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LICENTIATE T H E S I S

Luleå University of TechnologyDepartment of Applied Physics and Mechanical Engineering

Division of Fluid Mechanics

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Compression Moulding of SMC, Visualisation and Inverse Modelling

Torbjörn Odenberger

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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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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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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 flow-front 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……………………………………………………….……3PREFACE………………………………………………………………5LIST OF PUBLICATIONS…………………………………………….7

1. INTRODUCTION ........................................................................ 10 2. 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.

2. FIBRE REINFORCED POLYMERCOMPOSITES

These days when fuel consumption, performance and low cost are leading terms fibre reinforced polymer composites are moving into a new era withsharpened demands on efficient manufacturing of defect-free materials. The status of manufacturing and manufacturing defects will here be brieflyoutlined. 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 carryingpanels, 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 meterbarrier 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 polymercomposites 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

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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 exampleis the Scania truck P380, cf. Figure 2. where several details are made fromfibre composites.

Figure 2. Scania P 380 6x2*4 rigid, sleeper cab.

Other areas for fibre reinforced composites, where excellent mechanicalproperties 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 hasseveral 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 maincategories are defined by the material they are made from, glass, carbon andaramid. Since the fibres transfer the loads it important to locate and orient them

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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 print-through, 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

vision of this thesis. Since surface voids result either in costly after-treatmentsor 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:

1

1

2

2

12 V

TT

ppV . (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 temperatureT2. Thus this is of interest since both temperature and pressure are keyprocessing 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]:

tp

RRRR

pppHGD

atm

atmv

Svv

cr

ellln

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0

2

0

(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 givesthe saturated concentration, the density of the gas at atmospheric conditions ,the void radius Rv and the thickness of a stationary region Rs. For sphericallyshaped 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 someway. 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, lv, and uniform passages between the fibres will make it easier for the bubbles to move with the resin [2]. The smaller the

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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.

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 180-400 fibres. Following the demands on Class “A” appearance, in automotiveindustries, it is sometimes common to use somewhat more resin instead of low-profile additive and also add more filler than what is stated in Table 1.

Component wt %Isopolyester resin 16.4

Polystyrene 11.0Para-t-butyl peroxybenzoate 0.3

Zinc stearate 2.4Calcium carbonate 41.1Magnesium oxide 0.5

Fibreglass 30.0Table 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)

ijij

.

. (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 completedescription for many polymer composites [12,14]. Consequently more intricate models have to be used including effects such as shear-thinning and visco-elasticity. One example of such a model is the generalized Newtonian model (4)

ijij

..

)( . (4)

Here the non-Newtonian viscosity is modelled to be strain rate dependent

it self. The relation for are often set to the power-law formulation

according to:

)(.

)(.

1..

)(n

A (5)

where A and n are the material parameters. Another constitutive relation, that issometimes 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. Constitutiveparameters such as viscosity are often measured in rheometers. The actual cellsused for the measurements are designed to give a desired deformation of aliquid. 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 onepart of the tool and transferred by the liquid to the other is measured parallel tothe 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 smalland 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

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chalk suspension. Of this reason Vahlund [14] developed a method for large sample rheometry. A similar tool is here used as well for experimentalvisualisations 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 ),( 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 to d and to d it is given

by ddsin),( . Since one fibre end is indistinguishable from the other

),( is periodic and thus

),(),( . (6)

Since every fibre has a given direction the integral over all directions mustequal one as expressed below

0.1sin),(2

0 0

dd . (7)

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 compactmethod is used where tensors portray the distribution function. The second and forth order tensors, for the in plane case is the following:

dppa jiij )( (8)

dppppa lkjiij )( (9)

For the second order tensor we have random orientation distribution for the fibres when 5.0,0;0,5.0ija , 11-direction orientation when

and 45 degrees from the 11-dirction when

0,0;0,1ija5.0,5.0;5.0,5.0ija . This

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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

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 ofSMC-pressing can be divided into three phases, namely squish, flow andboiling. 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 timebetween each frame 0.04 seconds.

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0.00 s0.04 s0.08 s0.12 s0.16 s0.20 s0.24 s0.28 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 timebetween each frame 0.04 seconds.

In the later part of the flow process, when the moulds are almost completelyclosed, 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

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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 timebetween 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 momentumequation [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 computationallyprohibitive for a real case scenario as an automotive industry body panel.

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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

such as solid mechanics [26,27] and since the technique in it-self is the samefor 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 parametersthat should be estimated and the field of application [27].

Start Finite VolumeAnalyse

Solving Iteration

Output Finite Volume Analyse

Evaluation, RegularisationExpression

NO

YESExit

Experimental Output

STOP

Optimised DesignParameters 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. Onemethodology is thus to measure the pressure at a spatial location in simplegeometries and then find the viscosity distribution that matches these pressuresby 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 inPaper B is to verify and validate the numerical simulations and in order to further develop the inverse modelling technique suggested more experimentsmust be carried out. The procedure is to:

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

29

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: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 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: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.

From the studies with the inverse modelling system the following conclusions could be made.

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.

The initial values should be carefully chosen before a complete run including many time steps is carried out.

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.

More experiments must be carried out in order to get statistical value since every pressure curve is unique producing small oscillations.

30

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.

31

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 0-412-81960-0.

[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: 369-402.

[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 361-413.

32

[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.

33

[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 (Ti-2003 Science and Technology) Hamburg, Germany, 13-18 July, 2003

[28] CFX 4.4-manual. ANSYS, Inc., Southpointe, 275 Technology Drive, Canonsburg, PA 15317.

34

Paper A

1

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: [email protected]

Fax: +46 920 491047

2

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.

3

KEYWORDS

D. Process monitoring

E. Compression moulding

E. Resin flow

E. Thermosetting resin

4

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

5

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.

6

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

7

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 isophtalic-

based 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

8

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.

9

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

10

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

11

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

12

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

13

(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:

14

23

00

0 12

thV

hrVur (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,

ru 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

15

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.

16

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

17

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.

18

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

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:

19

ossible short cut which we are working towards is to introduce flow

simulations combined wi the material models.

B Plast. The chemical

nalysis was performed in collaboration with Bo Lindblom at the Division of

Process Metallurgy, Luleå University of Technology.

p

th inverse modelling regarding

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 A

a

20

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 Non-

Planar Parts. Intern. Polymer. Processing V 1990;2:79-87.

21

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.

22

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.






23

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 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.


and elapsed time between each frame 3.00 seconds. The black areas

on the right-hand figure denote formed voids.


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

24

of the flow front as computed from continuity, Equation (1). Both

velocities are normalised with the velocity of the press.


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



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


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,

25

Equation (1). All velocities are normalised with the velocity of the

press.

26

camera

mould

charge

Odenberger, Figure 1

27


28


29


30

0.00 s 0.04 s 0.08 s 0.12 s 0.16 s 0.20 s 0.24 s 0.28 s


31


32


33


34

0.00 s 0.32 s 0.64 s 0.96 s 1.28 s 1.60 s 1.92 s 2.24 s


35

0.00 s 0.04 s 0.08 s 0.12 s 0.16 s

Odenberger Figure 10

36


37


38

t [s]

0.00 0.05 0.10 0.15 0.20 0.25 0.30

v*

0

1

2

3

4

5

6


39

t [s]

0.00 0.05 0.10 0.15 0.20 0.25 0.30

v*

0

1

2

3

4

5

6


40

t [s]

0.0 0.2 0.4 0.6 0.8 1.0 1.2

v*

0

5

10

15

20


41

t [s]

0.0 0.5 1.0 1.5 2.0 2.5

v*

0

2

4

6

8


Paper B

1

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 multi-phase 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

2

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

3

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 sothat 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 adaptivemesh or two-dimensional flow through a semi-stationary mesh. Both these models are verified by theory while the trust in the actual simulations isincreased by grid refinement studies combined with the well known and widely used Richardson’s extrapolation method [10]. Finally the method is comparedto 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 placedbetween 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:

0dtm

(1)

a then becomes a direct function of h according to:

hh

aa 02

0 (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:

dtdhhh 0 (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:

4

zhzrGur2

(4)

if transient effects, axial flow and flow front phenomenon can be neglected. Here G is the pressure gradient, the viscosity and r and z the spatial co-ordinates along the radius and perpendicular to the disc, respectively. Continuity now yields that:

dtdh

hrrG

3

6 (5)

By setting the pressure to p0 at the flow front which is located at a thefollowing pressure distribution results:

2230

3 radtdh

hprp (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 schemeusing double precision and the AMG multi-grid solver. The geometry in focus for the simulations was generated in a cylindrical coordinate system (x, r, )and by applying axisymmetric conditions in the direction of , see Figure 1.

Figure 1. Axisymmetric flow domain.

5

Solid walls are set as boundary conditions on high and low x while atmosphericpressure 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 aone-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. Thenumerical 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 homogeneousmodel, 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 theanalytical case since the flow front will not move as a plug. The practicalmodel 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 foreach phase as described above for approximately 44 time steps where eachtime 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 isthat the residual error e of a quantityd

h .

dhh (10)

can be approximated from two grids with different numbers of elements as here stated:

122

phhd

h (11)

6

The order of the schemes used, p, is often two but due to the complicatedequation systems solved for it more or less simultaneously it is recommendedthat it is calculated with the following formula

2log

log2

42

hh

hh

p (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 middlemesh 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 andpressure 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 fluidand hence the pressure. One methodology is thus to measure the pressure and temperatures in simple geometries but in several points and then find theviscosity distribution that match these pressures by inverse modeling. With agood 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 co-ordinate, 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 isaltered with the aid of the CFX4.4 specified FORTRAN subroutine USRVIS and by using the following proportional regularization expression

erimentcalculatedoldnew pp exp2 . (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 thesame 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.

7

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 pressingproceeds.

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 correctmodel must be further developed before any conclusions on its usefulness can be made.

8

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 iterationcycle 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 to0.1 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 magnitudefor 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.

9

Figure 5. Left: Pressure error defined as the difference between experimentalvalue 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 alsodependent 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 maximumerror 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.

10

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 machineaccuracy since the proportional regularization will not stop until a desirednumber of iterations are reached. Leaving this for the moment to see if theother cases pointing in the same direction. The Sinus formed pressure curve is represented by the following expression

55*sin165 stepp (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.


11

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.

44281414

11165

2715165

14114

165

stepstepp

stepp

stepstepp

(15)

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.

12


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 experimentcarried out with a fjellman 310 tons press and under production like conditions.During pressing the pressure were captured with two Kistler pressuretransducer (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 chargecontains 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 theshear thinning behavior of SMC is exclusive, notice that a constant viscosity isset 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.

13

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 variationsa 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:

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 isproducing 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 runincluding many time steps is carried out.

14

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] Fibre Orintation, Rheological Behavior and Simulation of the Compression Moulding Process for Composite Materials, C.F.Vahlund. ISSN: 1402-1544.

[2] Compression molding, Tim A. Osswald and Shi-Chang Tseng, Flow and rheology in polymer composites manufacturing volyme 10, p 361-413.

[3] 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.

[4] Lundström, T.S., “Bubble Transport Through Constricted Capillary Tube with Application to Resin Transfer Moulding” Polymer Composites, 17, pp. 770-779 (1996)

[5] Lundström, T.S., “Measurement of Void Collapse during Resin Transfer Moulding” Composites Part A, 28A, pp. 201-214 (1997)

[6] Inverse Problem Theory. Tarantola Albert. 1987. ISBN 0-444-42765-1. [7] Concept and Computational Methods for Parameter Identification of

Inelastic Material Models, R.Mahnken, E.Stein. [8] 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.

[9] 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 (Ti-2003 Science and Technology) Hamburg, Germany, 13-18 July, 2003

[10] Computational methods for fluid dynamics, Joel H Ferziger, Milovan Peric´.

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