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Forming induced wrinkling of composite laminates: A numerical study on wrinkling mechanisms
Composites: Part A 81 (2016) 41–51
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Composites: Part A journal homepage: www.elsevier.com/locate/compositesa
Forming induced wrinkling of composite laminates: A numerical study on wrinkling mechanisms J. Sjölander a,⇑, P. Hallander b, M. Åkermo a a b
Department of Aeronautical and Vehicle Engineering, KTH Royal Institute of Technology, 100 44 Stockholm, Sweden SAAB AB, Linköping, Sweden
a r t i c l e
i n f o
Article history: Received 30 June 2015 Received in revised form 7 October 2015 Accepted 10 October 2015 Available online 30 October 2015 Keywords: A. Prepreg C. Process simulation E. Forming
a b s t r a c t When manufacturing composite aircraft components consisting of uni-directional prepreg laminates, Hot Drape Forming (HDF) is sometimes used. One issue with HDF is that, in contrast to hand lay-up where normally only one ply is laid up at a time, multiple plies are formed together. This limits the in-plane deformability of the stack, thus increasing the risk of out-of-plane wrinkling during forming. In this paper mechanisms responsible for creating different types of wrinkles are explained. It is shown through simulations how the wrinkles are created as a result of interaction between two layers with specific fibre directions or due to compression of the entire stack. The simulations are compared to experimental results with good agreement. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction In the aircraft industry weight is a critical property. Reducing the weight of an aircraft directly increases possible payload, which in turn gives a more fuel efficient transport system. For this reason composites have seen increased use in the past couple of decades due to their light weight, high stiffness and high strength. This increase has grown from a few percentage of the weight of an aircraft and is steadily increasing, up to this point where for example the latest Boeing 787 Dreamliner has 50% (by weight) composite material in its structural parts. The dominating material system when it comes to composites in structural aircraft components is pre-impregnated carbon fibres (prepregs). With the increasing use of prepregs, growing interest has followed in increasing the level of automation in production. To date several different automated processes have been developed for the lay-up and forming of prepregs, and these include Automatic Tape Laying (ATL), Advanced Fiber Placement (AFP) and Hot Drape Forming (HDF). However manual lay-up is still common, especially for more complex parts where automatic processes cannot achieve the necessary quality. The forming behaviour for these processes in general but in HDF in particular, is very dependent on the material properties of the prepreg. This is because it requires the forming of a multi-layer stack, where each ply through the thickness has a fibre angle which ⇑ Corresponding author. Tel.: +46 73 460 25 11. E-mail address: [email protected] (J. Sjölander). http://dx.doi.org/10.1016/j.compositesa.2015.10.012 1359-835X/Ó 2015 Elsevier Ltd. All rights reserved.
might be different to its neighbouring plies. Tam and Gutowski [1] showed that forming complex geometries using single unidirectional prepreg plies in the ideal case only requires non-area changing shear of the individual plies. This is because, unlike weaves where the warp is interconnected with the weft, a UD prepreg can, in theory shear without a reduction in area. Other studies have, however, shown that in practice due to tackiness, stacked UD prepreg materials normally form similar to woven material when it comes to inter-ply shear, but with the ability to also shear inbetween each separate layer. Earlier studies [2,3] have shown that material properties important to forming, such as inter-ply friction and intra-ply shear may vary significantly between seemingly very similar material systems, and these significantly change the forming outcome. In practice these materials are certified for use for the same type of applications, i.e. load-bearing aircraft parts. When forming a multi-layer stack over a complex tool geometry using a rubber diaphragm such as in HDF, forming forces and directions are determined by the geometry in combination with material properties and the stacking sequence of the material used. The latter means that while the stack undergoes the same global forming behaviour, separate plies adopt by moving relative to each other, since no deformation can occur parallel to the fibre deformation. The importance of using a stacking sequence that forms well over the geometry considered was first demonstrated by Hallander et al. in [4] where it was shown that, depending on which layers were combined, different forming results were obtained. In a later work [5], this was further exploited by studying the feasibility of using locally changed material properties, i.e. higher inter-ply
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friction, inter-ply shear or fibre stiffness, to steer the local forming behaviour in-between plies. Also separate plies were cut to reduce the fibre tension and shear forces developed in the material. In brief the study, which is later summarised as providing the experimental input to this paper, shows that although using locally different material properties may improve the forming outcome, using a good stacking sequence appears to be the only reliable method of overcoming any tendency of wrinkle development. This is partly supported by studies by e.g. Sun et al. [6], who examined the influence of changing friction in 2D forming, in this case forming a 90° angle. This was achieved by changing the forming temperature. Lower temperature meant higher friction, which in turn increased the defects after forming due to the layers not being able to slip sufficiently relative to each other. Also Lightfoot et al. [7] showed that, depending on the friction between the mould and the first ply, a wrinkle can be created. They also showed that, depending on the stacking sequence of the laminate, different wrinkles were formed, which also indicated that locally changing friction in an interface may change the global forming behaviour. Haanappel et al. [8] studied the forming of a complex, authentic geometry both in experiments and simulations. Both weaves and quasi-isotropic, uni-directional laminates were used. They saw that the two materials behaved quite differently where the unidirectional laminate showed a greater tendency to create wrinkles than the weave. They also noticed that a higher bending stiffness would lead to less wrinkles and more shearing in the material. Boisse et al. [9] performed both experiments and simulations of the forming of single layer, dry woven reinforcement onto a half sphere and a tetrahedral shape. They concluded that shearing of the material could lead to compressive stresses that in turn led to wrinkles. The magnitude of the bending stiffness decided how many wrinkles appeared, where low bending stiffness tends to lead to many small wrinkles while a larger bending stiffness led to a few, but larger wrinkles. Dodwell [10] developed a model for layered materials, which was able to predict out-of-plane wrinkling, in a case where a stack of prepreg were consolidated on a tool radius. Since HDF of multi-layer UD prepreg materials on a global level is highly dependent on the stacking sequence, detailed forming simulations are required considering the relative movement of each separate ply. Further, the simulations must predict the entire forming sequence, since wrinkles do not necessarily develop after the final forming step. However, while there is FE software that enables this kind of modelling, it is normally based on continuum mechanical approaches. It has been shown difficult to predict wrinkling in separate layers in critical areas. This has been commented by Larberg in e.g. [11]. According to Hallander et al. [4], such critical areas could be where separate plies undergo compression, while the stack globally is in tension.
Fig. 1. Geometry used in the forming experiments.
This paper aims to clarify the experimental findings in [5] by performing numerical simulations that enable the description of the forming sequence and the mechanical loads each separate must sustain during forming. Relating to the experimental findings, different kinds of wrinkles are discussed: those arising globally from excessive materials and those initiated locally due to single layers in compression. Further, for reasons explained above, since wrinkles developed due to local compressive stresses will not be detected in continuum-based simulations, the paper aims to find early wrinkle indicators that can be used in future simulations to detect wrinkle-prone areas. Experiments and numerical simulation are performed on a straight beam with a recess area, requiring 3D forming; however, the method developed based on wrinkle indicators is general and can be applied to any geometry used for forming of stacked materials.
2. Experimental background The numerical study presented in this paper aims to further the understanding of wrinkle development during forming of stacked UD prepreg. It is based on a experimental study, which is briefly summarised below. For further details the reader is referred to the study by Hallander et al. [5]. The aim of the experimental study was to examine whether wrinkle development could be avoided by either making the lamina more wrinkling resistant, or by reducing the compression developed in separate layers. The latter was achieved either by locally changing the friction properties in critical layers, by reducing the number of interfaces causing compression or by decreasing compression by reducing global tension. Improved wrinkling resistance was obtained by using locally stiffer fibres or using co-stacked layers. The experimental study was performed on a spar with a recess area in one flange according to Fig. 1. Two different 180 °C cure epoxy prepreg materials were used in the study: one containing HT (High Tenacity) fibre and the other containing IM (Intermediate Modulus) fibre. Except for having higher stiffness, the current paper shows that the IM fibre prepreg material has 40–50% lower inter-ply, prepreg–prepreg, friction and 30% lower intra-ply shear resistance than its HT counterpart, although the matrix is practically the same. A reference stacking sequence defined as [( 45, 0, 45, 90)4]s was used to manufacture samples containing either HT material, IM material or a combination of the two. Another stacking sequence: [(45, 45, 90, 0)4]s was used in order to halve the number of interfaces between the [±45] and [0] direction. In order to reduce the tension towards the centre of the recess area, the [0] direction was either removed from the stacking, as in [(45, 90, 45, 90)4]s stacking, or cut. Cutting was either performed throughout all the layers in the stack in a reference stacking or only on the [0] direction. Finally, as an attempt to increase the buckling resistance of the lamina, and at the same time reduce the numbers of expected critical interfaces, co-stacked layers were considered in two different configurations: [454, 04, 454, 04]s and [454, 904, 454, 904]s. After forming, wrinkles appeared in different positions: 1. horizontally in the centre of the recess area, 2. diagonally just below the radius at the start of the recess area, 3. vertically at the convex radius of the recess area and 4 on the centre of the web, across the beam. The results showed that appearance of wrinkles at position 1 was closely connected to the combination of 0° and 45° interfaces. It was shown that the wrinkles became smaller when reducing the inter-ply friction in-between these layers or just reducing the number of 0° and 45° interfaces. This seems to be caused by the tension provided by the 0° layer, since cutting this layer (or the entire stack) eliminated wrinkles developed in position 1.
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However instead, wrinkles in position 3 developed, which were not there initially. The same result was shown for the stacking having no 0° direction at all. In order to make a significant improvement, co-stacking of critical layers to increase buckling resistance was required. This created no visible out-of-plane wrinkling; however, micrographs of the cross-section showed out-of-plane waviness even for these samples. Total absence of wrinkling was only reached when using a different fibre stacking avoiding difficult fibre angle combinations.
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Fig. 2. Draping of a stiff ply into the recession area.
3. Wrinkle development When forming a stack of prepreg onto a geometry with double curvature, it is necessary for the stack to undergo in-plane deformation. This may be through shear or normal strain. If the degree of in-plane deformation is not sufficient for the stack to conform to the geometry at hand, out-of-plane wrinkling will occur. The authors of this paper are suggesting that the out-of-plane wrinkling of a laminate can be caused in at least two general ways: either the whole stack is put under compressive stress, leading to buckling of the stack. Alternatively a single layer in the stack is put in compression creating buckling, which then propagates and creates wrinkling of the stack. These two cases are explained further below.
Fig. 3. Shearing in zone B and the resulting strains. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Here we consider wrinkling of a laminate due to local compression of one layer in the stack. Consider an element subject to shear stress, the shear stress can be transformed into normal stresses rotated 45° from the applied shear stress by for example using Mohr’s circle. If the direction of the stress is aligned with the fibre direction, either tensile or compressive stress in the fibre will be created. While a tensile stress in the fibre direction is normally not critical for the forming outcome, significant compressive stresses in the fibre direction can cause buckling of the fibres, either in-plane or out-of-plane, and thereby causing wrinkling. This behaviour does not necessarily have to occur on a convex geometry, where it is more likely that global compression of the entire stack occurs. Hallander et al. [4] showed that this is a possible mechanism on a geometry requiring 3D forming, even in concave features that require global tension of the stack to form into.
As shown in Fig. 2, because of the recess area, the forming introduces shear by up to 2.86° in zone B. This is illustrated by the theoretical draping of a completely stiff fabric which has to be cut between zones A and B to conform to the geometry; from this it can be seen that it is necessary for some degree of shear in zone B to cover the ‘‘gaps” created by the forming. In Fig. 3 we see the ply after it has sheared to cover the gap. The shearing in zone B induces compressive stress in the 45° direction and tensile stress in the 45° direction. This holds independently of material used. However, it should be noted that while an isotropic generic material forms locally, forming of a stacked material with UD fibres in different directions causes fibre slippage and shear and thereby changes the material outside the actual forming area. Further, in multi-layer forming, each layer shows different deformability in zone B depending on its relative fibre angle. Focusing specifically on the 45° ply, it can be seen that the compressive stresses developed in zone B align with the fibre direction creating a risk of buckling. This should be the worst case scenario, since compressive stresses perpendicular to the fibres compact the fibre bed only and tensile stresses are easily carried by the fibres without buckling. The amount of compressive stress developed in zone B depends on the recess angle, i.e. the length to depth relationship of the recess area. Thus a reduction in recess angle should lead to a reduction in compressive stress. Now we consider a combination of layers as in a stack of UD prepreg. A 0° layer will deform closely to the ideal forming pattern since the fibres cover the gap completely, and this is shown in Fig. 4(a). The 90° on the other hand, as shown in Fig. 4(b), will form in a more geodesic manner since there is almost nothing stopping the ply to develop large transverse strains. Consequently the ±45° layers will fall somewhere in between. If we consider the pairing of layers, combining a 45° with a 0° will result in a relatively a high degree of shear and consequently high compressive stresses of the 45° since it is connected to the deformation of the 0°. Conversely pairing the 45° with a 90° will result in a lower degree of shear.
3.3. Forming onto a beam with a recess area
3.4. Proposed wrinkle indicators
The wrinkle development described here could be generic to any double curved geometry. However in this work the geometry in Fig. 1 is analysed. This is because it has been studied in [4,5] and the forming behaviour is therefore known. This gives the opportunity to study both the wrinkle development and different ways to mitigate it. It has a recess area on one flange with a depth of 6.25 mm. Since it is formed using hot drape forming the stack is placed on top of the beam and then gradually formed down onto the recess area marked A, B and C.
Based on the discussion of the material deformation above, the following assumptions are used when looking for wrinkle indicators in the simulation describing the forming of multi-layer UD prepreg:
3.1. Wrinkling due to global compression If the stack is formed over a convex geometry, wrinkles may be created basically because there is excess material that has to be collected in a wrinkle. Or in other words: wrinkling may arise from too high shear stiffness of the stack in relation to its bending stiffness during forming over any double curvature geometry requiring material shear. This type of wrinkling is general for all materials. 3.2. Wrinkling due to compression in a layer with a specific fibre direction
Local compressive stresses in the fibre direction in single layers during instants of forming are always an indicator that wrinkling may occur. In [5], it is shown that even if wrinkles cannot be seen from the outside due to the high buckling stability of
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the outer layers, microscope pictures indicate that it is difficult to avoid layer thickening and/or wrinkling inside the lamina at areas with high compressive stresses. When high local compression in single layers occurs and the FEmodel does not have enough fidelity to represent wrinkle development geometrically, the simulation outcome will naturally differ from the experimental findings. Instead indicators, such as stress in the fibre direction or apparent marcelling have to be used instead. Global compressive stresses resulting in wrinkling can most easily be determined by studying the compressive strain transversely to the fibre direction, since these areas will deform the most during wrinkle development. Fig. 4. (a) Ideal forming of a 0° ply and (b) geodesic forming of a 90° ply.
These indicators are general and may be used to study both locally and globally-induced wrinkling on a generic geometry. 3.5. FE-model The software Aniform v3.0.1 was used for the simulations [12]. This is a Finite Element software designed for composite forming. Aniform allows different models to be used for in-plane and outof-plane behaviour. This is an advantage because of the anisotropy of uncured prepregs. Additionally, friction between the layers and between the layers and the mould can be modelled with greater freedom by using combinations of different material models.
Table 1 Parameters used in the friction testing. Property
Value
Temperature Crosshead speed Normal pressure Relative fibre direction
70 (°C) 0.05 (mm/s) 80 (kPa) (0°/0°)
3.6. Overview of the FE-model The geometry in the FE-model consists of four parts: a base representing the fixed part of the HDF equipment, a forming tool, a stack consisting of 8 plies, and the rubber diaphragm. A schematic figure of the FE-model is shown in Fig. 7. The plies are discretized using linear triangle elements in which the in-plane properties are implemented, and these are coupled with Kirchoff shell elements where the out-of-plane properties are defined. The ply size is 180 480 mm with a thickness of 0.131 mm. Each ply is meshed with 86,400 elements. The rubber diaphragm size is 380 480 mm and is 1.5 mm thick. It is meshed with 16,590 elements. The mesh is refined around the radius of the forming tool. Modelling vacuum pressure being applied is done by setting a pressure load on top of the diaphragm. The pressure is increased incrementally during 60 s until the full pressure of 100 kPa is reached. The rubber diaphragm is constrained in x, y and z directions along the edges attached to the base. At the edges parallel to the y-axis the diaphragm is constrained in x direction. 3.7. Determination of material properties Following the experimental study, the same two aerospace grade prepreg systems were also used in the numerical study. They both contained the same matrix, which was reinforced with toughening thermoplastic particles. The difference between the materials was the fibres used. In one of the systems an Intermediate Modulus (IM) fibre was used, while in the other a High Tenacity (HT) fibre was used. The two different systems are referred to as IM and HT respectively. 3.7.1. Inter-ply friction properties The inter-ply friction properties of the materials were tested using the same method as described previously in [3]. The testing equipment consisted of a middle plate was sheets of prepregs are placed on each side. Using a pneumatic cylinder two smaller plates also covered with prepreg are pressed against the larger middle plate. The rig is positioned in an Instron tensile testing machine
Fig. 5. Friction coefficient versus displacement for the friction tests, the vertical bars represent one standard deviation. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
which displaces the plates relative to each other at a constant speed. The parameters used in this study are presented in Table 1. The results are shown in Fig. 5. Three samples were tested for each material. 3.7.2. Intra-ply shear testing The shear properties of the different materials were compared using bias extension testing, using the same method as in [13,2]. Here the prepreg is stacked with the stacking sequence [45/ 45/ 45/45]. The sample size was 200 50 mm. The samples were pulled at a constant speed of 0.05 mm/min. The resulting load curves can be seen in Fig. 6. 3.8. Material models The matrix is modelled with an elastic model and a viscous model in parallel. The fibres are modelled as linear elastic. One problem with this approach is that carbon fibres are much stiffer
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J. Sjölander et al. / Composites: Part A 81 (2016) 41–51 Table 2 In-plane material properties. Linearly elastic fibre (HT) E (MPa) 1000
Linearly elastic fibre (IM) E (MPa) 1220
Viscoelastic matrix (HT) E (MPa) 0.0071 m (–) 0.33 g (MPa s) 10.6
Viscoelastic matrix (IM) E (MPa) 0.0011 m (–) 0.33 g (MPa s) 12.8
Table 3 Out-of-plane material properties. Orthotropic bending E1 (MPa) E2 (MPa) m12 (–) G12 (MPa)
100 0.95 0.33 18.34
Fig. 6. Load versus displacement curve for bias extension tests, the vertical bars represent one standard deviation. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
than the matrix, and this difference in stiffness can lead to numerical instabilities. For this reason the fibre stiffness is downscaled so that the fibres still take a very large part of the load while the difference in stiffness is not so large as to cause numerical problems. The values used are shown in Table 2. The bending properties of a layer are separated from its in-plane properties. The bending properties were obtained by carrying out a cantilever bending test that was calibrated against a replication of the test in AniForm. The test was performed at 70 °C in the fibre direction and the transverse fibre direction according to the standard in [14]. The bending stiffness was modelled with an orthotropic elastic model to simulate the difference in bending stiffness in the fibre direction and the transverse fibre direction. However it has proved to be difficult to calibrate the bending stiffness correctly. Generally, tests with cantilever beam bending appear to overestimate the bending stiffness in the fibre direction. This could perhaps be due to anticlastic bending which increases the apparent stiffness of the ply but is not captured by the calibration. For this reason the stiffness in the fibre direction is assumed to have a lower value than the one obtained from the calibration. The out-of-plane properties are shown in Table 3. The inter-ply friction properties were modelled as a combination of viscous friction and Coulomb friction in parallel. It is
Table 4 Inter-ply material properties. Coulomb-viscous friction (IM)
Coulomb-viscous friction (HT)
Coulomb-viscous friction (Mould)
l (–) g (MPa s)
l (–) g (MPa s)
l (–) g (MPa s)
t (mm)
0.0116 0.005 0.01
t (mm)
0.0116 0.00710 0.01
t (mm)
0.00579 0.0025 0.01
impossible to create a friction model that captures the entire range of deformation speeds and pressures that are present in the forming. Additionally the friction is likely to vary depending on the respective fibre directions as well [15]. For this reason the values for the friction were chosen for a deformation speed and pressure that was representative for the forming process. For inter-ply friction the data were based on the tests shown in Fig. 5. The friction between mould and ply was not tested. However based on experience with similar materials it was assumed that it was around half of the inter-ply friction. Between the top layer and the diaphragm, a plastic film is placed which is assumed to result in zero friction in the top interface. The frictional properties used are shown in Table 4. The rubber diaphragm is modelled with a Mooney–Rivlin material model, calibrated against tensile tests. The parameters used are presented in Table 5.
Fig. 7. Overview of the FE-model. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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that are close to the centre of the stack are studied to reduce the effects of this simplification.
Table 5 Rubber diaphragm material parameters. Mooney–Rivlin model C10 C01
1.4265 0.1953
4. Results
To illustrate the differences and similarities between forming a stack of prepreg and an isotropic sheet, a simulation of the forming of an isotropic sheet was carried out, using a Young’s modulus of 1 GPa and a Poissons ratio of 0.33. The sheet thickness used was 0.1 mm. Note however that these parameters do not correspond to an experiment and are not taken from a real material, the simulation is used for illustrative purposes only.
The results of the FE simulations for the cases in Table 6 are presented starting with the isotropic material working as a reference for how the membrane stresses cause wrinkling during forming. Then, the simulated forming process is studied stepwise in order to detect how the strains on the material change during the forming sequence. Based on this simulation, conclusions are drawn that enable comparison of the simulated forming outcome for each of the simulated cases with photographs of the corresponding sample from the experimental work.
3.9. Sample configurations tested
4.1. Forming of an isotropic material sheet
The simulated configurations are presented in Table 6. Each configuration, except for the isotropic single-layer, corresponds to an experiment performed by Hallander et al. [5]; however, not all experiments are covered in this paper. Note that, in the table the number of layers in the simulation is reduced from 32 to 8. This is because it was not possible to perform the simulation of a 32 layer stack on the computer hardware that was available. This causes a reduction in overall thickness, which in turn leads to stresses created due to bending the stack over the radius are reduced. The loss of repeating units in the stacking sequence also means that some interfaces are not represented. In the results plies
Fig. 8(a) shows the simulated forming of a single isotropic sheet over the geometry considered. In the zone marked A, wrinkles are initiated due to being formed over a convex feature. In zone B, wrinkles as a result of the shear deformation in the recess area, are instead developed. In general, membranes wrinkle when exposed to a combination of shear and compressive stresses. Looking at the simulated shear deformation after forming it becomes clear that the material shears locally mainly where the recess area starts and in its centre, while compressive and tensile strains develop in zone B, as indicated in Fig. 3. The latter is shown in Fig. 8(b), showing the compressive (in blue) and tensile (in red)
Table 6 Simulated lay-ups. ID
Explanation
Lay-up experiment
Lay-up simulation
Overall used prepreg material
Locally used prepreg material
Iso QI Ref IM IM 0 QI DL
Isotropic layer Reference Reduced friction in 0° layer Re-stacking to distance the 0° layer from the 45° layer Removing the 0° layer Cutting the 0° layer between zone A and B
– [( 45, 0, 45, 90)4]s [( 45, 0, 45, 90)4]s [(45, 45, 90, 0)4]s
[Iso] [45, 0, 45, 90]s [45, 0, 45, 90]s [45, 45, 90, 0]s
– HT HT IM
– – IM –
[(45, 90, 45, 90)4]s [(45, 0, 45, 90)4]s
[45, 90, 45, 90]s [45, 0, 45, 90]s
IM IM
– –
No 0 QI 0 cut
Fig. 8. Iso: (a) overview picture of the hot drape forming of a single isotropic layer and (b) normal strain in the references to color in this figure legend, the reader is referred to the web version of this article.)
45° direction for the isotropic layer. (For interpretation of the
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Fig. 9. QI Ref IM: strains in the 45° degree layer and the 90° layer, shown in 5 steps representing forming at 20%, 40%, 60%, 80% and 100%. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 10. QI Ref IM: (a) hot drape formed sample, (b) shear strain in the 45° ply (layer 3), and (c) transverse strain in the 90° ply (layer 4). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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Fig. 11. IM 0: (a) hot drape formed sample, (b) shear strain in the 45° ply (layer 3), and (c) transverse strain in the 90° ply (layer 4). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 12. QI DL: (a) hot drape formed sample, (b) shear strain in the 45° ply (layer 2), and (c) transverse strain in the 90° ply (layer 3). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 13. No 0: (a) hot drape formed sample, (b) shear strain in the 45° ply (layer 3), and (c) transverse strain in the 90° ply (layer 4). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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Fig. 14. QI 0 cut: (a) hot drape formed sample, (b) shear strain in the 45° ply (layer 3), and (c) transverse strain in the 90° ply (layer 4). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
strains developed in the 45° direction of the isotropic material following forming. 4.2. Simulation of the forming process Previously, two different causes for wrinkling were suggested, one being global compression of the entire stack due to excessive material and the other being local compression in single plies with fibre angles aligning with the direction of the compressive stresses. During forming of the reference sample, the compressive and tensile stresses in the 45° ply increase to a maximum at around 20– 60% of the forming according to simulations presented in Fig. 9. However since the matrix is viscous, relaxation of these stresses tends to occur. It is shown that as the forming progresses, compressive strains become in-plane waviness which can be identified as alternating positive and negative shear. Since the software used is built on continuum mechanical formulation and the mesh is not fine enough to capture wrinkle initiation, these high compressive stresses resulting in alternating shear appear to be the clearest sign of potential wrinkling. Which measure should then be used to indicate the degree of wrinkling that might be appearing? The compressive stresses developed at different stages of forming or the resulting degree of alternating shear? The former is easier to quantify, but requires high resolution in the saving of numerical data during forming simulations, which will increase calculation time. Further, the degree of wrinkling depends on the viscous behaviour of the material, its interply friction and interlaminar shear properties as well as the stiffness of the fibres, since a lower degree of compressive stresses may cause severe wrinkling in a less stiff material. Therefore, the final degree of alternating shear has been used here to qualitatively measure/visualise the degree of wrinkling appearing due to local compression in single plies. This further enables comparison of the simulation outcome with the photographs from the different forming trials performed in the experimental study. The choice of showing the 45° layer in Fig. 9 is not coincidental. Since the wrinkles appear diagonally in the transition zone, the compressive stress in the +45° and 45° layer is of interest. The reason that the 45° layer has been chosen is that, in the stacking sequence used in the simulations, the 45° is embedded in the stack while the +45° is always the outer layer. This means that the 45° is more representative of the angled plies in the experimental stacking sequence. In addition to the alternating shear developing as the local compressive stresses are relaxed, large compressive transverse strains develop at the convex outer radius of the recess area. This appears
in Fig. 9 for the 90° layer at 100% as blue areas between zones B and C. According to the assumptions on suggested wrinkle indicators in the paragraph of the same title, this could be an indication of global compression and wrinkling due to excessive material. Based on the discussions presented above, the following measures are used when comparing the experimental outcomes with forming simulations: the photograph of the formed beam with the stacking sequence considered, final predicted shear deformation in the 45° ply and compressive deformation perpendicular to the fibre direction in the 90° ply. 4.3. Quasi-isotropic reference In Fig. 10 the reference forming is shown. This is a quasiisotropic stack with HT fibres used throughout the stack. In Fig. 10(a) three possible wrinkling locations are shown for future reference. In Fig. 10(b) marcelling in location 2 can be seen, indicated by the alternating positive and negative shear. Fig. 10(a) shows the corresponding experiment where out-of-plane wrinkling is seen at the same location. This is expected since the 45° and the 0° are next to each other which leads to compressive stress in the 45° layer. It should be noted that the wrinkle at location 1 is not directly represented by marcelling in the shear deformation plot. In a related ongoing study, it has been observed that this wrinkle appears to occur due to local bending underneath the rubber diaphragm when the vacuum pressure is only partially applied. This does, however, only occur when there is an indication of wrinkling from marcelling in the simulations. Looking carefully at the radius of the beam, marcelling can also be detected in the middle of the beam. However, it seems as it is not transferred into any visible wrinkles. Fig. 10(c) shows the compressive transverse strain in the 90° ply at location 3, demonstrating that there is compressive strain where the geometry is convex. This compares well with wrinkles developed due to excessive material at the same position in the experimental study. 4.4. Reduced friction and increased stiffness in 0° layer Fig. 11 shows forming simulations as well as a photograph of a formed sample with HT material in all layers except the 0° layer, where IM fibres were used. This was represented in the simulation by reducing the friction in the interfaces surrounding the 0° ply. Again marcelling of the 45° ply at location 2 can be seen, indicating wrinkling due to local compression parallel to the fibres.
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Although friction was reduced, there was only a minor reduction compared to the reference stack. It is however interesting to note that as the degree of marcelling reduces slightly at location 2, a larger wrinkle appears at location 3, thereby reducing the wrinkle at position 1 as discussed for the reference sample. These results are in line with the simulation and experimental outcomes of the Reference stacking of only IM fibre prepreg, which also shows no major difference compared to the Reference stacking with HT fibres. 4.5. Re-stacking to distance the 0° layer from the
45° layer
In Fig. 12 the stacking sequence was changed to [45/ 45/90/0] to reduce the effect of the 0° layer interacting with the 45° layer. Fig. 12 shows the effect of reducing the interaction between the 0° and 45° by re-stacking so that the layers are separated by a 90° layer. This essentially creates a cross-ply laminate. Compared to Fig. 10(a), the out-of-plane wrinkling is significantly reduced. This is also apparent in Fig. 12(b), which shows some marcelling behaviour but not as severe as in Fig. 10(b). Thus separating the 0° and 45° reduces the interaction which reduces the tendency for wrinkling. This is confirmed by looking more carefully into the simulation, where it can be observed that the compressive stresses in the 45° ply are still present, but significantly lower. For the beam geometry considered, it as if like re-stacking is a good option for reducing wrinkles. However, it should be noted that for a more aggressive recess geometry requiring higher a degree of shearing, this might not be enough. Fig. 12(c) shows little compressive transverse strain at location 3 in the 90° ply which is now connected in an interface to the 0° ply, leading to it following a more ideal forming path. This is supported by the lesser degree of wrinkles observed on the experimental beam after forming. 4.6. Removing the 0° layer In Fig. 13 the 0° layer was replaced with a 90° layer resulting in the stacking sequence [45, 90, 45, 90]s. Fig. 13(a) shows that the experimental sample is almost wrinkle free. There are wrinkles at location 2 indicating that there is no, or very low, compression of the ±45° layers. However, instead the wrinkles at location 3 become more pronounced. This is probably an effect of that the 90° and ±45° is able to take more geodesic paths during the forming since there is no 0° layer present creating tension towards the middle. This behaviour is confirmed by the simulation (Fig. 13(b)) which shows that the 45° layer forms largely geodesic. There is no signs of marcelling at location 3, which is related to the total absence of a 0° layer, leading to less tendency of the 45° to shear in that area. Fig. 13(c) shows that there is a considerable degree of compressive strain at location 3. This is likely because the removal of the 0° ply allows for a larger degree of geodesic fibre pathing in the plies, resulting in excessive material in the convex areas. 4.7. Cutting the 0° layer between zones A and B In the sample shown in Fig. 12 a cut in the 0° layer was implemented by splitting the nodes along the two lines that separate zones A and B on the flange, marked with red lines in Fig. 14. This was done to investigate whether it was only the fibre tension from the 0° layer that caused wrinkling, or whether the layer itself influenced the forming outcome. In Fig. 14(a) the formed sample with the cut 0° layer is shown. As for the sample with no 0° layer, no wrinkles at location 2 are present, which also corresponds well with the simulation shown in Fig. 14(b) where no alternating shear can be seen. This is
because a cut in the 0° layer leads to a higher degree of folding outwards, reducing the tension in the middle and thereby reducing the amount of alternating shear of the 45° layer. Fig. 14(c) shows that the compressive transverse strain in the 90° layer is smaller for the cut sample than for the sample without the 0° layer, shown in Fig. 13(c), although the actual wrinkles are larger. This is probably related to the fact that the stack is more sensitive to buckling when there are fibres (in this case the 0° layer) parallel to the load. 5. Conclusions This paper addresses experimental findings on wrinkle development during forming of multi-layer UD prepreg onto a 3D beam geometry. Two different causes for wrinkle development are presented, referred to as global buckling of the entire stack of material or local compression of single layers. Global buckling is assumed to occur due to excessive material during forming of e.g. convex geometries. Local compression followed by wrinkling, on the other hand, is shown to occur as the material shear during forming, causing compressive stresses in the material. The plies with fibres parallel to the compressive stresses are more likely to buckle, which incite out-of-plane wrinkles. FE-simulations performed show that the compressive stresses develop in critical layers of a stacked UD material during forming. However, as forming proceeds, these stresses relax into in-plane wrinkling shown as alternating positive and negative shear strain, also known as marcelling. Comparing the forming simulations to the experimental forming study, it becomes clear that local compression followed by marcelling coincides with wrinkles appearing during forming. Global wrinkling that typically occurs on convex features of the geometry, could in the FE-simulations be identified as transverse strains. It is shown that by changing the stacking sequence, removing or cutting the 0° ply, wrinkles at certain locations can be avoided. The changed stacking is also corresponded to a lower degree of marcelling these locations in the simulation. The simulations show good predictions considering when and where different kinds of wrinkles appear during the forming of the geometry considered. However, the methodology used is generic and should therefore be applicable for predictive forming on other geometries and with a greater variety of material systems than considered herein. Acknowledgements The work was funded through VINNOVA under the program Green Flying Demonstrator (GF Demo). Funding was also generously provided by the strategic research program LIGHTer SRA1. References [1] Tam AS, Gutowski TG. The kinematics for forming ideal aligned fibre composites into complex shapes. Compos Manuf 1990;1(4):219–28. [2] Larberg YR, Åkermo M, Norrby M. On the in-plane deformability of cross-plied unidirectional prepreg. J Compos Mater 2012;46(8):929–39. [3] Larberg YR, Åkermo M. On the interply friction of different generations of carbon/epoxy prepreg systems. Compos Part A: Appl Sci Manuf 2011;42 (9):1067–74. [4] Hallander P, Åkermo M, Mattei C, Petersson M, Nyman T. An experimental study of mechanisms behind wrinkle development during forming of composite laminates. Compos Part A: Appl Sci Manuf 2013;50:54–64. [5] Hallander P, Sjölander J, Åkermo M. Forming induced wrinkling of composite laminates with mixed ply material properties; an experimental study. Compos Part A: Appl Sci Manuf 2015;78:234–45. [6] Sun J, Gu Y, Li M, Ma X, Zhang Z. Effect of forming temperature on the quality of hot diaphragm formed C-shaped thermosetting composite laminates. J Reinf Plast Compos 2012;31(16):1074–87. [7] Lightfoot JS, Wisnom MR, Potter K. A new mechanism for the formation of ply wrinkles due to shear between plies. Compos Part A: Appl Sci Manuf 2013;49:139–47.
J. Sjölander et al. / Composites: Part A 81 (2016) 41–51 [8] Haanappel SP, ten Thije RHW, Sachs U, Rietman B, Akkerman R. Formability analyses of uni-directional and textile reinforced thermoplastics. Compos Part A: Appl Sci Manuf 2014;56:80–92. [9] Boisse P, Hamila N, Vidal-Sallé E, Dumont F. Simulation of wrinkling during textile composite reinforcement forming. Influence of tensile, in-plane shear and bending stiffnesses. Compos Sci Technol 2011;71(5):683–92. [10] Dodwell TJ. Internal wrinkling instabilities in layered media. Philos Mag 2015:1–19. [11] Larberg Y. Forming of stacked unidirectional prepreg materials. KTH, Lightweight Structures; 2012. QC 20121204.
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[12] AniForm Virtual Forming Tool.. [13] Potter K. Bias extension measurements on cross-plied unidirectional prepreg. Compos Part A: Appl Sci Manuf 2002;33(1):63–73. [14] ASTM D1388-07. Standard Test Method for Stiffness of Fabrics. West Conshohocken, PA: ASTM International; 2007. [15] Åkermo M, Larberg Y, Sjölander J, Hallander P. Influence of interply friction on the forming of stacked UD prepreg. In: Proceedings of the 19th international conference on composite materials; 2013. p. 919–28.
Contents lists available at ScienceDirect
Composites: Part A journal homepage: www.elsevier.com/locate/compositesa
Forming induced wrinkling of composite laminates: A numerical study on wrinkling mechanisms J. Sjölander a,⇑, P. Hallander b, M. Åkermo a a b
Department of Aeronautical and Vehicle Engineering, KTH Royal Institute of Technology, 100 44 Stockholm, Sweden SAAB AB, Linköping, Sweden
a r t i c l e
i n f o
Article history: Received 30 June 2015 Received in revised form 7 October 2015 Accepted 10 October 2015 Available online 30 October 2015 Keywords: A. Prepreg C. Process simulation E. Forming
a b s t r a c t When manufacturing composite aircraft components consisting of uni-directional prepreg laminates, Hot Drape Forming (HDF) is sometimes used. One issue with HDF is that, in contrast to hand lay-up where normally only one ply is laid up at a time, multiple plies are formed together. This limits the in-plane deformability of the stack, thus increasing the risk of out-of-plane wrinkling during forming. In this paper mechanisms responsible for creating different types of wrinkles are explained. It is shown through simulations how the wrinkles are created as a result of interaction between two layers with specific fibre directions or due to compression of the entire stack. The simulations are compared to experimental results with good agreement. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction In the aircraft industry weight is a critical property. Reducing the weight of an aircraft directly increases possible payload, which in turn gives a more fuel efficient transport system. For this reason composites have seen increased use in the past couple of decades due to their light weight, high stiffness and high strength. This increase has grown from a few percentage of the weight of an aircraft and is steadily increasing, up to this point where for example the latest Boeing 787 Dreamliner has 50% (by weight) composite material in its structural parts. The dominating material system when it comes to composites in structural aircraft components is pre-impregnated carbon fibres (prepregs). With the increasing use of prepregs, growing interest has followed in increasing the level of automation in production. To date several different automated processes have been developed for the lay-up and forming of prepregs, and these include Automatic Tape Laying (ATL), Advanced Fiber Placement (AFP) and Hot Drape Forming (HDF). However manual lay-up is still common, especially for more complex parts where automatic processes cannot achieve the necessary quality. The forming behaviour for these processes in general but in HDF in particular, is very dependent on the material properties of the prepreg. This is because it requires the forming of a multi-layer stack, where each ply through the thickness has a fibre angle which ⇑ Corresponding author. Tel.: +46 73 460 25 11. E-mail address: [email protected] (J. Sjölander). http://dx.doi.org/10.1016/j.compositesa.2015.10.012 1359-835X/Ó 2015 Elsevier Ltd. All rights reserved.
might be different to its neighbouring plies. Tam and Gutowski [1] showed that forming complex geometries using single unidirectional prepreg plies in the ideal case only requires non-area changing shear of the individual plies. This is because, unlike weaves where the warp is interconnected with the weft, a UD prepreg can, in theory shear without a reduction in area. Other studies have, however, shown that in practice due to tackiness, stacked UD prepreg materials normally form similar to woven material when it comes to inter-ply shear, but with the ability to also shear inbetween each separate layer. Earlier studies [2,3] have shown that material properties important to forming, such as inter-ply friction and intra-ply shear may vary significantly between seemingly very similar material systems, and these significantly change the forming outcome. In practice these materials are certified for use for the same type of applications, i.e. load-bearing aircraft parts. When forming a multi-layer stack over a complex tool geometry using a rubber diaphragm such as in HDF, forming forces and directions are determined by the geometry in combination with material properties and the stacking sequence of the material used. The latter means that while the stack undergoes the same global forming behaviour, separate plies adopt by moving relative to each other, since no deformation can occur parallel to the fibre deformation. The importance of using a stacking sequence that forms well over the geometry considered was first demonstrated by Hallander et al. in [4] where it was shown that, depending on which layers were combined, different forming results were obtained. In a later work [5], this was further exploited by studying the feasibility of using locally changed material properties, i.e. higher inter-ply
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friction, inter-ply shear or fibre stiffness, to steer the local forming behaviour in-between plies. Also separate plies were cut to reduce the fibre tension and shear forces developed in the material. In brief the study, which is later summarised as providing the experimental input to this paper, shows that although using locally different material properties may improve the forming outcome, using a good stacking sequence appears to be the only reliable method of overcoming any tendency of wrinkle development. This is partly supported by studies by e.g. Sun et al. [6], who examined the influence of changing friction in 2D forming, in this case forming a 90° angle. This was achieved by changing the forming temperature. Lower temperature meant higher friction, which in turn increased the defects after forming due to the layers not being able to slip sufficiently relative to each other. Also Lightfoot et al. [7] showed that, depending on the friction between the mould and the first ply, a wrinkle can be created. They also showed that, depending on the stacking sequence of the laminate, different wrinkles were formed, which also indicated that locally changing friction in an interface may change the global forming behaviour. Haanappel et al. [8] studied the forming of a complex, authentic geometry both in experiments and simulations. Both weaves and quasi-isotropic, uni-directional laminates were used. They saw that the two materials behaved quite differently where the unidirectional laminate showed a greater tendency to create wrinkles than the weave. They also noticed that a higher bending stiffness would lead to less wrinkles and more shearing in the material. Boisse et al. [9] performed both experiments and simulations of the forming of single layer, dry woven reinforcement onto a half sphere and a tetrahedral shape. They concluded that shearing of the material could lead to compressive stresses that in turn led to wrinkles. The magnitude of the bending stiffness decided how many wrinkles appeared, where low bending stiffness tends to lead to many small wrinkles while a larger bending stiffness led to a few, but larger wrinkles. Dodwell [10] developed a model for layered materials, which was able to predict out-of-plane wrinkling, in a case where a stack of prepreg were consolidated on a tool radius. Since HDF of multi-layer UD prepreg materials on a global level is highly dependent on the stacking sequence, detailed forming simulations are required considering the relative movement of each separate ply. Further, the simulations must predict the entire forming sequence, since wrinkles do not necessarily develop after the final forming step. However, while there is FE software that enables this kind of modelling, it is normally based on continuum mechanical approaches. It has been shown difficult to predict wrinkling in separate layers in critical areas. This has been commented by Larberg in e.g. [11]. According to Hallander et al. [4], such critical areas could be where separate plies undergo compression, while the stack globally is in tension.
Fig. 1. Geometry used in the forming experiments.
This paper aims to clarify the experimental findings in [5] by performing numerical simulations that enable the description of the forming sequence and the mechanical loads each separate must sustain during forming. Relating to the experimental findings, different kinds of wrinkles are discussed: those arising globally from excessive materials and those initiated locally due to single layers in compression. Further, for reasons explained above, since wrinkles developed due to local compressive stresses will not be detected in continuum-based simulations, the paper aims to find early wrinkle indicators that can be used in future simulations to detect wrinkle-prone areas. Experiments and numerical simulation are performed on a straight beam with a recess area, requiring 3D forming; however, the method developed based on wrinkle indicators is general and can be applied to any geometry used for forming of stacked materials.
2. Experimental background The numerical study presented in this paper aims to further the understanding of wrinkle development during forming of stacked UD prepreg. It is based on a experimental study, which is briefly summarised below. For further details the reader is referred to the study by Hallander et al. [5]. The aim of the experimental study was to examine whether wrinkle development could be avoided by either making the lamina more wrinkling resistant, or by reducing the compression developed in separate layers. The latter was achieved either by locally changing the friction properties in critical layers, by reducing the number of interfaces causing compression or by decreasing compression by reducing global tension. Improved wrinkling resistance was obtained by using locally stiffer fibres or using co-stacked layers. The experimental study was performed on a spar with a recess area in one flange according to Fig. 1. Two different 180 °C cure epoxy prepreg materials were used in the study: one containing HT (High Tenacity) fibre and the other containing IM (Intermediate Modulus) fibre. Except for having higher stiffness, the current paper shows that the IM fibre prepreg material has 40–50% lower inter-ply, prepreg–prepreg, friction and 30% lower intra-ply shear resistance than its HT counterpart, although the matrix is practically the same. A reference stacking sequence defined as [( 45, 0, 45, 90)4]s was used to manufacture samples containing either HT material, IM material or a combination of the two. Another stacking sequence: [(45, 45, 90, 0)4]s was used in order to halve the number of interfaces between the [±45] and [0] direction. In order to reduce the tension towards the centre of the recess area, the [0] direction was either removed from the stacking, as in [(45, 90, 45, 90)4]s stacking, or cut. Cutting was either performed throughout all the layers in the stack in a reference stacking or only on the [0] direction. Finally, as an attempt to increase the buckling resistance of the lamina, and at the same time reduce the numbers of expected critical interfaces, co-stacked layers were considered in two different configurations: [454, 04, 454, 04]s and [454, 904, 454, 904]s. After forming, wrinkles appeared in different positions: 1. horizontally in the centre of the recess area, 2. diagonally just below the radius at the start of the recess area, 3. vertically at the convex radius of the recess area and 4 on the centre of the web, across the beam. The results showed that appearance of wrinkles at position 1 was closely connected to the combination of 0° and 45° interfaces. It was shown that the wrinkles became smaller when reducing the inter-ply friction in-between these layers or just reducing the number of 0° and 45° interfaces. This seems to be caused by the tension provided by the 0° layer, since cutting this layer (or the entire stack) eliminated wrinkles developed in position 1.
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However instead, wrinkles in position 3 developed, which were not there initially. The same result was shown for the stacking having no 0° direction at all. In order to make a significant improvement, co-stacking of critical layers to increase buckling resistance was required. This created no visible out-of-plane wrinkling; however, micrographs of the cross-section showed out-of-plane waviness even for these samples. Total absence of wrinkling was only reached when using a different fibre stacking avoiding difficult fibre angle combinations.
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Fig. 2. Draping of a stiff ply into the recession area.
3. Wrinkle development When forming a stack of prepreg onto a geometry with double curvature, it is necessary for the stack to undergo in-plane deformation. This may be through shear or normal strain. If the degree of in-plane deformation is not sufficient for the stack to conform to the geometry at hand, out-of-plane wrinkling will occur. The authors of this paper are suggesting that the out-of-plane wrinkling of a laminate can be caused in at least two general ways: either the whole stack is put under compressive stress, leading to buckling of the stack. Alternatively a single layer in the stack is put in compression creating buckling, which then propagates and creates wrinkling of the stack. These two cases are explained further below.
Fig. 3. Shearing in zone B and the resulting strains. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Here we consider wrinkling of a laminate due to local compression of one layer in the stack. Consider an element subject to shear stress, the shear stress can be transformed into normal stresses rotated 45° from the applied shear stress by for example using Mohr’s circle. If the direction of the stress is aligned with the fibre direction, either tensile or compressive stress in the fibre will be created. While a tensile stress in the fibre direction is normally not critical for the forming outcome, significant compressive stresses in the fibre direction can cause buckling of the fibres, either in-plane or out-of-plane, and thereby causing wrinkling. This behaviour does not necessarily have to occur on a convex geometry, where it is more likely that global compression of the entire stack occurs. Hallander et al. [4] showed that this is a possible mechanism on a geometry requiring 3D forming, even in concave features that require global tension of the stack to form into.
As shown in Fig. 2, because of the recess area, the forming introduces shear by up to 2.86° in zone B. This is illustrated by the theoretical draping of a completely stiff fabric which has to be cut between zones A and B to conform to the geometry; from this it can be seen that it is necessary for some degree of shear in zone B to cover the ‘‘gaps” created by the forming. In Fig. 3 we see the ply after it has sheared to cover the gap. The shearing in zone B induces compressive stress in the 45° direction and tensile stress in the 45° direction. This holds independently of material used. However, it should be noted that while an isotropic generic material forms locally, forming of a stacked material with UD fibres in different directions causes fibre slippage and shear and thereby changes the material outside the actual forming area. Further, in multi-layer forming, each layer shows different deformability in zone B depending on its relative fibre angle. Focusing specifically on the 45° ply, it can be seen that the compressive stresses developed in zone B align with the fibre direction creating a risk of buckling. This should be the worst case scenario, since compressive stresses perpendicular to the fibres compact the fibre bed only and tensile stresses are easily carried by the fibres without buckling. The amount of compressive stress developed in zone B depends on the recess angle, i.e. the length to depth relationship of the recess area. Thus a reduction in recess angle should lead to a reduction in compressive stress. Now we consider a combination of layers as in a stack of UD prepreg. A 0° layer will deform closely to the ideal forming pattern since the fibres cover the gap completely, and this is shown in Fig. 4(a). The 90° on the other hand, as shown in Fig. 4(b), will form in a more geodesic manner since there is almost nothing stopping the ply to develop large transverse strains. Consequently the ±45° layers will fall somewhere in between. If we consider the pairing of layers, combining a 45° with a 0° will result in a relatively a high degree of shear and consequently high compressive stresses of the 45° since it is connected to the deformation of the 0°. Conversely pairing the 45° with a 90° will result in a lower degree of shear.
3.3. Forming onto a beam with a recess area
3.4. Proposed wrinkle indicators
The wrinkle development described here could be generic to any double curved geometry. However in this work the geometry in Fig. 1 is analysed. This is because it has been studied in [4,5] and the forming behaviour is therefore known. This gives the opportunity to study both the wrinkle development and different ways to mitigate it. It has a recess area on one flange with a depth of 6.25 mm. Since it is formed using hot drape forming the stack is placed on top of the beam and then gradually formed down onto the recess area marked A, B and C.
Based on the discussion of the material deformation above, the following assumptions are used when looking for wrinkle indicators in the simulation describing the forming of multi-layer UD prepreg:
3.1. Wrinkling due to global compression If the stack is formed over a convex geometry, wrinkles may be created basically because there is excess material that has to be collected in a wrinkle. Or in other words: wrinkling may arise from too high shear stiffness of the stack in relation to its bending stiffness during forming over any double curvature geometry requiring material shear. This type of wrinkling is general for all materials. 3.2. Wrinkling due to compression in a layer with a specific fibre direction
Local compressive stresses in the fibre direction in single layers during instants of forming are always an indicator that wrinkling may occur. In [5], it is shown that even if wrinkles cannot be seen from the outside due to the high buckling stability of
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the outer layers, microscope pictures indicate that it is difficult to avoid layer thickening and/or wrinkling inside the lamina at areas with high compressive stresses. When high local compression in single layers occurs and the FEmodel does not have enough fidelity to represent wrinkle development geometrically, the simulation outcome will naturally differ from the experimental findings. Instead indicators, such as stress in the fibre direction or apparent marcelling have to be used instead. Global compressive stresses resulting in wrinkling can most easily be determined by studying the compressive strain transversely to the fibre direction, since these areas will deform the most during wrinkle development. Fig. 4. (a) Ideal forming of a 0° ply and (b) geodesic forming of a 90° ply.
These indicators are general and may be used to study both locally and globally-induced wrinkling on a generic geometry. 3.5. FE-model The software Aniform v3.0.1 was used for the simulations [12]. This is a Finite Element software designed for composite forming. Aniform allows different models to be used for in-plane and outof-plane behaviour. This is an advantage because of the anisotropy of uncured prepregs. Additionally, friction between the layers and between the layers and the mould can be modelled with greater freedom by using combinations of different material models.
Table 1 Parameters used in the friction testing. Property
Value
Temperature Crosshead speed Normal pressure Relative fibre direction
70 (°C) 0.05 (mm/s) 80 (kPa) (0°/0°)
3.6. Overview of the FE-model The geometry in the FE-model consists of four parts: a base representing the fixed part of the HDF equipment, a forming tool, a stack consisting of 8 plies, and the rubber diaphragm. A schematic figure of the FE-model is shown in Fig. 7. The plies are discretized using linear triangle elements in which the in-plane properties are implemented, and these are coupled with Kirchoff shell elements where the out-of-plane properties are defined. The ply size is 180 480 mm with a thickness of 0.131 mm. Each ply is meshed with 86,400 elements. The rubber diaphragm size is 380 480 mm and is 1.5 mm thick. It is meshed with 16,590 elements. The mesh is refined around the radius of the forming tool. Modelling vacuum pressure being applied is done by setting a pressure load on top of the diaphragm. The pressure is increased incrementally during 60 s until the full pressure of 100 kPa is reached. The rubber diaphragm is constrained in x, y and z directions along the edges attached to the base. At the edges parallel to the y-axis the diaphragm is constrained in x direction. 3.7. Determination of material properties Following the experimental study, the same two aerospace grade prepreg systems were also used in the numerical study. They both contained the same matrix, which was reinforced with toughening thermoplastic particles. The difference between the materials was the fibres used. In one of the systems an Intermediate Modulus (IM) fibre was used, while in the other a High Tenacity (HT) fibre was used. The two different systems are referred to as IM and HT respectively. 3.7.1. Inter-ply friction properties The inter-ply friction properties of the materials were tested using the same method as described previously in [3]. The testing equipment consisted of a middle plate was sheets of prepregs are placed on each side. Using a pneumatic cylinder two smaller plates also covered with prepreg are pressed against the larger middle plate. The rig is positioned in an Instron tensile testing machine
Fig. 5. Friction coefficient versus displacement for the friction tests, the vertical bars represent one standard deviation. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
which displaces the plates relative to each other at a constant speed. The parameters used in this study are presented in Table 1. The results are shown in Fig. 5. Three samples were tested for each material. 3.7.2. Intra-ply shear testing The shear properties of the different materials were compared using bias extension testing, using the same method as in [13,2]. Here the prepreg is stacked with the stacking sequence [45/ 45/ 45/45]. The sample size was 200 50 mm. The samples were pulled at a constant speed of 0.05 mm/min. The resulting load curves can be seen in Fig. 6. 3.8. Material models The matrix is modelled with an elastic model and a viscous model in parallel. The fibres are modelled as linear elastic. One problem with this approach is that carbon fibres are much stiffer
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J. Sjölander et al. / Composites: Part A 81 (2016) 41–51 Table 2 In-plane material properties. Linearly elastic fibre (HT) E (MPa) 1000
Linearly elastic fibre (IM) E (MPa) 1220
Viscoelastic matrix (HT) E (MPa) 0.0071 m (–) 0.33 g (MPa s) 10.6
Viscoelastic matrix (IM) E (MPa) 0.0011 m (–) 0.33 g (MPa s) 12.8
Table 3 Out-of-plane material properties. Orthotropic bending E1 (MPa) E2 (MPa) m12 (–) G12 (MPa)
100 0.95 0.33 18.34
Fig. 6. Load versus displacement curve for bias extension tests, the vertical bars represent one standard deviation. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
than the matrix, and this difference in stiffness can lead to numerical instabilities. For this reason the fibre stiffness is downscaled so that the fibres still take a very large part of the load while the difference in stiffness is not so large as to cause numerical problems. The values used are shown in Table 2. The bending properties of a layer are separated from its in-plane properties. The bending properties were obtained by carrying out a cantilever bending test that was calibrated against a replication of the test in AniForm. The test was performed at 70 °C in the fibre direction and the transverse fibre direction according to the standard in [14]. The bending stiffness was modelled with an orthotropic elastic model to simulate the difference in bending stiffness in the fibre direction and the transverse fibre direction. However it has proved to be difficult to calibrate the bending stiffness correctly. Generally, tests with cantilever beam bending appear to overestimate the bending stiffness in the fibre direction. This could perhaps be due to anticlastic bending which increases the apparent stiffness of the ply but is not captured by the calibration. For this reason the stiffness in the fibre direction is assumed to have a lower value than the one obtained from the calibration. The out-of-plane properties are shown in Table 3. The inter-ply friction properties were modelled as a combination of viscous friction and Coulomb friction in parallel. It is
Table 4 Inter-ply material properties. Coulomb-viscous friction (IM)
Coulomb-viscous friction (HT)
Coulomb-viscous friction (Mould)
l (–) g (MPa s)
l (–) g (MPa s)
l (–) g (MPa s)
t (mm)
0.0116 0.005 0.01
t (mm)
0.0116 0.00710 0.01
t (mm)
0.00579 0.0025 0.01
impossible to create a friction model that captures the entire range of deformation speeds and pressures that are present in the forming. Additionally the friction is likely to vary depending on the respective fibre directions as well [15]. For this reason the values for the friction were chosen for a deformation speed and pressure that was representative for the forming process. For inter-ply friction the data were based on the tests shown in Fig. 5. The friction between mould and ply was not tested. However based on experience with similar materials it was assumed that it was around half of the inter-ply friction. Between the top layer and the diaphragm, a plastic film is placed which is assumed to result in zero friction in the top interface. The frictional properties used are shown in Table 4. The rubber diaphragm is modelled with a Mooney–Rivlin material model, calibrated against tensile tests. The parameters used are presented in Table 5.
Fig. 7. Overview of the FE-model. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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that are close to the centre of the stack are studied to reduce the effects of this simplification.
Table 5 Rubber diaphragm material parameters. Mooney–Rivlin model C10 C01
1.4265 0.1953
4. Results
To illustrate the differences and similarities between forming a stack of prepreg and an isotropic sheet, a simulation of the forming of an isotropic sheet was carried out, using a Young’s modulus of 1 GPa and a Poissons ratio of 0.33. The sheet thickness used was 0.1 mm. Note however that these parameters do not correspond to an experiment and are not taken from a real material, the simulation is used for illustrative purposes only.
The results of the FE simulations for the cases in Table 6 are presented starting with the isotropic material working as a reference for how the membrane stresses cause wrinkling during forming. Then, the simulated forming process is studied stepwise in order to detect how the strains on the material change during the forming sequence. Based on this simulation, conclusions are drawn that enable comparison of the simulated forming outcome for each of the simulated cases with photographs of the corresponding sample from the experimental work.
3.9. Sample configurations tested
4.1. Forming of an isotropic material sheet
The simulated configurations are presented in Table 6. Each configuration, except for the isotropic single-layer, corresponds to an experiment performed by Hallander et al. [5]; however, not all experiments are covered in this paper. Note that, in the table the number of layers in the simulation is reduced from 32 to 8. This is because it was not possible to perform the simulation of a 32 layer stack on the computer hardware that was available. This causes a reduction in overall thickness, which in turn leads to stresses created due to bending the stack over the radius are reduced. The loss of repeating units in the stacking sequence also means that some interfaces are not represented. In the results plies
Fig. 8(a) shows the simulated forming of a single isotropic sheet over the geometry considered. In the zone marked A, wrinkles are initiated due to being formed over a convex feature. In zone B, wrinkles as a result of the shear deformation in the recess area, are instead developed. In general, membranes wrinkle when exposed to a combination of shear and compressive stresses. Looking at the simulated shear deformation after forming it becomes clear that the material shears locally mainly where the recess area starts and in its centre, while compressive and tensile strains develop in zone B, as indicated in Fig. 3. The latter is shown in Fig. 8(b), showing the compressive (in blue) and tensile (in red)
Table 6 Simulated lay-ups. ID
Explanation
Lay-up experiment
Lay-up simulation
Overall used prepreg material
Locally used prepreg material
Iso QI Ref IM IM 0 QI DL
Isotropic layer Reference Reduced friction in 0° layer Re-stacking to distance the 0° layer from the 45° layer Removing the 0° layer Cutting the 0° layer between zone A and B
– [( 45, 0, 45, 90)4]s [( 45, 0, 45, 90)4]s [(45, 45, 90, 0)4]s
[Iso] [45, 0, 45, 90]s [45, 0, 45, 90]s [45, 45, 90, 0]s
– HT HT IM
– – IM –
[(45, 90, 45, 90)4]s [(45, 0, 45, 90)4]s
[45, 90, 45, 90]s [45, 0, 45, 90]s
IM IM
– –
No 0 QI 0 cut
Fig. 8. Iso: (a) overview picture of the hot drape forming of a single isotropic layer and (b) normal strain in the references to color in this figure legend, the reader is referred to the web version of this article.)
45° direction for the isotropic layer. (For interpretation of the
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Fig. 9. QI Ref IM: strains in the 45° degree layer and the 90° layer, shown in 5 steps representing forming at 20%, 40%, 60%, 80% and 100%. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 10. QI Ref IM: (a) hot drape formed sample, (b) shear strain in the 45° ply (layer 3), and (c) transverse strain in the 90° ply (layer 4). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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Fig. 11. IM 0: (a) hot drape formed sample, (b) shear strain in the 45° ply (layer 3), and (c) transverse strain in the 90° ply (layer 4). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 12. QI DL: (a) hot drape formed sample, (b) shear strain in the 45° ply (layer 2), and (c) transverse strain in the 90° ply (layer 3). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 13. No 0: (a) hot drape formed sample, (b) shear strain in the 45° ply (layer 3), and (c) transverse strain in the 90° ply (layer 4). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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Fig. 14. QI 0 cut: (a) hot drape formed sample, (b) shear strain in the 45° ply (layer 3), and (c) transverse strain in the 90° ply (layer 4). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
strains developed in the 45° direction of the isotropic material following forming. 4.2. Simulation of the forming process Previously, two different causes for wrinkling were suggested, one being global compression of the entire stack due to excessive material and the other being local compression in single plies with fibre angles aligning with the direction of the compressive stresses. During forming of the reference sample, the compressive and tensile stresses in the 45° ply increase to a maximum at around 20– 60% of the forming according to simulations presented in Fig. 9. However since the matrix is viscous, relaxation of these stresses tends to occur. It is shown that as the forming progresses, compressive strains become in-plane waviness which can be identified as alternating positive and negative shear. Since the software used is built on continuum mechanical formulation and the mesh is not fine enough to capture wrinkle initiation, these high compressive stresses resulting in alternating shear appear to be the clearest sign of potential wrinkling. Which measure should then be used to indicate the degree of wrinkling that might be appearing? The compressive stresses developed at different stages of forming or the resulting degree of alternating shear? The former is easier to quantify, but requires high resolution in the saving of numerical data during forming simulations, which will increase calculation time. Further, the degree of wrinkling depends on the viscous behaviour of the material, its interply friction and interlaminar shear properties as well as the stiffness of the fibres, since a lower degree of compressive stresses may cause severe wrinkling in a less stiff material. Therefore, the final degree of alternating shear has been used here to qualitatively measure/visualise the degree of wrinkling appearing due to local compression in single plies. This further enables comparison of the simulation outcome with the photographs from the different forming trials performed in the experimental study. The choice of showing the 45° layer in Fig. 9 is not coincidental. Since the wrinkles appear diagonally in the transition zone, the compressive stress in the +45° and 45° layer is of interest. The reason that the 45° layer has been chosen is that, in the stacking sequence used in the simulations, the 45° is embedded in the stack while the +45° is always the outer layer. This means that the 45° is more representative of the angled plies in the experimental stacking sequence. In addition to the alternating shear developing as the local compressive stresses are relaxed, large compressive transverse strains develop at the convex outer radius of the recess area. This appears
in Fig. 9 for the 90° layer at 100% as blue areas between zones B and C. According to the assumptions on suggested wrinkle indicators in the paragraph of the same title, this could be an indication of global compression and wrinkling due to excessive material. Based on the discussions presented above, the following measures are used when comparing the experimental outcomes with forming simulations: the photograph of the formed beam with the stacking sequence considered, final predicted shear deformation in the 45° ply and compressive deformation perpendicular to the fibre direction in the 90° ply. 4.3. Quasi-isotropic reference In Fig. 10 the reference forming is shown. This is a quasiisotropic stack with HT fibres used throughout the stack. In Fig. 10(a) three possible wrinkling locations are shown for future reference. In Fig. 10(b) marcelling in location 2 can be seen, indicated by the alternating positive and negative shear. Fig. 10(a) shows the corresponding experiment where out-of-plane wrinkling is seen at the same location. This is expected since the 45° and the 0° are next to each other which leads to compressive stress in the 45° layer. It should be noted that the wrinkle at location 1 is not directly represented by marcelling in the shear deformation plot. In a related ongoing study, it has been observed that this wrinkle appears to occur due to local bending underneath the rubber diaphragm when the vacuum pressure is only partially applied. This does, however, only occur when there is an indication of wrinkling from marcelling in the simulations. Looking carefully at the radius of the beam, marcelling can also be detected in the middle of the beam. However, it seems as it is not transferred into any visible wrinkles. Fig. 10(c) shows the compressive transverse strain in the 90° ply at location 3, demonstrating that there is compressive strain where the geometry is convex. This compares well with wrinkles developed due to excessive material at the same position in the experimental study. 4.4. Reduced friction and increased stiffness in 0° layer Fig. 11 shows forming simulations as well as a photograph of a formed sample with HT material in all layers except the 0° layer, where IM fibres were used. This was represented in the simulation by reducing the friction in the interfaces surrounding the 0° ply. Again marcelling of the 45° ply at location 2 can be seen, indicating wrinkling due to local compression parallel to the fibres.
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Although friction was reduced, there was only a minor reduction compared to the reference stack. It is however interesting to note that as the degree of marcelling reduces slightly at location 2, a larger wrinkle appears at location 3, thereby reducing the wrinkle at position 1 as discussed for the reference sample. These results are in line with the simulation and experimental outcomes of the Reference stacking of only IM fibre prepreg, which also shows no major difference compared to the Reference stacking with HT fibres. 4.5. Re-stacking to distance the 0° layer from the
45° layer
In Fig. 12 the stacking sequence was changed to [45/ 45/90/0] to reduce the effect of the 0° layer interacting with the 45° layer. Fig. 12 shows the effect of reducing the interaction between the 0° and 45° by re-stacking so that the layers are separated by a 90° layer. This essentially creates a cross-ply laminate. Compared to Fig. 10(a), the out-of-plane wrinkling is significantly reduced. This is also apparent in Fig. 12(b), which shows some marcelling behaviour but not as severe as in Fig. 10(b). Thus separating the 0° and 45° reduces the interaction which reduces the tendency for wrinkling. This is confirmed by looking more carefully into the simulation, where it can be observed that the compressive stresses in the 45° ply are still present, but significantly lower. For the beam geometry considered, it as if like re-stacking is a good option for reducing wrinkles. However, it should be noted that for a more aggressive recess geometry requiring higher a degree of shearing, this might not be enough. Fig. 12(c) shows little compressive transverse strain at location 3 in the 90° ply which is now connected in an interface to the 0° ply, leading to it following a more ideal forming path. This is supported by the lesser degree of wrinkles observed on the experimental beam after forming. 4.6. Removing the 0° layer In Fig. 13 the 0° layer was replaced with a 90° layer resulting in the stacking sequence [45, 90, 45, 90]s. Fig. 13(a) shows that the experimental sample is almost wrinkle free. There are wrinkles at location 2 indicating that there is no, or very low, compression of the ±45° layers. However, instead the wrinkles at location 3 become more pronounced. This is probably an effect of that the 90° and ±45° is able to take more geodesic paths during the forming since there is no 0° layer present creating tension towards the middle. This behaviour is confirmed by the simulation (Fig. 13(b)) which shows that the 45° layer forms largely geodesic. There is no signs of marcelling at location 3, which is related to the total absence of a 0° layer, leading to less tendency of the 45° to shear in that area. Fig. 13(c) shows that there is a considerable degree of compressive strain at location 3. This is likely because the removal of the 0° ply allows for a larger degree of geodesic fibre pathing in the plies, resulting in excessive material in the convex areas. 4.7. Cutting the 0° layer between zones A and B In the sample shown in Fig. 12 a cut in the 0° layer was implemented by splitting the nodes along the two lines that separate zones A and B on the flange, marked with red lines in Fig. 14. This was done to investigate whether it was only the fibre tension from the 0° layer that caused wrinkling, or whether the layer itself influenced the forming outcome. In Fig. 14(a) the formed sample with the cut 0° layer is shown. As for the sample with no 0° layer, no wrinkles at location 2 are present, which also corresponds well with the simulation shown in Fig. 14(b) where no alternating shear can be seen. This is
because a cut in the 0° layer leads to a higher degree of folding outwards, reducing the tension in the middle and thereby reducing the amount of alternating shear of the 45° layer. Fig. 14(c) shows that the compressive transverse strain in the 90° layer is smaller for the cut sample than for the sample without the 0° layer, shown in Fig. 13(c), although the actual wrinkles are larger. This is probably related to the fact that the stack is more sensitive to buckling when there are fibres (in this case the 0° layer) parallel to the load. 5. Conclusions This paper addresses experimental findings on wrinkle development during forming of multi-layer UD prepreg onto a 3D beam geometry. Two different causes for wrinkle development are presented, referred to as global buckling of the entire stack of material or local compression of single layers. Global buckling is assumed to occur due to excessive material during forming of e.g. convex geometries. Local compression followed by wrinkling, on the other hand, is shown to occur as the material shear during forming, causing compressive stresses in the material. The plies with fibres parallel to the compressive stresses are more likely to buckle, which incite out-of-plane wrinkles. FE-simulations performed show that the compressive stresses develop in critical layers of a stacked UD material during forming. However, as forming proceeds, these stresses relax into in-plane wrinkling shown as alternating positive and negative shear strain, also known as marcelling. Comparing the forming simulations to the experimental forming study, it becomes clear that local compression followed by marcelling coincides with wrinkles appearing during forming. Global wrinkling that typically occurs on convex features of the geometry, could in the FE-simulations be identified as transverse strains. It is shown that by changing the stacking sequence, removing or cutting the 0° ply, wrinkles at certain locations can be avoided. The changed stacking is also corresponded to a lower degree of marcelling these locations in the simulation. The simulations show good predictions considering when and where different kinds of wrinkles appear during the forming of the geometry considered. However, the methodology used is generic and should therefore be applicable for predictive forming on other geometries and with a greater variety of material systems than considered herein. Acknowledgements The work was funded through VINNOVA under the program Green Flying Demonstrator (GF Demo). Funding was also generously provided by the strategic research program LIGHTer SRA1. References [1] Tam AS, Gutowski TG. The kinematics for forming ideal aligned fibre composites into complex shapes. Compos Manuf 1990;1(4):219–28. [2] Larberg YR, Åkermo M, Norrby M. On the in-plane deformability of cross-plied unidirectional prepreg. J Compos Mater 2012;46(8):929–39. [3] Larberg YR, Åkermo M. On the interply friction of different generations of carbon/epoxy prepreg systems. Compos Part A: Appl Sci Manuf 2011;42 (9):1067–74. [4] Hallander P, Åkermo M, Mattei C, Petersson M, Nyman T. An experimental study of mechanisms behind wrinkle development during forming of composite laminates. Compos Part A: Appl Sci Manuf 2013;50:54–64. [5] Hallander P, Sjölander J, Åkermo M. Forming induced wrinkling of composite laminates with mixed ply material properties; an experimental study. Compos Part A: Appl Sci Manuf 2015;78:234–45. [6] Sun J, Gu Y, Li M, Ma X, Zhang Z. Effect of forming temperature on the quality of hot diaphragm formed C-shaped thermosetting composite laminates. J Reinf Plast Compos 2012;31(16):1074–87. [7] Lightfoot JS, Wisnom MR, Potter K. A new mechanism for the formation of ply wrinkles due to shear between plies. Compos Part A: Appl Sci Manuf 2013;49:139–47.
J. Sjölander et al. / Composites: Part A 81 (2016) 41–51 [8] Haanappel SP, ten Thije RHW, Sachs U, Rietman B, Akkerman R. Formability analyses of uni-directional and textile reinforced thermoplastics. Compos Part A: Appl Sci Manuf 2014;56:80–92. [9] Boisse P, Hamila N, Vidal-Sallé E, Dumont F. Simulation of wrinkling during textile composite reinforcement forming. Influence of tensile, in-plane shear and bending stiffnesses. Compos Sci Technol 2011;71(5):683–92. [10] Dodwell TJ. Internal wrinkling instabilities in layered media. Philos Mag 2015:1–19. [11] Larberg Y. Forming of stacked unidirectional prepreg materials. KTH, Lightweight Structures; 2012. QC 20121204.
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[12] AniForm Virtual Forming Tool.