WARPAGE SIMULATION OF INJECTION OVER-MOLDING PLASTICS ON
CONTINUOUS FIBER REINFORCED COMPOSITES
Zhihao Zuo, Zhiliang Fan, Franco Costa, David Astbury
Autodesk Australia Pty Ltd, Moldflow R&D Center, 259 Colchester Rd, Kilsyth VIC 3137, Australia
Abstract
Injection overmolding of thermoplastic over a continuous
fiber reinforced composite is one of the new manufacturing
approaches for automotive lightweighting which is
emerging as a potential way to increase vehicle fuel
economy. It not only takes advantage of excellent strength
and stiffness properties of continuous fiber reinforced
composite, but also has the advantage of forming complex
and intricate functional shapes with the injection molding
process. Warpage simulation of injection molding helps
designers optimize the part and mold design, material
choice and processing parameters, in order to meet tight
dimensional tolerances for assembly purposes. In this
paper, we extend our warpage simulations to account for
the effects of orthotropic and fully anisotropic mechanical
properties of continuous fiber reinforced composite inserts.
The feature enhancement includes buckling and large
deflection analyses of overmolded plastic components. The
numerical results from Autodesk Moldflow simulation for
two plastic parts injection over-molded onto continuous
fiber reinforced composites are presented.
Introduction
Lightweighting is a major trend in automotive industries
for reducing weight and environmental costs while
increasing performance. Recent developments in low-cost
advanced lightweight composite materials offer promising
potential in final product implementation. The field of
automotive composites is expanding rapidly to exterior,
interior, and under-the-hood structural, semi-structural,
non-structural and mechanical applications. Figure 1 shows
an example of a plastic part injection-overmolded onto a
thermoformed continuous fiber reinforced sheet.
Continuous fiber reinforced composites offer advanced
mechanical properties such as strength and stiffness,
however, they cannot be used for intricate functional
shapes such as ribs, bosses, bolt locations, etc. Addressing
this shortcoming, interest is rapidly growing in
technologies such as multi-material injection molding or
overmolding. In addition, overmolding is an excellent
approach to producing lightweight technical parts and can
reduce production and assembly costs. Applications of
over-molding plastic components help meet the current
demanding requirements from modern industries including
automotive and consumer products; further exploiting this
technology makes it possible to incorporate innovative
design features that are not possible with traditional
materials.
Figure 1. An injection overmolding plastics.
One of the key aspects of the production of automotive
components via the injection molding technology is the
need to meet tight dimensional tolerances for assembly
purposes. Towards the aim of optimizing designs for
improved product quality, warpage simulation predicts the
final shape of an injection molded part, and thus allows
designers to avoid potential problems early in the design
stage. To fully consider the complex effects introduced by
inserts in an injection overmolding process, a truly threedimensional finite element solution is required [1, 2].
In this paper, we extend our warpage simulations to
account for orthotropic and fully anisotropic mechanical
properties of continuous fiber reinforced composite inserts.
This feature enhancement considers buckling and large
deflection analyses of overmolded plastic components.
Simulation results are presented for two plastic parts
injection-overmolded onto continuous fiber reinforced
composites.
Warpage with Inserts
For injection molded parts, warpage is caused by
variations in shrinkage throughout the part, which is
largely determined by the varying pressure and
temperature histories coupled with the frozen layer growth
SPE ANTEC™ Indianapolis 2016 / 1249
[1, 2, and 3]. The presence of continuous fiber reinforced
composite inserts could significantly affect the warpage in
four ways: Firstly, it could affect the temperature and
pressure fields thus affecting the shrinkage of the injected
polymer. A continuous fiber reinforced composite insert
acts as an insulator and delays the cooling and
solidification of the injected polymer in the cavity.
Secondly, the injected plastic can solidify around the insert
while still being hotter than the insert. The subsequent
differential shrinkage between the injected polymers and
anisotropic composite inserts becomes a source of warpage
for injection over-molded parts. Thirdly, continuous fiber
reinforced composite inserts will provide significant
resistance to part warpage due to their great stiffness
property. Lastly, if the insert is thermoformed by the
closing action of the mold, residual stresses in the insert
itself may influence the final part shape after ejection.
In addition to many other assumptions associated with
general injection molding simulations [1, 2, 3], an
additional assumption used for over-molding with inserts is
that the continuous fiber reinforced composite inserts and
the injected polymer are well bonded.
Fiber Composite Properties
The mechanical properties of a continuous fiber
reinforced composite insert have a great influence on its
behavior under thermal expansion and forces/pressures
during the injection molding process, and thus have a great
impact on the shrinkage and warpage simulation of an
injection overmolded part.
There are many forms of common raw continuous fiber
composites, such as pultruded rods, woven mats and
unidirectional tapes; each consists of the reinforcing fibers
and a base matrix material (thermoplastics, thermosets etc.)
In most cases, it is likely that the fibers embedded in the
composite component are strongly oriented. As fibers
normally have very different physical properties than the
matrix materials, the fiber orientation introduces
significant anisotropy in the thermo-mechanical properties
of the composite fiber-matrix system. As a result, isotropic
constitutive models are not valid for continuous fiber
reinforced composites.
Not to lose generality, the full Hooke’s Law under a
spatial Cartesian coordinate system can be described in the
following form.
σ ij = Cijkl ε kl
contracted notations (subscripts 1 to 3 indicate normal
directions, and 4-6 the shear terms) as follows
⎧ε 1 ⎫
⎡C11
⎪ε ⎪
⎢
⎪ 2⎪
⎢
⎪⎪ε 3 ⎪⎪
⎢
ε kl → ⎨ ⎬ Cijkl → ⎢
⎢
⎪ε 4 ⎪
⎢
⎪ε 5 ⎪
⎢
⎪ ⎪
⎪⎩ε 6 ⎪⎭
⎢⎣
,
C12
C 22
Sym
C13
C 23
C14
C 24
C15
C 25
C33
C34
C 44
C35
C 45
C55
C16 ⎤
C 26 ⎥⎥
C36 ⎥
⎥
C 46 ⎥
C56 ⎥
⎥
C66 ⎥⎦
(2)
For a fully anisotropic material without any plane of
symmetry, e.g. combinations of multiple fiber sheets with
random alignment angles, all the 21 elastic constants in the
above stiffness matrix are independent of each other and
potentially non-zero. For an orthotropic material that has at
least two orthogonal planes of symmetry, the shear-normal
terms (e.g. C14 and C36) and the off-diagonal shear-shear
terms (e.g. C45 and C56) in the elastic matrix vanish, which
leaves only nine independent elastic constants.
Alternatively, the orthotropic properties can be described
by three Young’s moduli, three Poisson’s ratios and three
shear moduli, each defined on a principal direction.
Orthotropy can be found in fiber reinforced composites
with fiber layup in orthogonal directions, a typical example
is the continuous carbon fiber reinforced thermoplastic
composite tape.
Unlike for the transversely isotropic material model
commonly used for polymers, the coefficient of thermal
expansion (CTE) for an orthotropic fiber composite can be
different in all three principal directions. Consequently,
there are three independent CTEs for an orthotropic
composite. As for a fully anisotropic composite, the
number of CTEs becomes six, i.e. each corresponds to one
strain term as follows
(3)
ε kl = α kl ΔT
It is worth pointing out that an injection overmolded
design can involve fiber reinforced composite inserts of
very complex geometries and double curved surfaces, e.g.
from a thermoforming or draping process. As a result, the
fiber sheet direction and thus the composite principal
directions vary according to the insert surface normal and
any in-plane shear which has occurred during forming. It is
critical to define the local material axis correctly for use in
simulation.
Simulation Technology
(1)
Mesh Bonding
where the tensors of stress/strain σij/εkl and the elastic
stiffness Cijkl can be further order-reduced with the
SPE ANTEC™ Indianapolis 2016 / 1250
For numerical implementation and accuracy purposes,
an aligned mesh would be preferable at the interface of the
cavity and continuous fiber reinforced insert; this way, the
nodes on the cavity and insert interface would be perfectly
matched so that displacements can be shared on both
meshes of the cavity and insert. However, to enforce
perfect matching requires a significant effort during
meshing and may force the use of highly distorted
elements. An alternative and more practical solution is to
mesh the insert and cavity independently, and then force
consistent physical (e.g. displacement) results on the
interface. This latter approach was adopted in this work.
used which combines the AMG-CG equation solver with
the subspace eigenvalue iteration algorithm.
To bond the cavity-insert interface together in the
warpage solution, the analysis starts by identifying the
interface area between the insert mesh and the cavity mesh.
Based on the relative geometric position and the
displacement interpolation function of the element, the
relationships between the degrees of freedom at the nodes
of the cavity mesh and the nodes of the insert mesh can be
established. The relationships are typically described in
multi-point constraint (MPC) equations. The insert nodes
on the interface are regarded as the master nodes, and the
cavity nodes as the slave nodes. It is recommended that the
density of the insert mesh be coarser than that of the cavity
mesh. With these MPCs, the structural behavior is
expected to be identical to that of a perfectly matched mesh
of the combined system of inserts and cavities. Various
algorithms are available for dealing with MPC equations in
finite element methods. The elimination method based on
the Lagrange multiplier formulations is used in our
simulation. In this method, the constrained degrees of
freedom and multipliers are eliminated, thereby yielding a
lower order matrix equation for the unconstrained degrees
of freedom.
Case 1
Numerical Examples
Injection overmolding on orthotropic and fully
anisotropic inserts has been implemented in the Autodesk
Moldflow simulation package. Simulation results of two
examples with anisotropic continuous fiber reinforced
composite inserts are presented in the following to
demonstrate the effectiveness and efficiency of the
implementation.
The first case addresses a demonstration model shown in
Figure 2. The simple model consists of two overlapping Lshaped meshes, with one mesh representing the plastic part
(in green), and the other representing the continuous fiber
reinforced composite insert (in grey) onto which the plastic
part is overmolded. The insert material is an E glass fabric
with fibers at 0/90°. The material properties of the
isotropic polymer (a relatively flexible PFA polymer) and
the orthotropic composite insert are listed in Table 1.
Significant orientation can be seen from the composite
properties, which are locally defined, i.e. along the local
axes following the surface direction change. A practical
example of this type of insert would be a glass fiber angle
created from a peel ply fabric.
Buckling and Large Deflection
A typical plastic component injection overmolded onto
continuous fiber reinforced composites will be thin-walled
in nature. Buckling may occur with the injection molding
process. When the part is ejected from the mold, in-mold
residual stresses which depend on the time, temperature
and pressure history of the entire part [4, 5], have to be
rebalanced. Consequently the part may buckle. In our
simulation, the handling of anisotropic continuous fiber
reinforced composite inserts has also been extended into
the buckling and post-buckling warpage analyses [6, 7].
Classical linear buckling analysis generally yields a
sufficiently accurate buckling indicator for most practical
injection molding problems, where only small
displacements and deformations occur before an instability
point is reached. To deal with the large scale threedimensional finite element models of real-world injection
overmolded plastics parts, a fast parallel Eigen-solver is
Figure 2. An L-shaped part with a part insert.
Figure 3 shows the temperature history of the process on
a longitudinal cut section, including the progression of the
injected melt front. While surface temperature quickly
cools to the mold temperature, internal regions are seen to
cool much more slowly. Figure 4 shows the final warped
shape. For comparison purpose, two further tests were run
where the insert material was set in turn to a soft unfilled
polymer and a different fiber composite (see material
properties in Table 1). The analysis results are shown in
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Figure 5. Note that the stronger orthotropic insert restrains
the part from warping, when comparing cases (a) and (b).
On the other hand, when comparing cases (a) and (c), we
observe a larger warp angle and greater shrinkages in the Z
direction depending on the different fiber layup
orientations.
(a)
T = 0.17s
T = 0.56s
(b)
T = 2.98s
T = 30.64s
Figure 3. Temperature results at different times.
(c)
Figure 5. Warped shape and Z direction deflection with the
insert set as three different materials: (a) E glass fabric,
fibers at 0/90°, (b) PI X05, BIP-PF, (c) E glass fabric,
fibers at +/-45°.
Figure 4. Final warped shape of the part.
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Case 2
The second case shown in Figure 6 addresses the
simulation of a seat model with a PP material (in green)
over-molded onto a continuous fiber reinforced sheet (in
grey) and a polymer cushion (in yellow). The fiber
orientation of the insert is deliberately made nonorthogonal, i.e. with fibers at 0/45° to demonstrate
anisotropic behaviors. The insert has greater diagonal
terms in the elastic matrix than the overmolding polymer,
in order to demonstrate distinguished structural
performances between the two different components. Note
that the fibers of the insert run in compliance with the
curved surface.
T = 20.93s
T = 50.77s
Figure 6. An overmolded seat model.
Figure 7. Molding and insert temperature results at various
times during processing.
Figure 7 shows the temperature distribution on a crosssection of the polymer part and inserts at the end of filling
and at the ejection time. Figure 8 shows the predicted
warpage from a large deflection analysis. Since overall the
composite insert has much less shrinkage than the polymer,
it is forced to bend outwards. Consequently, the angle
between the seat back and bottom becomes larger after the
warp deformation. It is also noticed that, despite the
symmetry of the geometry and injection location, the
deformed shape of the insert shows an asymmetric pattern
about the part center line as shown in the contour plot in
figure 9. This is caused by the anisotropic mechanical
properties which result from the non-orthogonal fiber
layup orientations.
Figure 8. Final deformation of the warped part (large
deflection analysis).
SPE ANTEC™ Indianapolis 2016 / 1253
fiber orientation effect. Meshes of the cavity and inserts are
bonded with MPC in the finite element formulation. Large
deflection analyses were employed to predict part warpage.
Numerical results show that the present 3D simulation
technology is capable of predicting the warped shape of
injection overmolded parts with continuous fiber
reinforced composite inserts.
References
1.
2.
3.
Figure 9. Contour plot of insert deflection showing
deflection asymmetry.
4.
Summary
5.
We have extended the Autodesk Moldflow 3D warpage
simulation of injection overmolded parts to consider
continuous fiber reinforced composite inserts. Orthotropic
and fully anisotropic constituent relations can be specified
for the composite inserts in order to take into account the
6.
7.
P. Kennedy, R. Zheng, Flow Analysis of Injection
Molds (2nd edition), Hanser Gardner Publications, New
York (2013)
Z. Fan, C. Kietzmann, S. Ray, F. Costa, P. Kennedy,
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S. Ray, F. Costa, SPE ANTEC Proceedings, 49: 632636, Nashville (2003).
R. Zheng, P. Kennedy, N. Phan-Thien, X-J. Fan, J.
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Table 1. Material properties of the polymer and insert (Moduli E/G, Poisson’s ratio v, thermal expansion coefficient a,
thermal conductivity k).
Polymer:
PI X05, BIP-PF
Insert:
E glass fabric, fibers@0/90°
Insert:
E glass fabric, fibers@+/-45°
E1 = E2 = 600,
E1 = E2 = 25000, E3 = 1200,
E1 = E2 = 12200, E3 = 1200,
G12 = 204.08
G23 = G13 = 600, G12 = 4000
G23 = G13 = 600, G12 = 8000
v
v12 = v23 = 0.45
v23 = v13 = 0.4, v12 = 0.2
v23 = v13 = 0.4, v12 = 0.2
α (1/C deg.)
a1 = a2 = 0.00013
a1 = a2 = 7.4×10-6, a3 = 0.00012
a1 = a2 = 1.0×10-5, a3 = 0.00012
κ (W/mK)
0.19
0.3461
0.3461
E, G (MPa)
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