Plastication in injection moulding : Principles, Numerical ... school presentations... · ALPlastics oyonnax 10/07/13 Plastication in injection moulding : Principles, Numerical modeling

ALPlastics oyonnax 10/07/13

Plastication in injection moulding :Principles, Numerical modelingand in line Visualisation

Yves Béreaux1,a, Jean-Yves Charmeau2,a, Thuy Linh Pham2,a

Jean Balcaen2, Maël Moguedet3, Richard Apaloo

1LaMCoS UMR5259, INSA-Lyon2IMP@INSA UMR5223, INSA-Lyon3PEP,Centre Technique de la PlasturgieaFilière Génie Mécanique Procédés Plasturgie, INSA-Lyon

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Outline• Polymer Processing : Challenges

• Injection Moulding

• Plastication in injection Moulding

– Physics

– Visualization

– Modelling

– Fibre breakage

• Flow in screw channel



Thermo-Plastics Processing : Challenges

liquid solidpart

aspect

plastication

pressure, flow rate, viscosity

moulding

shear rate, Tfusion

solidepellets, powder

melting

molten polymer

solidificationgeometry

mechanical properties

flow and shaping

temperature, rpm Tcryst., Tmould

Heat transfer Mechanics Physics, Heat transfer

• Processing bears an impact on thermo-mechanical history from material to part

• Processing parameters 6= Physics variables

• Analysis on the product (consequences)→ Physics causes

• Instrumented machine 6= Scientific instrument



Injection-MouldingCyclic Process : widely used for making thin parts (not hollow)

1 plastication

3 injection

5 holding

2 metering

4 packing 6 cooling

7 part ejection

Research group’s main interests :

Plastication & Flow in screw barrel system

Surface defects of injection-molded parts not today



VisualisationLooking for a visualization device :

• Scale relevant to polymer processing machines

• Applicable to screw barrel units

• continuous in line flow visualisation : 3D, no blind spots

• Automated particle tracking ( particle : pellet, fibre, fluorescent tracer )

• Post-treatment of position : Velocities

Literature review• Extruder with glass windows to observe solid bed motion and plasticising:

Wong (1999) [WLLZ99], Gao (2000) [GJC00].

• Transparent barrel with (one or two ) video cameras to record a particle motion:Campbell 1992 [CSF92], Choo 1980 [CNP80].

• Magnetic Resonance Imaging (MRI) on a non-metallic barrel and screw unit :Amin (2003) [AHH+03], Agemura (1995) [AKM95].



Visiovis Data acquisition

camera V2

camera V1

led

camera H1

camera H2

calibrator

computer V

computer Hmobile rack

firewire

firewire

clock

usb

usb

particle

barrel

led

Barrel : PMMA Fluorescent Particle (0.4 mm)

Screw D400.4 mmlength 6D continuously monitored by 2 over 4 cameras

Silicone oil 100Pas recording two sets of 2D pathlines

[Mog05]M. Moguedet. Développement d’un outil d’aide à la conception et au fonctionnement d’un ensemble vis/fourreau

industriel -Application à l’injection de thermoplastiques chargés fibres de verre longues. PhD thesis, INSA-Lyon, 12

Décembre 2005



Visiovis : Pathlines reconstruction

Data sets of 2D positions are : filtered from noise, corrected from refraction combined to give a 3D pathline

Particle moving down and up the channel : slow near the barrel fast near the screw root





Visual Barrel design

Standard size barrel with :

3 optical glass windows

3 plane surfaces for visualization

and lightening (laser sheet option)

3 cameras monitoring :

plastication , flow charge dispersion

[Pha13]T.-L. Pham. Plastification des polymères fonctionnels et chargés. PhD thesis, INSA-Lyon, 2013. en cours



Transparent Barrel Plastication

melt poolsolid bed

channelflow

flight

Solid bed width increases with screw frequency Lateral film increases when screw is idle



Plastication

rpm

barrelsolid bed

melt film melt pool

pellets

hopper

nozzle

screw

Pellets melt along the screw following Maddock/Tadmor model : [Mad59, TDK67]

• Solid bed of compacted pellets with continuously decreasing width

• Molten polymer film at the barrel inner surface ...

• ... continuously wiped by the screw flights ...

• accumulates in a melt pool

Unresolved issues :solid bed permeability [NOF04], Solid bed velocity and acceleration, [FkSN82], lateral melt films[Lin85]?



Plastication in extrusion: Tadmor’s model

��

��

Tb

Vbx

δ

vis

fourreau

W

Vsy

XTm

• Fusion : contact and melt renewal

• Thermo-dependent power-law viscosity η =

K exp(−a(T − Tm))γn−1

• Solid bed : width X, velocity Vsz. Channel H,W . Mass flow rate mlt :

mlt =d

dz(ρsHXVsz)

mlt =

√√√√VbxU2ρmkm(Tb − Tm) (1 +BrU1)X

∆Ethlpy

• dimensionless numbers : Br self heating (vis-cous dissipation), A Thermo-dependence

Br =KV n+1

r δ1−n

km(Tb − Tm)

A =a(Tb− Tm)

n

• Melt film thickness :

δ =mlt

ρmVbxU2(A)



Plastication : Results

Solid fraction X/W along the screw length :

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

2 4 6 8 10 12 14 16 18

Sol

id b

ed W

idth

/ C

hann

el W

idth

N screw/turn

Pryltex

PP

HDPE

Feed Transition Metering

rpm 40

screw 90mm

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

2 4 6 8 10 12 14 16 18

Sol

id b

ed W

idth

/ C

hann

el W

idth

N screw/turn

screw 90mm

Transition MeteringFeed

Pryltex rpm 40 Tb 240C

rpm +50%

rpm +50% BP +50%

Tb +50C

Plastication length :

• increases with shear rate (increase viscous dissipation) (at a given throughput)

• decreases with higher screw rpm

• higher barrel temperature conflicting : increases conduction but decreases viscosity



Plastication in Injection Moulding

Specifics :

• not continuous (steady state) but cyclic

• sequence of steps : rotation (extrusion-like), dwelland forward injection

• melting depending on the time when pellets enterfeed zone

Modelling Nunn’s approach [Nun86]

• screw forward motion: additional melting (no solidbed motion)

X = X0 exp

(−∆tinj

km(Tb − Tm) + ηS2inj

δHρm∆Ethlpy

)

• dwell : film thickness increases by transient con-duction

δ =

√km(Tb − Tm)∆tdwell

ρs+ δ0

• At the beginning of rotation the solid bed reorgan-ises

00,10,20,30,40,50,60,70,80,9

1

0 5 10 15 20

InjectionExtrusionInjectionExtrusion

10,90,80,70,60,50,40,30,20,10

1 5 10 15 20

melting length shorterresidence time is much longer[Apa05] R. E. Apaloo. Plastification en injection. simplast.

Master’s thesis, Insa-Lyon, GMPP, 2005



Fibre Breakage• Fibres anchored at one end in solid bed, submitted at the other end to intense shear

��

��

��

��

��

��

��

l d

Vbx

θ

fourreau

δ

lit solide

vis

• Mittal’s [MGS88] model extended to power-law fluid :

σapplied =128δ3−nKV n

r

d3An−1

(exp(A)− 1)n

∫ lδ

0

(1− exp(−Ax))x

log(7.4Re

)dx

depends on film thickness δ, shear rate, viscosity K, fibre diameter d and orientation l

• Fibre breaks when σapplied > σmax

• New layer of fibres uncovered as the solid bed is melting

• Fibre length distribution obtained starting from a uniform distribution with random orientation



Fibre breakage in extrusion

Screw extraction and fibre length measurement Gupta [GMS+89]

Comparison between measured and calculated mass (Lw) and number(Ln) averaged fibre length

Ln =

∑i niLi∑i ni

Lw =

∑i niL

2i∑

i niLi

0

2

4

6

8

10

0 5 10 15 20

Ln,L

w (

mm

)

N D_Vis

Ln expLn calcLw expLw calc

0

5

10

15

20

25

30

35

40

0 1 2 3 4 5 6 7 8 9

fra

ction e

n m

asse %

longueur fibre (mm)

Lw exp = 3.85 mm

Lw calc = 3.60 mm

0

10

20

30

40

50

60

70

80

0 1 2 3 4 5 6 7 8 9

fra

ction e

n n

om

bre

%

longueur fibre (mm)

Ln exp = 1.05 mm

Ln calc = 1.10 mm

PP LGF 9mm on a 38mm diameter screw

agreement is good at low rpm, less so at higher rpm[Mog05]M. Moguedet. Développement d’un outil d’aide à la conception et au fonctionnement d’un ensemble vis/fourreau

industriel -Application à l’injection de thermoplastiques chargés fibres de verre longues. PhD thesis, INSA-Lyon, 12


ALPlastics oyonnax 10/07/13Décembre 2005



Flow in a screw channelFlow provoked by screw rotation and back pressure of the die downstream

φ

H

W

z

N

z

y

x

Vz

φVx

V

x

y D

L

Parallel Plates Model :

• Rotating barrel around a static screw : steady-state problem

• Unwound Channel: H � RB : no direct effects of torsion and curvature

• High aspect ratio: H � W : no direct effects of screw flights



Single screw throughput calculations

LmeterLcomp

Pressure

Lfeed

BackPressure

Scre

w Di

amet

er Hfeed

rpm

Q ?

Hmeter

• 3 zone screw viewed as a melt pump where :

– screw forward displacement (drag flow),

– pressure gradient in the screw channel.

– Pressure development begins at atmosphericpressure and ends at Back pressure imposedon the screw

BackPressure = ∆Palim + ∆Pcomp + ∆Pmeter

•

m = ρmQliq + ρsVszHX

=W−XW

1− HXαHalimWalim

ρmQ

• 1D relationship between flow rate and local pres-sure gradient for power-law fluids:

Q =VbzWH

(1 + s)(1 + 2s)|6G|ssgn(G)f(λ)

G =Hn+1(z)

6KV n0

dP

dz



Throughput and Pressure profiles

20

30

40

50

60

70

80

90

100

20 30 40 50 60 70 80 90 100

modele

Debit (

kg/h

)

essai Debit (kg/h)

PS Styron, T 211C

PC Lexan, T 285C

−10%

0 0

5 5

10

10

15

15

20

20

25

25

30

30

0

35

5

40

10 0 15 5 20 10 25 15 30 20pre

ssure

(M

Pa)

N screw turn

model Md=35.9 kg/h

25

model + plast. Md=35.5 kg/h

30

exp. Md=32.2 kg/h

rpm=100rpm=40

pre

ssure

(M

Pa)

N screw turn

model + plast. Md=90.8 kg/h.

model Md=103.4 kg/h

exp. Md=99.6 kg/h

Throughput :

1. Screw geometry

2. Polymer Rheology

3. Plastication length[BCM09] Y. Béreaux, J.-Y. Charmeau, and M. Moguedet. A simple model of throughput and pressure development for

single screw. Journal of Material Technology and Processing, 209(1):611–618, 2009



Aims

Specific effects of helical geometry on flow of viscous and viscoelastic fluid

Hypotheses

• Incompressible fluid in steady-state creeping flow

• Screw channel :

– constant depth and pitch

– curvature, torsion

– flights

– rectangular cross-section

• No leakage flow through barrel/screw clearance

• Perturbation method

– pressure & drag flow of viscous fluids

– pressure flow of viscoelastic fluids



Rectangular helical screw channel

2πPy x

RW/2

θr

z

B

T

NH/2

Geometry Dimensionless Numbers

Hydraulic Diameter D = 2HWH +W λ = W

H

Curvature κ = RR2 + P 2 ε = Dκ

Torsion τ = PR2 + P 2 α = Dτ

Helix Angle tan(φ) = PR tan(φ) = α

ε



Applicability

Visiovis Extruder (pumping zone)

Aspect ratio λ 6.9 21.8

Curvature ε 0.44 0.15

Torsion α 0.16 0.05

tan(φ) αε 0.36 0.33

• Curvature ε and torsion α are small but not negligible dimensionless parameters

• Aspect ratios λ are very large



Overview

Fluid Flow type Flow direction Helicity

viscous drag down-channel w curvature ε

viscoelastic pressure cross-channel u, v, ψ torsion α

Ducts

XZ

y

ZYX

Z

y

Tore (ε) Helix (α, ε) Straight twisted duct (α)



Pressure flow/Newtonian fluid

w0 w0 + α2wα2 w0 + εwε + ε2wε2

λ = 1

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

outer wall <--- x --> inner wall

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

y

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5


-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

y

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5


-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

y

λ = 1/5

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5


-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

y

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5


-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

y

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5


-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

y

Curvature : max velocity shifting towards the inner wall

Torsion : max velocity decreases



Pressure flow, curvature effects

0

0.5

1

1.5

2

2.5

−0.5 −0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4 0.5

w/w

0av

x, y

w plfw, y = 0

w plfw, x = 0

w0 + εwε + ε2wε2 , y = 0

w0 + εwε + ε2wε2 , x = 0

w0 + εwε, y = 0

ε = 0.66, α = 0, λ = 0.5

large shift of the down-channel velocity w towards the inner wall (deep channel)



Pressure flow, torsion effects

Down-channel velocity w Cross-channel velocity u, v, ψ

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

−0.5 −0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4 0.5

Z

y

w/w

0av

x, y

w0 + α2wα2 , y = 0

w0 + α2wα2 , x = 0

w0, y = 0w0, x = 0

w plfw, y = 0

w plfw, x = 0

x

y

−0.25

−0.2

−0.15

−0.1

−0.05

0

0.05

0.1

0.15

0.2

0.25

−0.5 −0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4 0.5

u/w

0av

x, y

y

x

u plfw, y = 0.25

αuα, y = 0.25

u plfw, x = 0αuα, x = 0

u plfw, x = 0.25αuα, x = 0.25

λ = 2, α = 0.6, ε = 0 λ = 5, α = 0.15, ε = 0

Narrower w profile Secondary flow created

uα scales like α 1+λ4w0av when λ > 1



Drag & pressure flow, down-channel velocity w

Visiovis design λ = 7 α = 0.16 ε = 0.52, at closed discharge

drag pressure flow - W

0dp - aspect 5

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

0.0 -0.1 -0.2 -0.3

-0.5-0.4

-0.3-0.2

-0.1 0

0.1 0.2

0.3 0.4

0.5

outer wall <--- x --> inner w

all

-0.5

-0.4

-0.3

-0.2

-0.1

0 0.1

0.2

0.3

0.4

0.5y

w0d −GPw0

drag pressure flow - W

dp - aspect 5

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

0.0 -0.1 -0.2 -0.3

-0.5-0.4

-0.3-0.2

-0.1 0

0.1 0.2

0.3 0.4

0.5


all

-0.5

-0.4

-0.3

-0.2

-0.1

0 0.1

0.2

0.3

0.4

0.5y

w0d + εwεd + α2/εwα2/ε −GP (w0 + εwε + ε2wε2 + α2wα2)



Drag & pressure flow, cross-channel velocity V , λ = 1

−0.5 0 0.5−0.5

0

0.5

V 0

x

y

−0.5 0 0.5−0.5

0

0.5

−0.5

V

x

y

Cavity-lid driven flow (unwound channel) perturbation solution (helical geometry)

At closed discharge with λ = 1, α = 0.25, ε = 0.5



Drag & pressure flow, cross-channel velocity V , λ = 7

−0

.50

0.5

−0

.5 barrel

screw

0

0.5−

0.5

V αε

x

y −0

.50

0.5

−0

.5 barrel

screw

0

0.5V

x

y

Visiovis design

α = 0.16, ε = 0.52

Large change in cross channel velocity for large aspect ratio.

Back pressure effects visible at closed discharge.



Viscoelastic fluid flow

• Differential viscoelastic model : Upper-Convected Maxwell

S + λr5S +2ηλr

5d= 0 (1)

5S=

∂S

∂t+∇S · v − S · ∇vt −∇v ·S (2)

• First normal stress difference & constant shear viscosity

• Developed in Frenet basis ( 1000 terms)

• Zero order analytic solution available in pressure flow only

• Expansion of each stress component in power of α, ε

• At a given order, stress components are now explicit functions of known velocity gradients

• Creates specific contribution to the flow :

– Deborah number: De = <w>0

D

– w = . . .+ αDewα + εD2ewε

– ψ = . . .+Deψε



Viscoelastic fluid, pressure flow, w

Curvaturepressure flow - Wp Newton - aspect 1

2 1.5 1

0.5

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5


-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

y

pressure flow - Wp Maxwell - aspect 1

2 1.5 1

0.5

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5


-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

y

λ = 1, ε = 0.5 w0 + εwε with De = 0 w0 + εwε + εD2ewmxwlε with ε = 0.5, De = 1

Torsionpressure flow - Wp Newton - aspect 1

2 1.5 1

0.5

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5


-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

y

pressure flow - Wp Maxwell - aspect 1

2 1.5 1

0.5

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5


-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

y

λ = 1, α = 0.25 w0 + α2wα2 with De = 0 w0 + α2wα2 + αDewα with α = 0.25, De = 1




pressure flow - W

p Maxw

ell - aspect 5

1.6 1.4 1.2 1 0.8 0.6 0.4 0.2

-0.5-0.4

-0.3-0.2

-0.1 0

0.1 0.2

0.3 0.4

0.5


all

-0.5

-0.4

-0.3

-0.2

-0.1

0 0.1

0.2

0.3

0.4

0.5y

Curvature, w0 + εwε + εD2ewmxwlε with ε = 0.5, De = 1, λ = 5

Large change in contours of w near the side walls

pressure flow - W

p Maxw

ell - aspect 5

1.6 1.4 1.2 1 0.8 0.6 0.4 0.2

-0.5-0.4

-0.3-0.2

-0.1 0

0.1 0.2

0.3 0.4

0.5


all

-0.5

-0.4

-0.3

-0.2

-0.1

0 0.1

0.2

0.3

0.4

0.5y

Torsion, w0 + αDewα + α2wα2 with α = 0.25, De = 2, λ = 5

Small twist in contours of w near the side walls



Viscoelastic fluid, pressure flow, cross-channel velocity u, v

ε = 0.5, Deborah De = 1

aspect ratio max u<w>0

max v<w>0

1 0.176 0.107

5 0.085 0.058

2 vortices appearing,

moving towards

the side walls

with higher aspect ratio λ

−0.5

ou

ter

wa

ll

inn

er

wa

ll

0 0.5

−0.5

0

0.5

V ε Maxwell

x

y

−0.5

ou

ter

wa

ll

inn

er

wa

ll

0 0.5

−0.5

0

0.5

V ε Maxwell

x

y




0

0.5

1

1.5

2

2.5

−0.5 −0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4 0.5

w/ < w >0

x

w0 + εwε, y = 0

w0 + ε(wε +D2ewmxwlε), y = 0

w pflw y = 0

w0 + εwε, y = 0.25

w0 + ε(wε +D2ewmxwlε), y = 0.25

w pflw y = 0.25

ε = 0.2, De = 0.73 : shift towards the outer wall validated by F.E. Calculations



Conclusions• 2D 1/2 viscous & viscoelastic fluids flow has been solved in a screw channel

– constant pitch and depth, rectangular cross-section

– with torsion and curvature taken into account

• New model backed precisely by 3D F.E. calculations

• Pressure flow is more sensitive to helical geometry than drag flow

• In pressure flow, torsion of the helical channel puts the fluid in cross channel motion

• Torsion effects are important for aspect ratio larger than one

• Curvature effects diminish with large aspect ratios for Newtonian fluid ...

• ... but remain present for viscoelastic (UCM) fluid

• Strong corrections to the PPM model are needed in view of finer

– calculations of mixing efficiency and overall residence time

– and screw design[BMR+04] Y. Béreaux, M. Moguedet, X. Raoul, JY. Charmeau, J. Balcaen, and D. Graebling. Series solutions for viscous

and viscoelastic fluids flow in the helical rectangular channel of an extruder screw. Journal of Non-Newtonian Fluid

Mechanics, 123(2-3):237–257, 2004



Plastication: synthesis and perspectives

Visiovis Barrel Windows

screw design

transient non−isothermal3D

1D Flow Analysis Network

non−Newtonian

1D plastication extrusion and injection

fibre breakage (solid/melt)

stationnary (static vis, rotating barrel)

2D 1/2 helicoidal

viscoelastic

velocity field

Newtonian

temperature parameterisothermal

plastication profilescrew characteristicsdistribution longueur fibres

buckling

criterion pathlines

heat transfer

non−newtonian melting multiphasic

non−isothermal

fibre

melt

breakage



Thank You for your attention



References

[AHH+03] M H G Amin, A D Hanlon, L D Hall, C Marriott, S Ablett, W Wang, and W J Frith. A versatilesingle-screw-extruder system designed for magnetic resonance imaging measurements.Measurement Science and Technology, 14(10):1760–1768, October 2003.

[AKM95] Cynthia K. Agemura, R. J. Kauten, and K. L. McCarthy. Flow fields in straight and taperedscrew extruders using magnetic resonance imaging. Journal of Food Engineering, 24:55–72, 1995.

[Apa05] R. E. Apaloo. Plastification en injection. simplast. Master’s thesis, Insa-Lyon, GMPP,2005.

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