____________________ * Corresponding author: K. Vanclooster, kristof.vanclooster@mtm.kuleuven.be

SIMULATION OF MULTI-LAYERED COMPOSITES FORMING

K. Vanclooster1*, S.V. Lomov1 and I. Verpoest1

1Katholieke Universiteit Leuven Dept. of Metallurgy and Materials Engineering (MTM)

Kasteelpark Arenberg 44, B-3001 Leuven, Belgium

ABSTRACT: The contact behaviour during forming of woven reinforced thermoplastic composites determines the quality of the formed product. This paper evaluates different descriptive models for the ply-ply and tool-ply frictional properties of thermoplastic woven composites under process conditions. An alternative descriptive model, based on the experimental observation of the traction behaviour during tool-ply and ply-ply slip is presented. This model is implemented in ABAQUS-explicit and forming simulations are performed. The maximum compressive stress during forming is found to heavily depend on the orientation between adjacent plies.

KEYWORDS: inter-ply slip, tool-ply slip, thermoplastic composite, forming, ABAQUS 1 INTRODUCTION The formability of multi-layered thermoplastic composites heavily depends on the relative orientation between the plies [1]. Moreover, it has been shown in [2] that the inter-ply slip properties between the plies play a determining factor in whether wrinkling will take place. When inter-ply slip prevents intra-ply shear from occurring, this usually results in a heavily wrinkled final product. The inter-ply and also tool-ply contact behaviour has been investigated previously in [3]. Several descriptive models have been developed for inter-ply and tool-ply slip [3, 4]. All of these models are based on the fact that the viscous interlayer plays a determining role in the inter-ply shear slip behaviour. An important drawback, however, is associated with the need to determine the thickness of the interlayer and the flow behaviour of the matrix. In this study, both the inter-ply and tool-ply slip behaviour of a woven thermoplastic composite are evaluated. Three types of descriptive models are considered. Afterwards, the traction model is implemented into ABAQUS using a VFRIC subroutine. The formability of a double-layered stacking is evaluated using the maximum compressive stress as an indication on the probability of the occurrence of wrinkling. 2 DESCRIPTIVE MODELLING OF

FRICTION DURING FORMING Due to the complex nature, i.e. a strong dependence on the process conditions of the inter-ply slip behaviour no predictive models exist, phenomenological models were

developed instead. All of these models are based on the fact that the viscous interlayer plays a determining role in the inter-ply and tool-ply slip behaviour. 2.1 MODEL OF LAMERS Lamers [4] proposed to define a viscous slip law that is able to describe the sliding of the individual plies. This law is expressed by the velocity difference, v, between adjacent plies. He assumed a friction law with the stress depending linearly on the velocity difference v between the plies, the interface stress or the traction τ is defined as:

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τ =1β⋅ν (1)

Where β is defined as the slip factor, which is calculated as:

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β =hη

(2)

Here h is the averaged thickness of the interface layer and η the viscosity of the interface layer. This formulation is derived from Newton’s law of viscosity. The main drawback of this formula is the need to identify the interlayer thickness for different process conditions. Lamers assumed that this interlayer thickness is constant throughout the whole specimen. To determine the interlayer thickness equations 1 and 2 are combined together with an Ellis-Arrhenius model of the viscosity, which can be found in [5]. The peak traction measured in the pull-out experiments in [5] forms the input for the right-hand side of Equation 3. These experiments are performed using Twintex P PP 60 1485 1/1 [6].

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τv

=η0(T)

1+v

h ⋅C(T)

n−1

⋅ h

(3)

A Newton-Raphson approach is used to calculate the representative interlayer thickness.

a

b

c

Figure 1: Influence of (a) the pressure, (b) the temperature and (c) the velocity on the representative interlayer thickness In Figure 1 the influence of the different process conditions on the representative interlayer thickness are examined for both tool-ply and ply-ply contact. An increase in normal pressure decreases the thickness of the interlayer. Applying pressure makes the matrix material flow away from the region where the pressure is high and thus makes the interlayer thinner. A rising temperature hardly affects the interlayer thickness. The slip velocity, however, has a great influence on the interlayer thickness. It increases with about 100% when the velocity increases from 0.33 to 8.33 mm/s. Table 1: Average representative interlayer thickness

Contact type Average representative interlayer thickness (mm)

Ply-ply 0.0622 ± 0.0242 Tool-ply 0.0387 ± 0.0134

The average representative thickness, indicated in Table 1, for ply-ply contact is found to be approximately two times thicker than the representative thickness for tool-ply. This can be explained by the fact that 2 layers of composite come into contact for ply-ply contact, while for tool-ply contact only one layer of composite is present, thus the interlayer thickness diminishes.

Figure 2: Cross-section of a ply-ply pull-out specimen From the µCt-image presented in Figure 2 it is seen that the interlayer (indicated by red borderlines) for ply-ply contact has a width spectrum of heights. Therefore, the assumption made by Lamers to consider a constant average interlayer results in a too cumbersome approach to derive a descriptive model. 2.2 STRIBECK CURVE Gorczyca et al. [3] introduced a second descriptive modeling approach for tool-ply friction based on the lubrication theory of Stribeck. In the Stribeck curve the friction coefficient is plotted as function of the Hersey number He, which is defined as:

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He =η ⋅ vFN

€

m−1[ ] (4)

Where η equals the shear viscosity, v is the speed of sliding and FN is the applied normal force. A high Hersey number usually means a relatively thick lubricant film, whereas a small number results in a very thin film. The Stribeck curves, shown in Figure 3, are constructed for both ply-ply and tool-ply contact. In order to calculate the Hersey number, the thickness of the interlayer needs to be known, since the viscosity is shear rate dependent. An interlayer thickness of 0.0622 mm for ply-ply friction and 0.0387 mm for tool-ply friction is assumed. It is clear from the Stribeck curves, that with increasing Hersey number, the friction coefficient increases. This agrees with the hydrodynamic regime of lubrication and endorses the fact that the matrix dominates the contact between the plies. As proposed by Gorczyca a linear relationship is found between the Hersey number and the friction coefficient:

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µ = c1 ⋅He + c0 (5)

a

b

Figure 3: Stribeck curve for (a) ply-ply friction and (b) tool-ply friction The fitting parameters c1 and c0 are shown in Table 2. Table 2: Fitting parameters for the Stribeck curves

Contact type c1 c0 Ply-ply 71.102 0.0863 Tool-ply 115.900 0.1064

2.3 TRACTION MODEL In this section a descriptive model for the traction will be developed for both tool-ply and ply-ply friction. It is assumed that the flow behaviour of the matrix material and the height of the interlayer are not known. In [5] it is shown that the traction-velocity behaviour can be described by a power-law, while the influence of the temperature is related to an Arrhenius type of equation. The following model is now proposed:

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τ = τ 0 ⋅ k ⋅ v( )na (6)

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τ 0 = B1 ⋅ exp B0 ⋅ P( ) ⋅ exp A0 ⋅ P + A1T

(7)

Where τ is the peak traction in Pa, v is the slip velocity in mm/s, k equals 1 s/mm, P is the pressure in bar and T is the temperature in K. Eq. 6 and 7 are implemented in MatLab and a multiple regression analysis is done using all the experimental data to find the parameters A0, A1, B0, B1 and na of the model. The results of this analysis are shown in Table 3. For both contact types high R2-values of more than 0.98 are found. Table 3: Fitting parameters for traction descriptive model

Contact A0 [K/bar]

A1 [K]

B0 [bar -1]

B1 [Pa] na

Ply-ply -3400 4338 8.07 0.53 0.52 Tool-ply -3816 4507 8.80 0.54 0.52

When evaluating the model, it is noticed that at high pressures the friction coefficient increases dramatically. This unanticipated increase in friction is due to the fact that the factors determining the influence of the pressure on the traction lie within an exponential function. Although, these pressure values lie out of the range tested in [5], previous studies mention low friction coefficient at high-pressure values. To compensate for this increase a boundary condition is added:

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P > Pcr :µ = µcr (8)

When a critical pressure Pcr is reached, the influence of the pressure on the friction coefficient µ is neglected. The temperature is found to have a big influence on the value of Pcr. To not increase the complexity of the model, the Pcr is taken independent of the temperature and as the average of the Pcr’s at 180, 195 and 210°C. Table 4: Pcr for different contact types

Contact type Pcr [bar] Ply-ply 1.16 Tool-ply 1.67

This extra boundary condition results in the friction-pressure plot shown in Figure 4.

Figure 4: Evaluation of traction descriptive model 2.4 COMPARISON

a

b

c

Figure 5: COMPARISON between traction model and Stribeck model for (a) the pressure, (b) the temperature and (c) the velocity dependence

Two of the presented descriptive models, the Stribeck and the traction model, are compared to each other over a wide range of process conditions in Figure 5. The Stribeck curve leads to a good approximation of the contact behaviour for the pressure dependence, though it falls short in describing the thermal influence on the friction coefficient. The traction model seems the most appropriate in and will be implemented into a FE-code. 2.5 IMPLEMENTATION INTO ABAQUS The traction model is implemented into ABAQUS explicit using a VFRIC subroutine. Figure 6 shows the comparison between the force-displacement curves obtained via ABAQUS and the experimental measurements. A good agreement is found.

Figure 6: Force-displacement curve The VFRIC is used in combination with a meso-scale model for fabric draping developed by Willems [7]. Simulations are performed where a multi-layered stacking of two laminates is deepdrawn using a hemispherically shaped punch (see Figure 7). These simulations are linked to the experimental work presented in [1]. The difference in warp direction between the adjacent plies of the laminate is changed from 0 to 45° with steps of 15°.

Figure 7: Minimum principal (maximum compressive) stress field for the forming of a laminate with a 45° orientation between the warp directions of the plies Wrinkling of a membrane is found as a structural answer in order to avoid compression stresses. Generally any wrinkling or folding phenomenon in a membrane can be explained by a buckling process. The resolution of such process always requires sophisticated tools and the solution needs sufficient numerical resources. A wrinkling criterion was developed in [8], where the principal stresses are used to evaluate the wrinkling. Here the approach is simplified and the maximum compressive stress is taken as an indication for the probability wrinkling occurs. The higher the maximum

value of the compressive stress, the higher the chance of wrinkling is. Table 5 summarizes the maximum compressive stress found at the end of the forming step for different orientations. Here, the same observations are made as in the experimental work presented in [1]. An increase in the orientation between two adjacent plies leads to more severe wrinkling of the laminate during forming. Table 5: Maximum compressive stress as function of the orientation between two adjacent plies

Orientation 0° 15° 30° 45° Max(σc) [Pa] 7.11 8.86 10.73 19.16

3 CONCLUSIONS Different descriptive models for the contact behaviour of ply-ply and tool-ply friction have been presented. An alternative model is proposed. This model offers the benefit of no need of the matrix flow properties or the interlayer thickness, but needs an extensive experimental investigation of the contact behaviour. The descriptive model is implemented into ABAQUS and forming simulations have been performed which indicate the same trend as the experimentally formed shapes. ACKNOWLEDGEMENT The Fund for Scientific Research Flanders (FWO Vlaanderen) is acknowledged for supporting this work. REFERENCES [1] Vanclooster, K., S.V. Lomov, and I. Verpoest. On the

formability of multi-layered fabric composites. in ICCM - 17th International Conference on Composite Materials. 2009. Edinburgh, United Kingdom.

[2] Vanclooster, K., et al. Optimizing the deepdrawing of multilayered woven fabric composites. in 12TH ESAFORM Conference on Material Forming. 2009. Twente, the Netherlands.

[3] Gorczyca-Cole, J.L., J.A. Sherwood, and J. Chen, A friction model for thermostamping commingled glass-polypropylene woven fabrics. Composites Part A: Applied Science and Manufacturing, 2007. 38(2): p. 393-406.

[4] Lamers, E.A.D., Shape distortions in fabric reinforced composite products due to processing induced fibre reorientation. 2004, Universiteit Twente: p. 134.

[5] Vanclooster, K., S.V. Lomov, and I. Verpoest. Investigation of interply shear in composite forming. in 11TH ESAFORM Conference on Material Forming. 2008. Lyon, France.

[6] http://www.ocvreinforcements.com [7] Willems, A., Forming simulations of textile reinforced

composite shell structures. 2008, Katholieke Universiteit Leuven: Leuven. p. 299.

[8] Raible, T., et al., Development of a wrinkling algorithm for orthotropic membrane materials. Computer Methods in Applied Mechanics and Engineering, 2005. 194(21-24): p. 2550-2568.