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# Numerical modelling of compression moulding with SMC for the improvement of mechanical properties

Moo Sun Kim, Woo Suck Han, Alain Vautrin, Woo Il Lee

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Moo Sun Kim, Woo Suck Han, Alain Vautrin, Woo Il Lee. Numerical modelling of compression moulding with SMC for the improvement of mechanical properties. 8e Colloque national en calcul des structures, CSMA, May 2007, Giens, France. hal-01495623

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# Numerical modelling of compression moulding with SMC for the improvement of mechanical properties

Moo Sun KIM*,**, Woo Suck HAN*, Alain Vautrin*, Woo Il LEE**

*Mechanical and Materials Engineering Department, Ecole Nationale Supérieure des Mines de Saint-Etienne, 42023 Saint-Etienne
{moosun, han, vautrin}@emse.fr

**School of Mechanical and Aerospace Engineering, Seoul National University, Seoul 151-741, South Korea

RÉSUMÉ. L'objectif principal de cette étude est d'optimiser les conditions du procédé de moulage par compression de SMC en vue de prédire et d'améliorer les performances mécaniques des structures composites. La phase préliminaire de l'optimisation globale est basée sur un programme de simulation du procédé faisant appel à la méthode CV/FEM et un programme de calcul des structures par éléments finis avec un élément DST, en vue de prendre simultanément en compte les contraintes mécaniques et celles du procédé de fabrication. A travers quelques exemples simples, nous avons montré que les propriétés mécaniques dépendent de la localisation du matériau initial.

ABSTRACT. The main goal of this study is to optimize processing conditions so as to predict and improve the mechanical performance of composite structures manufactured by compression molding process with SMC. As the preliminary step of optimization, we developed a processing simulation program by CV/FEM and a structural analysis program by DST element to consider simultaneously the mechanical requirements and the manufacturing process. Through some simple cases of molding shape, the dependence of the mechanical properties on the precharge location as processing parameter was verified.

MOTS-CLÉS: Moulage par compression avec SMC, localisation de la précharge, optimisation simultanée, propriétés mécaniques.

KEYWORDS: Compression molding with SMC, mechanical properties, precharge location, simultaneous optimization.
# 1. Introduction

Compression Moulding is the manufacturing process by compressing precharge in the mould. One of the advantages of this manufacturing process is its very short process time to satisfy mass production indispensable for automobile manufacturing, for example. Also, the mechanical properties of the final product is relatively fine and the process is simple. The representative thermoset material for compression moulding is SMC (Sheet Moulding Compound) in the form of thin plate. The charging process gives great influences on the mechanical properties of the final product. Fibre states, such as fibre volume fraction and fibre orientation can change the mechanical properties of the final product. Non-uniform distribution of the fibre volume fraction, due to the fibre separation or the change of fibre orientation, gives rise to non-uniform mechanical properties in the product. Therefore, the accurate prediction of fibre states and the optimisation of process conditions are demanded to obtain the required mechanical properties of the final structure. There are two models suggested for the flow analysis of compression moulding process: the generalized Hele-Shaw (GHS) model (Folgar *et al.*, 1983) and the Barone-Caulk model (Barone *et al.*, 1986). In this study, the numerical analysis of the flow of GHS model for 2-dimension has been completed using the CV/FEM (Control Volume FEM). Fibre separation is caused by the fibre-matrix and fibre-fibre interaction (Yoo, 1997). As well as fibre volume fraction, fibre orientation is the main cause for uneven properties in the product. As the methods to represent the state of fibre orientation, the fibre orientation distribution function (Jackson *et al.*, 1986) or the fibre orientation tensors (Advani *et al.*, 1987) can be used. To predict the mechanical properties of short-fibre composite, first of all, estimation of properties of a material with unidirectional properties must be computed. Halpin-Tsai equations are the most popular to predict the properties of short-fiber composites (Halpin *et al.*, 1976). Then, the properties of the composite are taken as an average of these unidirectional properties over all direction. The final fibre orientation tensors obtained from the processing simulation are used for the “orientation averaging”(Advani *et al.*, 1987). A series of triangular elements has been introduced based on Reissner-Mindlin assumptions. As the robust triangular elements for thin and thick plate, DST (Discrete Shear Triangle) element (Batoz *et al.*, 1989) and DRM (Discrete Reissner-Mindlin) element (Zienkiewicz *et al.*, 1990) are suggested. The final objective of this research is to find out the pattern of changes of structural properties depending on the structural parameters and processing parameters, and based on these pattern, by choosing the proper optimization techniques, to suggest the optimization methodology to get the better structural properties.

# 2. Modelling for flow and fibre states

For GHS model, it is assumed that the inertia of the material is negligible, the material is incompressible and the variant of shear stress in z-direction and the
variant of pressure are the dominant terms in the momentum equation. SMC is assumed as isotropic and incompressible. The flow velocity is defined as the in-plane velocity averaged through the thickness of material. With the above assumptions, from the continuity equation and momentum equation, one governing equation is described as the following.

$$ \frac{\partial}{\partial x}\left(\frac{S}{h} \frac{\partial P}{\partial x}\right)+\frac{\partial}{\partial y}\left(\frac{S}{h} \frac{\partial P}{\partial y}\right)=\frac{\dot{h}}{h} \quad [1] $$

where $P, h, \dot{h}$ are pressure, thickness and compression speed, respectively and $S$ is defined as flow conductance. For fibre separation phenomenon, each different velocity of flow and fibres must be understood. It can be said to be the relative velocity between resin flow and fibre flow. Due to the relative velocity of them, the initial homogeneous fibre content (i.e. fibre volume fraction) in precharge becomes non-homogeneous. The relative velocity is caused by the external force on fibres due to the pressure distribution dominantly. The network force as frictional force on a fibre tow, which is caused by the contacts of peripheral fibre tows, acts as a resisting force. Then it can be assumed that the drag force on fibre by the resin flow is balanced with the frictional force on a fibre tows. The difference of velocity between fibre and matrix owing to this phenomenon, can be determined by using the equivalence of drag force and network force. For fibre orientation, Advani(1987) developed an efficient method to represent fibre orientation using orientation tensors. This technique reduced the computational requirements. A compact and general description of fibre orientation state is provided by the tensors $a_{ij}$. It is symmetric and its trace is equal to unity. The advantage of using the tensor representation is that only a few numbers are required to describe the orientation state at any point in space. For planar orientations there are four components of $a_{ij}$, but only two are independent. Folgar and Tucker's equation of single fibre motion in a concentrated suspension can be combined with the equation of continuity to produce an equation of change for the probability distribution function and/or the orientation tensor.

### 3. Structural analysis

By using fibre volume fraction and fibre orientation tensors, which are obtained in the processing simulation, mechanical properties of composite structure can be considered as those of a homogenized material. First of all, to estimate unidirectional fibre-matrix material, Halpin-Tasi equation is used. And then, the unidirectional properties of fibre-matrix material are averaged over all direction to compute the fibre-matrix composite material. The unidirectional fibre-matrix
material is considered as transversly isotropic. Therefore, it has only 5 independent
stiffness tensor elements. The plate-like structure manufactured by compression
molding process must be correctly analysed as the shell problem. But shell finite
elements are among the most difficult to formulate. For the practical purposes,
instead of shell element, flat element approximation can give the adequate answer.
Typical flat element is considered to be subject to plane stress and plate bending
action. Therefore, stiffness matrix is formed by assembling the plane stress and plate
bending stiffness matrices. Also, plate bending stiffness matrix is composed of two
different stiffness matrices from bending moments and transverse shear forces. In
this paper, DRM element is used for plate bending problem.

**4. Case study of processing parameters**

By applying fibre separation and fibre orientation model to numerical analysis program, fibre volume fraction and fibre orientation are computed according to the processing conditions. We considered precharge location as the processing parameter for two cases of mold shape. For a simple rectangular plate under the loading condition as in Fig.1, maximum deflection is calculated for the fiber states induced from different processing condition.

<figure><img src="image_2.png" /><figcaption>Fig.1. Geometry of clamped plate and loading conditions</figcaption></figure>

Two cases of precharge locations are considered. One is to have the precharge
on the left side of the mold and the other on the right side as shown in Fig.2.
Resulting of maximum displacement are compared with a result in case of
homogeneous fiber volume fraction and isotopic fiber orientation in Fig. 3.

<figure><img src="image_3.png" /><figcaption>Fig. 2.(a)left-located precharge (30% covered mold, 30% fibre volume fraction)
(b)right-located precharge (30% covered mold, 30% fibre volume fraction)</figcaption></figure>

For a rectangular plate with hole as another consideration as in Fig. 4., three
cases precharge locations are considered in Fig.5. In Fig.6., maximum
displacements of cases are compared.
<figure><img src="image_4.png" /><figcaption>Fig.3. Maximum displacement of structure
Case 1: homogeneous fiber volume fraction and isotropic fiber orientation
Case 2: left-located precharge condition
Case 3: right-located precharge condition</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Fig.4. Geometry of clamped plate with hole and loading conditions</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Figure.5. Three</figcaption></figure>

<caption>Figure.6. Maximum displacements of structure</caption>
**5. Conclusion**

By flow simulation code, we could calculate fibre states and predict mechanical
properties of composite structure. We compared maximum displacements of simple
structure under loading to find out that final mechanical properties depend on the
processing conditions(in this case precharge location) to show different mechanical
properties. Other parameters such as thickness of structure and precharge dimension,
which influence mechanical properties, can be also considered. Final objective of
this research is to find the best optimization algorithm for the aforementioned
problem.In conclusion, our simulation tool will help engineers to design products
manufactured by compression molding through giving the guideline to determine
the processing conditions and design parameters of structures, and eventually to
save the development costs.

**6. Bibliographie**

Advani, S.G., C.L. Tucker III, «The use of tensors to describe and predict fiber orientation in short fiber orientation in short fiber composite», *Journal of Rheology*, vol.31, n° 8, 1987, p.751-784.

Advani, S.G., C.L. Tucker III, «A Numerical Simulation of Short Fiber Orientation in Compression Molding», *Polymer Composites*, vol.11, n° 3, 1990, p.164-173.

Barone, M.R., D.A.Caulk, «A model for the flow of a chopped fiber reinforced polymer compound in compression molding», *Journal of Applied Mechanics*, vol.53, 1986, p.361-371.

Batoz, J.L. and Lardeur, P., «A discrete shear triangular nine d.o.f. element for the analysis of thick to very thin plates», *International Journal for Numerical Methods in Engineering*, vol.28, 1989, p.533-560.

Folgar, F., Tucker III, C.L., «A Model of Compression Mold Filling», *Polymer Engineering and Science*, vol.23, n°2, 1983, p. 69-73.

Halpin, J.C., Kardos, J.L., «The Halpin-Tsai Equation: A Review», *Polymer Engineering and Science*, vol.16, n°5, 1976, p.344-352.

Hojo, H., C. Nagatsuka, E.G. Kim., K. Tamakawa, «Separation of matrix and fibers during molding of long fiber-reinforced thermoplastics», *Proceedings of the Third Japan-U.S Conference on Composite Materials*, 1986, p.605-612.

Jackson, W.C., C.L. Tucker., S.G. Advani., «Predicting the orientation of short fibers in thin compression moldings», *Journal of Composite Materials*, vol.20, 1986, p.539-557.

Yoo, Y.E., A Study on the analysis of compression molding process of composite material structures. Ph.D.Thesis, Seoul National University,1997.

Zienkiewicz, O.C., Taylor, R.L., Papadopoulos, P., Onate, E., «Plate bending elements with discrete constraints: new triangular elements», *Computers & Structures*, vol.35, n°4, 1990, p.505-522.