Description and modeling of fiber orientationin injection molding of

fiber reinforced thermoplastics

Michel Vincent

Centre de Mise en Forme des MatériauxUMR CNRS 7635

Ecole des Mines de ParisSophia Antipolis

France

Short / Long fiber reinforced thermoplastics

Short fibersLength : 0.2 - 0.5 mm

10 mm5 mm

1 cm

ProcessingFlow

Fibres :• orientation• length• curvature• dispersion

Mechanical propertiesShrinkage, warpageAspect

Outline

0

2,5

5

7,5

10

12,5

E (G

Pa)

0 30 60 90Angle θ

θ

Fibre length

Measurement: pyrolising + image analysis

plastication (melting zone) and nozzle: 55 % of the total length reduction, gate: 31 %flow in the cavity: 13 %

short fibers in polystyrene - Tremblay et al. (2000)

Fiber degradation when fiber concentration Kamal et al (1986)

Injection speed: significant effectInjection, mold temperatures: negligible effect

Tremblay et al. (2000)

0

0.05

0.1

0.15

0.2

0.25

0.3

0 1 2 3 4 5 6 7 8

Longueur (mm)

Fréquence

PlasticationinfluenceLong fibers PP 30 %

Standard plasticationLn = 0,77, Lw = 2,24 mm

Slow plastication (Ω , bp )Ln = 1,05 Lw = 3,51 mm

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0 1 2 3 4 5 6 7 8 9

Longueur (mm)

Fréq

uenc

e

ESDASHSTAMAX

Comparison short and long fibres

Short fibersLn = 0,41 Lw = 0,50 mm

Long fibersLn = 0,87 Lw = 3,62 mm

Fibre length

Fibre concentration

Measurement: pyrolising + weight

Concentration is nearly homogeneous in the molding:

along the flow directionin the thickness (some authors found a lower concentration in the skin).

Flow direction Flow direction

Fiber orientation

Flowdirection

Skin

Core

1 mm underthe skin

LGF PP 30 %

Observations - Long fibers

Orientation rulesShear flow

0

1

2

3

4

5

6

7

0 0,25 0,5 0,75 1time / period

angl

e (ra

dian

)

β = 10β = 40

ratioaspect

T

:

12

ββ

βγπ

⎟⎟⎠

⎞⎜⎜⎝

⎛+=

&

Orientation rules

Flowdirection

Shear flow Elongational flow

rotationsStable

position

0

10

20

30

40

50

60

70

80

90

0 1 2 3 4

time (s)

angl

e θ

(deg

ree)

β = 10β = 40

Transparent mold

PS + few fibres Long fiber PP

Many fibers: interactions

l/d = 16 c = 0.08: γ = 84

o : γ = 140

Folgar et Tucker (1983)

shear

Interpretation of orientation

elongation

z

Quantification of orientation

Polishing Microscopy

P2

P1

φ

3

1

2

φ +180

θa

b( , )x yc c

P

P3

x

z y

Imageanalysis

Orientation tensoraij = <pi pj >

1

3

2

θ

φ

pp1p2p3

a11 = 1 // axis 1

Isotropy in plan (1,2)

Description of the orientation1

a11 = 0 ⊥ axis 1

a11 = 0.5

Dimensionless thickness

axx

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

3 mm

Short fibers (PAA) 50 % - Plaque

1.1 mm1.7 mm

5 mm

xz

y2 mm

20 mm, 50000 fibres

Flow direction

Short fibers - Influence of the fiber concentration

1,7 mm 5 mm

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

Dimensionless thickness

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1Dimensionless thickness

axx

axx

30 %

50 %

Long fibers - PP 30 %600

1 2 3 42 ou 4

200

Position 1 leeds

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Epaisseur mm

Tens

eur a

33

Position 2 leeds

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Epaisseur mm

Tens

eur a

33 Position3 leeds

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Epaisseur mm

Tens

eur a

33

4 mm 12 mmPellet length :

Fiber orientation modeling

Flow and orientation are decoupled

Flow computation Fiber motion computation

Mold filling software

Jeffery (1922), Folgar, Tucker (1984)

( ) ( )2422222 32:2 aICaaaaa

dtda

I −+−++Ω−Ω= εεεελ &&&&

Fiber orientation modeling

)( 24 afa =

Closure approximationf(concentration, aspect ratio)≈ 10-2 - 10-4

( ) ( )2422222 32:2 aICaaaaa

dtda

I −+−++Ω−Ω= εεεελ &&&&

• quadratic aijkl = aijakl aligned• linearaijkl=-1/35(δijδkl+ δikδjl + δilδjk)+1/7(aij δkl + aik δjl + ail δjk + akl δij + ajl δik +

ajk δil)• Hybrid• Natural (Verleye, Dupret)• Orthotropic (Cintra, Tucker)

• Better fit with experiments• Some theoretical analysis

– CI=f(inter fibre spacing)– Direct simulation

Shear flow

Folgar, Tucker (1984)

Orientation: comparison exp./computation

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

Thickness

axx

1,7 mm5 mm

0

0.10.20.3

0.4

0.5

0.6

0.7

0.8

0.9

0 0.2 0.4 0.6 0.8 1

Thicknessax

x

Ci0.5 Ci

10 Ci

Short fibers PAA 30 %

Gate

numerical results

axx

ayy

azz

x

y

z

5 mm plaque

axx

ayy

azz

1.7 mm plaque

influence of the interaction coefficient Ci

x

y

z

Ci = 10-3

Ci = 10-2

Ci = 10-3

Ci = 10-2

x

y

z

1.7 mm plaque 5 mm plaqueaxx

Comparison with exp.axx 12

3

0

0,2

0,4

0,6

0,8

1

0 1 2 3 4 5

y (mm)

axx

0

0,2

0,4

0,6

0,8

1

0 1 2 3 4

y (mm)

axx

0

0,2

0,4

0,6

0,8

1

0 1 2

y (mm)

axx

2

3

1

Exp.

Comp.Ci : 10-2 & 10-3

50 % - 1.7 mm

Influence of the fibers on flow

Without fibres

Lipscomb et al. (1988)

0,11 % fibres

Effect of the fibres on the rheological behavior

cut fibers

400030002000100000

50

100

150

200

Time (s)

Tor

que

(g c

m)

62,6 g cm

0 wt %

20 wt %h = 4.6 mm0.01 s-1

initial

final

Behaviour laws

• Newtonian fluid, dilute or semi-concentrated

( )[ ]εεεεησ &&&& 224:2 aaNaNpI spI ++++−=

r1c

r12 <<

isotropiccontribution

(fibres + fluid)

anisotropic contribution(fibres)

),,cos(,, ratioaspectionconcentratfibreityvisfluidfNN spI =η

• Some attempts to account for shear thinning effects, viscoelasticity

Fibre - flow coupling

Without fibres With fibres

Conclusions• Fiber orientation is qualitatively understood

• Skin - core• Shear - Elongation

• Quantification : 2D3D : X ray microtomography ?

Clarke et al.

Conclusions

• Orientation model : often correct, but not always• Rheological behavior :

• Strong assumptions• Qualitative agreement

Acknowledgements

S. Flouret, T. Giroud, A. Clarke, A. Megally, A. Redjeb, T. Coupez, P. Laure

Arkema, Plastic Omnium, Schneider Electric, Solvay