Appl Compos Mater DOI 10.1007/s10443-015-9461-4
Design and Manufacture of Conical Shell Structures Using Prepreg Laminates Regina Khakimova 1 & Florian Burau 1 & Richard Degenhardt 1,2 & Mark Siebert 2 & Saullo G. P. Castro 3
Received: 13 July 2015 / Accepted: 21 July 2015 # Springer Science+Business Media Dordrecht 2015
Abstract The design and manufacture of unstiffened composite conical structures is very challenging, as the variation of the fiber orientations, lay-up and the geometry of the ply pieces have a significant influence on the thickness imperfections and ply angle deviations imprinted to the final part. This paper deals with the manufacture of laminated composite cones through the prepeg/autoclave process. The cones are designed to undergo repetitive buckling tests without accumulating permanent damage. The aim is to define a process that allows the control of fiber angle deviations and the removal of thickness imperfections generated from gaps and overlaps between ply pieces. Ultrasonic scan measurements are used to proof the effectiveness of the proposed method. Keywords Prepreg . Buckling . Finite element modelling . Lay-up Abbreviations AFP Automated fiber placement ATL Automated tape laying CFRP Carbon-fiber-reinforced polymer FI Failure index GFRP Glass-fiber-reinforced polymer KDF Knock-down factor
* Regina Khakimova
[email protected] 1
DLR, Institute of Composite Structures and Adaptive Systems, Lilienthalplatz 7, 38108 Braunschweig, Germany
2
PFH, Private University of Applied Sciences Göttingen, Composite Engineering Campus Stade, Göttingen, Germany
3
Brasilian Aerospace Company, EMBRAER, 12227-901 São José dos Campos, SP, Brazil
Appl Compos Mater
List of Definitions BAs-designed^ structural model
BAs-to-be-built^ structural model
BAs-built^ structural model
reference numerical description of the physical structure without any manufacturing imperfections, deviations, mistakes, repairs. For composite structures, the Bas-designed^ structure includes the description of the lay-up and all kinds of details as they are planned to be on the physical object. Bas-designed^ structure model enriched by additional data to describe the reference manufacturing process and any physical elements that are added to the Bas-designed^ structure for manufacturing reasons under standard conditions. For composite structures, this shall include the technology to lay down the plies, the machine programming and also any additional details that are added to the as-designed structure in order to ensure manufacturability. numerical representation of the real(physical) structure. It numerically gathers the Bas-designed^ model, the Bas-to-be-built^ model and any numerical information captured during the manufacture and of interest to describe the specific history of this structure manufacturing process. This can include manufacturing parameters recorded for this specific part (autoclave curve), NDT information captured for this part (C-scan with specific defect distribution to be considered for simulation, geometric measurement using photogrammetry, laser shape measurement, etc).
1 Introduction Thin-walled conical structures are widely used in aerospace, offshore, civil and other engineering fields. An important characteristic of laminated conical shells is the challenge to establish a manufacturing process capable to achieve reasonable levels of ply angle deviation and thickness/geometric imperfections. This is due to the inherent ply angle variation produced by the variable radius along the meridian. Bert et al. [1, 2] presented research work that includes experimental buckling tests of cylindrical and conical sandwich shells made of aluminium honeycomb core and GFRP face sheets. The face sheets [1] were manufactured by the prepreg/autoclave method, where no fiber angle deviation problems were reported because the semi-vertex angle α of the sandwich cone is quite small (the structure’s geometry is very close to a cylinder). The conical shells in [3] were manufactured by filament winding using the horizontal helical winding machine and a stainless steel conical mandrel. The fabrication method, however, delivered specimens with quite a significant thickness deviation, where the shell is thicker where the conical radius is smaller. Mahdi et al. [4] investigated crashed behavior of GDFRP cones manufactured by wet filament winding The detailed
Appl Compos Mater
manufacturing process and inspection of the structures were not described and discussed in [4]. In [5] the conical shells that were produced by 6-axis gantry-type AFP machine equipped with the thermoplastic fiber placing head were not carefully inspected and measured. Most likely, in that case the problem of the thickness and fiber angle deviation is not faced because of a negligible semi-vertex angle that makes the structure close to a cylinder. However, normally the AFP produces gaps and/or overlaps for structures with higher semi-vertex angles. The literature survey reveals a clear lack of publications dealing with the manufacture and test of laminated composite truncated cones. To the author’s best knowledge, the few experiments available were carried out on cones of semi-vertex angle α never bigger than 18°, as summarized in Table 1. Therefore, in [1–3, 5, 6] the investigation of the manufacturing parameters on the fiber angle deviation and its minimization was not the main focus. The present study applies the prepreg/autoclave method, widely used in the aerospace industry to render high quality laminates [7]. Many alternative manufacturing methods such as AFP and ATL are prone to generate unavoidable gaps and overlaps already in the Bas-to-be built^ structural design phase [8]. ATL is used mostly in manufacturing of large simple structures with the relatively flat surface. AFP is used in producing structures with complicated curved surfaces that requires steering of the fibers. As soon as the surface has some curvature, material strips in AFP and tapes in ATL cannot be exactly parallel to previous ones, because the surface area changes as the course traverses across it. For example, on a shape that is smaller at one end and bigger at the other, courses have to converge at the smaller end and diverge at the bigger end. As courses converge they begin to overlap. If two courses completely overlap then the ply at this location would have two layers, instead of one, which is undesirable. Using prepreg/autoclave process one can avoid such gaps and overlaps by cutting the prepreg into pieces with the right shape, herein referred to as ply pieces. It will be shown how the ply topology parameters are optimized in order to control and minimize the fiber angle deviation and thickness imperfections. This paper deals with the manufacture of conical structures that are designed as buckling test structures for validating a design approach called the Single Perturbation Load Approach (SPLA) [9]. It is assumed in the SPLA that a single buckle caused by a certain minimum perturbation (lateral) load represents the realistic geometric imperfections and the design load is reached. Recently, numerical studies were carried out investigating the applicability range of the SPLA with conical shells [10–12]. The optimization objective of the ply topology design is to find optimal fiber directions and shape of ply pieces which are manufacturable and deliver minimal fiber angle deviation and no thickness deviation in the Bas-to-be-built^ structure. The next section presents in detail the manufacturing process itself. It needs to be mentioned that there exists no documentation related to manufacturing of cones. So in this part several possibilities were studied and are documented here. Table 1 Buckling experiments of composite cones Material
Fabrication method
α (degrees)
Year
Reference
Type of loading
1969
[1, 2]
Sandwich
Prepreg/Autoclave
5
Bending, torsion
1999 2003
[3] [4]
CFRP, GFRP GFRP
Filament winding Filament winding
9 6–18
Axial compression Axial compression
2012
[5]
Carbon/Peek
AFP
1–3
Bending
Appl Compos Mater
Fig. 1 Ariane 5 ME equipment bay structure [13] with the top radius=890 mm, bottom radius=2702 mm, height=2064 mm, semi-vertex angle α=41.3°
2 Design of Conical Shell Structure The designed conical structures herein presented are based on a scaled-down version of a real part from the European Launcher Vehicle Ariane 5 ME, shown in Fig. 1. Although the design achieved a laminate with a stacking sequence differing from the real structures, the same angle family was kept: 0°, ±30°, ±45°, ±60°, 90°. At this design stage, three main criteria were considered: 1) Design close to real structures 2) Well-defined perturbation load curve using the Single Perturbation Load Approach (SPLA) 3) Elastic behavior of the structure up to the post-bucklingregime
2.1 Design Close to Real Structures Due to the constraints at the DLR testing facilities and while trying to keep the geometry of the scaled down version as close as possible to the real structure, two different structures with the same geometry but with a different lay-up were designed, given in Table 2. The height was
Table 2 Geometrical and material characteristics for L1 and L2 L1
L2
Stacking sequence
[30/0/-30/-30/0/30]
[30/-30/0/0/30/-30]
Top radius, Rtop
190 mm
Bottom radius, Rbot
400 mm
Semi-vertex angle, α
35°
Height, H
300 mm
Material properties
E11 =142.5GPa, E22 =8.7GPa, ν12 =0.28, G12 =5.1GPa, G13 =5.1GPa, G23 =5.1GPa
Appl Compos Mater Rtop
H/2
H
PL value α
Rbot
Fig. 2 Left: schematic mechanism of SPLA; right: geometric configuration of cone
chosen as long as possible in order to minimize influences of the boundary conditions on the buckling behavior during the axial compression tests. As in the case of real structures the laminate of the scaled-down cones should be symmetric and/or balanced. The applied material isthe unidirectional prepreg IM7/8552 characterized during the COCOMAT project [13] according to the German standards [14–17]. The material characteristic data is given in Table 2, which contains also geometry and lay-up data for two designs based on the extensive study that took into account the three design criteria above mentioned. During the manufacturability study it was found out that for this particular geometry the fiber orientation of 60° is not possible because the fibers would never reach the opposite edge. In general, the smaller the fiber angle direction is, the smaller the fiber angle deviation is. That is why only 0° and ±30° were considered in the design from the originally suggested angle family: 0°, ±30°, ±45°, ±60°, 90°.
2.2 Well-Defined Perturbation Load Curve Using the SPLA The Single Perturbation Load Approach (SPLA) is a deterministic method that uses a single lateral perturbation load (PL) to produce a representative geometric imperfection [9, 18, 19], as illustrated in Fig. 2. Idealization of a typical perturbation load curve obtained with the SPLA is shown in Fig. 3. When the value of the perturbation increases, the buckling load gets smaller
Fig. 3 Idealized curve of buckling load versus perturbation load copied from [9]
Appl Compos Mater
Table 3 FEA parameters
Element type
S8R
Element size
20 mm
Boundary conditions Damping factor
Clamped edges 1.e-7
Initial increment
0.001
Maximum increment
0.001
Minimum increment
1×10−6
Maximum number of increments
10000
down to a threshold where it remains nearly constant. The corresponding perturbation load of in Fig. 3) is called P1 and the corresponding buckling load the transition point (cf. point called N1, which is taken as the design load when using the SPLA. The perturbation load curve of the designed cones should show a well-defined value for the minimum perturbation load (P1 in Fig. 3), fulfilling the second required design criterion. For the Finite Element Analysis (FEA) of Bas-designed^ structures ABAQUS Standard 6.11 (Implicit) was employed. The non-linear solver selected is a Newton–Raphson iterative procedure with artificial damping stabilization, with the parameters shown in Table 3. The fulfillment of the criterion Bwell defined perturbation load^ is achieved according to the results shown in Fig. 4 for L1 and L2, where the minimum perturbation load P1 is well defined and relatively constant buckling load is observed after P1. For design L1 the knockdown factor (KDF) obtained with the SPLA is 0.84 with P1 of 5 N, whereas for design L2 the KDF is 0.85 and P1 is 7 N.
2.3 Stress Analysis An important requirement for a laminate that undergoes repeated tests is that no permanent damage can occur up to the post-buckling regime. Otherwise, created damages would propagate during the repeated tests, progressively degrading the mechanical properties. The Hashin failure criterion was applied to check the integrity of the laminate along the displacement controlled axial compression, and the four different damage initiation could be monitored:
a
b
L1 Fig. 4 Perturbation load curve
L2
Appl Compos Mater
Fig. 5 Hashin failure modes of L1 with different PL values
fiber tension, fiber compression, matrix tension, and matrix compression. Figure 5 shows the four failure modes for the load shortening curves obtained with PL=0.5 N and PL=10 N,
a
b
prebuckling
postbuckling
Fig. 6 Stress distribution (critical failure mode – Matrix Tension) of L1 with PL=0.5 N
Appl Compos Mater
a
b
prebuckling
postbuckling
Fig. 7 Stress distribution (critical failure mode – matrix tension) of L1 with PL=10 N
where matrix tension was identified as the critical failure mode, keeping the laminate failure indexless than 1 even after buckling.
Fig. 8 Hashin failure modes of L2 with different PL values
Appl Compos Mater
a
b
prebuckling
postbuckling
Fig. 9 Stress distribution (critical failure mode – matrix tension) of L2 with PL=0.5 N
Figures 6 and 7 show the failure modes for design L1 with PL=0.5 N and PL=10 N . Observations showed that with smaller values of the PL (region (a) from Fig. 3) the stress concentration is close to the edge, whereas for higher PL values (region (c) from Fig. 3) the critical stress concentration appears at the location of the perturbation load. Despite geometric imperfections were not considered, previous studies [10] showed that the difference between the KDF obtained with the SPLA and the KDF obtained with the SPLA plus the real geometric imperfections is not significant, meaning that the SPLA covers the knock-down produced by the geometric imperfections. The stress analysis for design L2 is given in Fig. 8, showing the failure criteria for two load shortening curves with PL=0.5 N and 10 N. From Fig. 8 it can be seen that the matrix tension failure mode increases quickly just after buckling, being however still on the safe side. Figures 9 and 10 show some representative stress distribution patterns.
3 Ply Topology Design The main challenge of the prepreg/autoclave manufacturing process for truncated cones is the right choice of the ply topology. One has to determine the ply pieces that minimize the fiber angle deviation, overlapping and gaps. A cylindrical coordinate system (r, ψ, z) is used to
a
b
prebuckling
postbuckling
Fig. 10 Stress distribution (critical failure mode – matrix tension) of L2 with PL=10 N
Appl Compos Mater
a
b α
α
s H
sbot
z
ζ
ϕ max
r
ψ
s ϕ
stop
rbot
η
Fig. 11 Left: cone in cylindrical coordinate system; right: coordinate systems of unrolled cone
describe the cone geometry, as shown in Fig. 11a. In order to get an unrolled cone surface, an imaginary cut is made through the cone at ψ=0 (Fig. 11a), resulting in two edges. The edge in the direction of ψ>0 (right edge in the figure) is mapped to the horizontal axis of the new coordinate system whereas the apex of the cone is placed at the origin. The layout of the unrolled surface is depicted in Fig. 11b, where a polar coordinate system (s,φ) is the twodimensional coordinate system used for the unrolled cone. ðs; φÞ ¼
r ; ψsinα sinα
ð1Þ
To facilitate geometrical operations, a Cartesian coordinate system (η,ζ) is also defined as depicted in Fig. 11b. ðη; ζ Þ ¼ s cos φ; s sin φ
ð2Þ
Several ply piece shapes were considered during the ply topology study. Trapezoidal ply pieces were designed in such a way to prevent overlaps or gaps in the laminate, and a typical example is shown in Fig. 12. The thin lines inside the trapezoid represent the fibers of each ply
Fig. 12 Design parameters for the asymmetrical trapezoidal cutting design
Appl Compos Mater
a
b
c
Fig. 13 Example of the maximum width a wmax =100mm b wmax =200mm c wmax =300mm
piece, being all fibers parallel to the ply piece upper edge. The cone is divided into three sections, being the upper and the lower parts used as supports and represented with dotted lines. The middle part is represented with thick lines, being the free part whose topology will be optimized.
3.1 Design Parameters The shape is defined by three independent design parameters: maximum width wmax, nominal fiber angle θnom and the distance between the apex and the position of the nominal fiber angle sθnom (Fig. 12). The maximum width wmax determines the largest width of the ply piece. In Fig. 13 three different examples for the maximum width are shown. The starting position sθnom defines at which s-coordinate the nominal fiber angle starts. The smaller the value is, the nearer starts the part at the cone vertex (Fig. 14). The maximum value is limited by the nominal fiber angle and the dimensions of the cone. Fig. 14c shows a ply piece design with the maximum value for sθnom. One can see that the shape becomes triangular and the acute tip of it touches the upper edge of the cone. If sθnomwould be further increased, the cone would not be fully covered.
3.2 Parameters Defining the Optimal Topology There are four different evaluation parameters used to determine which cutting design is optimal. These parameters are based on the assumption that all plies should have a maximum angle deviation 2°, as commonly adopted in the aerospace industry. When trapezoidal shapes
a
b
c
Fig. 14 Examples of the starting position a sθnom =330mm b sθnom =400mm c sθnom =491mm
Appl Compos Mater
Fig. 15 Ratio of continuous fibers
are used, not all fibers starting at the bottom reach the upper edge of the cone. The ratio of continuous fibers Rcont sets the number of fibers that are crossing the upper edge of the cone in relation to the number of fibers that start at the lower edge of the cone. Therefore, two lengths lcont,1 and lcont,2 (Fig. 15) are defined with their respective ratio calculated. The optimum value is 1, which can only be achieved with thin rectangular stripes. Rcont ¼
l cont;1 ; l cont;2
ð3Þ
Due to the variable cone radius, the real fiber angle differs from the nominal fiber angle. Baruch et al. [20] show that the fiber angle deviation on a conical structure depends on the chosen path. The simplest path is the geodesic one, defined as the shortest path between two points on a surface. This path is the mostly used in manufacturing because the laid up ply pieces will not exhibit residual shear forces. Goldfeld et al. [21, 22] [23] investigated the influence of the fiber angle deviation on the stiffness and the buckling of conical shells. They
Fig. 16 Fiber angle deviation problem
Appl Compos Mater
Fig. 17 Design parameters of the 0°-ply piece
described the local fiber angle as a function of the radial coordinate s (see Fig. 12) of the conical coordinate system: s θ ð4Þ θðsÞ ¼ arcsin nom ⋅sinðθnom Þ ; s where θnom is the nominal local fiber angle at sΘnom and θ(s) is the local fiber angel at s, see Fig. 13. This approach is only valid for single fibers which follow a geodesic path. Moreover, the local fiber angle model (Eq. 4) is only suitable for filament winding, and not for laminated cones produced by the prepreg/autoclave production method. This study considers ply pieces with a finite width and uses the angular coordinate φ of the conical coordinate system given in Fig. 12 to calculate the local fiber angle θðφÞ ¼ θnom −ðφθnom −φÞ;
ð5Þ
where φΘnom is the angular coordinate at which θnom can be found and can be considered as the reference angle of the ply piece (see Fig. 16). The area in which the fibers have a fiber angle deviation smaller than 2°is called effective area Aeff. The ratio of effective area RAeff is the relation between the effective area and the area of the ply piece. The optimum value for RAeff is 1, when all all fibers of the ply piece have a fiber angle deviation smaller than 2°.
Fig. 18 Left: defining the geometry of the cone; right: unrolled conical surface
Appl Compos Mater
Table 4 Geometric properties of the conical shape (Fig. 17)
Edge
rn in mm
sn in mm
E1
141
245.87
E2 E3
190 400
331.32 697.52
E4
449
782.96
The degree of coverage RDoC is also considered, but for this trapezoidal shape it is always 1. The ratio of total effectiveness Rtotal is the product of all three previously introduced evaluation ratios: Rtotal ¼ Rcont ⋅RAeff ⋅RDoC
ð6Þ
This ratio can be thought as the number of all fibers that are leading from the lower to the upper end of the cone with a fiber angle deviation smaller than 2° in relation to all fibers.
3.3 Concluding the Ply Piece Shape for the Design Cone For the ply pieces for the 0°-layer a symmetrical trapezoidal shape is used, shown in Fig. 17. The design parameter sθnom has no influence on the shape and therefore can be neglected. The only design parameter left is wmax. One can see that this shape is symmetrical to the origin fiber, drawn as dotted line. The symmetrical ply piece shape is sufficient to be employed only for nominal fiber angles smaller than 4°. If the nominal fiber angle becomes larger, the ply pieces have to be asymmetrical in order to minimize the fiber angle deviation. The truncated cone can be divided into three parts: the two support structures, which are needed for cutting and molding and the free cone, which is investigated. The conical structure is shown in Fig. 18a. The truncated cone has a half-cone angle of 35° and a total height of 440 mm. The free cone has a maximum radius of 400 mm and a height of 300 mm, each support part is 70 mm high. The support areas has to be partially cut away (to obtain straight edges) after laminating and the rest is molded in resin. These areas do need to be considered when discussing the ply placement process, however. The part has four edges which are numerated from top to bottom from E1 to E4. E1 is then the upper edge of the upper support part, E2 the upper edge of the free cone, E3 is the lower edge of the free cone and E4 the lower end of the lower support part. A common and convenient illustration for the fiber angle deviation is the unrolled cone surface with the two
Table 5 Optimization results for a fiber angle of 0° θmax, °
wmax, mm
Number of pieces
RAeff, %
Rcont, %
Rtotal, %
55
51.32
99.42
47.50
47.23
2.01
100
28.26
54.74
47.50
26.00
3.65
150
18.87
36.55
47.50
17.36
5.47
200
14.18
27.48
47.50
13.05
7.28
250
11.38
22.05
47.50
10.47
9.07
300
9.52
18.44
47.50
8.76
10.85
Appl Compos Mater
Fig. 19 Ply piece design for a fiber angle of 0° (wmax =55 mm)
dimensional Cartesian and the conical coordinate system, shown in Fig. 18b. The geometrical properties for all edges are shown in Table 4. The radius r is measured from the symmetrical axis and s is the distance between the edge and apex, as shown in Fig. 18a and b). In Table 5 the results for different maximum widths wmax are shown. In this table θmax is also introduced, which is the maximum local fiber angle for the design. One can see that Rcont for all widths has a constant value of 47.50 %, which is a consequence of the imposed nonoverlapping condition. With the increasing width, the number of required ply pieces decreases, simplifying the manufacture by reducing the time spent for cutting and laying the prepreg plies. In addition, there will be less geometry deviations of the plies due to cutting. However, the maximum local fiber angle increases from 2.01 to 10.85°. This also decreases the ratio of effective area RAeff and the total effectiveness Rtotal. The optimal design, considering Rtotal and the lowest value of θnom is the design with a width of 55 mm, highlighted in grey (Table 5). Special in-house software [24] is used for the calculation of the ply piece topology, their evaluation parameters and for visualization purposes. The tool allows setting the cone geometry, inputting design parameters, plotting the ply topology and outputting the evaluation parameters. The optimization procedure is an alternation of design parameters between certain limits with a certain step width. The results are then evaluated manually. For 0°-ply pieces and a symmetrical shape, the only design parameter is wmax. The lower limit is 50 mm and chosen so that the number of needed ply pieces would be reasonable in aspects of time consumption and prevention of manufacturing errors. The maximum value of wmax is caused by the roll width of the raw material, which is 300 mm. A step width of 1 mm leads to sufficient results. The design of the 0°-layer topology is satisfactory, because the fiber angle deviation is almost within 2° (see Fig. 19). However, for the 30°-degree layers it is more challenging to Table 6 Optimization results for the fiber angle of θnom =30° Name
wmax, mm
sθnom, mm
θlocal,max, °
θlocal,min, °
Δθlocal,max, °
Δθlocal,min, °
D1 D2
231 100
347 491
47.55 54.95
14.40 20.61
17.55 24.95
−15.60 −9.39
D3
99
394
43.58
16.41
13.58
−13.59
Rtotal
Appl Compos Mater 10% 9% 8% 7% 6% 5% 4% 3% 2% 1% 0% 250
wmax 50 mm 100 mm 150 mm 200 mm 231 mm 250 mm 300 mm 290
330
370
410
450
490
sθnomin mm Fig. 20 Influence of the design parameters on the ratio of total effectiveness for D1
find an optimal topology and within the chosen manufacturing method, it is impossible to obtain a ply topology design with the maximum fiber angle deviation within 2° on the entire cone surface. Therefore, the mechanical properties of this layer can be considered as homogenous. For the design of the cutting shape for the 30°-layers an unsymmetrical trapezoidal shape is proposed (Fig. 12). For the ply topology D1 the design parameters wmax and sθnom are changed between 50 and 300 mm, respectively between 250 and 490 mm. The maximum value of sθnom is a natural consequence of the premise that the whole cone should be covered. The upper edge of the cone has a value of s equal to 245.57 mm. A decrease of sθnom lower than 250 mm would lead to a decrease and even diminishing of the effective area especially for thin ply piece designs, see Fig. 12. Except for the degree of coverage all evaluation parameters are dependent on both design parameters. The finalized design parameters of D1 can be found in Table 6 and the geometric configuration of D1 is depicted in Fig. 23a. Figure 20 shows the effect of wmax and sθnom on the total effectiveness. One can see that the effect of sθnom on Rtotal depends also on the maximum width wmax. The progress of Rtotal shows for small widths like 50 mm three different gradients. This is caused by the changing ratio of effective area.
Table 7 Optimization results for D1 (fiber angle of 30°) wmax, mm
sθnom, mm
Number of pieces
RAeff, %
Rcont, %
Rtotal, %
θlocal,max, °
θlocal,min, °
50
491
57.07
19.02
33.29
6.33
51.43
20.61
100
491
28.92
23.82
32.49
7.74
54.95
20.61
150
440
19.53
24.25
35.44
8.59
52.18
18.39
200
383
14.83
23.58
38.15
9.00
49.24
15.93
231 250
347 327
12.93 12.01
22.99 22.35
39.60 40.32
9.11 9.01
47.55 46.76
14.40 13.56
300
271
10.13
19.53
42.13
8.23
44.52
11.20
Appl Compos Mater
Fig. 21 Location of the largest and lowest local fiber angle for trapezoidal shapes
In Table 7 results of the optimization of D1 for different maximum widths are shown. θlocal,min describes the minimum local fiber angle for the design. The reason for this is the low value of the ratio of effective area RAeff, which is lying between 19.02 and 24.25 %. The maximum local fiber angle θlocal,max can be found at the top end of the cone, while the minimum is at the lower end, see Fig. 21. This is also a consequence of the fiber angle deviation problem. One can see that both, the minimum and the maximum values are much larger than the allowed 2° deviation. The ratio of continuous fibers Rcont is not significantlyaffected by the design parameters, and further increase of this ratio can only be done by changing the basic shape to a rectangularpattern, but this would create overlaps. For 50 and 100 mm, sθnom is the highest possible value for this conical structure. The optimum design can be achieved for a maximum width of 231 mm and a sθnom value of 347 mm, as illustrated in Fig. 20. The total effectiveness is only 9.11 %, which is lower than for the 0° cutting design. During the optimization
a
b Local Fiber Angle in °
Local fiber Angle in °
60 50 40 30 20 10 0 250
60 50 40 30 20 10 0
300
350 400 450 sθnomin mm
wmax=100 mm
500
50
100
150 200 250 wmaxin mm
sθ nom =250 mm
Fig. 22 Influence of sθnom and wmax on the maximum and minimum local fiber angle
300
Appl Compos Mater
a
b
D1
c
D2
d
D3
Legend
Fig. 23 Fiber angle deviation for the three ply piece designs
procedure, it became clear that anincrease of the fiber angle produces an increase of the fiber angle deviation together with a decrease of the ratio of effective fibers RAeff, which ultimately leads to a less effective ply piece design. During the manufacturing of the first cones and the analysisof the first finite element model that considered the fiber angle deviation, it became clear that the first ply piece design (D1) leads to inhomogeneous mechanical properties of the resulting laminate. To minimize the effect of inhomogeneous mechanical properties two different designs were proposed with a maximum width smaller than 100 mm. The second design D2 is highlighted in light-grey in Table 6, and was obtained using the same optimization routine applied to determine D1. The third design D3 was chosen so that the fiber angle deviation is balanced, meaning that the maximum and minimum fiber angle deviations are equal. The largest and smallest local fiber angles can be found at the intersections of the ply piece with the cone edges, as illustrated in Fig. 21. The value of θlocal,min depends only on sθnom, but θlocal,max depends also on wmax, as shown in Fig. 22. It is possible to find for every value of wmax a corresponding value of sθnom so that the maximum and minimum fiber angle deviations are balanced. The value of wmax was set to 100 mm to ensure homogeneous material properties, a good handling and reasonable number of the ply pieces. The design parameters and the according maximum and minimum local fiber angles can be found in Table 7. The term Δθ is used to describe the fiber angle deviation and is defined as: Δθ ¼ θlocal −θnom
ð7Þ
Figure 23 shows the shapes for the three different designs and the distribution of the total fiber angle deviation. The maximum fiber angle deviation of D3 is smaller than the deviations of D1 and D2. Table 8 The five manufactured cones Cone
Lay-up
30°-Ply piece design
Vacuum bagging scheme
Mean thickness, mm
K01
L2
D1
A
0.66
K03
L2
D2
A
0.67
K05
L2
D2
B
0.74
K06
L2
D3
B
0.73
K08
L1
D3
B
0.73
Appl Compos Mater
Fig. 24 Cutting ply piece design D2 with the computer controlled automatic cutter
4 Manufacturing Process There are several reasons for choosing the prepreg/autoclave manufacturing method for the conical structures. First, there were CFRP cylinders successfully manufactured and tested previously at DLR by the prepreg/autoclave method [9, 25, 26]. Second, the method is considered to give a good quality laminate as discussed in Introduction. The prepreg/ autoclave technology delivers high component quality while requiring relatively low costs of tools. Last, there have been no publications describing the prepreg/autoclave manufacturing process applied to conical shell structures previously, as the authors have not found any publications related to it. For full-scale launch vehicle structures the ATL manufacturing process is usually applied [27]. However, it is not efficient to use the same method for the scaled-down structures. Moreover, the prepreg pieces in the ATL have a rectangular shape that would cause excessive thickness deviations for small structures.
a
b
D1 Fig. 25 Ply with the 30° fiber direction
c
D2
D3
Appl Compos Mater
Fig. 26 Ply with the 0° fiber direction
In the prepreg/autoclave fabrication method the CFRP part has to be laminated onto a single sided mandrel by hand lay-up. A plastic vacuum film is placed on top of the vacuum bagging and the laminate in order to form a vacuum-tight seal. A conical mandrel was designed and manufactured according to the dimensions given in Table 2. One should take into account at the design stage of the tooling that the height of the manufactured structure would be higher than the actual one of the design structure, in order to allow fixation prior to the test. Table 8 explains what lay-up, ply topology and vacuum bagging scheme was used for each one of the five cones manufactured. An automatic computer controlled cutter was used to cut the prepreg material into the desired ply shapes (Fig. 24) . Before cutting, one needs to prepare a CAD template and distribute the ply shape along the material fabric in such a way to minimize material waste. It is easier to handle laminating the pieces onto the mould using ply topology D1 because the ply pieces are bigger. During the lay-up, an additional source of fiber angle deviation exists while laying the pieces by hand onto the mould, and this error is minimized when using bigger ply pieces. Before starting the lamination process two reference lines were made on the tooling surface, around the circumferential direction. The opposite vertexes of the ply pieces should be coincident with these reference lines in order to assure the correct angle for each ply, as illustrated by the dotted lines in Figs. 12–17.
scheme A
Fig. 27 Vacuum bagging sequence
Appl Compos Mater
scheme B
Fig. 28 Vacuum bag moulding withs cheme B
Figures 25 and 26 show the laminating process with the prepreg pieces of the ply with 30° and 0° fiber orientations, respectively. Figure 27 shows the sequence of both vacuum bagging schemes. Different vacuum bagging schemes were applied in order to find the optimal quality of the laminate and the thickness close to nominal. The structures were measured and visually inspected after manufacturing each one. When using scheme A the thickness is about 12–13 % smaller than required. The reason is that the breathing fabric absorbs more resin during the curing process than foreseen. The optimal thickness and the visual quality of the laminate are obtained using the vacuum bagging by scheme B. The schematic vacuum bagging sequence on the conical structure is depicted in Fig. 28. The mean thickness values of the structures measured with dial thickness gages are given in Table 8. It is important to note that the fiber volume fraction of the structures produced with the three vacuum bagging schemes differs and that should be taken into account in the Bas-built^ structure properties. The curing cycle being used is the standard one for the Hexcel IM7/8552 that can be found in the official product data sheet of Hexcel. Figure 29 shows K07 before curing, after curing and after demoulding. Figure 30 shows ultrasonic (US) scans of all five Bas-built^ cones using the same contour scale for the distributed thickness. The laminate of the cones is homogenous with only minor
a
b
vacuum bagging Fig. 29 Manufacturing process of K07
c
after curing
after demoulding
Appl Compos Mater
a
b
K03
K01
c
K05
d
e
K06
K08
Fig. 30 Ultrasonic inspection scans as unrolled surface of a K01 b K03 c K05 d K06 e K08
gaps and overlaps. This pattern of the US scans is typical to shells laminated by prepreg/ autoclave and is very similar to the ones corresponding to cylinders produced by the same method at DLR [25]. It is also evident that K01 and K03 are thinner due to the fact that they
Appl Compos Mater
were produced with the vacuum bagging scheme BA^. The laminate quality of K08, K06 and K05, produced with the vacuum bagging scheme BB^ differ from each other, meaning that the laminate quality of Bas-built^ structures produced by prepreg/autoclave is depending very much on the ply piece design, skills of the worker and the curing process.
5 Summary and Conclusions Design and evaluation parameters were defined and proposed for the ply topology design for truncated cones produced by the prepreg/autoclave method. Constant thickness laminates are obtained in the Bas-to-be-built^ structural design phase. During the ply topology design study it was found that larger fiber angles result in larger fiber angle deviations and it was shown how to minimize the thickness imperfections created by gaps and overlaps of different ply pieces. Optimal ply piece design with the maximum fiber angle deviation less than 2° was achieved for the ply with the 0° degree orientation. For the ply with the 30° fiber orientation three different ply piece designs resulting from the optimization process are suggested. With the increasing width of the ply piece, the number of required ply pieces decreases, simplifying the manufacture by reducing the time spent for cutting and laying the prepreg plies. Besides, the number of gaps and overlaps is minimal. However, with a narrower ply piece, the deviations of both, the local minimal and maximum angles are smaller than with the wide ply piece. Thus, the optimal ply topology design is achieved with the D3 ply piece design where the deviation of both, the minimum and the maximum fiber angle orientation is kept minimal. The prepreg/autoclave manufacturing method was successfully applied to the conical structures herein design with a semi-vertex angle α=35°. Five geometrically identical laminated cones with different stacking sequence and ply topology design were manufactured and measured by ultrasonic inspection. Two vacuum bagging schemes were proposed and applied, showing that the vacuum bagging scheme B delivers laminates with the average thickness close to the nominal one. As a next step, selected test conical shells will be measured by photogrammetry and tested at DLR facilities under axial compression and geometric imperfections created by perturbation loads. The results will build the basis for the validation of new design concepts as part of the DESICOS project [28]. In the test validation stage, finite element simulations of Bas-built^ structural models are planned using the measured imperfections and the laminate properties corresponding to the individual shape of the ply pieces applied in the manufacture. Acknowledgments The research leading to these results has received funding from the European Community’s Seventh Framework Programme (FP7/2007–2013) under Priority Space, Grant Agreement Number 282522 (www.desicos.eu). The information in this paper reflects only the author’s views and the European Community is not liable for any use that may be made of the information contained therein.
References 1. Bert, C., Crisman, W., Nordby, G.: Fabrication and full-scale structural evaluation of glass-fabric reinforced plastic shells. J. Aircr. 5(1), 27–34 (1968) 2. Bert, C., Crisman, W., Nordby, G.: Buckling of cylindrical and conical sandwich shells with orthotropic facings. AIAA J. 7(2), 250–257 (1969)
Appl Compos Mater 3. Tong, L.: Buckling of filament-wound laminated conical shells. AIAA J. 37(6), 778–791 (1999) 4. Mahdi, E., Hamouda, A., Sahari, B., Khalid, Y.: Effect of residual stresses in a filament wound laminated conical shell. J. Mater. Process. Technol. 138, 291–296 (2003) 5. Shadmehri, F.: Buckling of laminated composite conical shells; theory and experiment, Montreal, Quebec, Canada: PhD thesis, Concordia University (2012) 6. Mahdi, E., Hamouda, A., Sahari, B., Khalid, Y.: Crushing behavior of cone-cylinder-cone composite system. Mech. Adv. Mater. Struct. 9(2), 99–117 (2002) 7. Bader, M.G.: Selection of composite materials and manufacturing routes for cost-effective performance. Compos. Part A 33, 947–962 (2002) 8. Lukaszewicz, D., Ward, C., Potter, K.D.: The engineering apsects of automated prepreg layup: History, present and future. Compos. Part B 43, 997–1009 (2012) 9. Hühne, C., Rolfes, R., Breitbach, E., Teßmer, J.: Robust design of composite cylindrical shells under axial compression - simulation and validation. Thin-Walled Struct. 46, 947–962 (2008) 10. Khakimova, R., Warren, C.J., Zimmermann, R., Castro, S.G., Arbelo, M.A., Degenhardt, R.: The single perturbation load approach applied to imperfection sensitive conical composite structures. Thin-Walled Struct. 84, 369–377 (2014) 11. Khakimova, R., Zimmermann, R., Di Pascua, M.F., Castro, S.G., Arbelo, A.A., Degenhard, R.: Buckling and postbuckling of truncated conical shells with varying semi-vertex angle: the use of the single perturbation load approach. 54th Israel Annual Conference on Aerospace Sciences, Haifa (2014) 12. Khakimova, R., Castro, S.G.P., Arbelo, M.A., Degenhardt, R., Rohwer, K., Zimmermann, R., Quappen, G., Hinsch, S.: Studies of imperfection sensitive conical composite structures. International Conference on Composites/Nano Engineering, Tenerife (2013) 13. DESICOS [Online]. Available: http://www.desicos.eu 14. www.cocomat.de [Online] 15. European Association of Aerospace Manufacturers: DIN EN 2561 Kohlenstoffaserverstärkte kunststoffe unidirektionale laminate zugprüfung parallel zur faserrichtung. European Committee for Standardization (1995) 16. European Association of Aerospace Manufacturers: DIN EN 2597 Carbon fibre reinforced plastics, unidirectional laminates - Tensile test perpendicular to the fibre direction. (1998) 17. The European Association of Aerospace Industries: DIN EN 2850 unidirektionale kohlenstoffaser-duroplast verbundwerkstoffe druckversuch parallel zur faserrichtung. (1997) 18. The European Associa tion of Aerospace Industries: DIN EN 6031. (1996) 19. Castro, S.G.P., Arbelo, M.A., Zimmermann, R., Degenhardt, R.: Exploring the constancy of the global buckling load after a critical geometric imperfection level in thin-walled cylindrical shells for less conservative knock-down factors. Thin-Walled Struct. 72, 76–87 (2013) 20. Castro, S.G.P., Zimmermann, R., Arbelo, M.A., Khakimova, R., Hilburger, M.W., Degenhardt, R.: Geometric imperfections and lower-bound methods used to calculate knock-down factors for axially compressed composite cylindrical shells. Thin-Walled Struct. 74, 118–132 (2014) 21. Baruch, M., Arbocz, J., Zhang, G.: Laminated conical shells - considerations for the variations of the stiffness coefficients. in AIAA-94-1634-CP (1994) 22. Goldfeld, Y.: The influence of the stiffness coefficients on the imperfection sensitivity of laminated cylindrical shells. Compos. Struct. 64, 243–247 (2004) 23. Goldfeld, Y., Arbocz, J., Rothwell, A.: Design and optimization of laminated conical shells for buckling. Thin-Walled Struct. 43, 107–133 (2005) 24. Goldfeld, Y., Arbocz, J.: Buckling of laminated conical shells given the variations of the stiffness coefficients. AIAA J. 42(3), 642–649 (2004) 25. Castro, S.G.P., Schor, P., Burau, F., Reichardt, J.: DESICOS improved software. 1 May 2015. [Online]. Available: http://desicos.github.io/desicos/ 26. Degenhardt, R., Kling, A., Bethge, A., Orf, J., Kärger, L., Rohwer, K., Zimmermann, R., Calvi, A.: Investigations on imperfection sensitivity and deduction of improved knock-down factors for unstiffened CFRP cylindrical shells. Compos. Struct. 92(8), 1939–1946 (2010) 27. Degenhardt, R., Bethge, A., Kling, A., Zimmermann, R., Rohwer, K., Teßmer, J., Calvi, A.: Probabilistic approach for improved buckling knock-down factors of CFRP cylindrical shells. In proceeding of: First CEAS European Air and Space Conference (2008) 28. Ahmed, T., Brodsjo, A., Kremers, A., Cruijssen, H., van der Bas, F., Spanjer, D., Groenendijk, C.: A composite engine thrust frame cone, made with novel cost-effective manufacturing technology. 12th European Conference on Space Structures, Materials & Environmental Testing, Noordwijk (2012)
