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FORMING PREDICTIONS OF UD REINFORCED
THERMOPLASTIC LAMINATES
S.P. Haanappel1, R. ten Thije2, R. Akkerman1
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University of Twente, Faculty of Engineering Technology, Chair of Production Technology, Drienerlolaan 5, P.O. Box 217 7500AE Enschede, the Netherlands
s.p.haanappel@utwente.nl, r.akkerman@utwente.nl
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Aniform Virtual Forming, Nieuwstraat 116, 7411 LP Deventer, the Netherlands www.aniform.com, r.tenthije@aniform.com
Abstract
A preliminary study was made of the thermoforming process of UD fibre reinforced thermoplastic laminates. Deformation mechanisms of the ply and the laminate were identified. Forming experiments were performed with a single dome to support this study. The experiments were also used to validate the forming predictions with finite element analyses. The laminates were modelled with Discrete Kirchoff Triangles combined with multiple membrane elements to describe the in-plane behaviour. The Ideal Fibre Reinforced Newtonian fluid Model was employed for the membrane terms, involving transverse and longitudinal viscosities. Different characterisation methods show large variations in magnitude of the measured viscosities. The effect of these variations on the forming predictions has been examined. A large effect was observed for cross-ply laminates, whereas the differences for the quasi-isotropic laminates were smaller. Moreover, wrinkling predictions show good agreement with the experiments.
1 Introduction
There is a growing interest in the application of uni-directionally (UD) reinforced thermoplastics in aerospace industry. For example, the Fokker Aerospace Group started the development of processing this material in floor beams since the year 2000. This development was supported by the increasing availability of tooling to process these materials. Since these products were successfully integrated in aircraft designs, it is tempting to process these thermoplastic materials in primary loaded structures. Strengths, stiffnesses, weight savings, and low scrap are points of consideration. These can be achieved by blank designs with locally varying thicknesses and ply orientations. The feasibility of such tailored blanks was presented by Burkhart [1].
Prediction tools that simulate the thermoforming process aim to reduce the number of optimisation cycles during the development phase of a product. In order to simulate the forming process of a tailored blank, at least a model is needed that successfully predicts the forming behaviour of a flat blank. As a first step, forming trials with a doubly curved shape will be performed. Then, a model will be developed in order to simulate this forming experiment. The model needs material property data for different deformation mechanisms. The sensitivity of the simulation results on intra-ply shear parameters will be assessed.
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2 Single dome forming trials
Forming experiments were performed with circular blanks, having a diameter of 217.5 mm, a polyetherketoneketone (PEKK) thermoplastic matrix, and a UD carbon fibre reinforcement. Two lay-ups are considered, namely a cross-ply [0/90]S, and a quasi-isotropic [0/90/45/-45]S
lay-up. These laminates were subsequently heated up to 360 οC and formed between a
pre-heated steel male and a cold rubber female part, as shown in Figure 1. The blanks were supported by four laminate holders as shown in figures 2 and 3. These holders locally restrict some deformation due to the resulting normal forces and lower temperatures.
Figure 1 Left, thermoforming set-up. Right, dimensions of the steel mould geometry.
Figure 2 shows the forming results of the cross-ply laminates at two instances. The mould parts were not fully closed in the left picture, in order to see the development of wrinkles. Out-of-plane buckling and subsequent folding mechanisms were observed. Most of them were concentrated near the blank holders. The right picture shows the final product. Some buckled zones were folded and converted to a wrinkle, whereas others disappeared. Figure 3 shows the forming results of the quasi-isotropic laminates. Buckled zones are more pronounced, compared to the cross-ply laminate results. They develop on both sides of each blank holder. Buckling, folding, and wrinkling results in a larger affected zone near one side of the holder, compared to the other side of the holder.
Previously, forming trials on similar domes with UD reinforcements were reported by McGuinness [2], Ó Brádaigh [3], and Friedrich [4]. These authors considered forming trials with a [0]8 lay-up, without a discrete clamping as depicted in Figure 2 and 3. Non-circular
footprints were reported due to fibre inextensibility, which was observed here as well (see Figure 2). However, Figure 3 shows a circular footprint due to the quasi-isotropic lay-up. In the literature, wrinkles in the doubly curved region were not detected for the [0]8 lay-up.
Nevertheless, wrinkles near the flanges that are oriented ±45ο to the fibre direction were
observed and termed as fibre buckling [5]. Literature on forming trials with simple doubly curved shapes with lay-ups other than uni-directional is scarcely available.
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Figure 2 Thermoforming results of the [0/90]S lay-up. Left, intermediate forming result,
distance between tools: 10 mm. Right, final shape of the formed dome.
Figure 3 Thermoforming results of the [0/90/45/-45]S lay-up. Left, intermediate forming result,
distance between tools: 20 mm. Right, final shape of the formed dome.
3 Deformation mechanisms
An excess of material appears when forming of a flat blank into a doubly curved shape, as can be observed from the thermoforming results. Mechanisms to deal with this excess are shown Figure 4. All these mechanisms appear simultaneously during the forming process. The ratio between the energies that are consumed by these mechanisms, determine whether or not and how defects such as wrinkling develop.
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Figure 4 Deformation mechanisms during thermoforming. From left to right:
axial intra-ply shear, transverse intra-ply shear, inter-ply and tool-ply slip, and bending.
Mechanisms as in Figure 5 were observed in sequence. Once it is favourable to buckle out-of-plane, a transition into another mechanism from Figure 4 is possible. As the mould parts approach each other, the buckled zone can be converted to intra-ply shear, moved to another zone, or folded to form a wrinkle.
Figure 5 Mechanisms that deal with out-of-plane buckling.
The well accepted Ideal Fibre Reinforced Newtonian fluid Model (IFRM) can be utilised to describe the in-plane deformation behaviour of a UD reinforced ply with a thermoplastic matrix material in its molten state. This continuum theory was initially developed for elastic materials [6] and adapted by Rogers [7] to account for viscous fluids. A decomposed stress tensor is found by assuming incompressibility and fibre-inextensibility. The stress is the sum of a hydrostatic pressure p, an arbitrary fibre stress T, and an extra stress tensor. Rogers [7] proposed a linear form of the extra stress tensor to describe the constitutive behaviour of a fibre reinforced viscous fluid, resulting in the following constitutive relationship:
) )( ( 2 2 D aa D D aa a a T I p + + T + L − T ⋅ + ⋅ − = η η η σ , (1)
in whichσ is the stress tensor, a is a vector that represents the fibre direction, and D is the rate of deformation tensor. The parameters ηT and ηL represent the transverse and
longitudinal viscosity of the uni-directional ply and are related to the shearing mechanisms of a fibre reinforced viscous fluid, as shown in Figure 4.
Several techniques were developed to determine the two viscosities in eqn. (1) for a UD fibre reinforced laminate at high temperatures. Some of them are described by Advani [8] and a comparison of many tests was presented by Harrison [9]. For example, plate-plate rheometry
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[10] and picture frame [11] tests were developed, but their resulting viscosities differ several orders of magnitude. However, do these differences result in deviating forming predictions?
4 Modelling
Several approaches can be followed to model the forming process [12]. For example, discrete approaches that are based on analytical mapping expressions were used by Tam [13] and Golden [14]. The mapping of an initially flat geometry onto a prescribed curved mould surface is in both cases obtained by assuming inextensible fibres and incompressibility. Although it is hard to obtain a single expression for complex mould surfaces, mapping is still useful via numerical techniques [15]. The main drawback to the mapping approach is the absence of material behaviour. This implies that effects of inter-ply friction cannot easily be accounted for. In this work, the Aniform finite element package [16] was utilised. Suitable constitutive models were implemented to describe the deformation mechanisms in Figure 4.
4.1 Ply modelling
The plies of the blank are modelled with 3-node triangular shell elements. Each node has 6 degrees of freedom, namely 3 displacements and 3 rotations. The element is a combination of a membrane (MEM) element and a Discrete Kirchoff Triangle (DKT) [17]. The elements are updated using a decoupled approach, as illustrated in Figure 6, showing a 1½D simplification of the shell element. Using the same constitutive models and values for both the membrane and bending part would results in a significant over-prediction of the bending stiffness and hence unrealistic bending behaviour. Therefore, different constitutive models are used for the MEM and DKT part of the element [18].
Figure 6 Decoupled update of the elements that form the ply.
An orthotropic elastic model is used for the DKTs to model the bending behaviour of the plies. The principal direction is aligned with the fibre direction in the ply. This model allows for modelling a higher bending stiffness in the fibre direction when compared to the direction
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perpendicular to the fibres. A ply thickness of 0.14 mm was used. The IFRM relation (1) was used to describe the constitutive behaviour of the membrane elements. Table 1 shows the material parameter values for the two constitutive models.
Table 1 Material properties for the bending and membrane part of the ply elements.
DKT bending part MEMbrane part Orthotropic elastic model IFRM relation
E1 [MPa] 25.0 simulation A simulation B
E2 [MPa] 12.5 Efib [GPa] 1.0 1.0
ν12 [-] 0.32 ηT [kPa⋅s] 4.0 300.0
G21 [MPa] 10.0 ηL [kPa⋅s] 6.0 300.0
4.2 Contact modelling
The penalty method was used to model contact logic on the tool-ply and ply-ply interfaces. In addition to the penalty method, a viscous friction model was used to model friction on the interfaces. This model assumes the presence of a fluid layer with thickness h between the two bodies. The traction τ
r
on the interface is then given by:
τ =η γ⋅
r r
&, (2) in which η denotes the fluid viscosity and γ
r
& the shear rate, which is given by:
v h γ = r r & , (3)
in which the vector v r
denotes the relative slip velocity of the two bodies.
The individual plies of the blank have the tendency to stick together. This ‘tackiness’ of the plies is modelled by an adhesive tension that is included in the contact logic. As long as the plies are not separated by more than a user defined threshold value, this adhesive tension is active. The parameters used are summarised in Table 2.
Table 2 Parameters for the contact interfaces.
tool –ply ply – ply Penalty model
penalty stiffness [MPa] 1.0 1.0 Viscous friction model
film thickness [µm] 7 7
viscosity [Pa⋅s] 700 700
Adhesion model
adhesion tension [MPa] -- 0.1
threshold [mm] -- 2
4.3 Simulations
Simulations were performed with a two layered [0/90] and a four layered [0/90/45/-45] configuration. The distribution and the interaction of the modelled entities are shown in Figure 7. The steel male and rubber female mould parts in Figure 1 were modelled as rigid surfaces, both having 13.000 elements. Each ply was meshed with 16.000 elements. Blank
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holders as shown in Figures 2 and 3, were represented by coupling the displacements of the nodes at the associated positions. Moreover, these coupled nodes were allowed to move as a rigid body. The forming process was simulated by moving the upper mould with 10 mm/s downwards. Per lay-up configuration, two simulations were done to determine the influence of the intra-ply shear parameters ηT and ηL. Calculations were done with an Amazone EC2
instance, having 8 virtual cores (20 EC2 Compute Units) and 7 GB of memory. Computing times varied between 10 and 48 hours.
Figure 7 Schematic representation of the modelled entities.
4.3.1 [0/90] Lay-Up
Figure 8 shows the simulation results for which the parameters in Table 1 and 2 were used. Varying the transverse and longitudinal viscosities in eqn. (1) by two orders of magnitude gives a clear difference. For the low viscosities (left), the edges of the laminate between the holders are sagging and quickly touch the male tool during the forming process. In combination with slack behaviour of the laminate, wrinkles develop globally. Less pronounced wrinkling develops when using the higher viscosities (right). Small buckled zones can be observed in the interior of the dome, however, these will disappear when the moulds are fully closed. The blank holders influence the wrinkling pattern significantly, as was also observed during the forming trials with the results in Figure 2.
Figure 8 Results of forming predictions of the single dome for a [0/90] lay-up. Distance between tools: 8 mm.
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4.3.1 [0/90/45/-45] Lay-Up
As shown in Figure 9, both results show large wrinkles that are originated from the blank holder positions. Smaller wrinkles develop next to the large wrinkles. Apparently, their length and positions depend on the viscosities’ magnitudes. Globally, the result with low viscosities (left) tends to the development of more minor wrinkling, compared to the high viscosity result (right). The large wrinkles next to the blank holders were also observed in the experimental results in Figure 3. Experiments show relatively large wrinkles on both sides of the holders. Indeed, both simulations show a tendency to form a smaller wrinkle. However, closing the moulds convert these small buckled regions into intra-ply shear.
Figure 9 Results of forming predictions of the single dome for a [0/90/45/-45] lay-up. Distance between tools:
12 mm. Left, ηT= 4.0 [kPa·s] and ηL= 6.0 [kPa·s]. Right, ηT=ηL=300 [kPa·s].
5 Conclusions and future work
Forming simulations were performed with UD fibre reinforced thermoplastic laminates. Cross-ply and quasi-isotropic laminates were considered. The transverse and longitudinal viscosities were varied for two orders of magnitude to illustrate their effect.
Small differences were found for the quasi-isotropic laminates between the two sets of material properties. Wrinkle behaviour was significantly influenced by the blank holders. In combination with a relatively simple geometry, it is expected that the dependency on the viscosities is not efficiently highlighted. However, the predicted wrinkling behaviour was affected significantly in case of the cross-ply laminates. In case of the higher viscosities, wrinkle predictions were in good agreement with the experiments.
There are various methods to characterise intra-ply shear. Large scatter in the measured viscosities was found [9]. Its influence on forming predictions has been shown. Some of the characterisation methods show difficulties due to the low integrity of the thermoplastic laminate at high temperatures. Dealing with the laminate’s integrity at high temperatures can probably be facilitated by exploiting the stiff and continuous nature of the fibres. The possibility of loading a fibre reinforced rectangular strip in torsion is currently investigated [19].
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Acknowledgement
This project is funded by the Thermoplastic Composite Research Centre. The support of the Region Twente and the Gelderland & Overijssel team for the TPRC, by means of the GO Programme EFRO 2007-2013, is gratefully acknowledged. Furthermore, the authors would like to thank Richard Roerink, Steven Teunissen, and Michael Wielandt from the Fokker Aerospace Group. Their help with the thermoforming experiments was highly appreciated.
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