:
L ICENTIATE T H E S I S
Compression Moulding of SMC,
Visualisation and Inverse Modelling
Torbjörn Odenberger
Luleå University of Technology
Department of Applied Physics and Mechanical Engineering
Division of Fluid Mechanics
:|: -|: - -- ⁄ -- 
Compression Moulding of SMC, Visualisation and Inverse
Modelling
By
Torbjörn Odenberger
Division of Fluid Mechanics
Department of Applied Physics and mechanical Engineering
Luleå University of Technology
SE-971 87 Luleå
Sweden
Luleå, June 2005
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2
ABSTRACT
Before presenting the Sheet Moulding Compound (SMC) process, which is the
primarily focus of this work, a literature survey is carried out to deal with fibre
reinforced polymer composites in general. Then the first part of this work is
presented and is primarily focused on experimental visualisation of the flow
during mould closure of SMC. Circular plates are manufactured with industry
scale equipment at close to production conditions. Special attention is given to
the advancing flow front, for which the full complexity is captured by means of
continuous high resolution close-up monitoring. From the experimental
visualisation of the flow front, three phases are defined, namely squish, flow,
and boiling. During the initial phase, squish, outer layers do not remain outer
layers, the actual flow is very complex and air is likely to be entrapped. The
governing process parameters during this phase are mould temperature, mould
closing speed and amount of preheating in the mould. During the second phase,
flow, the flow is stable and seemingly viscous. During the last phase, boiling,
bubbles are observed in the low pressure region at the flow front, favouring the
void content both internally and on the surface. Based on a chemical analysis
including mass spectrometry and thermogravimetry, the gas is probably
styrene.
In the second part it is investigated if an inverse modelling approach by
proportional regularisation can be applied to mimic the pressure distribution
during compression moulding of SMC. The process is simulated with
Computational Fluid Dynamics and the mastered parameter, the viscosity of
the SMC, is allowed to vary as a function of time. A grid refinement study of
two ways to model the process and for three fictitious pressure scenarios yields
that the suggested approach work very well and that the numerical errors can
be minimised as desired. Finally a validation process is carried out showing
that to get quantitative agreements of the whole pressure field more advanced
viscosity models must be used. In order to verify the inverse modelling system
have to important errors are studied. Firstly the error between calculated and
experimental pressure, secondly the discretisation error due to solving the
problem for many small volumes. Both have to be minimized and the later is
studied with Richardson’s extrapolation. The conclusions are that the initial
guess is very important for predictions in the beginning of the simulation.
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4
PREFACE
This Thesis was produced at the division of fluid mechanics at Luleå
University of Technology, Sweden. The work was supported by VINNOVA
through the framework of KEX, by the Swedish Research Council and the
Swedish institute of Composites SICOMP. The experiments were performed at
SICOMP AB with, as always, a very helpful staff, thank you very much!
A lot of people have been contributed to this Thesis and I owe them my
gratitude’s.
Professor Staffan Lundström my supervisor, thank you, for believing in me and
supporting me.
I am also grateful to Professor Håkan Gustavsson for the fruitful discussions
we have hade.
Allan Holmgren and Magnus Andersson, I couldn’t make this happen without
you.
Christer Lundemo, thank you for your ideas and the discussions we have had.
I am also grateful to all people involved in KEX, making my work possible,
thank you for your support.
Thank you my friends of RT-2002 and at fluid dynamics making the University
an interesting place to be at.
Thank you, Bo Lindblom for your support during the chemical analysis.
My wife Eva-Lis, my beloved daughter Alva, Mum, Dad, brothers and the rest
of my family, thank you for always being there for me.
Luleå 2005-06-17
_________________________
Torbjörn Odenberger
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List of Publications
The thesis comprises an introduction and the following appended
publications:
A. Odenberger P.T, Andersson H.M, Lundström T.S, Experimental flowfront visualization in compression moulding of SMC.
Composites Part A 35 (2004) p. 1125-1134.
B. Odenberger P.T, Lundström T.S. Inverse Modelling of Compression
Moulding of SMC with usage of Computational Fluid Dynamics.
Submitted for publication.
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CONTENTS
ABSTRACT……………………………………………………….……3
PREFACE………………………………………………………………5
LIST OF PUBLICATIONS…………………………………………….7
1.
2.
INTRODUCTION ........................................................................ 10
FIBRE REINFORCED POLYMER COMPOSITES ................... 11
2.1
Applications .......................................................................... 11
2.2
Constituents........................................................................... 12
2.3
Manufacturing....................................................................... 13
2.4
Defects .................................................................................. 14
3. SHEET MOULDING COMPOUND............................................ 17
3.1
Manufacturing route.............................................................. 17
3.2
Material composition ............................................................ 18
3.3
Defects .................................................................................. 19
3.4
Rheology ............................................................................... 19
3.5
Fibre orientation.................................................................... 21
3.6
Flow during moulding........................................................... 22
3.6.1 Experimental visualisations .............................................. 22
3.6.2 3D-simulation tools........................................................... 25
3.6.3 2D-simulations tools ......................................................... 26
3.6.4 Inverse modelling.............................................................. 26
4. CONCLUDING REMARKS........................................................ 29
5. SUGGESTIONS FOR FUTURE WORK..................................... 30
6. REFERENCER ............................................................................. 31
PAPER A…………………………………………………………….…1
PAPER B…………………………………………………………….…1
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1.
INTRODUCTION
This thesis deals with methods to visualise and model one particular method to
manufacturing fibre reinforced polymer composites namely the Sheet
Moulding Compound process often termed SMC. The vision is to be able to
predict and thereby minimize the void content. The manufacturing science, the
methods described and also the results presented are however generic and
apply in several aspects on as well other manufacturing methods of fibre
reinforced polymer composites as similar processes such as paper-making and
the formation of medium density fibre boards. The actual work performed is
reported in two papers but to start with a short overview of the subject is
presented. The summary is not meant to be complete in any sense but it will
hopefully introduce readers not familiar with composites manufacturing and
SMC to the subject of this thesis.
10
2. FIBRE REINFORCED POLYMER
COMPOSITES
These days when fuel consumption, performance and low cost are leading
terms fibre reinforced polymer composites are moving into a new era with
sharpened demands on efficient manufacturing of defect-free materials. The
status of manufacturing and manufacturing defects will here be briefly
outlined. Let us however to start with an overview of typical applications and
constituents.
2.1
Applications
Fibre reinforced polymer composites is a high performance type of material
that can be tailored for almost any needs. The way of combining low weight
and high strength makes it indispensable for marine applications such as hulls,
rigs and rudders, aerospace parts such as structural beams and load carrying
panels, sports equipment such as poles, golf-clubs and floor-ball sticks cf.
Figure 1. To exemplify 1942 Cornelius Warmerdams set the world record to
4.77 m in pole vault using a bamboo pole. This record did hold for, as much as,
15 years until it was increased by a few centimetres using metal rods. However
with the introduction of composite poles the athletics soon broke the 5 meter
barrier and have, as well known, even managed to pass 6 meters.
Figure 1. A typical floor-ball stick with a handle made of glass/carbon reinforced polymer
composites while the blade is pure thermoplastic.
Also in the automotive industries fibre reinforced polymer composites are
widely used. The reason for this is not only the high stiffness to weight ratio of
11
the material but also that the manufacturing tooling can be less expensive than
the ones used for parts made of steel. Hence, outer-panels to trucks buses and
some cars are often made of fibre reinforced composite materials. One example
is the Scania truck P380, cf. Figure 2. where several details are made from
fibre composites.
Figure 2. Scania P 380 6x2*4 rigid, sleeper cab.
Other areas for fibre reinforced composites, where excellent mechanical
properties are combined with different features of the material, are power
technology (insulation) house facilities (design freedom) construction
(maintenance) and cisterns (chemical sustainability).
2.2
Constituents
All polymer composites consist of a load carrier such as fibres or grains and a
binder holding the particles together here called the matrix. The matrix has
several tasks to fulfil. To start with a high bounding between the load carriers,
the fibres, is of importance. Then the fibres and particles have to be protected
against mechanical and chemical damage and finally the matrix itself needs to
be resistant to the ambient environment (chemicals etc.). Epoxies, vinylesters
and polyesters are often used as matrix where the polyester often is chosen of
economical reasons while epoxies, in many aspects, have the best properties.
The fibres and particles in their turn should naturally have a high strength and
stiffness. There are many types of fibres to choose from where the three main
categories are defined by the material they are made from, glass, carbon and
aramid. Since the fibres transfer the loads it important to locate and orient them
12
so that the usage of their mechanical strength is maximized. This will depend
on the load case and two examples are here presented.
Firstly consider the body panel of trucks where the load is due to pressures
generated by the relative speed of air during driving and also due to unknown
forces applied active during driving and maintenance. Such panels need to be a
fairly good load carrier in all directions which is often fulfilled by using
chopped strands of fibres, about 2-3 cm of length that are located randomly
throughout the whole part. The implication of this is that also the matrix will to
a large extend transfer loads. Secondly consider a high pressure fuel storage
bottle where the demands on the load carrier is much higher than in the panel
discussed above. Hence it is better to use continuous fibres than chopped
strands since the loads are then conveyed directly by the fibres giving the bottle
a high strength and stiffness.
There are numerous examples that could be mentioned based on their
application using different types of fibre length and fibre orientation but in
general the strength and stiffness of the composites is increased with fibre
length and fibre content. Chopped fibre systems are, however, more viable
when the formability and high volume production is in focus.
2.3
Manufacturing
There are numerous ways to manufacture fibre reinforced polymer composites.
One often makes a distinction between methods for high volume and high
performance products. The latter products have mainly been developed within
the defence industry resulting in that issues such as appearance and
manufacturing costs have been of secondary importance. Labour intensive
methods such as pre-preg lay-up form the basis for this type of composites. In
this extremely expensive method pre-impregnated fabrics (often unidirectional)
are laid-up on a mould manually in desired directions to get optimal
mechanical properties. The stack of fabrics is then covered and put into an
autoclave in order to bleed out resin and cure the part at high pressures and
temperatures. For automotive industry such methods are only of interest for
exclusive models and accessories. For bulk-parts it is essential that the
mechanical properties are good enough while manufacturing costs is often the
primary topic and for items such as outer panels mirror finish is a key issue.
These panels are traditionally made from steel but for cars in smaller series,
trucks and buses it has turned out that the costs becomes lower if the panels are
made from fibre reinforced composites by compression moulding of SMC. I
will return to this method in the next section but let me first shortly discuss a
few more methods.
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Resin Transfer Moulding is another relatively cost effective process where the
resin is impregnating fibres that are placed in a closed mould. The resin is
transfer by a pressurised system and after complete filling of the mould the
resin is cured. The process offers the possibility to tailor-make parts at
relatively low costs. In RTM the material used is also the common ones as
unsaturated polyesters, epoxies, vinylesters etc. Another method for high
performance composites is filament winding. This method is used for example
high pressurised tanks where the fibres are continues and wetted before winded
up to the desired shape. In addition there are methods for minor series
(prototype) with very little investment cost as with wet lay up and spray-up.
The benefit is that not much investment cost has to be made and that they
represent direct forward methods. While significant efforts in research and
development on manufacturing methods have resulted in a fundamental
understanding of many important mechanisms, composite processing science is
still far from completely investigated. Regardless of the manufacturing method,
the flow of resin impregnating the fibres, or in some cases the flow of already
impregnated fibres, is in general a very complex process. Furthermore, it
affects everything from fibre distribution and orientation to void content and
spatial variation in solidification. A fundamental understanding of the flow
processes is therefore essential in order to ensure optimum and robust
processing.
2.4
Defects
Unwanted fibre orientation, uneven fibre distribution, fibre crimp, fibre printthrough, fabric wrinkling, warpage, and formation of dry spots are examples of
defects that may be introduced during manufacturing of composites. This work
is however focused on another flaw namely voids. Residual voids in composite
parts can deteriorate properties of the composite such as the interlaminar shear
strength, flexural strength, electrical insulation and resistance to moisture. To
exemplify it has been shown that on average the interlaminar shear strength
decreases with 7% for each volume percentage voids [1]. Although this is a
crude generalization it shows on the importance of understanding the formation
of voids during composites manufacturing. Voids are most likely formed in the
processing of composite materials and may exist in the resin before the
processing, form during the impregnation, the filling of a mould and during
solidification. In addition to the formation of the voids the transport of them
has a large influence on the final void content and distribution in the
composite. During processing, enclosed gas (or volatile components in the
resin) may move as voids by advection or dissolve into the resin as molecules
by diffusion [2,3]. Knowledge of such mechanisms is fundamental for the
14
vision of this thesis. Since surface voids result either in costly after-treatments
or rejection of the parts.
Voids that are located in impregnated areas are certainly affected by the
ambient conditions. To start with voids will change in volume with the
pressure a relation that in its simplest form is described by the perfect gas law:
V2
p1 T2
V1 .
p 2 T1
(1)
An obvious conclusion from Eq. (1) is that raising the pressure p2 will result in
a smaller volume V2, hence this is also the case when lowering the temperature
T2. Thus this is of interest since both temperature and pressure are key
processing parameters. Please also notice that Eq. (1) does not account for the
capillary pressure which in most cases may be neglected, but for small bubbles
the capillary pressure should be added to both pressures in (1). Another
mechanism being important for the evaluation of the voids is diffusion of gas
molecules over the gas-liquid interface. It has, for instance been shown that
needle-shaped voids being located inside fibre bundles alter its length
according to the following relationship [4]:
ª
p0 º
2GDr H «1
»
p[ pc »¼
«¬
patm t
ª R R º
Rv2 ln « v S » U atm
¬ Rv
¼
l
l0 e
(2)
Where lo is the initial length of the void and where the indices atm, o and [ for
the pressure denote atmospheric pressure, degassing pressure and pressure at
position[, respectively. In the exponent some additional parameters appear.
These are the geometrical constant G, the diffusion coefficient Dr of the
specific gas in the resin, a constant H which multiplied by the pressure gives
the saturated concentration, the density of the gas at atmospheric conditions ȡ,
the void radius Rv and the thickness of a stationary region Rs. For spherically
shaped moisture voids alternative expressions have been derived to model void
growth and dissolution in pre-preg lay-up [2,3].
The critical volume must be correlated to the processing conditions in some
way. For instance, the voids may escape some entrapment in the fabric if the
pressure gradient is high enough. Without going into any details it is clear that
low liquid vapour surface tension, Jlv, and uniform passages between the fibres
will make it easier for the bubbles to move with the resin [2]. The smaller the
15
scale studied is, the higher pressure gradient will be required to force a bubble
through a constriction. Hence, for the same ratio between the void radius and
the constriction radius voids are more likely to be trapped within fibre bundles
than between them. Such voids are on the other hand naturally small and may
therefore just dissolve into the resin.
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3. SHEET MOULDING COMPOUND
Moulding compound is, when it comes to usage of raw material, the number
one manufacturing method of fibre reinforced composite materials [5].
Compression moulding is also the most cost-effective manufacturing methods
of load carrying fibre composites for long and very long production series.
Within automotive industry it is mostly used for panel constructions such as
hoods, fenders, roofs and tailgates cf. Figure 2 where the following details are
made form SMC, corner panels, tool cover panel, small and large roof spoiler,
side spoilers and low front panel. But also other areas are of interest with
applications such as lamp structures and restroom facilities. Thus the process
has a wide field of applications and benefits are not only cost effectiveness but
also low weight-, noise damping-, halogen free-, flame retardant-, electrical
insulated- and corrosion resistant products.
3.1
Manufacturing route
In the SMC-process a couple of male and female moulds are used. They are
mounted in a high capacity hydraulic press and heated up to the desired curing
temperature with for example electrical cartridge heaters. When the moulds
have reached this state a charge is prepared consisting of sheets of SMC
material stapled on top of each other and placed on the lower mould-half cf
Figure 3. The size of the charge is about 20-90 percent of the mould surface
and the mould temperature is between 120-180 °C for unsaturated polyester
based SMC-material. Now the press is closed as fast as possible to force the
charge to fill the mould. The hydraulic pressure is build up (3-20 MPa) and
held until the desired cross-linking is reached which typically takes about 1 - 4
minutes. The final part is now stable and can be demoulded enabling the start
of a new moulding, cf. Figure 3.
17
Charge
Molded Part
Figure 3. Schematic sketch of the SMC- process.
3.2
Material composition
SMC is a continuous sheet containing relatively long fibres and mineral fillers
embedded in a highly viscous thermosetting resin [6]. A typical SMC
composition can be viewed in Table 1. The fibreglass is normally chopped
strands of E-glass with a length of approximately 25 mm containing about 180400 fibres. Following the demands on Class “A” appearance, in automotive
industries, it is sometimes common to use somewhat more resin instead of lowprofile additive and also add more filler than what is stated in Table 1.
Component
Isopolyester resin
Polystyrene
Para-t-butyl peroxybenzoate
Zinc stearate
Calcium carbonate
Magnesium oxide
Fibreglass
wt %
16.4
11.0
0.3
2.4
41.1
0.5
30.0
Table 1. Example of a low-shrinkage SMC formulation.
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3.3
Defects
Although the SMC process has a very good reputation and is widely used there
are certainly areas that must be further studied. Fibre orientation and
distribution is set during the filling of the mould and the final state strongly
affects the mechanical properties of the part moulded. It has turned out that it is
very difficult to model the movement of the fibres regardless of which
approach that is used. [7,8,9,10]. One reason is that there is no good enough
model for the fibre to fibre interaction. Another type of defect, being the one in
focus in this thesis is pinholes and blowouts [11]. These defects the pinholes
and blowouts then emerge when the SMC-moulded part is painted and coated
and pinholes and blowouts emerge as small surface defects being approximate
300 μm and 600 μm in diameter, respectively. Such defects have to be treated
and the part repainted or even worse rejected. The origin to these defects is
probably bulk voids and hence methods to reduce the number of voids in the
bulk must be found such as, high pressures and high pressure gradients as
described in the previous sections. In order to define the appropriate level of
these quantities it is important to clarify the flow behaviour of the SMC. This
will be done in three parts.
3.4
Rheology
The actual flow during the pressing is rather complex involving, for instance,
high temperature gradients with corresponding gradients in viscosity of the
resin, near wall effects caused by relatively long fibres in a thin geometry, the
interaction of the four phases resin, fibres, fillers and air and an accelerated
cross-linking of the molecules in the resin [5,6,12-14]. It is also apparent that
the long fibres and the relatively high fibre volume fraction (30 %) lead to
interaction between individual fibres. Problems associated with this are
unwanted fibre orientation, uneven distribution of fibres and fillers, formation
of weld lines and formation of voids. In practice may this result in residual
stresses, warpage (shape distortions due to internal stresses), areas with low
mechanical properties and surfaces with flaws.
Since the pressure and pressure gradients [5,6,12-14, 15,16] are key process
parameters and are vital for a successful moulding it is of interest to have a
material model that can describe the SMC as good as possible. In fluid
mechanics there are several material models to choose from where the most
common one is known as the Newtonian model. This model states that the
strain rate is proportional to the stresses in the fluid by a constant that is known
as the viscosity (3)
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.
W ij
P J ij .
(3)
The fictive Newtonian behaviour is thus linear and can in most cases predict
fluids as water and air but it has been shown that this is not a complete
description for many polymer composites [12,14]. Consequently more intricate
models have to be used including effects such as shear-thinning and viscoelasticity. One example of such a model is the generalized Newtonian model
(4)
.
W ij
.
K (J ) J ij .
(4)
.
Here the non-Newtonian viscosity K (J ) is modelled to be strain rate dependent
.
it self. The relation for K (J ) are often set to the power-law formulation
according to:
.
K (J )
. n 1
AJ
(5)
where A and n are the material parameters. Another constitutive relation, that is
sometimes implemented, is the Carreau-Yasuda and Cross equations [14].
Naturally the viscosity is also dependent on other parameters such as
temperature, degree of cure and orientation state of the fibres. The latter is so
interesting so it deserves a section of its own since it also strongly influences
the mechanical properties of the moulded part. But before moving into this area
let us briefly review methods to measure the viscosity of SMC. Constitutive
parameters such as viscosity are often measured in rheometers. The actual cells
used for the measurements are designed to give a desired deformation of a
liquid. A rotating cylinder within a hollow one and a rotating or oscillating
coaxial cone or plate over a plane plate are typical tools used. By usage of
these kinds of geometries the measurements are carried out with well-defined
deformations and deformation rates. The force generated by the motion of one
part of the tool and transferred by the liquid to the other is measured parallel to
the deformation and can then be related to the viscosity. Another way of
measuring the viscosity is to let the fluid flow through a tube with well-defined
geometry under a known pressure gradient and simultaneously measure the
volumetric flow rate. Traditionally the tools used for rheometry are rather small
and the cavities filled with liquid thinner than the lengths of the strands used in
SMC hence rheometers are most suited for the pure polyester or the polyester
20
chalk suspension. Of this reason Vahlund [14] developed a method for large
sample rheometry. A similar tool is here used as well for experimental
visualisations in Paper A as inverse modelling in Paper B.
3.5
Fibre orientation
Except for being important for the mechanical properties of the part the fibre
orientation distribution will influence the flow and thus the pressure
distribution during moulding. Hence it is important to know that the fibre
orientation distribution function \ (T , I ) can represent the fibre orientation in a
polymer composite. It is a probability function that describes the probability
that an individual fibre is orientated within a certain angular interval [17]. For
example if the interval is T to T dT and I to I dI it is given
by\ (T , I ) sin TdTdI . Since one fibre end is indistinguishable from the other
\ (T , I ) is periodic and thus
\ (T , I ) \ (S T , I S ) .
(6)
Since every fibre has a given direction the integral over all directions must
equal one as expressed below
2S S
³ ³\ (T ,I ) sin TdTdI
1.0 .
(7)
0 0
This function is not used in numerical calculations, although it is describing the
fibre orientation for the fibres, since it contains more information than can be
handled in the computations. Instead a more straight-forward and compact
method is used where tensors portray the distribution function. The second and
forth order tensors, for the in plane case is the following:
a ij
³ p p \ (I )dI
a ij
³p p
i
i
(8)
j
j
p k p l\ (I ) dI
(9)
For the second order tensor we have random orientation distribution for the
fibres when a ij >0.5, 0; 0, 0.5@ , 11-direction orientation when a ij >1, 0; 0, 0@
and 45 degrees from the 11-dirction when a ij
21
>0.5, 0.5; 0.5, 0.5@ .
This
information can be found in Advani and Tucker’s paper “the use of tensors to
describe and predict fibre orientation in short fibre composites [17].
3.6
Flow during moulding
The two previous chapters have shown on ways to characterise the flow during
moulding. The flow is however very complex and when trying to model
phenomena such as entrapment of air and the evaluation of the formed bubbles
additional models are required. In order to form such models the actual
behaviour of the SMC during pressing must be clarified. This may be done by
experimental visualisations of real mouldings and by usage of simulation tools.
3.6.1 Experimental visualisations
Visualisations with multicoloured SMC-charges were first used by Marker and
Ford [18] and later adapted by Barone and Caulk [19]. The technique were then
refined by Costigan, Fisher and Kanagendra [20] who presented flow front
studies by the partial moulding technique by also setting-up an in-situ video
recording equipment. Based on this investigation they expelled the partial
moulding technique since it did not capture the true flow front behaviour. Their
presentation was instead based on their video-recordings leading to the result
that for high ram and flow front velocities the flow seemed more Newtonian
with more plug like flow front progression than in low mould closing speeds
where a tumbled fibre flow occurred. In 1986 Barone and Caulk [21] proposed
a mathematical model based on their earlier observations [19] changing focus
from experimental visualisations to theoretical and numerical modelling cf.
[22, 8, 23]. Hence, the visualisations done in the previous presented papers
have formed the basis for most models presented up to date. Today small high
resolution cameras are available for almost any needs making it possible to not
only look at one instant rate of deformation but also covering the span of
deformations in a short time. The high resolution camera has one other
advantage and that is that the true flow front behaviour is captured instantly not
after curing in the mould. A full report of a visualisation done with a high
resolution camera-system is presented in Paper A and the technique is
furthermore shortly presented in what follows.
It can sometimes be relatively costly to obtain a class “A” appearance of a
surface in automotive industries. One reason to this is the surface defects such
as voids as discussed above. And even with the fact that high pressures often
reduce the void content it should be preferable if they did not exist in the first
22
place. This was the main driving force for the investigation presented in paper
A. The main result of the experimental visualisation is that the liquid stage of
SMC-pressing can be divided into three phases, namely squish, flow and
boiling. During the initial moments of contact when moulding pressure is
building up, the first phase, squish, is defined as the first squirt of paste
emerging from the charge. The actual appearance of the squish is dependent on
the mould closing speeds and mould temperatures. For 15 mm/s and 135 ºC the
bottom layer yields to the pressure first; cf. Figure 4 and the corresponding
sketch Figure 5, where the elapsed time between each frame is 0.04 seconds.
Figure 4. Mould closing speed 15 mm/s, uniform mould temperature 135 ºC and elapsed time
between each frame 0.04 seconds.
23
0.00 s
0.04 s
0.08 s
0.12 s
0.16 s
0.20 s
0.24 s
0.28 s
Figure 5. Sketch over the flow front progression in Figure 4.
Initially the bottom layer rotates upward and it hits the upper mould before the
top layers even start to deform; cf. Figure 4. This violent behaviour persists
even for the higher mould temperature 165 ºC. The reason for this behaviour is
that the SMC was placed on the lower mould half and thus heated from this
side. Interestingly, for a lower speed on the press and if the lower mould
temperature is decreased to 135 ºC while keeping the upper at 165 ºC, then also
the top layer shoots out to meet the bottom layer, before the other layers start to
deform.
After the squish the flow front settles down in a seemingly stable and viscous
flow, this will be defined as the phase, flow, cf. Figure 6. When using a lower
mould closing speed it turns out that the squish produces loose fibre ends that
are pushed ahead of the flow front through the rest of the flow.
Figure 6. Mould closing speed 15 mm/s, uniform mould temperature 135 ºC and elapsed time
between each frame 0.04 seconds.
In the later part of the flow process, when the moulds are almost completely
closed, bubbles are observed originating from the SMC defining the phase,
boiling. It is important to notice that the boiling take place in a low pressure
24
region. A schematic sketch and snap-shots from the video-recordings of the
boiling is presented in Figure 7 and 8, respectively. The bubbles are also
observed in the cured part.
0.00 s
0.04 s
0.08 s
0.12 s
0.16 s
Figure 7. Sketch over the flow front progression in Figure 12. The view at 0.16 s (brown)
appears as dark hols in the SMC. Notice that the sketches of the first three time steps are only
possible scenarios.
Figure 8. Mould closing speed 15 mm/s, uniform mould temperature 165 ºC and elapsed time
between each frame 0.08 seconds. The encircled black area on the right-hand side figure is a
void.
3.6.2 3D-simulation tools
The pioneering work by Barone and Caulk [19,21] with coloured charge
visualisations indicated that the true in mould flow for SMC where very
complex with a high coupling between the energy equation and the momentum
equation [8]. Thus the true in mould flow are non-isothermal, this can also be
viewed in the previous chapter 3.6.1. This has become a stimulus for the
researchers to simulate and is done by for example Michaeli [24]. He uses a FE
model to simulate the third dimension (the height of the charge) but still for a
2D case since the true 3D flow would be too cumbersome and computationally
prohibitive for a real case scenario as an automotive industry body panel.
25
Hence only the phenomena are studied as the squish and not a real case
scenario.
3.6.3 2D-simulations tools
This is the method up to day to analyse the mould filling process by numerous
of different commercial simulation programs thus leaving the true in mould
flow for the future. For example a Volvo S60/V70 hood where simulated by
Vahlund [14]. The assumptions made are often based on experimental
visualisations where the walls have been studied and approximations of partly
slip are being implemented. This way of simulating the mould flow is an
approximation that up to day needs to be done, because of the limitation in
calculation recourses and computer performance. It has to be mentioned that
this simulations are often giving satisfied results regarding mould filling in
many cases but sometimes it would be of interest to scrutinize the true in
mould flow and then it is insufficient, i.e. when pressures, pressure gradients
and fibre orientation is sought for.
3.6.4 Inverse modelling
According to Tarantola [25] the scientific procedure for study a physical
system can be divided into tree stages. 1) Parameterization of the system:
choose a set of model parameters that can describe the system. 2) Forward
modelling: Discover the physical laws allowing for prediction of some
measurable parameter. 3) Inverse modelling: letting some measurements infer
the model parameters.
It is very tempting to reveal the viscosity during pressing by an inverse
modelling type of approach since the flow is very complex being affected by
several parameters. New materials are developed and there are endless
combinations for the chemical composition for a type of material. The material
parameters needs to measured in some way or estimated as by using an inverse
modelling technique. Thus the advantage with inverse modelling is that the
model parameters are tuned to best fit the experiments hence the inverse
modelling approach then has its clear area of usage. By a successful usage of
this approach it is possible to make predictions of parameters such as pressure
and pressure gradients even with model simplifications. It is, however, obvious
that such an approach must be carefully validated to confirm that it can account
for the very complex real in mould flow with many phases and large gradients
in physical parameters[12,13,14, 25]. Inverse modelling is widely used in areas
26
such as solid mechanics [26,27] and since the technique in it-self is the same
for any continuum, solid as well as fluid one could expect the same benefits in
this fluid mechanic approach that is presented by, for instance, Kajberg and
Westman [26,27].
When using the inverse modelling technique there are choices to be made that
influence the results. Before discussing these choices it is in place to present a
general schematic sketch of the process, cf. Figure 9. When studying this
figure it is important to know that an inverse modelling system can be build up
in numerous ways, depending on, for instance, how many model parameters
that should be estimated and the field of application [27].
Start Finite Volume
Analyse
STOP
NO
Solving Iteration
Exit
Output Finite Volume
Analyse
YES
Evaluation, Regularisation
Expression
Optimised Design
Parameters Output
Experimental Output
Figure 9. Schematic sketch for the inverse modelling system.
Finally the method in Figure 9 is below presented and a full report of results
obtained with this method can be viewed in Paper B.
To reveal the pressure and pressure gradients the viscosity needs to be known
as a function of time and spatial coordinates. This is important since from a
fluid dynamic point of view, the viscosity is the parameter that relates
deformation rate to stresses in the fluid and hence the pressure. One
methodology is thus to measure the pressure at a spatial location in simple
geometries and then find the viscosity distribution that matches these pressures
by inverse modelling. With a good enough model of the viscosity it is then
likely that the flow in more complex geometries can be found. An initial
inverse modelling procedure is presented in Paper B and without going into
any details it is shown that the procedure suggested can mimic any kind of
viscosity distribution in time while to fully capture the spatial distribution more
27
advanced viscosity models must be used. This is exemplified in figure 10 were
the centre experimental pressure is captured by the inverse modelling while the
simulated and experimental pressures obtained of-centre differs. The focus in
Paper B is to verify and validate the numerical simulations and in order to
further develop the inverse modelling technique suggested more experiments
must be carried out. The procedure is to:
x
x
x
x
x
Measure pressures at different spatial locations.
Simultaneous measure the true mould closing speed.
Choose an appropriate constitutive model.
Set up an inverse model calculation with the
measurements, revealing the viscosity, based on the
constitutive model.
Validate in some other experimental set-up.
Figure 10. Experimental centre pressure (C-exp), calculated centre pressure (C-sim),
experimental pressure (C-p1) located a distance 37.5 mm from centre and corresponding
calculated pressure (P1-sim) presented.
28
4. CONCLUDING REMARKS
The papers that follow have been partly reviewed above. As an additional
appetizer the main results from the papers are here summarized. From the
experimental visualisation of the flow front, three phases are defined, namely
squish, flow, and boiling.
During the initial phase, squish:
x The flow is very complex and air is likely to be entrapped.
x The SMC closest to one or both of the mould halves moves ahead of the
rest of the material and outer layers do not remain outer layers.
Interestingly the squish moves partly axially.
x Analysis also indicates that at least some of the air entrapped between
the SMC-sheets is released as the press hits the charge.
During the second phase, flow:
x A stable plug flow is formed.
x There is no indication of void entrapment for the simple geometry in
focus.
During the last phase, boiling:
x Bubbles are observed in the low pressure region at the flow front.
x Based on a chemical analysis, the gas leaving by the bubbles is
probably styrene.
From the studies with the inverse modelling system the following conclusions
could be made.
x
The inverse modelling with a proportional regularization for the
viscosity is producing results of which any desired error can be
achieved. The cost for small errors is the number of iterations needed
leading to time-consuming calculations.
x
The initial values should be carefully chosen before a complete run
including many time steps is carried out.
x
The suggested inverse modelling method will be developed to include
more complex material models as shear thinning material ones. Thus
the true SMC behaviour could be investigated.
x
More experiments must be carried out in order to get statistical value
since every pressure curve is unique producing small oscillations.
29
5. SUGGESTIONS FOR FUTURE WORK
Since the inverse modelling work as expected, with the rather simple model
used, it is of highest interest to test more advanced models. In this context it is
very important to do many enough experiments to, in a statistical sound
manner, find the constants to the models and to validate the expressions
obtained. More to come is that there is a lack of knowledge for the wall
interactions for very dense fibre and particle suspensions. Thus the wall
boundaries have to be investigated with PIV or LDV. The near wall velocities
will be implemented in the simulations and this will lead to even more accurate
results. It is furthermore very important to clarify the evaluation of formed
voids as a function of pressure and temperature. This can be done in set-ups as
those suggested in [4] and by simple theory. It is finally of interest to develop
innovative methods to reduce the void content in every stage of the process
including the manufacturing of the SMC.
30
6.
REFERENCER
[1]
Giorse, S. R. (1993). "Effect of void contents on the mechanical
properties of carbon/epoxy laminates." Sampe Quarterly(Jan): 54-59.
[2]
Lundström, T. S. (1996). "Bubble transport through constricted
capillary tubes with application to resin transfer molding." Polymer
Composites 17(6): 770-779.
[3]
Gutowski, T. G., Ed. (1997). Advanced Composite Manufacturing.
Cambridge, MA, John Wiley & Sons, Inc.
[4]
Lundström, T. S. (1997). "Measurement of void collapse during resin
transfer moulding." Composites Part A 28A: 201-214.
[5]
Manufacturing of Polymer Composites, B.T.Åström. 1997. ISBN 0412-81960-0.
[6]
Sheet Molding Compounds, H.G.Kia. 1993. ISBN 1-56990-154-6.
[7]
Folgar, F., Tucker III, C.L. (1984). "Orientation behavior of fibers in
concentrated suspensions." J. Reinforced Plastics and Composites 3:
98-119.
[8]
Osswald TA, Tseng SC. Compression Molding. In: Advani SG, editor.
Flow and Rheology in Polymer Composites Manufacturing.
Amsterdam: Elsevier, 1994. p.361-414.
[9]
Tucker, C. L., Advani, S.G. (1994). Processing of short-fiber systems.
Flow and rheology in polymer composites manufacturing. S. G.
Advani. Amsterdam, Elsevier.
[10]
Petrie, C. J. S. (1999). "The rheology of fibre suspensions." 87: 369402.
[11]
Pinholes and blowouts in SMC. A Sjögren. SICOMP TR04-005.
[12]
Compression molding, Tim A. Osswald and Shi-Chang Tseng, Flow
and rheology in polymer composites manufacturing volyme 10, p 361413.
31
[13]
Experimental flow-front visualization in compression moulding of
SMC, P.T.Odenberger, H.M.Andersson, T.S.Lundström,Composites
Part A 35 (2004), p1125-1134.
[14]
Fibre Orintation, Rheological Behavior and Simulation of the
Compression Moulding Process for Composite Materials, C.F.Vahlund.
ISSN: 1402-1544.
[15]
Lundström, T.S., “Bubble Transport Through Constricted Capillary
Tube with Application to Resin Transfer Moulding” Polymer
Composites, 17, pp. 770-779 (1996)
[16]
Lundström, T.S., “Measurement of Void Collapse during Resin
Transfer Moulding” Composites Part A, 28A, pp. 201-214 (1997)
[17]
The use of tensors to describe and predict fiber orientation in short
fiber composites. S.G Advani, C,L Tucker III. Journal of Rheology , 31,
1987 p. 751-784.
[18]
Marker LF, Ford B. Flow and curing behavior of SMC during molding.
Modern Plastics 1977;54:64-70.
[19]
Barone MR, Caulk DA. Kinematics of Flow in Sheet Moulding
Compounds. Polymer Composites 1985;6(2):105-109.
[20]
Costigan PJ, Fisher BC and Kanagendra M. The Rheology of SMC
During Compression Molding, and Resultant Material Properties. In:
Proceedings
of
40th
Annual
Conference,
Reinforced
Plastics/Composites Institute, The Society of the Plastics Industry, Inc.
Jan. 28-Feb. 1, 1985. Session 16-E. p.1-12.
[21]
Barone MR, Caulk DA. A Model for the Flow of a Chopped Fiber
Reinforced Polymer Compound in Compression Molding. Journal of
Applied Mechanics 1986;53:361-371.
[22]
Osswald TA, Tucker CL. Compression Mold Filling Simulation for
Non-Planar Parts. Intern. Polymer. Processing V 1990;2:79-87.
32
[23]
Mallick PK. Compression Molding. In: Mallick PK, Newman S,
editors. Composite Materials Technology. New York: Hanser
Publishers, 1990. p.67-102.
[24]
W.Michaeli, M.Mahlke, T.A.Osswald, M.N.Nölke, Simulation of the
flow in SMC. Kunststoffe 80(6) (1990) 717.
[25]
Inverse Problem Theory. Tarantola Albert. 1987. ISBN 0-444-42765-1.
[26]
Characterisation of materials subjected to large strains by inverse
modelling based on in-plane displacement fields. J. Kajberg, G.
Lindkvist. International Journal of Solids and Structures, v 41, n 13,
June, 2004, p 3439-3459.
[27]
Numerical and Microstructural Evaluation of Elevated Temperature
Compression Tests on Ti-6AI-4V. Westman E-L., Pederson R.,
Wikman B., Oldenburg M. 10th World Conference on Titanium (Ti2003 Science and Technology) Hamburg, Germany, 13-18 July, 2003
[28]
CFX 4.4-manual. ANSYS, Inc., Southpointe, 275 Technology Drive,
Canonsburg, PA 15317.
33
34
Paper A
EXPERIMENTAL FLOW-FRONT VISUALISATION
IN COMPRESSION MOULDING OF SMC
P.T. Odenberger*, H.M. Andersson, and T.S. Lundström
Division of Fluid Mechanics, Luleå University of Technology,
SE-971 87 Luleå, Sweden.
*To whom correspondence should be addressed.
E-mail: Torbjorn.Odenberger@mt.luth.se
Fax: +46 920 491047
1
ABSTRACT
This work is primarily focused on experimental visualisation of the flow during
mould closure in compression moulding of sheet moulding compound (SMC).
Circular plates are manufactured with industry scale equipment at close to
production conditions. Special attention is given to the advancing flow front,
for which the full complexity is captured by means of continuous high
resolution close-up monitoring. From the experimental visualisation of the flow
front, three phases are defined, namely squish, flow, and boiling. During the
initial phase, squish, outer layers do not remain outer layers, the actual flow is
very complex and air is likely to be entrapped. The governing process
parameters during this phase are mould temperature, mould closing speed and
amount of preheating in the mould. During the second phase, flow, the flow is
stable and seemingly viscous. During the last phase, boiling, bubbles are
observed in the low pressure region at the flow front, favouring the void
content both internally and on the surface. Based on a chemical analysis
including mass spectrometry and thermogravimetry, the gas is probably
styrene.
2
KEYWORDS
D.
Process monitoring
E.
Compression moulding
E.
Resin flow
E.
Thermosetting resin
3
INTRODUCTION
Compression moulding of Sheet Moulding Compound (SMC) is a viable and
paramount method to manufacture fibre reinforced composite materials. It is
stable and fast and has been in use for several decades. The practical
knowledge of the process is therefore close to being complete resulting in that
processing parameters can be tuned before production to obtain a high-quality
composite. To get a full set of generic rules in order to avoid the tuning and
further improve the quality of the composite some issues are still to be
explained. One unsolved and often studied matter is the reorientation of the
fibres during processing. Knowledge of this is of major importance since the
final fibre orientation distribution strongly influence on the strength of the
composite. We will, however, focus on another problem being vital for the
automotive industry, that is, the formation of surface voids during moulding.
Such voids may imply costly after treatment to enable a class-A appearance
after painting.
The mechanisms for void formation and removal are mapped for other
processes such as Resin Transfer Moulding (RTM). It is therefore well-known
that formed voids move with the pressure gradient and that gas molecules
originally trapped within a void can diffuse into the liquid resin. These results
indicate that there are at least two ways to remove voids that are formed during
4
compression moulding of SMC: i) high enough pressure gradient and/or ii)
high enough pressures. Knowing this it still remains to investigate the
mechanisms for void formation during compression moulding of SMC and to
find ways to accurately predict the pressure distribution during manufacturing.
SMC is a continuous sheet containing chopped fibres and mineral fillers
embedded in a highly viscous thermosetting resin. The general procedure in
compression moulding of SMC is as follows. First, plies of SMC are cut to
desired shape and size and stacked outside a preheated mould to form a charge.
The charge is then placed upon the lower mould half and the movable upper
mould half is brought down to close the mould. As the mould pressure builds
up, the SMC is forced towards the outer edges of the cavity. At the edges a
narrow vent is formed letting the air escape but trapping the SMC. Once the
mould is adequately filled, the mould pressure is kept during a preset time, i.e.
until a predetermined degree of curing in the moulded part is achieved. The top
mould half is then brought back up and the part is removed from the mould for
cooling and post mould curing. It has been shown that the final void content is
strongly dependent on the processing and material properties but the
mechanisms for the formation of the voids are not known. Residual voids in the
composite may originate from the SMC which often is very porous, be trapped
during lay-up and filling and/or form during the curing of the resin. We will
here narrow our focus and concentrate on the latter two of these issues.
5
In the late 1970’s Marker and Ford [1] performed a pioneering work on
visualisation of the filling of moulds by usage of multicoloured charges. This
method was later adapted by Barone and Caulk [2], who in 1985 performed
partial mouldings by insertion of steel shims between the mould stops. Both
layered and segmented charges were loaded and the stages of deformation were
examined in sections cut from the cured parts. The same year, 1985, Costigan,
Fisher and Kanagendra [3], presented flow front studies by combining the
partial moulding technique developed by Marker and Ford with in-situ video
recordings of the flow front during pressing. The partial moulding technique
was however discarded since it, according to the authors, failed to capture the
true flow front. Instead, Kanagendra and Fischer [4] presented schematic
drawings based on their video recordings. Then, in 1986 Barone and Caulk [5]
proposed a mathematical model based on their earlier observations [2], with
several different validated alternatives for the boundary conditions at the mould
surfaces. This is the starting point of a period where focus is changing from
experimental visualisation to development of mathematical models and
numerical simulations, cf. [6, 7, 8]. Eventually, in 1994 this trend led Tucker
and Advani [9] to identify some of the then existing models as adequate
analysis tools for predictions of microstructure and composite properties.
However, they stated that one of the major research challenges is to contrive
6
good ways to use these models as design tools, rather than for diagnosis, i.e. to
determine mould geometry, material properties and processing conditions
based on the desired part properties.
The work in this report is primarily focused on experimental visualisation of
the flow during mould closure. Hence we aim at continuing the work that was
postponed during the late 1980’s. Special attention is given to the advancing
flow front, for which the full complexity is captured by means of continuous
high resolution close-up monitoring.
EXPERIMENTAL SET-UP AND PROCEDURE
All experiments were performed on industry scaled equipment at close to
production conditions and the experimental procedure is as follows. The
material used in this study is a standard SMC with industrial applications. The
continuous sheets contain chopped strands of Vetrotex E-glass (average length
26 mm) from a 4800 roving with a 1,25 % size embedded in an isophtalicbased polyester. Magnesium oxide (MgO) is added to the resin paste as
thickener, polystyrene as low shrink additive, CaCO3 as filler and a zinc
stearate as mould release agent. The viscosity of the unprocessed SMC was
measured continuously during the experiments at ambient conditions (T ~ 20º
C) and was found to be approximately 40 Pas. Circular samples of SMC were
7
cut out using a sharp blade knife and a rigid template with a diameter of 100
millimetres. The circular shape was chosen in order to minimise effects of
anisotropy and to maximise the visibility of the flow front. Each sample was
taken randomly from the continuous sheet and the same cutting technique was
used throughout the experimental series. Five circular samples were carefully
stacked on top of each other to form a charge. Each charge was weighed
straight after being put together (160 ± 2g) and only fresh cut samples were
used in order to maintain similar initial material properties. A charge was then
placed centrally between two parallel and circular plates (Ø = 300 mm)
mounted in a 310 tonnes Fjellman hydraulic press, cf. Figure 1. In order to
ensure a high repeatability and to facilitate handling, the exact charge position
was indicated with a marker directly on the lower mould half. Of practical
reasons, 2 mm distances were used. An entire tool surface renovation was
performed before the experiments were started in order to obtain well defined
in mould flow conditions and to avoid disturbances of the flow front. Also,
because of the high surface finish, no additional mould lubricant was needed.
The interpretation of the results, such as anisotropy of the charge and final
surface evaluation was thereby simplified. In addition, the sides of the tools
were painted matt black to avoid optical reflections.
8
The process parameters that were altered are the mould temperatures of the
lower and upper tool and the mould closing speed. Three different mould
temperature combinations with industrial relevance were evaluated. First, a
uniform temperature of 135 ºC was used on the lower surface as on the upper
mould half. Second, the temperature of the upper mould half was raised to 165
ºC while keeping the lower mould at 135 ºC. Third and last, again a uniform
temperature was used, this time 165 ºC. For each temperature case, two
different mould closing speeds were applied, 2 and 15 mm/s. The in-mould
cure time was set to 180 seconds and held constant throughout the experiments.
The hydraulic pressure force was set high enough (approximately 600kN) to
prevent the tools from separating during curing of the SMC.
For high-resolution close-ups, a Panasonic F15HS video camera was used. The
camera was mounted on a fully adjustable tripod and equipped with a 135 mm
1:2 Nikon objective and two spacers (K3 and K5). A small torch with a narrow
beam provided proper illumination. Since this camera has no means of internal
storage, all video was transferred to a Panasonic NV-FS200 EC S-VHS
recorder. Digitised versions of the video recordings were obtained with aid of a
Pinnacle DC1000 combined with appropriate software. Individual frames could
then be extracted with a sampling frequency of 25 frames per second and a
resolution of 720 by 576 pixels. The horizontal and vertical extent of the field
9
of view is with this set-up approximately 31 and 17 millimetres respectively,
cf. Figure 2. Based on the geometry of the mould, a side view of the advancing
flow front was chosen, cf. Figure 1 and Figure 3. In the latter figure the
outermost edges of a typical circular charge can be spotted. Once the upper
mould half (not yet visible in Figure 3) reaches the top layer, the SMC will
deform and the flow will be from left to right. Due to the limited width of the
field of view, the whole flow distance could not be covered at once. Instead the
camera set-up was translated in a direction parallel to the movement of the
flow front, cf. Figure 1. In this manner the total flow distance was coved in
three steps. In addition the overall development was captured by a
supplementary video camera with a field of view approximately 100
millimetres wide, ensuring the global overview.
During the experimental work substantial gaseous emissions from the SMC
were observed. In order to clarify the contents of these emissions, an
investigation with a mass spectrometry system was carried out. The basic
principle of a mass spectrometry system is detection and identification of
ionised molecules. While the mass spectrometry system gives a qualitative
measure of the contents of the gaseous emissions, a quantitative measure is
given by running a thermogravimetry system in parallel. In this way the weight
reduction is monitored and correlated to the gas contents. In the analysis
10
performed in this paper the mass spectrometry equipment is a Quadropole mass
spectrometer system from Balzer Instruments and the thermogravimetry is
performed with a Netzsch STA409.
EXPERIMENTAL OBSERVATIONS
The main result of the experimental visualisation is that the liquid stage of
SMC-pressing can be divided into three phases, namely squish, flow and
boiling. Each one of these three phases will now be explained and dealt with
separately.
During the initial moments of contact, as the upper mould half reaches the top
surface of the charge, the first phase, squish, is defined as the first squirt of
paste emerging from the charge as the moulding pressure is building up. For a
high mould closing speed (15 mm/s) and a rather low mould temperature (135
ºC), the bottom layer yields to the pressure first; cf. Figure 4 and the
corresponding sketch Figure 5, where the elapsed time between each frame is
0.04 seconds. Initially the SMC nearest the lower mould half moves radially
towards the edges but already after a tenth of a second the direction changes
11
and it moves axially and hits the upper mould half before the top layers even
start to deform; cf. Figure 4. And increased mould temperature to 165 ºC does
not affect the principal behaviour of the squish. The pattern shown in Figure 4
is thus preserved, though with an augmented intensity, cf. Figure 6. With a
mould closing speed of 2 mm/s and a uniform mould temperature of 135 ºC the
bottom layer also leaves the charge first but now the axial movement is not so
dominant, cf. Figure 7 and note that the elapse time between each frame here is
0.16 seconds. Now, if the upper mould temperature is increased to 165 ºC and
everything else is held constant, then also the top layer shoots out to meet the
bottom layer, before the other layers start to deform, cf. Figure 8 and
corresponding sketch Figure 9 where the elapsed time between each frame is
0.32 seconds.
After the initial tumultuous phase, squish, the flow front settles down in a
seemingly stable and viscous flow, here defined as flow, cf. the last frames of
Figure 4. Any debris, such as loose fibre ends produced by the squish when
using a lower mould closing speed, is simply pushed ahead of the flow front
and later on easily identified along the edges of the final plates.
During closure of the mould, before complete cross-linking of the resin,
bubbles are observed emerging from the resin in the low-pressure region
12
(atmospheric pressure) at the flow front: it appears as if the resin is boiling, a
schematic sketch of the flow phenomena is submitted cf. Figure 10. Figure 11
shows the boiling near the flow front in a mould temperature of 135 ºC, and in
Figure 12 the mould temperature is 165 ºC. Observations made from the video
recordings indicate that the bubbles are larger for the higher temperature while
the number of bubbles is greater in the lower temperature, cf. Figure 11 and
Figure 12. Also, from the elapsed time between each frame, which is 3.00
seconds in Figure 11 and 0.08 seconds in Figure 12, it is clear that the outbursts
last longer in the lower temperature case than in the higher temperature ditto.
The difference in size of the bubbles is also confirmed by examination of the
final edges of the moulded parts. Still, the mere existence, and certainly the
origin of the bubbles are as intriguing as their physical appearance. We will
deal with this at the end of the next section.
DISCUSSION
The observations presented in the previous section will now be scrutinised. It
is, to start with, interesting to compare the velocity of the squish with the
average radial speed of the SMC. The former can be estimated from the figures
presented in the previous section while the latter is directly given by continuity
as stated by the following expression:
13
ur
V r0 §
V ·
¨¨1 t ¸¸
2 h0 ©
h0 ¹
3 2
(1)
where V is the speed of the press, t is time and r0 and h0 initial radius and
height of the charge. When the velocity of the press is 15 mm/s and the
temperature is 135 ºC, the squish accelerates as the press moves down, se
Figure 13. The velocity of the squish is about 2.5 times the average velocity,
ur when it reaches its maximum. This naturally coincides with the time when
the squish hits the upper mould half. Surprisingly, the initial speed of the
squish is lower than what is predicted by (1). The most likely reason for this is
that air entrapped between the sheets, and possibly in the sheets, is released
during the early stages of the pressing. Anyway, after the clash against the
upper mould half the speed of the squish is reduced towards the theoretical
averaged velocity.
The reason for the high speed of the squish can be traced to extreme gradients
in the viscosity of the SMC. When the SMC is placed on the heated mould the
viscosity of the SMC closest to the mould is naturally reduced with a
corresponding increase in velocity for a certain induced stress level. As
exemplified in Figures 14 and 15, the observed trends also hold for the other
cases with uniform velocity. The relatively extreme speed of the squish when
14
the press moves at 2 mm is due to that only a few fibres moves ahead; cf.
Figures 7 and 14. For the case of higher temperature on the upper mould half
and a speed of two millimetres the SMC moves on two fronts, cf. Figure 16.
The lower front takes the lead but as the pressing continue the upper front
catches up. Such behaviour is expected since although the contact with the
lower plate is longer, the higher temperature on the upper mould half can
eventually result in a lower viscosity in this area. It is clear from the discussion
above that the squish can be caused by a step gradient in viscosity. It still
remains to find out, however, if this is the reason for the SMC to move axially
during the pressing.
There are at least two practical implications of the squish. It is obvious that
there is a risk for air entrapment at the flow front. Since the shape of the flow
front is dependent on the processing parameters, the amount of air entrapped
will probably change when the processing parameters are altered. This
speculation is however yet to be validated. Another consequence of the squish,
worthwhile mentioning, is that the flow front will almost certainly consist of
the SMC that has been heated the longest time. This is important for the
subsequent curing.
15
In the next phase, flow, the flow front was observed to settle down in a stable
and seemingly viscous flow, probably due to a more evenly distributed
viscosity. There is therefore no indication on void entrapment during this stage,
as long as the geometry of the mould is simple enough. However, as a
consequence of the stability, it was observed that disorders created during the
squish, e.g. fibre entanglement at the flow front, are preserved during flow.
Such effects may make it difficult to directly fill geometries such as ribs and
bosses and hence air can be entrapped.
Considering the possible contents of the observed gaseous emissions during
and after mould closure, the boiling point of styrene under atmospheric
pressure is around 145 ºC [10]. In the chemical analysis based on mass
spectrometry and thermogravimetry that was performed, temperatures above
and below this value were investigated. First a 216.0 mg sample of SMC was
placed in a heated oven (135 ºC) during 10 minutes under atmospheric
pressure. The weight afterwards was 203.1 mg, i.e. a 5.6% weight reduction. In
the same manner the weight reduction was 4.5% when a 222.9 mg sample was
subjected to a temperature of 165 ºC for 10 minutes. The emitted gases were
meanwhile collected and analysed in the mass spectrometry system. The
ionisation spectra from empty reference samples subjected to the same
conditions were then subtracted from the obtained spectra for each temperature
16
in order to avoid surrounding noise. In both temperature cases, the final
ionisation spectrum matched perfectly the ionisation spectrum of styrene. Thus,
the ultimate outcome of importance here is that everything else but styrene
could be dismissed as originating from the samples of SMC. Regardless of the
contents of the bubbles, they are without doubt an important source of void,
both internally and on the surface. It is therefore important to keep the overall
pressure on the SMC higher than the pressure corresponding to the boiling
point at the prevailing temperature [10].
To summarize, two mechanisms for void formation during compression
moulding of SMC have been identified; entrapment during the initial phase of
pressing and boiling in low pressure regimes. Adjusting the pressing speed
and/or the temperature on the mould halves did only change the pattern of the
squish and the intensity of boiling. Based on earlier studies on processes such
as RTM [10, 11], the best solution to minimize the void content would be to
evacuate the mould before and during the initial phase of pressing and then
secure a high level of pressure all over the part when the mould has been filled.
CONCLUSIONS
From the experimental visualisation of the flow front, three phases are defined,
namely squish, flow, and boiling.
17
During the initial phase, squish:
the flow is very complex and air is likely to be entrapped.
the SMC closest to one or both of the mould halves moves ahead of
the rest of the material and outer layers do not remain outer layers.
Interestingly the squish moves partly axially.
Analysis also indicate that at least some of the air entrapped between
the SMC-sheets is released as the press hits the charge.
During the second phase, flow:
a stable plug flow is formed.
there is no indication of void entrapment for the simple geometry in
focus.
During the last phase, boiling:
bubbles are observed in the low pressure region at the flow front.
based on a chemical analysis, the gas leaving by the bubbles is
probably styrene.
In overall the observations presented here shows that the pressing of SMC is a
very complex procedure. Hence to model it properly and to be able to predict
the pressure distribution many mechanisms must be accounted for. One
18
possible short cut which we are working towards is to introduce flow
simulations combined with inverse modelling regarding the material models.
ACKNOWLEDGEMENTS
This work was supported by VINNOVA through the framework of KEX and
by the Swedish Research Council. The experiments were performed at
SICOMP AB with great assistance from their staff and the used material was
provided by ABB Power Technology Products AB Plast. The chemical
analysis was performed in collaboration with Bo Lindblom at the Division of
Process Metallurgy, Luleå University of Technology.
19
REFERENCES
1. Marker LF, Ford B. Flow and curing behavior of SMC during molding.
Modern Plastics 1977;54:64-70.
2. Barone MR, Caulk DA. Kinematics of Flow in Sheet Moulding
Compounds. Polymer Composites 1985;6(2):105-109.
3. Costigan PJ, Fisher BC and Kanagendra M. The Rheology of SMC During
Compression Molding, and Resultant Material Properties. In: Proceedings
of 40th Annual Conference, Reinforced Plastics/Composites Institute, The
Society of the Plastics Industry, Inc. Jan. 28-Feb. 1, 1985. Session 16-E.
p.1-12.
4. Kanagendra M, Fisher BC. Process Interactions for SMC Compression
Molding Under Microcomputer Control. In: Proceedings of 40th Annual
Conference, Reinforced Plastics/Composites Institute, The Society of the
Plastics Industry, Inc. Jan. 28-Feb. 1, 1985. Session 16-C. p.1-11.
5. Barone MR, Caulk DA. A Model for the Flow of a Chopped Fiber
Reinforced Polymer Compound in Compression Molding. Journal of
Applied Mechanics 1986;53:361-371.
6. Osswald TA, Tucker CL. Compression Mold Filling Simulation for NonPlanar Parts. Intern. Polymer. Processing V 1990;2:79-87.
20
7. Osswald TA, Tseng SC. Compression Molding. In: Advani SG, editor.
Flow and Rheology in Polymer Composites Manufacturing. Amsterdam:
Elsevier, 1994. p.361-414.
8. Mallick PK. Compression Molding. In: Mallick PK, Newman S, editors.
Composite Materials Technology. New York: Hanser Publishers, 1990.
p.67-102.
9. Tucker CL, Advani SG. Processing of Short-Fiber Systems. In: Advani
SG, editor. Flow and Rheology in Polymer Composites Manufacturing.
Amsterdam: Elsevier, 1994. p.147-202.
10. Lundström TS, Gebart BR and Lundemo CY. Void Formation in RTM.
Journal of Reinforced Plastics and Composites 1993;12:1339-1349.
11. Vahlund CF. Fibre Orientation, Rheological Behaviour and Simulation of
the Compression Moulding Process for Composite Materials. Doctoral
Thesis 2001:25, Luleå University of Technology, ISSN 1402-1544.
21
FIGURE CAPTIONS
Figure 1.
Schematic top view of mould-centred charge placement and flow
front side view monitoring
Figure 2.
Vertical extent of typical field of view.
Figure 3.
Side view of the outermost edges of a typical initial charge.
Figure 4.
Mould closing speed 15 mm/s, uniform mould temperature 135 ºC
and elapsed time between each frame 0.04 seconds.
Figure 5.
Sketch over the flow front progression in Figure 4.
Figure 6.
Mould closing speed 15 mm/s, uniform mould temperature 165 ºC
and elapsed time between each frame 0.04 seconds.
Figure 7.
Mould closing speed 2 mm/s, uniform mould temperature 135 ºC
and elapsed time between each frame 0.16 seconds.
22
Figure 8.
Mould closing speed 2 mm/s, lower mould half temperature 135
ºC, upper mould half temperature 165 ºC and elapsed time between
each frame 0.32 seconds.
Figure 9.
Sketch over the flow front progression in Figure 8.
Figure 10. Sketch over the flow front progression in Figure 11 and 12. The
view at 0.16 s (brown) appears as dark hols in the SMC. Notice that
the sketches of the first three time steps are only possible scenarios.
Figure 11. Mould closing speed 15 mm/s, uniform mould temperature 135 ºC
and elapsed time between each frame 3.00 seconds. The black areas
on the right-hand figure denote formed voids.
Figure 12. Mould closing speed 15 mm/s, uniform mould temperature 165 ºC
and elapsed time between each frame 0.08 seconds. The encircled
black area on the right-hand side figure is a void.
Figure 13. The dots denote normalised velocity of the squish as a function of
time when the press moves at 15 mm/s and the temperature is
135ºC on both mould halves. The line denotes normalised velocity
23
of the flow front as computed from continuity, Equation (1). Both
velocities are normalised with the velocity of the press.
Figure 14. The dots denote normalised velocity of the squish as a function of
time when the press moves at 15 mm/s and the temperature is
165ºC on both mould halves. The line denotes normalised velocity
of the flow front as computed from continuity, Equation (1). Both
velocities are normalised with the velocity of the press.
Figure 15. The dots denote normalised velocity of the squish as a function of
time when the press moves at 2 mm/s and the temperature is 135ºC
on both mould halves. The line denotes normalised velocity of the
flow front as computed from continuity, Equation (1). Both
velocities are normalised with the velocity of the press.
Figure 16. The dots denote normalised velocity of the squish (lower-filled
symbols and upper-open symbols) as a function of time when the
press moves at 2 mm/s and the temperature is 135ºC and 165ºC on
the lower and upper mould half, respectively. The line denotes
normalised velocity of the flow front as computed from continuity,
24
Equation (1). All velocities are normalised with the velocity of the
press.
25
mould
camera
charge
Odenberger, Figure 1
26
Odenberger, Figure 2
27
Odenberger, Figure 3
28
Odenberger, Figure 4
29
0.00 s
0.04 s
0.08 s
0.12 s
0.16 s
0.20 s
0.24 s
0.28 s
Odenberger, Figure 5
30
Odenberger, Figure 6
31
Odenberger, Figure 7
32
Odenberger, Figure 8
33
0.00 s
0.32 s
0.64 s
0.96 s
1.28 s
1.60 s
1.92 s
2.24 s
Odenberger, Figure 9
34
0.00 s
0.04 s
0.08 s
0.12 s
0.16 s
Odenberger Figure 10
35
Odenberger, Figure 11
36
Odenberger, Figure 12
37
6
5
v*
4
3
2
1
0
0.00
0.05
0.10
0.15
t
Odenberger, Figure 13
38
[s]
0.20
0.25
0.30
6
5
v*
4
3
2
1
0
0.00
0.05
0.10
0.15
t
Odenberger, Figure 14
39
[s]
0.20
0.25
0.30
20
v*
15
10
5
0
0.0
0.2
0.4
0.6
t
Odenberger, Figure 15
40
[s]
0.8
1.0
1.2
8
v*
6
4
2
0
0.0
0.5
1.0
1.5
t
Odenberger, Figure 16
41
[s]
2.0
2.5
Paper B
Inverse Modelling of Compression Moulding of
SMC with usage of Computational Fluid
Dynamics
P.T Odenberger , T.S Lundström
Department of Fluid Dynamics, Luleå University of Technology
971 87 Luleå, Sweden
SUMMARY: The purpose of this work is to investigate whether an inverse
modelling approach by proportional regularisation can be applied to mimic the
pressure distribution during compression moulding of SMC. The process is
simulated with Computational Fluid Dynamics and the mastered parameter, the
viscosity of the SMC, is allowed to vary as a function of time. A grid
refinement study of two ways to model the process and for three fictitious
pressure scenarios yields that the suggested approach work very well and that
the numerical errors can be minimised as desired. Finally a validation process
is carried out showing that to get quantitative agreements of the whole pressure
field more advanced viscosity models must be used.
KEYWORDS: Inverse modelling, SMC, Compression moulding, CFD,
Rheology.
INTRODUCTION
When manufacturing fibre composites by compression moulding processes
such as Sheet Moulding Compound (SMC) a mixture of fibres, chalk,
unsaturated resin and gas bubbles is forced to fill a mould. The resulting multiphase flow is affected by variations in viscosity that is due to steep temperature
gradients, a variable cure cycle and flow induced fibre orientation, Vahlund
[1]. Hence several mechanisms are active during the process and the full set of
governing equations does not have trivial solutions [2]. Thus the physical
behaviour is multifaceted with phenomena such as squish, flow and boiling,
Odenberger [3]. Although simplified models have shown to be efficient in
some cases when predicting flow front positions, for instance, there is really a
1
lack of models for accurate predictions of fibre orientation and void formation
and transport. While uncontrolled fibre orientation may result in uneven
strength and stiffness in a finished part, residual voids may appear on the
surface as flaws and great efforts must be spent on minimising the number of
them. This is certainly important in the automotive industries since their
applications often must have a class A appearance. The required models can be
obtained in a variety of ways, e.g. micromechanical modelling and
experiments. We will here present an alternative route namely inverse
modelling technique that can be used as one component to obtain the final void
distribution.
Voids may form as well during the forming of the SMC as during the
compression stage by different kinds of mechanisms. It is to start with well
known that the SMC contains voids that either have been entrained into the
polyester during mixing or created during the impregnation of the fibres.
Besides, air can be entrapped at the flow front during the pressing stage. Hence
by, as a first approach, assuming that these voids are located in the SMC
methods to remove them must be found in order to minimize the risk of surface
flaws. In principal, the voids can be transported out of the SMC or dissolve into
it, mechanisms that are strongly related to the spatial distribution of the
pressure [4,5]. It is even so that if the pressure is too low at a specific
temperature voids may form by boiling, of styrene, for instance [3]. Hence, it is
obvious that the pressure distribution must be known. This quantity is in its
turn directly related to the distribution in viscosity.
According to Tarantola [6] the scientific procedure for studying a physical
system can be divided into three stages. In the parameterization stage a set of
model parameters are chosen that, in an appropriate fashion, can describe the
system. Then to discover the physical laws that allow for prediction of some
measurable parameter, a forward modelling stage is suggested. In a final stage
some measurements are set to influence the model parameters, inverse
modelling. The advantage of studying the final stage combined with the first
stage is manifolded, [7]. One is that uncertain model parameters can be tuned
to best fit the experiments. Then it is possible to make predictions of
parameters such as pressures and pressure gradients even with model
simplifications. Such simplifications are sometimes necessary since the
computer capacity is still not enough for the very complex real in-mould flow
described above [1,2,3]. It is also stated by Tarantola [6] that success in one
stage often leads to success in another stage. The inverse modelling is also a
widely used technique in areas such as solid mechanics [8,9]. And since the
technique with inverse modeling is the same for any continuum, solid as well
as fluid, such work is giving synergy effects. Hence this leads to a very good
2
start and one could expect the same benefits in this fluid mechanic approach
that is presented by Kajberg and Westman [8,9].
The outline of this paper is as follows, a theoretical analysis is carried out so
that the simulations performed can be verified. Then three model cases are
defined that somewhat mimic a real moulding but where the pressure versus
time curves are simpler. These relationships are implemented in a numerical
model which in principal can be of two types: One-phase flow with an adaptive
mesh or two-dimensional flow through a semi-stationary mesh. Both these
models are verified by theory while the trust in the actual simulations is
increased by grid refinement studies combined with the well known and widely
used Richardson’s extrapolation method [10]. Finally the method is compared
to the experiments and the results obtained are discussed and some conclusions
are presented.
THEORY
Of interest is a disc of a Newtonian liquid having a radius a that is placed
between two parallel plates being a distance h apart. Then let the upper plates
move towards the lower one at a constant speed and study the resulting flow.
By continuity:
wm
dt
(1)
0
a then becomes a direct function of h according to:
a
a0
2
h0
h
(2)
where the zeros indicate initial values. The evaluation in height of the disc
may in its turn simply be described by the following relationship:
h
h0 dh
dt
(3)
Now when the disc is allowed to move towards the plane the velocity profile,
at each r, may be assumed to take the following form:
3
ur
G r z h z 2P
(4)
if transient effects, axial flow and flow front phenomenon can be neglected.
Here G is the pressure gradient, P the viscosity and r and z the spatial coordinates along the radius and perpendicular to the disc, respectively.
Continuity now yields that:
G r 6 Pr dh
h 3 dt
(5)
By setting the pressure to p0 at the flow front which is located at a the
following pressure distribution results:
p r p0 3P dh 2
a r2
h 3 dt
(6)
By the assumptions made this equation gives the pressure distribution in the
disc at an arbitrary time or flow front position.
NUMERICAL PROCEDURE
All computations were done with the commercial software CFX4.4 which
solves the flow in geometries modeled with structural elements. The
computations were carried out with a high order upwind differencing scheme
using double precision and the AMG multi-grid solver. The geometry in focus
for the simulations was generated in a cylindrical coordinate system (x, r, Į)
and by applying axisymmetric conditions in the direction of Į, see Figure 1.
Figure 1. Axisymmetric flow domain.
4
Solid walls are set as boundary conditions on high and low x while atmospheric
pressure is set on high r. To drive the flow the upper solid wall is allowed to
move at a velocity of 15 mm/s according to proper production conditions in the
press. Now two techniques are used to simulate the pressing. To start with a
one-phase fluid model with a full remeshing procedure is applied by usage of
continuity and by assuming that the flow front moves as a plug, cf. theory. The
numerical model uses the Eulerian description and solves for a plate with the
same dimensions as in the analytical solution. Thus there are two moving
boundaries, high x and high r. The way of treating these moving boundaries is
to remesh in every time step. The domain is solved for three grids 4000, 1000
and 250 element, Secondly a two phase flow model is used where a Newtonian
liquid displaces a gas (air). This numerical model also uses the Eulerian
description. It is a two phase description that is based on a homogeneous
model, which means that the two phases are sharing the same velocity field,
and are continuous. The domain is as well in this case solved for three grids
2400, 600 and 150 elements. The initial charge is placed in the domain by
setting its volume fraction to 1.0 and the other phase to 0.0. The only moving
grid boundary is the high x moving wall and thus the remeshing is only carried
out in the x-direction. This way of solving the problem is not the same as in the
analytical case since the flow front will not move as a plug. The practical
model difference is that the charge is only placed at the initial condition and
not at each time step as in the other two cases. Hence if the real flow front
behavior can be captured, this way of modeling better act as the real physics. It
will however turn out that the numerical treatment of the liquid-gas interface at
the solid walls strongly influences the results. The calculations are solved for
each phase as described above for approximately 44 time steps where each
time step is 0.01 s.
In order to investigate the quality and trust of the simulations and to find a grid
independent solutions Richardson’s extrapolation is used [10]. The concept is
that the residual error e H hd of a quantity ) .
)
) h H hd
(10)
can be approximated from two grids with different numbers of elements as here
stated:
H hd |
) h ) 2h
2 p 1
5
(11)
The order of the schemes used, p, is often two but due to the complicated
equation systems solved for it more or less simultaneously it is recommended
that it is calculated with the following formula
p
§ ) ) 4h
log¨¨ 2 h
© ) h ) 2h
log 2
·
¸¸
¹
(12)
This Equation is valid if the refinement is done in equal steps, that is, that the
quote between the number of elements between the crudest and the middle
mesh is equal to the quote between the middle and the finest mesh.
INVERSE MODELING
The main aim with this modeling is to be able to predict the pressure and
pressure gradients accurately during pressing in any geometry. To be able to do
that the viscosity as a function of time and spatial co-ordinate needs to be
known. This is important since from a fluid dynamic point of view, the
viscosity is the parameter that relates deformation rate to stresses in the fluid
and hence the pressure. One methodology is thus to measure the pressure and
temperatures in simple geometries but in several points and then find the
viscosity distribution that match these pressures by inverse modeling. With a
good enough viscosity model it is then likely that the flow in more complex
geometries can be found. To demonstrate the model the viscosity is assumed to
be constant and is solely fitted to pressure measurements in one spatial coordinate, the center of the disc. Once proven to work for this case it is only a
matter of hard work for making it function for a general case. The viscosity is
altered with the aid of the CFX4.4 specified FORTRAN subroutine USRVIS
and by using the following proportional regularization expression
P new
P old 2 ˜ p calculated p exp eriment .
(13)
This seemingly simple expression will first be tested for three bogus scenarios
for the mid-point pressure during a radial flow pressing. These scenarios are i)
a half sinus curve with a maximum of 16.5 MPa, ii) a ramped step up to the
same value iii) and a step function also with a maximum of 16.5 MPa. Then the
method will be applied to one real measurement performed enabling a
comparison to pressure measurements performed at other locations.
6
RESULTS
Verification
In order to reveal how good approximation the numerical model is, the one
phase model presented above is compared to the corresponding analytical
expression, cf. Eqn. 6. It is seen that the numerical solution produce accurate
and reliable result even for the coarsest grid, but the extrapolated value by
Richardsons extrapolation is closest to the analytical solution as the pressing
proceeds.
Figure 2. Left: Pressure presented for three grids where 4h = 250 cells, 2h =
1000 cells and h = 4000 cells. The analytical and Richardson’s extrapolated
curve is also included. Right: Error between analytically and numerically
derived pressures.
For the two-phase formulation the discrepancy from the analytical solutions is,
as expected, much larger, see Figure 4. This is probably not only due to the
different geometries at the flow front but also a result of numerical problems at
the contact lines formed between the liquid, gas and solids. The lagging of
these contact lines is much larger than what is physically reasonable, see
Figure 3, and it is not possible to extrapolate the pressure by Richardson’s
extrapolation, since the error tends to increase. Thus it is not possible to get a
grid independent solution in this case. Hence this more physically correct
model must be further developed before any conclusions on its usefulness can
be made.
7
Figure 3. Volume fraction presented with cusp formation. Here red denote the
solid phase and blue the gas phase.
Figure 4. Left: Pressure presented for three grids 4h=250 cells, 2h=1000 cells
and h=4000 cells. The analytical solution is also included.
Right: Error between analytically and numerically derived pressures.
Inverse modeling
An inherent effect of the inverse modeling is that at least one extra iteration
cycle is brought into the simulation procedure. Hence, it is of interesting to
scrutinize the convergence for as well the governing variables as the adapted
ones here represented by the pressure and the viscosity, respectively. This
convergence study is evaluated for the first time-step for the constant pressure
case, 16.5 MPa by setting the initial viscosity to 0.25 MPas, initial pressure to
0.1 MPa and initial velocity to zero. Setting unreasonable values on these
parameters will affect the result. A total of 2500 iterations were carried out but
as shown in Figure 5 about 800 iterations will produce 1 % error of magnitude
for the pressure and not much happens after 1500 hundred iterations. Hence,
this is the maximum number of iterations that will be used henceforth. Please
also notice that the first 50 iterations are dismissed since the errors are large
during these initial steps.
8
Figure 5. Left: Pressure error defined as the difference between experimental
value and calculated value. Right: Viscosity alterations for the same interval.
The next thing to do is to derive the error as a function of flow front position or
equivalently time. This is done first for the constant pressure case 16.5 MPa. In
the initial phase of the compression this error is relatively large but it soon
decreases as the process continues. The maximum value calculated is also
dependent on the grid and is 2.1 % for 250 cells, 1.6% for 1000 cells and 0.2%
for 4000 cells, see Figure 6. Interestingly with the finest mesh the maximum
error is relatively small also for 500 iterations, 3.1%.
Figure 6. Left: The error between experimental and calculated pressure for
500 iterations presented. Right: Corresponding plot but for 1500 iterations.
The corresponding viscosity curves for the constant pressure, presented above,
are here presented cf. Figure 7.
9
Figure 7. Corresponding viscosity curve for the constant pressure 165 bar
case.
So far it seems to be possible to minimize the error down to almost machine
accuracy since the proportional regularization will not stop until a desired
number of iterations are reached. Leaving this for the moment to see if the
other cases pointing in the same direction.
The Sinus formed pressure curve is represented by the following expression
p
S ·
§
165 ˜ sin ¨ step * ¸
55 ¹
©
(14)
where step is the current time step and where the initial values are set to p = 0.1
MPa, μ = 7 kPas and the velocity to zero. Again the maximum error is small,
cf. Figure 8.
Figure 8. Left: The error between experimental and calculated pressure for
500 iterations presented. Right: Corresponding plot but for 1500 iterations.
10
The corresponding viscosity curves for the sinus formed pressure, are here
presented cf. Figure 9. The Richardson’s extrapolated curve is also included.
Figure 9. Corresponding viscosity curve for the sinus formed pressure curve.
The Step formed pressure curve is as follows.
­
step
° p 165 ˜
14
°
® p 165
°
1 step ·
§
¸
° p 165 ˜ ¨1 © 14 14 ¹
¯
1 d step t 14
15 d step t 27
(15)
28 d step t 44
The initial values are set to p = 0.1 MPa, μ = 15 kPa and velocities = 0 this will
give us a maximum error between the simulated and experimental pressure to e
=1.55 % for 250 cells, e = 1.2% for 1000 cells and e = 1.0% for 4000 cells cf.
Figure 10. Also here the errors produced are plotted for a 500 iteration case.
11
Figure 10. Left: The error between experimental and calculated pressure for
500 iterations presented. Right: Corresponding plot but for 1500 iterations.
The corresponding viscosity curves for the step formed pressure curves,
presented above, are here presented cf. Figure 11. The Richardson’s
extrapolated curve is also included.
Figure 11. Corresponding viscosity curve for the step formed pressure curve.
Validation
As a final activity the method verified above is validated with an experiment
carried out with a fjellman 310 tons press and under production like conditions.
During pressing the pressure were captured with two Kistler pressure
transducer (6153C) located in the center of a plate to plate mould and at a
distance of 37.5 mm from the center, respectively. The mould closing speed is
set to 15 mm/s but in reality it ends up with a mean value of 8 mm/s, off course
the velocity profile is measured and implemented in the simulation. The charge
contains 5 layers of circular sheets with a diameter of 10 cm on top of each
other with the height measured to 13 mm.
The Pressure curves are here presented, Figure 12, for the real case scenario. It
can be seen that when using the Newtonian model as constitutive relation the
shear thinning behavior of SMC is exclusive, notice that a constant viscosity is
set trough the whole domain. There are two pressures included first the center
pressure, presented as C, second the pressure at from the center, presented as
P1. When comparing the results from the simulation and experiment it is
obvious that the trend with increasing pressure in point P1 are there, although
the simulated pressure evaluation is more flat.
12
Figure 12. Experimental center pressure (C-exp), calculated center pressure
(C-sim), experimental pressure (C-p1) located a distance 37.5 mm from center
and corresponding calculated pressure (P1-sim) presented.
Since it has been seen that the pressure are not stable and have large variations
a statistical pressure, maybe median or mean value, based on several shoots,
would be the right experimental input to the numerical model. Then the
correlation for the pressure in P1 could be even better, or a more sophisticated
material model could be developed. This is a hot burning topic for the future to
reveal. Thus the procedure is as follows for a real case scenario based on
several shoots:
x
x
x
x
x
Measure pressures at different spatial locations.
Simultaneous measure the true mould closing speed.
Choose an appropriate constitutive model.
Set up an inverse model calculation with the
measurements, revealing the viscosity, and based on the
constitutive model.
Validate in some other experimental set-up.
DISCUSSION AND CONCLUSION
The inverse modeling with a proportional regularization for the viscosity is
producing results of which any desired error can be achieved. The cost for
small errors is the number of iterations needed leading to long calculation
times.
The initial values should be carefully investigated before a complete run
including many time steps is carried out.
13
This method will be developed to include more complex material models as
shear thinning material ones. Thus the true SMC behavior could be
investigated.
More experiments must be carried out in order to get statistical value since
every pressure curve is unique producing small oscillations.
REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
Fibre Orintation, Rheological Behavior and Simulation of the
Compression Moulding Process for Composite Materials, C.F.Vahlund.
ISSN: 1402-1544.
Compression molding, Tim A. Osswald and Shi-Chang Tseng, Flow
and rheology in polymer composites manufacturing volyme 10, p 361413.
Experimental flow-front visualization in compression moulding of
SMC, P.T.Odenberger, H.M.Andersson, T.S.Lundström,Composites
Part A 35 (2004), p1125-1134.
Lundström, T.S., “Bubble Transport Through Constricted Capillary
Tube with Application to Resin Transfer Moulding” Polymer
Composites, 17, pp. 770-779 (1996)
Lundström, T.S., “Measurement of Void Collapse during Resin
Transfer Moulding” Composites Part A, 28A, pp. 201-214 (1997)
Inverse Problem Theory. Tarantola Albert. 1987. ISBN 0-444-42765-1.
Concept and Computational Methods for Parameter Identification of
Inelastic Material Models, R.Mahnken, E.Stein.
Characterisation of materials subjected to large strains by inverse
modelling based on in-plane displacement fields. J. Kajberg, G.
Lindkvist. International Journal of Solids and Structures, v 41, n 13,
June, 2004, p 3439-3459.
Numerical and Microstructural Evaluation of Elevated Temperature
Compression Tests on Ti-6AI-4V. Westman E-L., Pederson R.,
Wikman B., Oldenburg M. 10th World Conference on Titanium (Ti2003 Science and Technology) Hamburg, Germany, 13-18 July, 2003
Computational methods for fluid dynamics, Joel H Ferziger, Milovan
Peric´.
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