If is Of()oertv should be evaluated in discrete eX1Jerlmlents.

ADjfJen:au

137

I

Inverse radius

A1.2 Apparent shear rate related to inverse radius:

4x

velocity

J Pressure and Temperature Effects

assoCl.ate:o with

and

extrusion leads to an Isoen1troPIC reduction in for a pressure of could and introduce an error of order 10 to 50 per cent in

A1.3 Exit temperature

die wall at same ten'lperature as melt on

138 COlmbllDU1lll the tenloerature "',U,""""''''''' ture be "f' ...r",\ ... II" (Jlst\lrbe(J, the wall which are to llreatest deterrnininll the resistance to estima1te that would cause an pff,Pt"'tnlP tenlperature which would reduce the " •., ..."',,'.i-'"

I

--:;I---~---""":"-Average

I I I I

Entry

AlA

Low

I Exit

inside a

t"~nll'~'n!

extent mULLUl::my carlcelllm:R. magDltucle of the errors due to nrl~I:!'.!1!1rp and ooltenUal ma,llDl,tucle of which effects outis to minimise the the dies should not pr(.ce~iSlt1Ig C()nClltU)nS are

Al.5

~(]llan!-eIUrV

die: streamlines and extrudate

non-laminar flow

ADDell~alX

139

1

4 Shear Modification Effects

The action of &>cvlrru,rh'l1llJ' the melt may and/or mc.rpJ110Jogllcal structure of the Thus excessive and so exc:esslv,elv should be that the volume average total shear

4 5 Non-laminar Flow

the NO]tl-l(!lmlJtlar flow in the flow lTH1lrlr,pnllu from those which are is convenient to use DOS;Slble .... ">1,.,,.., of extrudate rnC~Ol~()JUCal information. apl:Jropnate for studies. made under non-laminar flow c.11sUnJ~Ul:sne:c.1

as

REFERENCES

of molten

3. 4. 5. 6.

Ch~lUtf!ourleaux.

Aottend.ix 2

Interpretation of Extensional Viscosity from Flow through an Orifice Die

A2 Extensional flow

thrlom~h

an orifice die

def:orrnation is 1'3"."""__ ~'" flow received most use and " ' ......... L_

so

a

...... 4

eIoln2~iti(J'n

value has been

rate, i = at a flow rate of = '1 is the n is the power law

r

Polymer Melt If this

is to the orifice .... r"."" •• rt3 above the U!:Ilirtii'u of the intC:!fPret:ati<m flow measurements is be treated with caution. more tUflC1alm(mtaJ C1Dniunlatlon

l(n~f!Ol(1JlV

must be taken over the method is a transducer

.... r." .."'rr""rI

elcmg;atlonal response from i"i"I1!1Vl"rcrllncr results so obtained must or

REFERENCES

1.

COl1l1ptlabon, Journal

A01penlClIx 3

The Inference of Elastic Modulus from Post-extrusion Swelling

Several authors have sU2,ges:teCl intleroretinJ! DOI~t-c:~xt]rusllon able deformation. If extensional flow is then it is apl)rOpnate orifice flow as recoverable ex1:enlSlOltl, is the ratio of extrudate/die Olame:ter

SWf~lllIU!

+ leadmlJ! to extensional mo,duJlus.

E

+ swc:mUUl ratio from a

] die and

rR is the recoverable shear at

144

Polymer Melt Rheology

1/

6. 0

5. 0

.0

.0

L ./

.0

/

/

V

/

/ V

V

,/

.0

/ ~

/

1.0

1.2

1.4

1.6

1.8

2.0

Ratio of solidified extrudate to die diameter, BL

A3 Plot of recoverable shear

swelling ratio

There are several possible ways of making a measurement of sweHllnil ratio. One method is as follows:

L The extrudate is cut flush with the die. is obtained which may be transferred to a water bath to facilitate cooling. 3. The diameter is measurea with a mlC~rometer in two dtrc~cUons at right angles end. within 1 cm of the 4. The readings are and the result is taken as the extrudate diameter.

2. A new

Swell ratio is the ratio of extrudate to die diameter. Certain corrections would be necessary to obtain a true sweUllnil ratio. These arise from: on CO()11I112 under

ShJrinJka~~e

Sa~~2lfI2

to h'~'~7'lnn Diametral increase to surface tension flow conditions not established mutually carlcelUIll2 is that a These errors are, to some meaningful measurement can be obtained if the folJm'JlinlD CC)nClltlC)DS are met:

AD.Del1tarx

4

dI8.me:ter to die diameter >5: 1. when

REFERENCES

elastic deformations in polymier melts. Plastics and

.R.ppel1lOlX 4

Rupture Behaviour

Most observers now at the stress COlllcc:~ntlratJlon of flow into an orifice as a str()n21v e:x:tension:al of 'melt through stress at which the melt rUt)tUlres.

Yolvm~ers •

AP1penl(llX

5

Data Sheet for Capillary Flow

Extruder

Die diam. 2R

N/m 2

y=

0so =

By courtesy of lei Limited (Plastics """1"1;:>''''''"1

Ns/m 2

1/=

147

AD.oen:au 5

Extrudate N/m2

G

+

L

E=

Extrudate

o

APiDel11(11X

6

Comparison of the Rheological Properties of Two Samples of Low-density Polyethylene

Fl(ltlres A6.1-6 COD1D3Jre

same as

Cone and plate rheometry 103

10·

Shear stress (N/m2)

shear at 170°C

10- 1

Angular velocity (rad/s)

A6.2 nvnalnlC viscoelastic

nrClnp'rti,"'''

at 170°C

The elastic modulus results recovery on a cone and inference of elastic response from Dost-«~xtJruslon swell:mS! cone and plate measurements at low stress are agreement with dynamic measurements and with the normal stress measurements in flow A6.4), on the assumption l that re.~o"erahle

shear

N

E

"-

Cone and plate recovery measurements·

~

(!)

0' :::J

"5

10'-

"0 0

E "CIS Q)

.t::.

en

--10 3

10 4

Shear stress (N/m2)

reSl)On:se at 1700C on work of S. Citroen at UCW 1979 Orifice die G == E/3 where E is the elong,ltional modulus

150 Table A6 Data for Post-extrusion Swelling

10 30

2-0

1·5

2·4

100

2·7

1·7 2·7 distorted

~

/

2·6

).;'

If V

'/

I

"

10'

Stress (N/m2)

A6.4 First normal stress difference at 17WC: results of P. J. Daniells2

Non~laminar

flow

104Stress (N/m2)

A6.5 Orifice pressure

from

",a ...iU",r'l1

flow at 1700C

AO,oen:dLX

6

151

CD Ii..

:s ....Q.

3 x zero shear viscosity

.......

-

:s

-1-- __

----!---- -'"- ~~ I 10- .......

a: •

1 .....

.....

I "',

Based on orifice flow

103

104

105

Elo'ng4!1tiCtnal stress (N/m2)

A6.6 Elcm2;lltiornal flow at 170°C

REFERENCES

Elastic MSc

L.tUIUI"u,J,

1964.

Rubber Te(;hmcJlotzv 1977.

Appendix 7

Typical Processing Property Data for a General-purpose Low-density Polyethylene Polymer with Moderate Branching

Melt Flow at

2-0

5·3 x Table A7 Temperature

Density

Bulk modulus

Heat content relative to lCrC

3·1 130 170 210

Table A 7 lists diffusivity data

Heat in adequately per

762 746

1·10 1()9 0·96 x 1()9 0·83 x 109

±10

±0·03 x 1()9

Coefficient of tbermal dilTusion

x lOS

3·8 x lOS 4·8 x 105 5·8 X 105

1·1 x 1·1 10- 7 1·1 x

lOS

±0·1 x 10- 7

±0·1

bulk modulus and also beat content and tbis polymer. otber tbermodynamic data we bave

is cOl1l1plc~x near tbe but witbin tbe melt from above to below 70°C tbe beat eX(:hall1~e a of tbermal diffusivity of 1·1 x 10-7 m2/s

AO,rJen:atx 7 tel1[lpe:rat:un~s

above the while may tend to SClliSlc'n may dominate. These are minimised by the exclusion

coc~ftjlcleJr1t

of friction rises from a value of 0-4 at 20°C to a and then faUs to a minimum of at of about 0-45 as the polymer melts.

N

E -,

~

Q.

...0 "a ...:::J

10"

II)

fII

:...

Q.

II) (,)

!E ...

}I~ -1-_--

0

10&

104

Stress

of a oprlpr~ll_nnrT'ln~p Dol.vethvllene with moderate oranctlung

A7

Swell ratio at 15(f'C

10

100

(N/m2)

1·4 1·6

2·1 2·5

of

Appendix S

Typical Processing Property Data for General-purpose Grade Polypropylene Homopolymer

Melt Flow Rate neD'atj"e

3-0

mcrealses the and its effect may be corlsJdlen:~d as a such that

t"~'n1",\~"":lt"'''A

=S·6x on

uuu'nc't'tu

as reclucJing tenlperat1ure

Table AS Temperature

Density

Bulk modulus

Heat content relative to 20°C

Coefftcient of thermal diffusion

0·76 x 109 0·70 X 109 0·67 109 0·61 x 109

0 4·5 X 105 5-0 X 105 5·6 x 105 6·3 x 105

1·4x 0·9 X 10- 7 0-9 X 10- 7 1-0 x 1-0 10- 7 1-0 x

±0·03 x 109

±0·1 x 105

20 180

200 220 240 260

±1O

Table AS lists nAnC!li'u bulk modulus and also heat content and thermal diffusivity data for this nolvmler cornOl'esSlon or de(;Orrlprc~ssion: = 2·2 x 10-7C>ClNm-2

Pressure bmld-l1n/lrele:ase

ne~lttnlg

or

CO(U1n:2

at constant volume:

Polypropylene which melts at 165°C as a melt. presence of intense stress may the of sut)erc::oollin,g. most purposes it may assumed that polypropylene will

at

Aooelltau 8

155

water. The coettlcllent of of ooJvoJ'no'vlerle other this value can be very

Q,

...

0 "0

106

...::::J

Q)

fI) fI)

...

Q)

Q, II) (J

!E

105

0

.-<

C 0 ';;

cII)

A

)(

II)

"0 C

'"s;::.:

'"

II)

s::. fI)

,5

..:

=

s::. fI)

,5

10'"

10 5

Stress

(N/m2)

A8 Kheolo£!\! of a aelleral·l[JUJ''Oose oohi'Of{)o\rlerle homOOCllv1ner Swell ratio at 2rxrC

10 100

1·5 1·6

2-0

2·6

Appendix 9

Typical Processing Property Data for a General-purpose Grade Acrylic Polymer

Melt Flow Rate

4-0

HV4::irol§tatic DJress.ure IDCreal8eS melt "i'''''.n'''t" and it is cOIlVenient to coolsidler a teorlpe:raturc:/p!'ess,ure equivalent

=3·3x which implies that a hydrostatic pressure of 108 N/m 2 (1000 atm) effect on as a drop in of

the same

Table A9 Temperature

Density

20 180 200 220 240 260 280

1180 1130 1110 1100 1080 1070 1050 ±10

Bulk modulus

1·35 x 1·25 x 1·15 x 1·05 x 0-95 x 0·85 x

1()9 1()9 1()9 109 1()9 109

±0·03 x 1()9

Heat content relative to lOClC

0 2·7 x 3·1 x 3·5 x 4·0 x 4·5 x 5·0 x

lOs lOS lOS lOS lOS lOS

±0·1 x lOS

Coefficient of thermal diffusion

1·1 x 10-7 0-7 X 10- 7 0-7

±0'1 x 10-7

Table A9 lists typical bulk modulus and heat content and thermal diffusivity data for this polymer_ OccasionaUy relevant are the thermodynamic tulllctl()oS:

= 1-2 x and

iDl-,enau

157

9

C1eJlratClatlon can occur_ aPt)rmnmate.ly constant up to 1300C a malXll1nUID value of 0-8 at about

-

N

E

~

Q.

...

0 "0

10'

!:J

,

= !

/' /'

Q.

8

~

101i

0

200°C

..:

..,

«t

.s::. fI)

.5

~ 102~--------r---------+---~----~--------~

~

\ 104

105

Stress A9

(N/m2)

ofaOp.flp.r:~I-rvlrnn':p

Swell ratio at 2(J(f'C

10

1·3

100

1·6

1·5

2·5

10'

Apt)endlix 10

Typical Processing Property Data for an Injection Moulding Grade of 6-6 Nylon at 285°C

Flow curves at different and pressures are SUt>erlPos,ablle vertical at constant stress. Within the pr()Cel,SIIlI~ shift the axis is proportional to the tenl1pe:rature cmmge. '(1t~{'n~11"'(1 is summarised by 1·36 Similar remarks A hvc:1ro!datlc

pf()Ce:SSll1l~

range. as a

Vls(~ositv

=3·2x

Table AIO Temperature

Density

Bulk modulus

Heat content relative to 20 C

Coemcient of thermal diffusion

Q

285

In

1010

1·5 x 1()9

7-0 x lOS

±10

±0'1 x 1()9

±0·3 x lOs

form 6·6 bulk modulus at relative to 20°C are The rise in

of 1·14 x 103 pressure and

11&>.,..c... t'(1

atnl0sphc~nc

AIO. bulk cornPI'eSS,lOn 1·2 x 10- 7 °C/Nm- 2

±0·1 x 10-7

at 20°C. The melt heat content

Quc~nCJllea

159

10

AO.oen:QlX

melts at about may SUI)er·cO(). of orientation 1"&:!>t'ilnt",:o", by a reversible cOlule:nScltlcm so that eClllilibri1Llm water content are reflected chja.n~~es in molecular nylon 6·6 may to thermal Above Drc;~sellce

The coefficient of kinetic friction at 20°C is about but falls l"'.U"urlll" to 0·1 in the Above 200°C friction to a maximum to a value of O· 25 at 250°C.

N

E

~

e.

0 I"0

106

I»

:; rn rn l-

e. I» (,)

-.: 'C

105

0

.< C 0 '0 c:::

W 104

C

V

/ /

I»

/ /' ",

",

"...

.....

,/

1; and Ell

/'

-

:

0

... '0...c::: I» )(

)(

I»

I

c: ea

"0

s;::-

ea 103

t.:

ea

I»

.c: rn

.S N

c:::

A

ci

.: ea

I»

.c: rn

-----

.S N 102

-E

rn ~

I

I»

I»

"0

E

~ rn :s

~

:;

"0 0

:e

it

~

10 5

106

Stress (N/m2)

AIO

KDleOI4Jgy

of an

lnl,F>l'i'1Inn

mouldinJZ

of 6·6 nylon

APtJen(lllX 11

Typical Processing Property Data for an Injection Moulding Grade of Polyethersulphone

VIS(;OSltv on pressure is such has the same effect on v ......,.tu 'l1 • •

6·7 x Table All Temperature

Density

Bulk modulus

Heat content relative to

20°C

+10

1·4

1()9

4·7 x lOS

±0·1

9

±0·3 x lOS

10

Coefficient oftberma. dltTuslon

±0·1 x 10-7

heat content and thermal crO~):SllrIK

after orolon2ec:l exposure to telTlpelratllLres

11

161

-

N

E

~

Q.

0

"-

"0

106

f

:::s en en f.)

"-

Q.

E/3

f.)

"

Ot: 't:

--

106

0

t<

320°C

C

0

'in cf.)

.... )it( f.)

320°C

"0

c cc

"0

F"

ci

CC

.:

.: f.)

.c en

.:

N

E fh

~

....> "iii 0

:>" en

370'C } A

C

cc

3

10

CC

f.)

.c (I)

370°C

,: N

E

102

~ (I)

:::s

3

"0

0

::E 104

105

105

Stress (N/m2)

All

of an

of

APt,endllX 12

Typical Processing Property Data for a Rigid and a Plasticised Grade of PVC ViSC:OS11tv on pressure is such that tnCJrea~;tnJl the pressure has the same effect on at recluc:mJl tenlperatlure

=3,1 x

Table Al2 Temperature

Density

+10

Bulk modulus

Heat content relative to

Coemdent of thermal

20°C

dift'usion

105

1·9x1()9 1·6x1()9

2·1 x lOS

±O'l x 1()9

±O·1 x lOS

1·6

heat content and thermal

and ......."""' ........""

nIIIUC1-nn

lle,ltuluz at constant volume

2000C. The friction of PVC dec'emis CIulcauy on the lubricant formulation.

ADl'ena~lX

t<

C 0

..

'ii

12

w

C 104

0

c:

'ii

)(

....Ci

Ci Ci

"0

c:

ca

F"

.: ca Ci

.c: fA

.S N E

-

c:

)(

Ci

"0

c:

ca

103

C)

.:

=

.c: fA .S

102

fA

~

fA

:::J

:; "0 0

:E 104

105

106

Stress (N/m2) A12.1 Rh,eoll()2V of a Swell ratio at 17(f'C

10

100

1·05 1·10

1·35 1·50

PVC

164

""".1""",,,,,. Melt Rheology N

e

~

Q.

...

0 'C

e...

po

10&

:::J

/""I.-

1~

0 0

...e

Q.

e

\

190°C

(J

It:

'l:

0

...

10 6

"" ,,\ '" \

""",'

1

\

/ /

,..

G and E/3

\ \170 0 C

.<

C

C 104

c

'0

'0

....e )(

e 'C c as

0

c ....e)( e 'C c as

ci

170°C 103

to:

as

e

.52

'"

w

0

.t::. 0

.52 N

-

e 10

2

\

,

A\

'\190 0 C

\

\

1~\

\~

~ 0

:::J

"S 'C 0

::! 10 4

106

10 5

Stress (N/m2)

A12.2 Rheology of a highly

PVC

on K69 nol1vme:r 1

APJ,endtlx 13

Empirical Observations of Flow in Channels of Complex Cross-section

\ \

AB.l Flow

For the

9n~llv~!I~' p~lral1[lete:rs

PUJ~OOl~e

c0I111plc~x

dleSCtibiI12 die channels

channels may

desc;;ribc~d

of of

by

area area

the dmlen.Slo'oie:ss ratios

From these Pat'ameters we may

x y

and for a slot die X a set of the two flows

= 0 and Y = 1.

col111plc~x

for can cJltaIJlDels can

166

In ae(lUCJn2

relati4ems.hil)S we note the established !or:mu.lae: Slot

4QlaA

rate Stress ~ .......lru'....

shear y=

+

(i)

shear stress,

+

0s=

Pressure drop through dies of zero ."".. ,.po, ...... ,

+ 1)

=4(1+

= = = 1-0 Swell

for YR>

{ dies Swell

B~b

(Br) x

1 + 0'4(1

= =

-0-8)

(iv)

(vi)

for dies of zero

aBb

Dies of zero

r

Ba = (Br)X =

(viii)

drop in a long die and the ratio of extrudate to n is the power in is the in YR is the recoverable shear and eR the recoverable extension as .....,.U.'~IJL''"'.1 2. The to y have values 0 nr~..C!'alrp

Sigllific~s

been determined and short dies cornbi.nil112 three rods to form a

in addition to standard cross-section and tn~mgle with concave sides. and that their tension-

Shear rate

(8- 1 ) utl:!..'nc:!ttu

stifJfeDllng,

nolvnrnm/lerle

Working Shear Rate The intersection reference at

flow curves

in-

temsion-tlmlnlllg and

of the flow curves Ol)ltalIleCl wc.rk:lD2 shear rate is ael:lDe~a

Table At3.t Data for Calculation of Working Shear Rate Shear rates at Intersections p == 1 and q== i DIe cross-section

Circle

Concave

factors points Ol)1tau1leCl

x

y

1·06 1-00

3·2 3-8 2·2 2·3

23 28 32 23

420 360

1·62

3-8

35

480

1-00

1-00

0-80 0-28 0-11

1·28

I tOO

380 300

Table All.2 Data for Calculation of WorkiDg Shear Stress Shear stress X Circle

Concave

PoIy(methyJ methacrylate)

y

10 S-1

100 S~l

1000 8- 1

10 S-l

1-00 1·28 1·06 1-00 1·62

26 26 25 27 24

110 120 110 100

260

17 18 15 17 18

90

Table All.l Predicted Value Compared with Observed in Dies Function 1% high 2% high as observed

250 230

Polyethylene

100 8- 1 1000 8- 1 61

160

64

55 56 59

150 140

Polypropylene

108- 1 31 34 32 31 38

100 8- 1 1000 S-l 84

130

80 77 82 81

110 130

Table A13.4 Predicted Value Compared with Observed in Dies of Zero Length

Standard deviation

Standard deviation

8% 8% 7%

7% 10% 7%

169 calculated are on average 9 cent.

cent

with a stand,ard deviation Y=

WOlrkJlnJ! shear

26 per

.lI..-_.-+---==-

Working Shear Stress From the at defined values of WOlriOllJ! for rand s of equation obtained r =s =i obtained of cif(;uhu CJrOSl;-se~CtJi[)n. are, on average, 2 per cent Thus wOlrkuU! shear

Other Rheological Functions In a similar manner the other empUllcal IUIlICtll:ms are defined such that pressure

mf~aS1L1re;d

Post·extrusion

value of from

{ Dies of zero length

Cal,CuJlatc~d,

standard deviation 8 per cent.
=

(

above may be used as a to oornol1tulJ! C4()mple:x ducts and also as an aid to The same and in nQ1rtll"nhu" intterslectin2 flow curves, may be used ,to the shear rates of cOJnp,lex svs,terns--f()r e;"antlpl1e, in mixing devices where torque may be tbrl()uJl~b

AOttenClllX 14

Flow through a Tapered Slot or Annular Die to give Uniform Velocity of Extrusion with Varying Thickness Profile

-+ HN ........ A14

die

For small cp, tan cp = --w,__...t.:.

(i)

In section N, pressure = constant in all seCtlOllS

shear rate, where

y

is volume flow rate per unit width shear stress, 'tl""I£1I£11TV

(J

=

at die

velocity of oar'isOlrl, VN = swell

=1

(¥1A

N

= constant

B, assumed constant (but variable in principle)

(v) (vi)

AD,venaLX 14

171

From (vi) and (v), constant

BVN

whence

From (iii),

=

x

From (iv),

From

and (i),

~~......-;;.;..;;;;;.;.""":' ~

-(~JJ=

constant

Then 1

Example. Wall thickness in side walls approximately double reCluurect thu;Kfiiess. With a variable thickness inflation will first occur in If the side wall thickness were reduced to half, on mtJlahon, these walls would become thin. SU22ests that a side wall about IW()-I1UTlIS the 2: 1 on thickness of inflation.

Original =10mm = 4 mm-f> 15mm

2·7mm

n=O·3 To

equation

(247)O'31~"""""0·82 whence

12·3 mm.

Author Index the

Ballman, R. L. Barrie, L T. 1 130 Bartos, O. 98 Benbow, J. J. 18,19 101,102 Berens, A. R. 10 (13) Berl~ol12:oni.

A.

32

tOllc')wuzg in Darlenth'l!St!3

56 (38)

104 (110)

Bird, R. B. 1 (4), 52 BloodeD, D. J. 97 L. L. 104 D. C. 52 Bol1ltinck. W. J. 32, 33

Daniells, P. l.

35

H.C. 47 93

Borocz, L.

Edwards, S.

73

E. 91 Busse, W.F.

~lI":Ui:lu.R.

Caron. I. M.

,cVC;;li:ljl!,C;;,

A. E.

102

H.

Cancio. L. V. Casson,N.

R.V. Chauffoureaux, J. C. 136 Chen,S.l. 120(131) Chen, Y. 87 (90)

Choi, S. Y. 44(68) Christiansen, R. L. 52 Oark, H. O. 58 P. L. 33 105

40

113

130 Oallo, R. l.

64

47 (68)

174 Kratz, R. F. 52 Kraus,G. 84 Krul, N. 32,33 Kubat, J. 93 Kuhfuss, H. F. 11

Galvin, P. 21 Gieniewski, C. 104 VU111:>1:'1::>. A. 84 Gottfert Feinwerke-Buchen 32 Gould, R. W. 10 50 Ura,essliey W. W.

34 58 102,103 (109),

84

Hessenbruch, H. Hirai, N. Holdsworth, P. J. 97 Holmes-Walker, W. A. Hoiomek, J. 136 Hori, Y. Howells, E. R. 102 Hubbard, D. 49 Huck,N. D. 113 Hudson, N. E. 32 Hulimann, H. P. 101 T.W. 98 Hutton, J. F. 20 Huxtable. J. 87.88 (90) Ide, Y. 23 ..... ,"""u... Chemical In(j!ustrie:r-Welw~rn Garden 54 91 Ito, K. 44 Ito, Y. 52 Jackson, W. J. 11 Jacovic, M. S. 83 J. C. 64 (70) Janieschitz-)'rie:gl, H. Johnson, J. F. Jones, T. E. R. 18 Jung,A. 44 Kamal, M. R. 138 Karl, U. H. 44 Kase, S. 32 Khan, A. A. 103 Klein, I. 129 W. 101

76,84

130

104 (110)

49,

Lamb,P. 32 97,98,99 Lamonte, R. R. Landel, R. F. Laun, H. M. 23 Leblanc, J. L. 34 Lee,B. L. 93 Lenk, R. S. 1 A.S. 7 Lord, H. A. 130 Lund, J. K. 32 Maack, H. 104 Macdonald, I. F. 47 McGowan, J. C. 44 McFarlane, F. E. 76,84 McJ!Celvlev J. M. 1 Mackie, P. 32 Mackley, M. R. Maerker,J. M. MaiUeffer. C. Markovitz, H. Masken, S. G. Matovich, M. A. 104 Matsuo, T. 32 Maxwell, B. 21,24 Meier,D. J. 84 Meissner. J. 20 23, 32 Mendelson, R. A. 40 (67) Menges, G. 94 Men, E. H. 98 A.P. 98 Metzner, A. B. 32 Mewis,J. 87 Middleman, S. MilIer,J. C. 104 Miller, W. R. Minnick, L. A. 18 Moore, D. R. 47,52 "UV'I.!f,GU, P. W. 76 M.E. 98 Nakajima, N. 130 Nazem, F. 20 (36) Newman, S. 86, 87 (90) Nicely, V. A. 76,84 Nielssen, L. E. 1

84

130

47

83

52

97

175 Schulken, R. M. 18 Scott Blair, G. W. 5 W.E. Semljonl[)V V. 44 Shah, Y. T. 99 Sbc:t>bc::rd. G. W. Shida, M. 141 Shishido, S. 52 Shroff, R. N. 141 Smit, P. P. A. 84 Southern, J. H. 97 A.J.B. 87 J.A. 32 J.E. 97 Swerdlow, M. S. 32,33

86,87

136

den Otter, J. L. 34 D.F. 67 Y. 87 " V i t l • .,..,,,, . .

J. 62 Paul, D. R. 86,87 Pearsall, G. W. 58 Pearson, J. R. A. 1 129 C. 44 Petrie, C. J. S. 23

55

J. M. 10 50 Plazek, D. J. 52 Plochocki, A. P. 86, 87 Pollock, D. 83 Poolak, T. 83 Porter, R. S. 44 Prest, W. N. 85 Pritchett, R. J. 62 Proctor, B. 96

130

104

104

Tadmor, Z. 94 Throne, J. L. 129 Tordella. J. P. 98,100,101 Trevena, D. H. 49 Truesdell, C. 5 Turner, S. 87,88 Tyabin, N. V. 57 Uhland, E.

85

98

97 98

H.

Raadsen, J. 84 Rabinowitsch, B. 135 Ra~:upa,tbi. N. 52 Rao, A. 129 Reid, G. C. 18 Reiner,M. 5,8 Reinhard, R. H. Rheometrics--Frankfurt 18,23 Rice, P. D. R. 62 130 van J. 136 Rokudai, M. 53 Rubin,1. 130

L.S. 136 Walters, K. 15, 18, 19 Warner, H. R. 52 Wasiak, A. 97 van Wazer,J. R. 15,19 Webb, P. C. 130 Weeks, J. C. 18 WeilsSellbeJ]t, K. West,D. 98 Westover, R. F. 33 White, J. L. 23 87 93,97 18

Schmidt, L. Schowalter. W. R. 64 Schrenk, W. J. 104 Schroeder, E. 83

49,50

104

Whorlow. R. W. 15,19,21 Williams, G. 130 Williams, M. L. 40 Willmouth, F. M. 97 Winter, H. H. 57 Wissbrun, K. F. 105 Worth, R. A. 58 Yearsley, F. 72 Ziabicki, A.

97

50

26

25

58

Subject Index

Adhesion 21,56,101,118 Weld lines

26 63,95,96 screw 120 10,78,84,93 11,12,54,63,65,79,104,105, 112,115, detailed studies 130 52,81,84 Bulk coolpre:ssi(JD

55,100,124 detailed studies 130 E '"".... 11 ..... ," H ....,_, rheometers 24, 146 amranlta2ces and limitations 34 errors and corrections 56 Cavitation 54, 107. 129 Chemical 11,41,92 Chemical structure 2, 71 Choke sections 96 Cluster flow 83 Coextrusion 102 Compression moulding 112 Cone rheometer 19 advantages and limitations 22 Contamination 50, 67, 104, 107 2 100

1,111 106,114,119.123 Data representation of 18,28, 146

152-163 spaces 11,61,92,101,114 Deborah number 48,95. 127 11,35,92,102,120 Density 9, 10,54, 106

2

'Draw resonance'

104 Shear, oscillal:ory

adventitious effects of 94 de)>endelrlce on stress 51 enhancement 97 inferred 30 in filled systems limited 52 measurement of 22,28, 143 of 104,127 see also M(J.duJlus; Orientation; Strain recovery Elc,ngliltioinal flow, see flows 11,150 Entropy 44 5 Strt~tcl:ling flows Extrusion 12, 56, 100, 121 detailed studies 129 of monofilament 61 58,63,167,170 105

11,51,54,91,93,97,104,126, Fibre 127 detailed studies 129 Fillers 10, 87. 102, 119 Film 11,12,34,51,53,54,65,93,104. 113, 127

177 Normalstress 7.19,20,103

detailed studies 130 rupture in 15 Film casting 11,104,127 Flow 32 9, 54,126 Fourier number 9 Friction 113 Gelation 35 Gell)m4~trv of deformation 54 Heat transfer 9. 34 at surface 10 34,50,53.81,93,120 114

10,11,34,52,53,54,55, 56,67,100, 107,112,115,121,123,128 detailed studies 130 orientation in 46,54,81,94,118 Instrumentation 2,34,39,133 94 crystal 10, 76, 83 Lubricallts 88 Maron~Pierce

87

Maxwell model 8, 18, Mechanical 32,53,83,84,88,97,105, 133,139 Melt Flow Indexer 33 'Melt fracture' 100 see also Non-laminar flow 92,113 52,75 definition 8 Molecular dimensions 73 Molecular models 71 Molecularstructure 2,71 Molecular theories 11 73, 77 distribution 52, 73, 78. 102 11, 71, 83, 91,133 'Neck-in' 106 Newtonian behaviour 8 Non-laminar flow 31,50,56,97,99,100,114, 139,145 Non-Newtonian flow 2,22,40,47, 75, 76 de~~n(lenc~onmo'leculajr~ej21~t

79

Orientation 3,21,46,52,54,58, 118 Orifice flow 30, 141 U~ciHlrdOlry flow and short time-scales 47 superposit:i.on on steady flow 47 Shear, oSCliJlatory

75,91,94,

111 Ph~ ~para1tion

93 88 Poisson'STatio 52 42,45 42,45,76,86 data 158 98 42,45,85 Pol,ydime1thyl siloxane 45,76 42,45,16 data 160 Polyetl~ylc;~ne, branched 3,29,42,44,45,48, 50,55,61,81,83,86,106,113,111.148, 167 Plastici~rs

42,45,71,74,80,81,98 42,45,16,83 74,78,85 Pol;v(meth:yl mlethacr:vlatle) 40,41,42.45,58, 83, 167 11,76 Polyptlen:ylelle oxide 45, 85 30,42,45.74,83,86,97,98,

74,83 10,42,45,50,53,74,83,91 Droces!~in2 aids for 10, 50 typical data 162 Post~extrusion 21,30,93,94,91,105, 143 32 see also Mechanical Pressure 44,96,97,137 43

178 Rabinowitsch correction Reclaim 11 Rheometers classes of 16

135

concentration 82, 107 overshoot 20 Stretch rate

125

123

35 in fibre and film coDilparisc1n of data from different 148 purposes of 15

112,113 detailed studies 129 8,15,49,93, 127,145 67

Sandwich

11,34 Screw extruder 56,57,113,121 as rheometer 34 effects of scale 11 twin 125

instabilities in 24, 52, 104, 127 rheometers for 23,32, 141 Structural foam 91 Structure, see Chemical structure; Molecular structure; MClrpll0l«lgy 91, Surface Surface 31,99,101,104,105,106,114 Surface 133 Surface tension 51 Swell ratio, see Post-extrusion

and 20 3, 11, 71, 79, 88, 91, 97, 134 97,101 Shear 6,56

see Viscous diSlsiplilticln 17, 18, 19 57 52, see also Non-Newtonian flow

oSClillatory

Shear rate forbidden 98 in 125 in extrusion 121 in 121 in screw extruder 121 Shrink 3 Sink marks 91

115 Slip 23,98,129,136 see also Adhesion Spaghetti model 52, 73 heat 9 mandrel 96

93 Strain 6 rateof 6 recovery 8,19,21,75,79,143 Streamlines 32, 100, 101, 114 Stress 6,49

126 52,81,125

39,41 75

transition

99 TeDSCIr notation 7 Thermal diffusion 9 Time 46 of 95 natural or characteristic of material

48,75,

95 natural rbeometers 35 Transients of stress and strain

11,34,48 19

54,65,104,127 32 oatcn-i[O-[)aI(:n variation 93 dellendellce on stress 52 common materials 7 Viscous dissipation 9, 10,23,41,56, 120, 137 Voiding, see Cavitation Voigt model 17

3,52,81,107,124 3,11,93,95,96,114,118,133 116,123

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