Polymer Melt Rheology F.N.Cogswel.pdf

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

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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

Notation

Introduction

1 Fundamental concepts

1.1 2e('me~trv of deformation rlleolof21cal response of materials

1.2 Thermal and tlle:rmtodymlmJic response

1.3 "'h\'<i;tI("~1 and chemical

1 Rheometry for polymer melts

2.1 Cat,aDle of measurement Vi~iCOjelal)tic response of melts to deformation

shear flow in a cone and rheometer J::,1(Jn~:atlon;al flow rheometers

2.2 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

2.3 Process simulators

2.4 Priorities and costs for upa

xi

xiii

1

5

5 6 7

9

10

15

17 17 19 23

24 25 30 30 31 31 32 33 33

34

35

3 Physical features and Dow

3.1 'emtl)eJratl11re and rtu:~01()2V

3.2 Pressure effects

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

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

3.5 Deformation 2e()mc:~trv and rh(~01()2V 3.5.1 Bulk deflormlatl<m 3.5.2 hlongatloIlLal flow 3.5.3 flow

39

39

44

46

49 49 51 52 53

54 54 54 56

3.6 Flows 57 3.6.1 flows 57 3.6.2 Pressure-driven flows in channels of other than circular cross-section 58 3.6.3 flows 60 3.6.4 sections of thickness 63 3.6.5 Biaxial extensional flows 64 3.6.6 The interface 65

4 Rheology and structure

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

4.2 Chain distribution

4.3 Chain branctlmg

4.4 M(uptloJl02Jical structure in melts

4.5 plasti(~sers and lubricants

5 Adventitious Dow phenomena

5.1 Plasticisation

5.2 Chemical

5.3 Instabilities associated with a in vis,~ositv

71

71 73 73 73

77

81

83

84

91

92

92

93

ix

5.4 Instabilities in 93

5.5 Melt 94

5.6 Melt memory 95

5.7 in structured materia1s 97

5.8 effects 97

5.9 induced instabilities 99

5.10 Non~laminar flow 100

5.11 Die exit instabilities 101

5.12 Coextrusion instabilities 102

5.13 flow instabilities 104

5.14 Phenomena associated with solidification 106

6 in polymer 111

6.1 Introduction 111

6.2 Low flow processes 115 6.2.1 115 6.2.2 Deformation of an extrudate under 116 6.2.3 Processes associated with relaxation of after flow 118 6.2.4 of a surface a melt 118

6.3 119 6.3.1 119 6.3.2 Distributive 120 6.3.3 120 6.3.4 Work 120

6.4 Constrained flows 121 6.4.1 Screw extruders 121 6.4.2 Wire 123 6.4.3 Pressure-driven flows in dies and moulds 123 6.4.4 Constrained flows defined pressure 124

6.5 Free surface flows 125 6.5.1 126 6.5.2 Film and blow 127 6.5.3 Vacuum 127

6.6 Bulk deformations 128

6.7 Select 129

x

7 Future developments in polymer rheology

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

Appendix 2: Int,,,.rn,r,,.tl:ltl(,\n of extensional vi"{~n"jtv from flow through an orifice die

Appendix 3: The inference of elastic modulus from Dosit~extnlsicm s\lVellin2

Appendix 4: RUlptUJre behaviour

Appendix 5: Data sheet for l"llflHI!::.rv flow

Appendix 6: COlnp(llris<)O rhe:ololgic,al proJJtert:ies of two

Appendix 7:

Appendix 8:

Appendix 9:

Appendix 10:

Appendix 11:

Appendix 12:

prc.celisiIllg nrnr)eT1tv data for a geJler,al-I'urpol~e

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

prC)Celisirlg property data for an In.l lectllon

pr()Ce:sslrlg property data for a and a

Appendix 13: Emlpirlcal observations of flow in channels of cOIlnplc,x

of low-

of

of

of

cross-section

Appendix 14: Flow a slot or annular die to thickness

uniform of extrusion with

Author index

index

133

135 135 136 137 139 139

141

143

145

146

148

152

154

156

158

160

162

165

170

173

176

Preface

rne:OI()IlV and the assoc].ate:d sciences and tnc:~rD110a'v",amlC rc:~srx)nSie. DJIlVS]lCal and chemical

which form the methods of meaSlJlnl1tll the flow of on the

InS>UJflYU 1981 F.N.C.

Notation

R L R' L' Q p

y n 11

recoverable elong,lU(Jtnal

Introduction

material.

raw efficieltlcy in the

de~U2rled nolvn1er to suit a move towards

interaction ae\relCtn new or

na."m()flU)US raw

literature both in trade and m()flO'2fC1PtIS:.l-· I :.l have been

tne:or~v-ess,en1tlal as a basis from which we can progress t"n~efi()m~en()IOjglCl(l1 and discuss effects

��

2

The OOlectlvc:!s of the res:eaJrcn from which this book l1p.lrn.l~"C are:

ext,erien(:e of a material in a t'"'ru'ulp.:I""irln nlrnl","'Cc'

response of the

ort~all;:t the 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 into a cOJllplex

nOlvn1er rnf~OI()OV cur'rerltlv ~nr,p~rc to be in and the first the final clalntl(~atton.

��

3

more £1&>"'11"''.11'\1"" then~ 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

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 been laid on construction of between those and several books 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

9. 10. 11.

12.

1966.

.... 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

..... .,.£'\11" .. "'" is to geJleral1~;ea materials

eQtlatllon of state. The 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::

llratnular-1the form in which materials are fed to the process melt -the form in which are nC!11!:llllu Sllat:.e<1 solid -the form of the final one in which some Sbalpll1lg

may

��

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

1.1

stress

strain

rate

y

1 Ii

shear: area A and distance h remain constant

1

deformation

(b) In simple extension stress is a01)l1e~a normal to the surface of the material

stress UE:=

strain (unity) E:=

rate of strain e

��

7

extension: cross-sectional area A and I both vary

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

lUH1'3111"U 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

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 10-5

Water 10-3

Olive oil 10-1

loo 1()2

1 (lLl 06 1()9 stiff

Glass 1()21

��

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

riA· ............... '" 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

Stress

Time

1.4 Hookean behaviour

11 ..... 1" ...... £0 .. melts delIDons1tra1te elastic:o-~rjsc~()US reSDO]tlSe to stress. The Max-well model in Hookean elastic <:tn'"lnc:,O

illustrated in

in a

m(jltel~ial will as a Matx\\reH aOl)arlent "'""ro ..... .:""'" an modulus which tel1[)Dc~ra1tune. pressure, stress, of deforma-

nrl'\np,rtll'"'<:t which we record and use are thus the nnJrlnf"pnt

anl')arent Maxwell modulus. more viscous than most

very

��

Fundamental Lo,nce'DlS

a

Strain

Stress

b

Dashpot

Raversible deformation

Spring

Time

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

9

....... h,"'''''.,. prc)Ce!,SlIllj! it is frequently interactions elastu;ity rupture phenomena which determine the

1.2 THERMAL AND THERMODYNAMIC RESPONSE

is as pressure. For a aplueC:lation of tOIl~etller with the nowned as msulClltlJ1lj!

cOlnpres,sio'ilit:y of materials we have ~lr''''~£1I'll

and in viscous flow, rI"" • .,."d'" and SPt'~Clt:lC

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

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.

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

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

in a meltll1l2 omnI-local hot "~a.~~£~~ nrnt\lplm when

m(]~le(:UUlr ",""'''''_HL. RUlnnmg the extruder cold and so hot any material prone to

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 variations as a result of or of meJUIlUl instabilities in the screw. are at their most severe in which the extrudate to be or to stretch and blow where local variations in result in amounts of stretch. The of 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 undegraded polymer in a matrix of material. While the 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"'<l of it is rnf~OI()1!V interacts with the

��

Fundamental Concepts

RBFBRENCBS

5. 6. 7. 8 ..... "', ..... ".

13

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. Demonstration of a pn~en('m(~n(Jln mvestllgalte its and its DOltentIal

effect. The of new which into novel

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 measure-ment are 'Is it and 'Is it sufficient?'. If a is the only one 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

PV1,.....,."·.A .... I"'A for a more review of rtu~onl1eters undelrlyiin,g their use several texts are available ,1-4

��

16 Melt

Table 2.1 Classes of Rheometer for Melts in Common Use

Classllkation Method Variables Limitations

ROTATIONAL Eccentric Strain shear Near to linear METHODS disc and and and

'balance' Strain rheometer PRECISE DATA

Strain Strain rate Strain recovery Normal stress Stress PRECISE DATA Stress Stress relaxation Time

Torsion As above

SQUEEZING Penetrometer Parallel

EXTRUSION Melt flow rate

flow Flow rate Pressure

flow Swell ratio Extrudate APPARENT PROPERTIES

appearance COMPARATIVE

ENGINEERING DATA

TORQUE Instrument COMPARATIVE extruder

'Brabender'type force Resistance to flow volume

fREE Extensional SURFACE and FLOWS

PRECISE DATA Strain rate <1 s-1

Extrudate force Drawing

CoMPARATIVE

Sheet inflation PRECISE DATA difficulties Bubble inflation Biaxial extension

COMPARATIVE

��

17

2.1 RHEOMETERS CAPABLE OF PRECISE MEASUREMENT

2.1.1 Viscoelastic Response of Melts to SmaU.amplitude Deformation

The and measurement of

rate in

of oDtalllllDl2 nrpr'IClP

mOlduJusarerreQuen4~-IOel)erldent.

amlpJlltu4je-.aepeJ()d4~nt because maximum strain sut:t1C1~entjly small that from

are rare, "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

int1en:.re1tatjion rest on whether stress or strain assumed to be the co]tltr1oUiin2 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

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.<lel1t on treQujenc:y ui~£"ru:!itu and m(~aUIUS

re~)re!)entat:i.on .of the same data may be made

the material is reS'P.on<lltn2 and

.of a these

..... ".rt.li" lIJltelrchanjlea.ble and contain the same mt.onna1tl.ol[}. rer're~;entatli.on of data is an in their <ll2.,estl.on

J.UUi...,...,,", at sul11Clenttlv t.o a Maxwell m.odel.

noilvnler melts use the Maxwell 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 the .. h",.file,,,,,·., of melts are:

tecnmQuces have received and may be used to .obtain on~Cls:e in the linear over a very wide range of treQU4enc:y

(ii) a direct measurement of elastic as well as viscous Dr()Oertu:~s--anld

��

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 g£'Tln<lifi'"

nr£"'I,.,-t",C! a solution-

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 this method of has an <lirl'"<li.."tO€~'''

stress variant in that, when the reaches constant re~IOlJn2.

Cone and instruments may also be used to determine the elastic reSPO]llse of melts. Several measurements can be stress and

transients to and from normal stresses and recovery. The between such responses and measurements has been the subject of numerous those and .l.,.;v'""J'.'..,.

evidence can be found to of COI[lcIUSlon:s.

��

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

That thrust is most measured instruments in which the strain rate is accounts the common for that class 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

��


Strain rate

a

b

As set up and running with no 'overshoot'

Time

'Overshoot' evident

21

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

b ~eciondlarv

the of the measured. rheometer higher stress

cone and rheometer

""'.1"1"''''' and so on the stress in a double cone

ins,trtJlm~ent to be used at much argument «~«lU"" the of the

stress OVcerSJno(lt for eX~imlple 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 measure of elastic has the additional while it is meastJlreci, it is the thing which is nallJPCmlJng. ae~;tgJ)ea to measure strain recovery after constant-rate aeJtormaltlOin

��

22

Measured

c .~ (/)

Applied

Time

Time CONSTANT STRESS

Yn.I\IJt1"1Pl' Melt K/1;eo,tolJ.'V

Time

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.''' .... T' ••

ment at constant rate is that it time to reach equlllorlUln response. This difference in demonstrated for a Maxwell model under constant is attained instan-

while under constant strain rate the to condi-slow

oPleraltlOifl is that most

at constant shear stress are more Ois.criimj,natoJ~y shear rate in non-Newtonian svs;telns.

The of cone rhc~OInetrv are:

nrf~Clselv defined flow at low shear stress. on both aDd in a of

As a measure of under low stress it is sensitive to the structural characteristics of the which structure may break down 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 of has advanced more t"!u'\U11Iv

than flows. This progress

The slmtph~cltv how it <lerrOrnlS and the ten.<leltlcy reh:ativelv crude lnstrume~nt~i.l;)"lO while more SOt)hl~;:tlcate<l mlaCJt1lnleS""I-.;)V on a broader range of ma:ter'lal:S,

measurement are now COlrnntler'CUllUy

flow measurements have a measurements in that the measurement does not involve an with the wall of the so that is not a Such measurements are of direct as of the ............................... r1T'!:l'lll1nrtT tions and are of considerable thf~orebcal sig,ni11cCllDc:e ret)reSerltII1U! the of irrotational flows which are rurlaa.memt~:lUy from shear flows. the of measurement desirable to carry it out.

��

24

2.7 blongatlOnlal strain rate, E

Stress

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<l.

ments the small reSltOUal unrc:~coveJreo may be tnt'p.rr\ ..... lt ... rt

aetonnatlon in ClrlCUtnstaflices where Ul~lt1t'IIO achieved would allow the to neck.

recovery aDI)ar~ent rate of viscous

conditions to be

The most important in favour of direct measurements of elon~(Jltlonal flow is that such measurements can one Oflieself of the between shear and extensional flows between materials in flows. Both these a crucial role in the which follow. The trenchant such

that they require a deal of and that is a very

2.2 MEASUREMENT OF APPARENT RHEOLOGICAL PROPERTIES BY CAPILLARY FLOW

The that we can only determine the nrf"{'n~p rJle()lOI~IC;al ft ...... .-.""' .. 1· .... '" of polymer melts under a limited range of are of limited interest leads to a quest for other of measurement. The criteria which these methods should meet are:

should cover the strain rate range of interest in PfilCtl.caJ prc.ce~)sml~ (up

measured should reCluurea so that it may be

The should be {,{,U'1VP'ntf"ntllv

(better than 5

property

It should be pm'SIO.le of less than 100 g and Drc:~feI'abllv as little as 1 g.

Capillary flow meets many of these reQluir·em,en1ts.

��

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 POSSlltJle cOllVe~nl~~ntlv to measure shear stresses in 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 equilibrium, will take a of size to accommodate a melt pressure transducer near to

Intlerpretl!ltlC'll of Cal)lll:ary rne:Ofiletlry the PoiseuiUe eOllatlon aPI)ar,ent rather a true measure of uu:r .... nc"f"u at the op,eraltlnl2 f"'.rn .. ""' ... :l_

of corrections is the true 'ittl;! .... nc:l .. u

.. 'V" .. """"' .... "u. is recommended:

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 Inlluc~nc:e 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

��

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

27

L

POI,st[,le. measurements when the measured

.,.,., ....... ,,~~ nh~~p."'llP.<1 that a

Pressure

L/R correction

wall shear rate shear stress

col're(~tlv as gn:ullcent may be of several but this extensive

poL "',_,,"' __ , the choice of two dies The colmlJ-im,ne; a die an orifice

where is the pressure Some eX]:>erlm1ent:ers

��

L/R a b

L/R

Error band in pressure

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

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 land

Die exit pressure drop

2.12 The ends correction is a COfnOC)Ullld of entrance and exit pressure

10" 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 'i (,-1) J

1000 fI) • • 100

• 10

2.14 Effect of die lentnD-to··ra<uus ratio on po~.t-extrllsi(m SVveHlnil: DolvDf'OD'vlerle 230/2 15 at 210°C

��

Vr..h'"'Ior Melts 31

2.2.4 Observation of Extrudate Appearance

extrudate from ........ ""cu."".. ",,'rn'U,.rt.,. useful non-laminar flow or sUlta(;e nnDer1:ec'tlons. non-laminar flow occurs the

for nr£,\n.,.rf'u"'C! no hold and data 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 app~arance, Where .", are the index, shear viscosity

capillary at the same volume flow rate.

��

32

2.2.6 Accessories to CapllJary Rheometers

Stretching Flow

Polymer Melt Rheology

An obvious access~orv to an extruder is an instrumented haul-off. Measurements of in-line tension, and rate can of value in comparing the stretchability of polymers. to carry out such the use which has been in many

demonstrated that clipping a weight on a sample and allowing it to draw it solidifies is a method of comparing highly viscous in stretching flows, and no of measurement could possibly be less that an extruder exists. The main drawback of all such measurements is the difficulty of the flows, 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 influence of that important, though often parameter may be evalu· 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 direct measurement of the streamlines and of stress during flow. 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 Polymer Melts 33

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 cornpJ·es~.jbi.lity of melts. In a study it is

cb~lrec~s different volume to allow correction for tantgellt bulk modulus, is VdPldV where

2 .. 2.7 The Melt Flow Indexer as Rheometer

The Melt Flow Index is a control test used to assess the of a standard conditions. a melt flow rate is extremely

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 can be miniaturised to allow measurements to be made as 0·1 g of In a small the of

leaKa,~e become severe if a ram-driven is used: gas pressure is more A of miniaturised and

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

a COlnpanlUv'e test.

��

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.

are ne~cessal~V favour of pnlctlcal flow in mOlulcts su[nec:n\ire assessment of

2.3 PROCESS SIMULATORS

Sh(utlcolmrl2S mean

caJ,aOle of ....... L",.,rh..,in

Avir ... n,rt~jr ... on which a

shc)rtc:omlmjl~s: a the shortest time time-scales often

so that the melt may

mlrlUte$. These

may aUow a true response of the in out rheometric measurements at a best we can do with is at best an "'". ............. " nr~(" .. Il·A

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 as ...... <>10"" control tests when eV~llmltjrlg

.,,,,o.l'''I~-UU of ext:)enefl(~e

value in establlshmg two materials. The rt ........... "' ... of such teC:hnlqlles which may of itself ob~;CUlre

which may be prc~mlnerlt pr()OllctltOn eql.npment, and versa.

��


The geJilitlOtn of all polymer prclceS.Slng. AV~IUAnle to make qualitative and co[np~lral1ve measure-

nrr'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

and it is often to 'run in' the surface is attained. Although it

the instruments they are commonly used for rate of gelation is a critical feature to the process.

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

laboratory with all the equipment which would be nnl'urn,ar p]rocc.:~SSU12 could cost £250000 (1980

r13£1'I1U-13 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.

Essential. A Melt Flow Index tester for measurements and OUiuu:a-tive assessment of behaviour. Such equipment is obtainable for about

Very highly desirable. A .. <3 ...... _,,, .. .,."'; • ., c~lPi1llarv rne:O[[lett~r

ducer located in the barrel above including a orifice die _ This will allow the measurement of enJnn4eerm2 erties according to Standard recommendation and is currently AV~ulAnle at a cost of about

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 recom-menae: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 tech-niques, 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 labora-tory for a modest a second becomes 'Can we afford not to have such a labOratto['vT

��

36

RBFBRBNCBS

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

6.

7.

8.

9. 10. 11. 12.

13. 14. HenDOw

15. 16.

17.

18.

19.

20.

21. MaJrcwell.

22. Coi!'sweIL

23. 1979.

1975. J(n~wl'~Klcal 1 j~chj~iql.teS, Ellis Horwood (di~.trit)Ute~d

dyrlamic response of

and

IS9,

Plastics J::.,n,~lneer'InK

Research Notes in Mathematics No.

24. 'Munstedt hl()ntl;atl0nlll Flow Rheometer' built Rheometries, Frankfurt and New

25. R. Extensional flow of nnllvlO:1'vrf'np

1965. 26. .....V11I."""'U. rhc:~ol()gy of ool'vmc~r melts under Plastics and

��

37

27. Rheometer zur der deformationsmechanischen schaften von Kunststoffschmelzen unter

28.

29.

30.

31. 32.

1961. 33.

34.

35. 36.

39. ""-Vj","""",u,

40. 41.

42.

43.

44.

45.

47. HJLQ<l'A"''',

48. :swcerclJ[ow

49.

50.

51.

8 1969.

bl()n~:atlon.al behaviour of a low

The realities of Plastics and

""-Vil:.i:ln,""u. F. N. and Krul,

elong~ltiofnal flow and failure of 1978.

"",.."",lVILI. Godwin, 1981. 34,

Doilve'thv'lel1te melt l"h" ..... II', .. nr

t"vtl"l1".""n sWleUiln2. Journal

8

phcenc~m(m(J~n of draw resonance in 1966.

SpiJlnillg of molten oolvetJllvl4enes. '"TJ.r".J.l.Lh 1972. spInning, Transactions

Dolvethvliene melts in and Rubber

Pn/vlH ... ,. l<fleC»lo"rv and

biaxial extensional

nolvtl1lene. in The J(fl,eoliO"RV

��

38

53. l,;Ofl:sweU.

55.

1975. 60. 'Brabender PJ~COltnar~nh7, made

61. Saddle

W pJ\lnrn Garden

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 environment of two is quite different so 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 ll;re:att:~r at low tenlPerature

very much less seIlsltlve

39

��

40

\

Shear stress

\ \ \ \ \ \ ,

terno.~ratll1·e is the of close theoretical

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

de'velooiine: master curves have also

the different are cOlnmlonllv orocesse<l. several melts may be found in the aplt)elll<ll(~es.

Because of the non-Newtonian character melts the SUI)er'Dositllon of flow curves at different a at constant stress means that there is not a at constant shear rate. For a shear

material on appears to decrease at shear rate

��

P,,"u"'I"'rll Features and Flow

, " " ......

Modulus ......

41

- --

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 for an Increase in of 10°C

Test Polymer RFI*

Branched 150 1·35 200 1·3 250 1·25

Linear 200 1·2

200 1·2

200 1·7

200 2·5 250 1·9

250 1·5

350 1·5

6:6 275 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

Rotational

Pressurised concentric

Extrusion

Pressurised

Double-die method

Non-linear plot

the InOuence of Pressure on Viscosity

Operator

MaxweU9

Westover10

Choi11

Porter12

measurement lDClep'eneJellt of pressUlrisirlg

Direct descendent of l"1U'llll!"TV rheometer

modification of l"Q1'\ .. II,:.ru rheometer

Problems

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 1"Arlln"", .. ,· both free volume and leaClullg to an in VISiCOS~ltv

of pressure on

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

nr~~c!c!ln"p may be corlSldlere:Cl ore:SStlLre. increases the Vl!O:lr-nC:ltv'

50 40

30

necessary to bring the melt back to its on:gm.aJ '''IQr'r''QY,..'1T

turlctllon as

4·8 3·9-5·3

4·0

4-0

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 close these functions that if no direct

measure of the influence of is then the thermo-ClVlrlarmC 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 3·1 3·2 6·7 5·1 5·7 3·6 6·7

5·0 SO 1·7

1·6 X 10-7

1·5 2·2 1-5 1·2 1·1 1·2 1·9 1·4

1·4 SO 0-4

3·3 2·8 4·0 2·7 2·8 2·8 2-7 3·5 3·6

3·1 SO 0-5

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 ccent:12r~l(te theoretical texts asume that inc:olIlpr!essiblle, nrn1.rU1'lnn

excuSle for the

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

have a cornplete aPlueC:latlon how that rh""r.lr"nu mt'eralcts essential to gn'nr~>"l~::t1'~

and

Maxwell is achieved.

time-scale of real be filled order of

Evaluation of creep eXlpel"lm,ents under constant stress before flow is

...... -

0.11' l' 101'

Time

3.6 Im~e-aepfmC.1ent apparent Maxwell parameters

��

Ph\J(,I,f'nl Features 47

109

10·

107

/

106 / /

105 / G /

10· /

/ 10-2

Cvclic loading ~ (s/rad) Creep loading (s)

3.7 compan!mn of and osc:lllaltOl:y shear flow: at 20ne

established allows the mtC:!fPret,ltlo,n of tllTle-cler)endelflt alDoBlrellt Maxwell pal~alTlet~~rs:

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

where stress and strain are nr .. "nr\rt1nn!:l1

evaluation of as a first

llelrWf~en ani~UUU I1'eQUellCV and time texts, for eXclm1ple 1-<1"'11*"11,)

a series measureCH}SS'-DI10IS at constant maximum

tlnle-1C1el)erldent, response in the non-linear

t1vln~rnlr aplprC)ache:s, and from are consistent

time-scale response is truncated.

��

48

10 Time (s'

Modulus (N/m2)

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

Time (s'

Stress (N/m2)

- -

10

3.8 DVflamjc response data in the non-linear 0-3 at

retllectlna the of the time-Df()Derti~~s is the memory which the

nmle-~iCaJLe for which a material has a the natural time of the the

ratio the vU::,f"nc:tth,

time-scale of a mattet"tal Deborah number, mountains melted from

flow. the 11""1'"'1'1\, .. ,11 the

process

such that if > 1 the process is dominantly < 1 the orC)CelSS a)lal~(SIS it essent:lalllv In use of this COflceltn

material. If we COI1SI(ler comer fol:loVl,ed

consider two Df()cesses:

since the

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

material characteristic of the

of a low stress deformation round a we must

I 100 s

= 10

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

the stress levels which liquid ~v~tenl~ cOlnp.an~,on with useful solids. water will cavltalte"U

Tnr'I"P/~rf"~ at often an indication of telltsiotn tliinnilltg t)ien2IVI()Ur

and a transition to SU),ertlclalJly lDcrealS1I112 the rate at

a b

3.10 a ~UI>erJtJClciUy brittle failure b failure

even when all contamnnants, the

��

50

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

Experiment

Constant-force extension24

Orifice flow

die

Shear

Shear modified

There is also some indication

150 190

150 190

::::=10 atm

::::=100 atm

bmefrilnglenc;e at the entrance nnll"C'f'''r~''np COJTef>Do'nome: to a maximum

IO\:4/-c1I~ns;ltv nnlh.lp·th'lI'lp."p the

0-3 0-7

slgmtlca.ntJy increased by a small of crj"staJIlS'atJOn.

presence of toreuz:n V-V\.IJ,,,,.,, increases the to

assoclate:o with such contaminants.

��

Physical Features and

0' 3.0 '';; ., ... ~ ., ... " 2.0 c:

c: •• ... ... en

o 1 3 5

10

51

PVC at 170"C

OOSSll[)!e 2eller,al e~J(pl,amltlCJ~n of rupture behaviour is that it is associated n""i~u1l' ..... 1r on a scale of about 100 nm. Provided the tensile stress

enOUJlln. surface tension suffices to such faults stable. Ho,mC.2elmSlil-In'u'U'n1lTPri gel:atlCm in PVC achieved use of orC)Ce!iSllll2

nVIClrc.st::ttlc pressure all to reduce characteristic of Whether

tun:Clalnelltal to theOff:tic.al work .

material or an artefact remains to be estaOJIISJ"lteCS

... , .... 'V~' ... L.., is the ultimate method of failure both in thin sections such as and fibres due to rlr!UXT1ln('r thick sections where the solidification stresses cause in both those extremes normal is most cornmonlty an intermittent effect with stress and is most ... .:><::.£UII"

achieved notches both in the material and in the is also the critical in the initiation of 10c:llmln2.

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 The same qualitative reSPOI!1se

For nn,l"rr.,,,,,,.. melts the bulk mc.csuJUS t1'''''''.'.:lt-.,.... than the shear mCJtCSutus

a nnl"n,,,,,,r melts.

some five orders of for purposes,

��

""rulc!c!L'l.n'C! ratio may be taken as 1/2. The bulk modulus with hvclrm.tatic accord!1D2 to:

+9P

When is the bulk modulus at pressure P above atnlosphc~nc and is the bulk at atmlosptherlC pl'eSS111re.

The shear and

In may a critical role in ,",-"U.'U..,"'''''' 6), and the faster a process is

elastlc:JtV is also manifested in the have a

3.4.3 Viscous Response as a Fundion of Stress

The non-Newtonian behaviour of polymer under both shear and exten-rec: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 ~ Shear

Viscosity ~branched

linear

wide molecular _______ .........;;w=eight distribution

Stretch

3.12 irrotational flows

shear and extension: the distinction between rotational and

of course, to real rather than the cl1()Pt:)ed "c!1.~111" h,P'!:I'lftiU lubricated with tomato sauce. If a bowlful real

dj~:211112 in a fork and move it from

��

,..I-ntc-'p,,.,1 Features and 53

3.4.4 Modification of Rheology by Mechanical History

rl4>l'!~T'int1, .... n~ of assume an state as the nT'~'~Tl~~1 pr{)Ce~;su1Ig sItuattlO>DS, material response at any

nT'~.'t1U'Ul~ thermo-mechanical

reductIon in

eql1ilibri1um will reflect the eql1ilibrium nr ... ,.n""rt.,,,,~

eOl1ililbrilum may be Slgll1ltlcarltly imt>ro'ved me~cn,am,cal urr,.rv,"nn may be the most effectIve

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

Melt Dow Swell Thermomechanical rate ratio

0·28 1·47 Shear modified 0-66 1·14 After solution and 0-27 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

��

Physical Features

Cross·sectional area A

Force F

3.14 Stress variation in volume flow rate

Vo at die v

U.,.I,~t"ljr" at haul-off

Draw distance s v

ara.wU12 of an extrudate

55

stress sut)lej~t of a

close approximation to that the stress

(JE FIA

where has its maximum at the nalLU·IOII

The total in the process,

e

the time-scale of the process,

t slv

Comt)InJtn9; these we obtain aDllar,ent extensional vlscmntv

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 '. 'n .................... section of extrusion die

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

surfaces

lrnlnrn·t~t1t t1lttl"·t'Plnt"I"·":: 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

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

3.17 Shear effect a sQuleez:m2 flow

aDI)earS to

3.6 FLOWS HAVING COMPLEX GEOMETRY

of UI",,,,"OIl"hi i(len'tifit~d the fact that

.... ,..1'11 ...... .,... pr{)celssil1l2 we find many flows

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 pn~sslJre-dr'ive:n tnrlOlUlrn an annulus the mandrel is .. " .. ,.. .. "",rl4,,*

is the volume flow rate and !J is the rate of rotatilon.

extrusion shear

rotational shear rate,

normal addition pr()celc:tur'es.

total shear rate,

= 2n:RDIH

= +

��

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 rate

Rotatiooal Total shear Pressure drop, P

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 of the minor axis of the included 2b of the axis of the included 2c chord the axis of the die

of of

area area

��

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

Ull" ..... tr .... u.. shear

Shear rate Stress

y= 1

WOlrklf:l2 re~latjion:)hiI~fur can

cOlnolex cl1,mnels can

estjibli.she~d formulae:

y= + shear

Pressure

= 1-0

Swell ratios for YR >

dies (

��

60

Swell ratio for zero ."",.,,~ ..... ,

( B.,B b : (exponential (vii) Dies of zero

3.6 .. 3 Converging Flows

In rnl'V""rOllno

flow is sUJ)el1po~,ed 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

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

the interaction between the flows addition of the shear and extensional

One cyfmdlrtcal flow:

ilie fur

pressure + where is the COfltrilt>utton due to Sh€~arl!Dg flow and is the contribution due to ex1:en:SlOlnal flow and

tan 8

where ro is the die radius rl is the die exit radius 8 is the half of convergence OSI is the ,shear stress to the shear rate at die wall at the

Yt = the volume flow n is power in the relation:ship OBI is the extensional stress average extensional

strain rate, £1 = tan

��

1.1£ .. , ... "",,1 Features and Flow 61

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

for streamline

therefore

whence the half

shear is the dominant flow rel:atl()nSblp between flow rate

COlnp()llelnt At about

mm

130 S-1

tan (J = 2 x 7/130 = 0-1

of convergence 6 rI"' ..... "',"'.,

If

stn~tcl1liD1:t rate rupture, the

At the becomes

we

��

62 Melt Rheology

were used to effect the whole of the reduction from 20 mm to the length of the would be such that 91 L = 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

tan i.e. 7

i.e. r = we may dele1u(;e 14 = (4 x

m and ro=2·2mm nr~,.tprrp,rI die for this extrusion is one that reduces the overall by

and from extension;

Pressure Swell ratio

Further optimisation may in be by

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

exp ERI

COJrre:soCtndine to the stress at the die exit COlrre!mcfndine to the extensional stress at

value

.... """,11""''''' and dies with contraction U!:ll"'!t1'1i'" from 0-01 to 1·57

deviation 16%

for flow

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 Flow 63

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 thickness is This can, of the die to the non-uniform jntlatllon

8 b

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 cannot be To overcome this

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 <>, .. ",." ... £'1 the die we see a Qua1i1tatiive

��

64 I'rtl\1"",(1'" Melt KnleOlc:»gv

Pressure equa'

~

1 Thin section

1 " " .. -'-

Thick section at

at low -+ HN +-velocitv

Uniform velocity

c

velocity b

a

~tt"~lt,,"{nr has been used to obtain a variation of 50 per cent in pal~ISOln tJlllCKness~ 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

shear extension

Pure shear or Uniform

Modulus G

3G 4G 6G

much less I.U'-''''""U some indication of the (JeICluc!eO from studies on solids

Ilm.lUrlg elastic response in 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

If a melt flows dltter,ent uu:!,f'nc:!.tu one of two

Slt1Jatlofls can occur. the before whereas

through If we cOllsuier the of the central of the interface then we

define an acceleration factor N such that of the interface is where Vis the of the in uniform VISICOS,ltv tube.

if M is the of viscosities of new and old studies mdlca1te values for N as shown in Table 3.8-a may be

��

8

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 Centreline

1()4 0·55 1()2 0-65 10 0-80 1 1·00 Stable 0·1 1·20 0-01 1·32 0·0001 1·40

Skin too viscous

Skin too fluid

b

3.27 Sandwich mould!m~

��

Phuc;ronl Features

The above

REFERENCES

of nr.I""",,,r

pffiPrtlvP if the new is of lower a

on the wall of the machine from which it viSicm.ltv of melts is sensitive to teIlt1oe~ra1turc~,

own source of non-

this COlnoletle. it indicates that that

oot:imi~ationandex~.loi1tation,

L N. and Bulk "tel'ne.t" of Dolvmc~ric ':)1'':)I',",U',:). Journal tJ(..lir;;;ru,;.r;;;. 37,

2. J, D., Viscoelastic Prl'linprtiPfl Pn#Vn1prfl 2nd "''''''''U,II. ,",uat.Jt,",l

3.

5. Johnson.

6. Malrkm,ritz.

9. Ma~"weIL

��

68 Polymer Melt Rheology

to.

11. Determination of melt VIs(~OSlty an extrusion Journal

12. R. R. S.

13.

14. Lm~SWE~1I

15.

16. MelLssnler extension of pOIvmc~r 1972.

17. Macdonald, I. the Khlf!0IC1R'V

18. J. J., '-'Vi~W""U. viscoelastic

19. Deborah and Barak in H. K. 1960.

20. D. C. F. and

21.

22.

23.

24. Swcerdltow

27.

28. ShtJrrk.f,kin.

29.

31.

pb~rsic()·ctlemlical pro,perties of

extensional rheometer for uniaxial 16

Transactions Small deformations

International on H. Influence of

non-Newtonian

dVlllamlc response of

LJetorP1Ultiol't. Fracture and

Rip'pfr;no"pn/~p to Studies communication, 1979.

me:tl:Ulcr:vla1te C4Do()lvlnelrs as aids

nolvmcer melts, Plastics and PnlvmpY<il.

Comparllion of the elongcltio:nal constant strain

colnp;ari!son between YnIVPn,r:-r bnJllrneC:!rtfllJl and Science.

��

Physical Features and Flow

32.

33.

35.

36.

39. AJ .... " ...... "'.

40. Middleorlan, 41.

44.

45.

46. 47.

48.

52.

(with 382

pOI,vm,ers in uni· 11

rhe:olo~e;lcal ec::tuatl011S of state, rr()Cec~all'tgS

mtc~e;nlttea strain 1966.

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

Applicatic)O No.

elone;,ltIOtnal flow of nnlvml,,:r

Plastics

��

70

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

54.

55. '-AJ1i/:;:)WCU.

56.

57.

58.

59.

60. 61.

62.

63. 64.

·nn\/.,.,.'lYln,n flow and flow: a cOl1npilabon. Journal 4, 23--38, 1978.

of melts in extrusion

lDI1ectJIOn mould

R., Biaxial extension of an elastic

of non-Newtonian fluids-a "T.J.J--.. ... u. 1971.

conlmutnic,abon, 1974.

Plastics

Sandwich Plastics and Pn,fllnlfPY!.C 39,

��

Rheology and Structure

Easy

Difficult Service properties

Poor -----1 ___ -- Excellent

4.1 ..... n/ ... .,. .. ,h.,." and ease of prClcesismg: a common

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 C C/ Polyethylene

/ \ / \ / H H H H 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.

��

4.1.1 Chain Length

For a nn·lun""" ..

from

L=

where is the and

4.1.3 Molecular Aspect Ratio

Returning to the we may an1ticioalte

to a first aPlprctxiJnaltiolll, ratio of

molecular

the

is the molecular

73

is oDltaule<l

of the unit.

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

D M Polymer (m)

9·1 x 10-12 -20 180 770 5·5xl0-10 60000 1-2x 1()3 2-0x 1()4 6·0x 1()4 3 0-06 6·0 10 210 770 6·7 110000 0-8 1·0 4·0 4 0-08 4-1 50 250 730 8·4 200000 0·4 0-5 2-0 4 0·08 2·4 100 300 950t 9·6 400000 0-3t 0-5t 2-0t 4 0-06 4-0 60 260 BOOt 6·4 160000 0-3t 8-1 -10 190 1190 4·7 58000 3·0 10-0 20·0 2 0-03 7·6 60 260 1010 5·3 69000 2-0 10-0 10-0 1 0-02 5·6 70 270 1210 5-6 100000 5-0 10-0 30-0 4 0-06 5·3 40 240 1086 6-1 120000 2·0t 10-0 30-0 3 0-02 2-6 110 310 1020 8-5 330000 3·0t 2·0 8-0 4 0-15 4·5 220 420 1060 6·7 150000 4-0 8-0 30·0 4 0-05 3·2 -120 80 950 8·3 260000 1-0 1-0 2-0 2

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

��

Structure

For the sake of this cOlnp:aru;on we in the form of three pal'amlet{;~rs:

the at a shear stress of

a sinlplifie:d view of

the at a shear stress of 1()3

at, the shear stress at which

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 the latter an elastic shear strain or function.

Melt rne~olol!V <l~eDen<ls

Table 4.1 magmtueJle for rioT"''''''',,,,,,,,,,,, nnihln'&>r~'

makInlg as necessary to make any

The choice

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

metnet<l of measurement an the ",,,,,, ... +1,;,,, •• ,,,,.,. values I work from that

we of the structure. attribute the chain stiffness to the t1e'~ibilitv

ratio at 200°C above but variation

H.lVUU.JlU.". 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,

The which seems least consistent with the is one

��


Table 4.2 related to Molecular Weight: PoIy(metbyl methacrylate) at 210°C

Weigbt ... .,..,.n" .. ..,

molecular

34000 75000

160000 360000

2x1()4

tleJnlJlle comonomer in tenlJ)erature and so the ",,,,£,,,,,£,"tu

600 16000

400000 8000000

30 x 1()4 8 x 1()4 3xl()4 2xl()4

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 non-Newtonian 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 and the~exc~pltlolns.

One such exception calculated that rodlike

predlc1:lOn has ��

Xhleol<,R'Y and Structure 77

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

4.2 CHAIN LENGTH AND LENGTH DISTRIBUTION

Molecular det.ermliniJlg the

eXI)rel)sictn as

That rell:lltIOlrlSnllJ) true for a narrow range of molecular wp:tottt~· a

that the 01"P'!:lt&> ..

the orCIOalJlllltv down under

Molecular and number average

sug,ges,ted aJ)l)earS more aJ)1:)r01Pn,lte:

+

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

Mw== ==

average

one which may different m,ole,CUHlf weiolhtliL For

to

��

a

b

104 105

Shear stress (N/m2)

ble~ndin~ s8nllplces of different molecular

Number Oft molecules

COlnoc)ul1ld blended conrtoound blended

..... " , ,

4.4 a Molecular - - broad

b Narrow en1tan2lements per chain c Broad MWD,

��

Rheology and Structure 79

Molecular Distribution A major variant on molecular is molecular distribution (MWD), usually poJlydlspiennty index as the ratio of to number aVf~ra"e molecular

sarnplle has a narrow molecular a similar of so that

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.

causes elastic response in those which is retarded by viscous resistance as the smaller molecules conform. in a <HU'nnll"" of broad molecular distribution there is more elastic response than in a of with narrow mCllec:Ul,lr dis.triltlut:iOll. but that elastic response is OelaVf!O

c: .~ -(/) j ... Q.)

> 8 Q.)

-- - - -~~ __ L-__________________ __

Time

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

If we assume that it is stress which orients the so reduces enltangle~mc~nts, a second consequence of the uneven stress is that the at a lower average stress tail is in on of a of low molecular the flow curve shows two distim:t 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<r;!1hl under Melt Flow

be several orders of malgnltU.de tTr""<lf'~ .. r

dis1triblubon. while at sel,ectmg materials for such aplPllc::atlOI1lS

pf()ce:ss(llbi1lity low stress form I:!tl:lhilihT

the molecular distribution. Howe'ver these ad'vaf;lta,~es str,eDllltn pr()perti~~s associated with the low mCIlec:ulclr

��

a

b

4.6 a

-

, ,


" , , , " -

103 104 10'

, , , \

Shear stress (N/m2)

\

\ \

\

104 106

Shear stress (N/m2•

\ \ • I \' •

1\

I I , •

- -. 185000 15000

��

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

4.3 CHAIN BRANCHING

a

b

c

Linear molecule Branched molecule

--------- -+ .-

4.7 a Branched and linear molecules b Shear flow c flow

81

��

N 106

E 'fii ~ ~ 8 .!! 106 >

a

b

104

Stress (N/m2)

---'""1.""",----

Stress concentration

/ ~

106

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 flows. The for the of to increase with stress means that local stress concentrations are less in

��

H.1l~eolof}.~v and Structure 83

flow br<llncJllln:g, it is far

trec]uency and how the OfalnCJlleS

"'.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

ch~m2Ie. 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

nnl11I'1'1'''''' that is cornmonJly plroc~~sst~d ,..,..,'"+'',110 .... ''' 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

��

84

cry'staJltIle polymers often po!)se~)s a remarkable memory of that rec~ry!itajllisling in the same to tenrtpe:ra-

tures several tens of above nnl!vrnIPr.;: is accentuated

to In we noted three ditteren~t::es

in extensional flow h"",t'Hnl'I011r

in the of the rhe:ol()gy history. features SUJ1~ge:)t determined

me~ch:amsm is identified. While all these responses are highly spe:CltllC be considered an

exception rather than a rule, there is nOltnlJ!1f.l. sensitivity to thermomechanical which distmgUlSh(~s rlle(JllO'~Y of such "'v~tp",,,, 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

It with be noticed that nnl'l1rnp.n:z

pla,stl(~S but combination with ad(llti'ves serioulslv deficient.

��

103

102

, , \

" \ ,,\ ,\

'\ \,

85

\\ \ \

104

Shear stress

higll1-visco:sitv incl[)mlpatjlble nnhilrnprc at 275°C

staOUlsers, mould release

nnllvrntprc aimed at COfltiD:nilllg refine

O'TP'!:ltl'"r S()Ptllstlc3ltion in the

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

"'n ... "'t ... nrot ..... n vu.,uu,.:t. it is desirable that the continuous u.", .... .-u,d-" 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

��

86

.: .. ~ ...... ~ .. ". . .. ". " . ...

Shear stress (N/m2)

4.10 Blend of InUJr_v1'i:t"n.~ihl DOI,,,mers at 285°C 66

... "Irtn" ........ blend

lOW'-Vl!,CO!mv cornp!Jnfmt. The of blends is

the concentration of the A review of the

- -- - , " \

\

10"

Shear stress (N/m2)

4.11 Effect of low ratio filler Base MFI 20 at 130QC 0·29 volume cone. aspect ratio filler

��

f(hlf!OIC1.2'V and Structure 87

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

Molecular

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

Log shear stress

resistance to COIIIUloction with

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 gellerau~,eCl with

the other factors mtluenC]lng 'liQ,('ru~thl

1'">-.,._ ..... ,"', the mtJlueloce microstructure of the ...... ".£'1 .. "'1-

factor, The pr(.ce~)sil1lg ht",t", .. ..,

��

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.

10. Uraesslc!v

12.

14. J a\.uv li\..

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

11,

on the Structure

Journal Pn/u.,...." .. Science

��

90

19. C02:swell. On the Formation oresented at the

20.

22.

25.

26. 27.

28.

29.

30.

31.

32.

1980.

on fibre orientation in Journal Materials Science, 13,

Molecule Inrin"t,r'u C:on:ferienc:e on

sUS,peJIlSliOns from unimodal "l(:f'n<:lhr

of the effect of m IlectJlon fibre filled nolvnl'onv-

��

,-,"UIULI""'J. Five

Adventitious Flow Phenomena

The success of a plaS{I(~S pro(~eSSm2 opelratl!On .,.""run',-",£! not the aclue'vln,(1

a desired of energy, but also the 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

��


5.1 PLASTICISATION

All machines have a limited cal,at'1111tv incidence of a 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 this limit. The fact are continually pushed to 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 ~ueo'r~CJP time of a melt prclce~.smig oner'abon--t1vnil~alllv

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 cent of the total that we must treat, and with their three products: 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 remark-As well as product quality, may act as

strless,-concc~ntrating features nucleate other such as rupture in film or fibre pro~ce~isin2.

By serves to lubri-cate 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. When this a local of the flow is lubricated and eases the 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

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

exalgg~erated in appearance and may act as

��

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'' mouldine: by means of a that it is

lDllectlon uV,c"L.J .. ",. The mae:ni.tucle m<!lgnlitulde of the stress the of the mouldmj?;. orientation vary with ))Oslt1:on mechanical n ... ,(~n",.rl .. ::>",

That nr(1.C11](~e both

skin of the "" ... """'+"" ... + in the central

��

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

95

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

i round

~ across

~ round

i across

aU across

sec.anltIOfn occurs in the shear teJ111pt~ralturc~, nor pressure will ehInin.ate

dlsltnbute weld such PflltlCl[)leS

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 ""l"l1it'.1I'1'I;1 oDmple:x and

mtJrodluCltnf! a relax,ltio'n zone

In all these cases the relmjrernell1t in the material's 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.

��

Adven:tittc,us Flow Phenomena 97

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<llln2 should a ma1tenal

tp"'InPT!:ltuTP and shear than its ...... n •• ' .... .,

2eJlerate a new, smaller structure it cases the act of down the eXlstuI2

structure to form new structure may not occur so that the matenal is left with a he1terC)2e:ne~DUS structure which may to defects in the flow. In such materials a of at a low ternJ)jera,tUJ~e enhances tool in its

5.8 CRYSTALLISATION EFFECTS

..... QJt "",,",u.,,;u ... J high stress combined with most

below the nominal ...... "',rh" .. "'" structures which

Such and

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

associated the discOlltiIlU11ty 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

the effect has nnlll.1nrnrn/ll"nfl' of

swell output

��

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

--+ Coo, melt

--+

Hot wan

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 flow is tolloYveCl a constriction Here the VISiCOS:ltv ... 'f''''rI •• ~n .. eXl~O~leCl to the intense flow at the

break up the The flow flow is slow the whole a ternp1eraltulre ... 'rgrUPlr'lY

> 1, where a is coefficient of thermal dltfus;i0I1. x is the half or if it is fast en<)u~:n

��

100

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

As oligirlally 11.,,"Ci"'lMn,:,11

origil1latf~s with the very tensile stresses which accom-pany COllstJ~airled i"'r\1",u~ • .,.ftill'\c" flow at the entrance to extrusion dies

Recircullting .~I~ ~~~y ~ltJ or'dead

~(6 ~:;-Iamln.r ~~

I (,\> \ 1'"\ J \ .l

Rupture at entry Triggered in die

Chaotic Regular (tension-stiffening melts' (tension-thinning melts)

5.7 Non-laminar flow

��

Phenomena

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 remote from die the flow.

As a result of many prc'ce~;Slllt~ Oloerat14:>ns laminar flow at extrusion rates two would cause in

5.11 DIE EXIT INSTABILITIES

tensile stresses may also exist at the die where the surface

101

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, pf()CeSSlm~, when

corltarmnate the extrudate so

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" have led to err"''''"11'n in coextrusion This tec:nnol(~2Y with it a new range

tenaeltlcy for a maltenal 'l11<>,('>n<>,.i"u4L. makes it erA .. ' ...... ':1'II1.1 same

A -I "" 3

Shear rate

5.11 Inters,ecttnJ?; vis,:ositv/~,he(u rate curves of two oo)vmiers

��

Adventitious Flow t'n4~nOtmt:~na 103

As combined Shear rate profile 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 different elasticities interface may stress effects at the interface.

Secondary

Primary

5.13 """"JIJ""," formation where a stream meets a 'weak' stream

��


'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

A further form of coextrusion defect is a thickness of COCltlIll2 ... "",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

where h is the H is the of the sheet and N 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 a defect sometimes described as 'runny paint' other observers have that it can a effect for decorative finishes'.

5.13 STRETCHING FLOW INSTABILITIES

processes blow and vacuum TrU'rn"nn to 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

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

c: .~ ';: tU >

tralllsition to a more favQuJrabJle

~OS,SiblUtv of break bV

\ \

:: Viscosity , Elasticity dominated

...... ~ dominated .¥ u :.c Rupture -~ ',~---=~----------------------~~~~L-

Haul-off/extrusion rate

5.14 Thickness variation as a function of haul-off rate

.,.'V ........... ,u· local variations in Vlscm.ltv'-lthe £1T'!:tUTllno more the more vis:cous--lieaclID2

to local variations in Vlcf'nc:dv

relJtresent real dltitercmcles but may reflect diflrercmctes ture or variations in structure from the thermomechanical process

the

The conlblflatU)n annular die and a SUl)seawent dralWIlUZ

from a thin or narrow may lead to a "'11.,·t-tu~T' form of

I

I

I

If the melt

bead

5.15

of the die or the

Curtaining

bead and ·cnrtaj.ninlJ;f

cirlculnfe~re)lCe 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 1 I

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 at room ternpleraltUlre melt can be as much as 25 per cent.

:rYistaUls,atlion is a nucleated cOlnp()Sitlonorofpn)ce!~Slf;lg

be nlcrtnrtpn

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 Phenomena 107

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

and thick secltIOlltS. of the section

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

Conclusion

elliptical section

5.18 Defects

Void

of thick sections

The and the

that of 'melt fracture' and rp£1I11U'P IIlst(;~ad

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

REFERENCES

1.

sur'nr~ess1ion and eXJ)IOI.tatlon aSSOCJlat~~a with .... r.llu ..... "" ...

Structural foam mouldm~ with 1979.

from the more phl.lOS,optlV of

surface

2. Note PP TD leI J..-IUIUI;#'U.

1972. 3. Borocz, L and Kubat, J., Phase seV1anltiotn

Plastics and Rubber 4

��

4.

5. :SChmldlt.

6.

7.

8.

9.

10.

11.

12.

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

15.

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

17. MaCklc~v

18. :southern.

19. D.

Dollvolefitn films

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

behaviour of stress crvstailltsc;:d 1977.

20.

21.

22. Meltzger.

1964.

flow of 19

and

Modern Plastics

4,

23. Unstable flow of amorplbOl11S n.nlv:me'rll: tttrmlgb caa: .. n~tnes, l!,n.gmeermg and 11

��

Adve1i~titijC1US Flow t'hj~nO'mE~na

27. "t:lIIUlcUU,

28.

29. 30.

3L

32.

33.

34.

37. HulilmBLnn,

38.

1975. 43.

polvm~ers: a second site of melt frt}lr-tnlrp

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

Transac-

Plastics

Transactions and

Plastics

Journal

Transactions and

��

110 Melt

44. Interfacial flow 35th Annual

45.

46.

47.

48.

49.

50.

51.

52. in molten 8

53. Science and 1967.

54. effects on

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"'<l1

aD1,rO,aClles to such processes material response so that the n'lllrr1!:U:rp

be most fruitful. IJ'nl"ft'1i""r(.' are converted to en(l-oroclucts

prc.ce~iSU112 operatlO[lS are directed at 1l1".Up·UU110'

mCJWlng·-llut in many cases a orcJduct I1nJ,prc~p tc:~cnnOJ021les. open container could

pressure tec:hnolc)2V

filament welded from vacuum formed from blow moulded from tubular &l>vf· .... ,-i<lt""·

mould

Dn~c11.1de the

��

112

-Q!)

o u

A

, 0 "'I,;

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

Number of mouldings

c

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<ltInlg to a substrate or oxidation to achieve a nrilnt~hl"" surface. is often the rate-cletl:!rnlininsz process.

��

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

or uneven because of ex~cessiv'e reliance on heat l'f""""'1"<:at""rI local shear regIons, may as a DOlrri(h!e-lil~e in

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

may be uneven. CO()llDr2 rate interact-

or or result from

CO()JlDISt air may cause a of the

mspec;tlCtn of the ...... r,rln,,..t and of the pr('ce~)s .rI""nt.lh" 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 1'h.,>",lr' .. ,."

��

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

Each class of flow may include response.

6.2 LOW FLOW PROCESSES

viscous or

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.

elastic

uu .. ,,""' ....... JiioJ 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

t t t , t t Heat

Powder

Melt tension

t t t t t t Heat

6.4 The smt:emlg process

resistance

This reJfltlOJDSh.ip nrt"V"A,t:'C! is not heat transfer as it may be if the n'2l1 .... 1t"·I#'OC! are too eX3.mple is in Table 6. L

Table 6.1 Slnlerinl of Low-density Polyethylene MFI 20

Thickness

3 X 10-3

Temperature

130 170 210 250

Surface tension

31 X 10-3

25 20 16

Viscosity at zero shear

5·4 x 103 1·8 0-6 0-2

Time to form a glossy surface

(s)

Calculated

1600 640 270 120

Observed

1400 780 390 300

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- IU!cnnlinll' medium -

6.5 Buoyancy causes of a central core to float UmJlar4:is in a bath

For a 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 of an extruded tube under

thickness of coattm:~. Thus

total deformation = shear rate x time shear stress x tmle/'V1SI~m.1tv

and is The sag an ~vt ... nrl~rI blow m()UIIQlIl12 is another

eX,lmlPJe of deformation under ,., .... ".ud'u

In such a process

where I is the A is e is the rlPlrt<l:t1'v

stress

g is the constant.

l'vrnr;;.Uv this stress is in the order

extensional

paJ'lSCJ1n t)ec(J,mc:~s taLPe1reo so that a smanc:~r Clross·sc~ct]lon must c ............ n ......

stress = i Strain rate = i Total strain = ! Total deformation =!

eX~lml)le, total deformation of 0-1 m would be obltalIleO

l

��

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 in sJ1t~aflln2 and cJ1~lrajctelnstlc

10"

Modulus / (N/m2;"

Shear stress

103

Characteristic 'time (s)

\T , \

104 105

Shear stress (N/m2J

6.7 Relaxation of orientation after flow: 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 IOlIlL2 applltC:iltl<mS where a lack of orientation is .. ""'e ...... ""rf

rJ1(~Oll()glcal response which must

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 n¥~ ... ftrl

oel,lRller can manoeuvre. The need to locate if low flow processes

have a very

6.3 MIXING PROCESSES

The of flows unclerstalllOlnR. Almost every plasttC:IS1I1R lflaCJiUuery manujfac1tun~r

element so there is a COlfl1PoundjlnJl: machines based on varied prInCIples.

discern four "~¥nAtC'·

apJ)llc:atl()Q of energy

6.3.1 Dispersion

He:SlO«es the method of actlllevlDll OlSlperSlOlll. at which it is attiempte:d is also critical. If the lDs:reclleJllts the matrix is moUeJIl. p:artJculate malteJ~lal and extended chain t"¥'l'C't~lC' sut)seIQuc~ntlv difficult to melt.

h@l~~Vllrv worked aJl:J~10me:ra1:e or suffer "'f'f' .. ·.f'.r.'" nnllvlTl@lr11f' substances which are

plasti(;isaltio,n and more difficult to In .. .,o.,,:>Illu ideal to add fillers to the melt rather than to solid feeds.

��


dlsIPer:,e a small amount of low-viscosity material in a U1(!j"'n~:ihl __ ,t 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.

6.3.2 Distributive Mixing

Distributive mixing, aimed at is achieved the interruption of streamlines. by rows of

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 n1"{"t1n,('f' 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 may break be UlrlOUfl~n the extruder without melting. The barrier 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 the die This nalrf'f~.lhl and prOlmOttes

6.3.4 Work Input

to tp",np1"tltII1I'P to increase in the same way.

tenlPeratlure build-up due to heat n ... r''''1''~:lht'.n

which is more stable.

All kinds of work input. Excessive work input is it may also lead to heat generation and to If the work input 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 pn~SS1ilre·ClI]V€m and the shear rates at much SOlllletlmc~s e'tcec~atrle; 100 000 The shear rates in such flows have described in an

kn<)wleClil~e of flow rate

where M is the D is the

shear rate =

T is the time N is the number of u .. " ........ "lIVU

��

122

a

b

c

6.10 Selection of die diameter for wire cm/eT'in~ a too restricted b Die too c Die correct size

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

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

as a check that more have not gone

6.4.2 Wire Covering i"'cnJP,r,na nrr,i"'P,c~C! the choice of diameter Iml)OSC~S a need to

shear at the i.,.+,.,.ri""'''A

I'h'~'Ult1lnU1n 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

��


...... ...

6.12 Strc~tcl1lina flows in inie~cti()D mIOu,IQUlf!;

warping or ..... <l' ... 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 nrf~!il!ililre 2ra:(J1e~nts 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 (ll1l''\ ... r'nn,~ ... rI

I I

Pressure I I

I

#,pumPing I I I

Drag I I I

Shear stress r

Pressure profile Shearing field

Tensil!t I

Stretching flow

Figure 6.13 Constrained extensional flow in caumoienlllg

��

to a dominant sn~~ar]tng flow7 as a first aplprc.xlInaltlolll,

y 2VIH

stretch rate, t = 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

125

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 qualitative-c!ln"1l1~" bubble blowing process in polythene film. Film blowing reaumes

a

b

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

��

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 nlnWlrlO the whole of material is to a strletchlI1lg

of such processes is described in

maximum stress

total strain

the

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,

3 stress "2

��

n""'CCII .. ':> remains constant, the stress bubble size increases. characteristic allows than smaller ones-a which is eSt)eClaJJIV e:"ag;gel'ate~d deformation decreases with stress. In we observed that branched materials have a resistance to deformation which increases with stress that such materials should a more uniform cell 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 inevit-stress and so to the of balance to

a delicate one. The ODltlOllS !t111!tIII!thilp to stabilise a are in the of may not available.

However the context, we must defer to the advice of the Bard: .. , 'twere well it were done 1'1 ........... '1'"

6.5.3 Vacuum Forming

One process which is almost ",nt', .. ",hl

where a sheet is sucked into a the most extreme tlnlwllnf!

are at their minimum thickness and strain

6.16 Vacuum IOflrnl11lg

process, of the

��


the sheet. In this process the stress is limited to about one atrnO!)pJ1lerc~, (rlh) x for processes, rlh::::::: stress level of 1 ()6 for the nl"r\l"p,~"

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

Conclusion

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

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

6.6 BULK DEFORMATIONS

but cnCllngC;!S of

COInOlres~)ed per

nl"l"""11rp is al"~111111~1_ such an opti

as PY{"P"':IVP the quality usually better than that of

in building up or relteasin2 dlsplacernellt from an accumulator

��

6.18 Observed in nmlla-tln to predeternlJnc~d flow rate

aettencls on the volume of the acc;unlul,atofr--a the accumulator will .. ", ... :>Ilt",

relaxation will be more prc:deterllDiIled flow rate. Bulk cornPl'ess,ibillity

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

��


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 ." ..... 1' •• ;

1975.

C;alen(JrraR.~e, ...... ' .. "' ........ "" Francais .... PL ....... ,,.,"',, et

��

REFERENCES

1.

2.

3.

4.

5.

6.

7.

8. 9.

1966.

131

lDl lect:lon m()tul(llDJ~. Plastics and Rubber

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

in Journee Apph<=aUons des

��

��

Future Developments in Polymer Rheology

of the interaction between rnC;~OJ()1!V decades

in

��

134

The last have seen a nrn,u" ... ",

mitigalte the major flow defects

REFERENCE

1. ,V ....... cfv'ev J.

such as their train a new f(erlenltlCln

gnt,\pgrg"i"'p will COIltulUe

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 psc:::uaopJ.astlc nature of

made to take into account the fact that the melt means that the aSSUITlea pa)~aJ:)jOl1c 'Us:>lnl"'l'hl

the die is DIUIl-lIKe. This ,..,..· .. 0'''' ..........

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

(i) Where data are to be used for COlnOfilra1:tve n",~nn,Q"'<l aD11J1v]IDSZ the correction win not alter the COlrnpanlbllllty Where the data are to be used as enJllDleerlDi data to calculate pressure iralOle~nts in different it can shown that the maximum error in n""'QQ1!1"'" gra.Ole:nt, occurs when data from a are

takes the form + + has accuracy of most

measurement. Where the data are to be used as fundamental or for the of other than the other ooltentlal sources of error

unlt1011bteOJly a proper one to from aPl)earS unrf~W(lrOlDSZ in terms of the effort lDvolveO.

an index the of pse:uOioplastllc rheol<ltglcal piarame:ter which may be

enJllD4eerlDg ",allfvUJ,aU\.JUi) and may nQl1~111"

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 I 137

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 out-

is 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 1 139

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

c.11sUnJ~Ul:sne:c.1 as

REFERENCES

3.

4.

5. Ch~lUtf!ourleaux.

6.

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

of molten

��

��

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".""" __ ~'" "' ......... L_ ...... 4 flow

received most use and

eIoln2~iti(J'n rate, i =

at a flow rate

so a

value has been

of r = '1 is the n is the power law

��

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

REFERENCES

1.

Polymer Melt l(n~f!Ol(1JlV

must be taken over the .... r." .. "'rr""rI method is a transducer

elcmg;atlonal response from i"i"I1!1Vl"rcrllncr

results so obtained must or

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 SWf~lllIU! 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

+

leadmlJ! to extensional mo,duJlus.

E

+ ]

swc:mUUl ratio from a die and rR is the recoverable shear at

��


0 1/ V

6.

5. / 0

V / .0

V / .0

/ L .0

./ /

.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. 2. A new 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

within 1 cm of the end. 4. The readings are and the result is taken as the extrudate diameter.

Swell ratio is the ratio of extrudate to die diameter. Certain corrections would be necessary to obtain a true sweUllnil ratio. These

arise from:

ShJrinJka~~e on CO()11I112 Sa~~2lfI2 under

to h'~'~7'lnn Diametral increase to surface tension

flow conditions not established

These errors are, to some mutually carlcelUIll2 is that a 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 Yolvm~ers •

.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.

��

AP1penl(llX 5

Data Sheet for Capillary Flow

y= 0= so

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

Die diam.

2R

Extruder

N/m2 Ns/m2

1/=

��

AD.oen:au 5 147

Extrudate Extrudate

N/m2 L o

G + E=

��

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 agree-ment with dynamic measurements and with the normal stress measurements in flow A6.4), on the assumption l that

N E "-~ (!)

0' :::J "5 "0 0 E "-CIS Q)

.t::. en

10'-

re.~o"erahle shear

Cone and plate recovery measurements·

---103 104

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

100

2-0 2·4 2·7

~ ).;'

If / V

'/

" 10'

Stress (N/m2)

1·5 2·6 1·7 2·7

distorted

I

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

Non~laminar

flow

104-Stress (N/m2)

A6.5 Orifice pressure from ",a ... iU",r'l1 flow at 1700C

��

AO,oen:dLX 6 151

CD Ii.. :s .... Q. :s

3 x zero shear viscosity a: -1-- __ •

....... - 1 .....

-'" 10- ....... I "',

----!---- ~~ ..... - Based on orifice flow

I 103 104 105

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

A6.6 Elcm2;lltiornal flow at 170°C

REFERENCES

Elastic L.tUIUI"u,J, 1964. MSc Rubber Te(;hmcJlotzv 1977.

��

Appendix 7

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

Melt Flow at

Table A7

Temperature

130 170 210

Table A 7 lists diffusivity data

2-0

5·3 x

Heat content Coefficient Density Bulk modulus relative to of tbermal

lCrC dilTusion

3·1 x lOS

1·10 1()9 3·8 x lOS 1·1 x 762 0·96 x 1()9 4·8 x 105 1·1 10-7

746 0·83 x 109 5·8 X 105 1·1 x

±10 ±0·03 x 1()9 ±0·1 lOS ±0·1 x 10-7

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

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

��

AO,rJen:atx 7

tel1[lpe:rat:un~s above the may tend to while 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 of

N E -, ~ Q. 0 ... "a II) ... :::J fII : ... Q.

II) (,)

!E ... 0

and then faUs to a minimum of at of about 0-45 as the polymer melts.

10"

104

-1-_--

10&

Stress (N/m2)

}I~

A 7 of a oprlpr~ll_nnrT'ln~p Dol.vethvllene with moderate oranctlung

Swell ratio at 15(f'C

10 100

1·4 1·6

2·1 2·5

��

Appendix S

Typical Processing Property Data for General-purpose Grade Polypropylene Homopolymer

Melt Flow Rate 3-0

mcrealses the and its effect may be corlsJdlen:~d as a neD'atj"e t"~'n1",\~"":lt"'''A such that

Table AS

Temperature

20 180 200 220 240 260

Density

±1O

=S·6x

on uuu'nc't'tu as reclucJing tenlperat1ure

Heat content Coefftcient Bulk modulus relative to of thermal

20°C diffusion

0 1·4x 0·76 x 109 4·5 X 105 0·9 X 10-7 0·70 X 109 5-0 X 105 0-9 X 10-7 0·67 109 5·6 x 105 1-0 x 0·61 x 109 6·3 x 105 1-0 10-7

1-0 x

±0·03 x 109 ±0·1 x 105

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

water. The coettlcllent of of ooJvoJ'no'vlerle

other this value can be very

Q, 0 ... "0 Q) ... ::::J fI) fI) Q) ... Q,

II) (J

!E 0

.-< C 0 ';; c II) -)( II)

"0 C

'" s;::-.: '" II)

s::. fI)

,5

..:

= s::. fI)

,5

106

105

10'" 105

Stress (N/m2)

A

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

155

��

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/m2 (1000 atm) the same effect on as a drop in of

Table A9

Heat content Coefficient Temperature Density Bulk modulus relative to of thermal

lOClC diffusion

20 1180 0 1·1 x 10-7

180 1130 1·35 x 1()9 2·7 x lOs 0-7 X 10-7

200 1110 1·25 x 1()9 3·1 x lOS 0-7 220 1100 1·15 x 1()9 3·5 x lOS 240 1080 1·05 x 109 4·0 x lOS 260 1070 0-95 x 1()9 4·5 x lOS 280 1050 0·85 x 109 5·0 x lOS

±10 ±0·03 x 1()9 ±0·1 x lOS ±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 9

N E -~ Q. 0 ... "0

! :J

= ! Q.

8 ~ 0

..: «t ..,

.s::. fI)

.5

157

C1eJlratClatlon can occur_ aPt)rmnmate.ly constant up to 1300C a

malXll1nUID value of 0-8 at about

10'

, /'

/'

101i

200°C

~ 102~--------r---------+---~----~--------~ -~ 104 105

Stress (N/m2)

\

A9 ofaOp.flp.r:~I-rvlrnn':p

Swell ratio at 2(J(f'C

10 100

1·3 1·5

1·6 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.

Similar remarks A hvc:1ro!datlc

Table AIO

Temperature

285

'(1t~{'n~11"'(1 is summarised by

1·36

=3·2x

Heat content Density Bulk modulus relative to

20QC

1010 1·5 x 1()9 7-0 x lOS

±10 ±0'1 x 1()9 ±0·3 x lOs

pf()Ce:SSll1l~ range. Vls(~ositv as a

Coemcient of thermal diffusion

±0·1 x 10-7

In form 6·6 11&>.,..c ... t'(1 of 1·14 x 103 at 20°C. The melt bulk modulus at atnl0sphc~nc pressure and Quc~nCJllea heat content

relative to 20°C are AIO. The rise in bulk cornPI'eSS,lOn

1·2 x 10-7°C/Nm-2

��

AO.oen:QlX 10 159

melts at about may SUI)er·cO(). Drc;~sellce of orientation 1"&:!>t'ilnt",:o",

by a reversible cOlule:nScltlcm so that eClllilibri1Llm water content are reflected chja.n~~es in molecular

Above nylon 6·6 may to thermal

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 I» :; rn rn I» l-e. I» (,)

-.: 'C 0

.< C 0 '0 c::: I» ... )( I» "0 c: ea s;::-t.: ea I» .c: rn .S N E -rn ~

106

105

W 104

C : 0 '0 c::: I» ... )( I» "0 c::: ea 103

ci .: ea I» .c: rn .S N 102 E -~ rn :s :;

"0 0 :e it

/ V

/ /' ,/ .....

"...

/ -

I

----- ~ ~

105

Stress (N/m2)

AIO KDleOI4Jgy of an lnl,F>l'i'1Inn mouldinJZ

/' ",

", 1; and Ell

I

A

106

of 6·6 nylon

��

APtJen(lllX 11

Typical Processing Property Data for an Injection Moulding Grade of Polyethersulphone

Table All

Temperature

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

6·7 x

Heat content Density Bulk modulus relative to

20°C

1·4 1()9 4·7 x lOS

+10 ±0·1 109 ±0·3 x lOS

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. f.) E/3 " Ot:

106 't: --0

t< 320°C C

370'C } A

0 'in c f.) .... )it( f.)

320°C "0 c "0 cc C

cc F" ci 103

.: CC .: f.) CC .c f.) en .c .: (I)

370°C N ,: E N fh E 102

~ -~ > (I) .... "iii :::s 0 3 " "0 en 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

Table Al2

Temperature

ViSC:OS11tv on pressure is such that tnCJrea~;tnJl the pressure has the same effect on at recluc:mJl tenlperatlure

Density

+10

=3,1 x

Heat content Bulk modulus relative to

Coemdent of thermal dift'usion

1·9x1()9 1·6x1()9

±O'l x 1()9

20°C

1·6 105

2·1 x lOS

±O·1 x lOS

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 12

t<

C w 0 C 104

'ii 0 c: 'ii Ci c: .. Ci )( .... Ci )(

"0 Ci

c: "0 ca c:

ca F"

C) 103

.: ca .: Ci

= .c: fA .c: .S fA

N .S E

102 -fA

~ fA :::J :;

"0 0 :E

104 105

Stress (N/m2)

A12.1 Rh,eoll()2V of a PVC

Swell ratio at 17(f'C

10 100

1·05 1·10

1·35 1·50

106

��

164 """.1""",,,,,. Melt Rheology

N e -~ Q. 0 ... 'C e 10& ... :::J 0 0 e ... Q. e (J

It: 'l:

p /"" o I.-

1~ \ " 190°C '" " G and E/3 ,,\

0 106 ... """,' \

1 / \ / ,.. \

\1700 C .< C w 0 C 104

'0 0 c '0 e .... c )( e e ....

)(

'C e c 'C as c

as ci 103

to: as e

.t::. .52 0

.52 N e 102 -~ 0 :::J

"S 'C 0

'" A \

\ , 170°C '\1900 C

\ \

1~\ \~

::!

104 105 106

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 9n~llv~!I~' p~lral1[lete:rs dleSCtibiI12 die channels

For the PUJ~OOl~e

From these Pat'ameters we may

c0I111plc~x channels may desc;;ribc~d by

x y

of of

the dmlen.Slo'oie:ss ratios

area area

and for a slot die X = 0 and Y = 1. a set of for

the two flows can col111plc~x cJltaIJlDels can

��

166

In ae(lUCJn2 relati4ems.hil)S we note the established !or:mu.lae:

rate Stress

4QlaA Slot

~ ....... lru' .... shear

shear stress,

y= +

0= s

(i)

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

Swell

Swell

=4(1+

= = = 1-0

for YR>

{ B~b 1 + 0'4(1

= dies (Br) x =

for dies of zero

raBb

Dies of Ba = zero

(Br)X =

nr~ .. C!'alrp drop in a long die and Sigllific~s the ratio of extrudate to

+ 1)

-0-8) (iv)

(vi)

(viii)

is the in n is the power in YR is the recoverable shear and eR the recoverable extension as

.....,.U.'~IJL''"'.1 2. The to y have values 0

been determined in addition to standard and short dies cross-section and

cornbi.nil112 three rods to form a tn~mgle with concave sides. and

that their

tension-

��

Shear rate (8- 1)

utl:! .. 'nc:!ttu flow curves

stifJfeDllng, nolvnrnm/lerle temsion-tlmlnlllg and

Working Shear Rate The intersection reference at

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

DIe cross-section x

Circle 1-00 0-80 0-28 0-11

Concave ItOO

factors

points Ol)1tau1leCl

y

1-00 1·28 1·06 1-00

1·62

Shear rates at Intersections p == 1 and q== i

3·2 23 380 3-8 28 300 2·2 32 420 2·3 23 360

3-8 35 480

in-

��

Table All.2 Data for Calculation of WorkiDg Shear Stress

Shear stress

Circle

Concave

PoIy(methyJ methacrylate) X y 10 S-1 100 S~l

1-00 26 110 1·28 26 120 1·06 25 110 1-00 27 100 1·62 24 90

Table All.l Predicted Value Compared with

Function

Observed in Dies

1% high 2% high

as observed

Standard deviation

8% 8% 7%

1000 8-1

260

250 230

Polyethylene Polypropylene 10 S-l 100 8-1 1000 8-1 108-1 100 8- 1

17 61 160 31 84 18 64 34 80 15 55 32 77 17 56 150 31 82 18 59 140 38 81

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

Standard deviation

7% 10% 7%

1000 S-l

130

110 130

��

169

calculated are on average 9 cent.

cent with a stand,ard deviation 26 per

WOlrkJlnJ! shear Y = .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 value of Post·extrusion from

Dies of zero length

{

(

Cal,CuJlatc~d, standard deviation 8 per cent. <YR<10:

0-8)

=

above may be used as a to oornol1tulJ! tbrl()uJl~b 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

��

AOttenClllX 14

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

For small cp,

In section N,

pressure

-+ HN ........

A14 die

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

= constant in all seCtlOllS

shear rate, y where is volume flow rate per unit width

shear stress, (J =

'tl""I£1I£11TV at die

velocity of oar'isOlrl, VN = = 1 (¥1AN

= constant

swell B, assumed constant (but variable in principle)

(i)

(v)

(vi)

��

AD,venaLX 14 171

From (vi) and (v),

BVN constant

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 thickness of about IW()-I1UTlIS the 2: 1 on inflation.

Original

n=O·3

To equation

whence

=10mm = 4 mm-f>

15mm 2·7mm

(247)O'31~"""""-

0·82 12·3 mm.

��

��

Author Index

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. 32 104 (110) Bird, R. B. 1 (4), 52 BloodeD, D. J. 97

L. L. 104 D. C. 52

Bol1ltinck. W. J. 32, 33 H.C. 47

Borocz, L. 93

Busse, W.F.

Caron. I. M. 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. 33 105 113

56

130

the

(38)

Daniells, P. l.

Edwards, S. 73 E. 91

~lI":Ui:lu.R. ,cVC;;li:ljl!,C;;, A. E. 102

H.

Oallo, R. l. 64

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

35

40 47 (68)

174

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),

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

84

..... ,"""u ... Chemical In(j!ustrie:r-Welw~rn Garden 54 91

Ito, K. 44 Ito, Y. 52

Jackson, W. J. 11 76,84 Jacovic, M. S. 83

J. C. 64 (70) Janieschitz-)'rie:gl, H. 130 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

Kratz, R. F. 52 Kraus,G. 84 Krul, N. 32,33 49, Kubat, J. 93 Kuhfuss, H. F. 11

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

104 (110)

84

130

47

52 83

97

86,87

den Otter, J. L. 34 D.F. 67

"Vitl • .,..,,,, .. Y. 87

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

136

104

104

Porter, R. S. 44 85 Prest, W. N. 85 Pritchett, R. J. 62 Proctor, B. 96

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

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

18

130

97

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

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. 98

H. 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. White, J. L. 23 33

87 93,97

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

175

49,50 104

98

50 58

26

25

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

Data

2 100

1,111 106,114,119.123

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 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

97

Fibre 127

11,51,54,91,93,97,104,126,

detailed studies 129 Fillers 10, 87. 102, 119 Film 11,12,34,51,53,54,65,93,104.

113, 127

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

definition 8

92,113 52,75

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

177

Normalstress 7.19,20,103

Orientation 3,21,46,52,54,58, 75,91,94, 118

Orifice flow 30, 141 U~ciHlrdOlry flow

and short time-scales 47 superposit:i.on on steady flow 47

Shear, oSCliJlatory

111 Ph~ ~para1tion

Plastici~rs 88 Poisson'STatio 52

93

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

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 135 Reclaim 11 Rheometers

classes of 16 35

coDilparisc1n of data from different 148

purposes of 15 112,113

detailed studies 129 8,15,49,93, 127,145

Sandwich 67 11,34

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

and 20 3, 11, 71, 79, 88, 91, 97, 134

97,101 Shear 6,56

see Viscous diSlsiplilticln oSClillatory 17, 18, 19

57 52, see also Non-Newtonian flow

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

Strain 6 rateof 6

93

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

concentration 82, 107 overshoot 20

Stretch rate 125

123 in fibre and film 126

52,81,125

instabilities in 24, 52, 104, 127 rheometers for 23,32, 141

Structural foam 91 Structure, see Chemical structure; Molecular

structure; MClrpll0l«lgy Surface 91, Surface 31,99,101,104,105,106,114 Surface 133 Surface tension 51 Swell ratio, see Post-extrusion

39,41 transition 75

TeDSCIr notation 7 Thermal diffusion 9 Time 46

of 95

99

natural or characteristic of material 48,75, 95

natural rbeometers 35

Transients of stress and strain 19

54,65,104,127 32

oatcn-i[O-[)aI(:n variation 93

dellendellce on stress 52 common materials 7

11,34,48

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

11111111111111111111111111 9 781855 731981

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