Description and modeling of fiber orientation in injection molding … · 2018. 12. 11. · Flow...
Transcript of Description and modeling of fiber orientation in injection molding … · 2018. 12. 11. · Flow...
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