Evaluation of composite materials for space structures

Transcription

1 Evaluation of composite materials for space structures H. Eskandari and D. Nikanpour Canadian Space Agency, Canada Abstract This study examines the effects of materials on the stiffness of space structures and addresses pitfalls in materials selection. Moreover, the effect of structure's configuration and methods of finite element modeling of honeycomb-core sandwich structures on the structure's stiffness are evaluated. The focus of the study is the structure of a small satellite made of three square decks and nine tubular beams. The study demonstrates that designing a structure with seemingly superior composite materials may not always lead to a better performance in comparison to conventional materials. The use of composite materials (especially anisotropic ones) instead of conventional materials (usually isotropic) requires careful examination of the concerned application in order to avoid improper use of composite materials. The results reveal the degree of the importance of the material's shear moduli on the overall performance of a stiffness-driven structure. Introduction An important objective in design of space structures is to reduce mass without compromising their performance. Although this is a desirable goal in any design, it becomes of paramount importance for space applications, since the economical and environmental costs of launching space vehicles are significantly high. It is therefore understandable that advanced composite materials are targeted as means of achieving this goal (Grastataro et al [1], Garvey [2]). Structural loads on spacecraft are of two types: static and dynamic. Forces due to steady acceleration are referred to quasi-static forces. Dynamic loads have

2 J4 Advances in Composite Materials and Structures VII, C.A. Brebbia, W.R. Blain & W.P. De Wilde (Editors) Advances in Composite Materials and Structures III transient nature. For instance, dynamic lateral forces can arise from two sources: when two or more rockets don't fire simultaneously, and when launch mounts are not released simultaneously. Significant lateral force can be generated in these cases (Sarafin & Larson [3], Larson & Wertz [4]). The magnitude of load imposed on the payload depends on the stiffness of the structure. For large structures, a load cycle analysis is usually needed to reach a convergence in evaluating structural load. However, for small structure like the one considered in this study, this dependence can safely be ignored. With regard to the dynamic nature of loading conditions described above, a minimum natural frequency for the structure is usually required, which is dictated by vibrational characteristics of launch vehicles. The natural frequency is proportional directly to the square root of stiffness and inversely to the square root of mass. The minimum natural frequency conditions, drives the design of space structure to be primarily stiffness limited. In general, stiffness of a structure can be manipulated by controlling parameters associated with the following attributes of the structure: 1) material, elastic constants; 2) structural elements, optimum section with respect to structural load; 3) structure, arrangement of structural elements within a structure with respect to structural load; 4) Joints: flexibility of joints. All the above issues have been investigated; however, in this manuscript the emphasis is mainly given to the first issue, i.e., the effect of materials on the stiffness of a structure, a comparative analysis of performance of aluminum and graphite-epoxy. In addition, the influence of structure's configuration and methods of finite element modeling of sandwich panels with honeycomb core are addressed. Accordingly the following three sections examines each of this issues followed by conclusions. Evaluation of material selection This part examines the effects of materials on stiffness. The focus of the study is a structure of a small satellite made of three square decks and nine tubular beams as shown in Figure 1. The decks are made of aluminum honeycomb plates with core thickness of 18 mm and face-sheets of 1mm thick. They are square shape, 500x500 mm in size, with an overall thickness of 20 mm. The tubular beams are considered to be made of either unidirectional graphite-epoxy with E%=130, Ey=Ez=14 GPa, Gxy=Gyz=Gxz=5 GPa, and density of 1590 Kg/nf or aluminum with E=70 GPa, G=27, and density of 2700 Kg/ml Tubes are 25 mm in outer diameter, 2 mm in thickness and 500 mm in length. The finite element technique is used to evaluate the natural frequencies of the satellite structure. The commercial software IDEAS was used for all analyses. Finding an efficient method of finite element meshing for the structure is very important. Due to the relatively large structure of the satellite, the analysis of the complete structure requires careful and economy meshing to

3 Advances in Composite Materials and Structures 17J 15 Figure 1. Solid model of the 9-tube hexahedral structure of the satellite. avoid shortage of computer memory or software limitations. This implies modeling the structure with the best-suited elements for a specific analysis. For modal and vibration analysis one can use beam elements for tubes and shell elements for decks and mass elements for subsystems. Although very efficient for modal analysis (in terms of computer time and memory), the beam elements would not be appropriate for further local stress analysis, e.g. stress at the tubedeck joints. An alternative to beam elements is the use of shell elements, which are more suitable for evaluating local stresses; however, they require more CPU time and computer memory. The face sheets of the decks and tubes are modeled using shell elements, and the core of the deck is modeled with hexahedral solid elements. A total of 7500 elements are used in constructing the finite element model. Frequencies are evaluated for free-free boundary conditions. In the following results, fi, the first mode of vibration, is a torsion mode and ^ is the first mode of lateral bending, f] is equal to f% but associated with the mode of vibration in a plane perpendicular to that of ^ and t* is the second mode of lateral bending. The first mode of vibration is shown in Figure 2. All frequencies are in Hertz. Considering the large difference in elastic modulus of Al (E=70 GPa) and that of Gr-Ep (E%=130 GPa), also lower density of Gr-Ep, one may expect that the natural frequencies of the structure with Gr-Ep tubes be higher

4 16 Advances in Composite Materials and Structures VII than those of the Al-tube structure. However, as the Tabel 1 shows, the opposite is the case. RESULTS: 1- B.C. l.normal_mode l.displacement_l /caisz/hamld/satlo.mfl MODE: DISPLACEMENT 1 - FREQ: MAG MIN: DEFORMATION: 1- B.C. l.normal_mode 2.86E-04 MAX: l.displacement_l 3.27E-01 MODE: DISPLACEMENT 1 - MAG FREQ: MIN: FRAME OF REF: PART 2.86E-04 MAX: 3.27E-01 VALUE OPTION:ACTUAL 3.27E-01 Figure 2. First mode of vibration of the satellite, torsion mode. Table 1. The effect of tube's materials on natural frequencies (Hz) of the structure. Gr/Ep tube Al tube fi f f To justify these unexpected results, one explanation seems plausible. The tubes act as beams in the structure and the length-to-depth ratio of the tube used in the model is relatively small, the length (from deck to deck) is less than 10 times of the diameter. For short beams, shear deformations are considerable, and hence, Timoshenko beam theory, in which shear stiffness of the beam is accounted for, applies instead of Euler beam theory. When shear deformations are significant, uniaxial graphite-epoxy tubes are not very efficient since they possess a low transverse shear stiffness. The along-fiber elastic modulus of the tube is 130 GPa and that of aluminum is only 70 GPa, but the shear moduli of the tube are very low (5 GPa) while the shear modulus of aluminum is 27 GPa, approximately five times higher. This raises an important issue: the use of composite materials (especially composite laminates) instead of conventional

5 Advances in Composite Materials and Structures VII materials (isotropic) requires careful analysis of the application in hand in order to exploit full advantages of composite materials. To verify above explanation, the shear moduli of the Gr-Ep was increased from 5 GPa to 15 GPa (still 12 GPa less than that of Al). The natural frequencies increased to values very close to those obtained for aluminum-tube structure as given in Table Table 2. The effect of shear modulus on natural frequencies (Hz) of the structure. Gr-Ep, Gxv=Gxz=Gvz= 15 GPa Aluminum fi fi f* In order to compare performance of the Gr-Ep and aluminum tubes with equal mass, the thickness of the Gr-Ep is increased, while the outer diameter is kept the same as that of Al tubes, so that mass of both tubes are the same. This yields a thickness of 3.65 mm for Gr-Ep tubes. The results are shown in Tabel 3. Table 3. The effect of Al and Gr-Ep tubes with equivalent mass on natural frequencies (Hz). Gr-Ep, G=5 GPa, t=3.65mm Aluminum fi fz f From these results, it is evident that the uniaxial Gr-Ep tubes, as used here, do not offer any advantage over aluminum tubes, one way to obtain Superiority is to use high-modulus uniaxial Gr-Ep plies (with a minimum modulus of 220 GPa) arranged in a quasi-isotropic lay-up. This lay-up would result in increase of G%y to approximately 50 GPa, however, the G%z and Gy% remain as low as 5 GPa. The result of the analysis using this type of lay-up are compared with those obtained using aluminum tube in Table 4. Table 4. The effect of a quasi-isotropic lay-up on natural frequencies (Hz). quasi-isotropic Gr-Ep, t=2mm Aluminum fi f ft The results show that the quasi-isotropic lay-up would offer better stiffness compare to aluminum. However, it should be noted that the high-modulus graphite fibers are significantly more expensive than the low modulus fibers. Furthermore, this type of lay-up can only be produced with the filament winding technique. Despite the better stiffness offered by the quasi-isotropic lay-up, the fact remains that in the application here, the full advantage is not taken of

6 18 Advances in Composite Materials and Structures VII graphite-epoxy composites. It is therefore reasonable to use aluminum tubes for this application, unless the design is modified (for example, changing the lengthto-depth ratio if no restriction is applied). The results reveal the degree of the importance of the effect of shear stiffness on overall performance of a stiffnessdriven structure. To further study the effect of the tube's material on the stiffness, a single tube isolated from the structure is examined. The tube is modeled as a clamped beam to resemble its function and conditions in the satellite's structure. The tube has a diameter of 25mm and a wall thickness of 2mm as used in the satellite's structure. Five different lengths were analyzed: 100, 200, 300, 400, and 500mm. The 200mm length is very close to the length of tubes connecting the two adjacent decks in the satellite's structure. The beam is clamped at both ends and is loaded in the middle with a 1KN force. In order to avoid local deformation, the load is distributed over all constituent nodes of the middle section. Aluminum and graphite-epoxy, as described before, are compared in these analyses. As before, shell elements were used to construct the finite element model of the tube, which is shown in Figure 3. The maximum displacements at midsection for four lengths are shown in Table 5. Based on these results, the stiffness of the beam is calculated for each case and is plotted against the ratio of length to radius of gyration, R, a measure of length to depth ratio, in Figure 4. It is observed that in terms of stiffness, the graphite-epoxy is only advantageous to aluminum for lengths greater than 400mm, or ratios greater than 25. Figure 3. Finite element model of a tubular beam

7 Advances in Composite Materials and Structures VI'I Table 5. Maximum displacement at midsection of the tube. length (mm) Disp (10^ mm) Aluminum Graphite-epoxy E+08 (d.ooe E Figure 4 gyration. Bending stiffness of the tube versus the ratio of length to radius of Evaluation of structure's configuration As stated before the arrangement of structural members or overall configuration of the structure greatly affects the stiffness of the structure. Two configurations were compared for their stiffness efficiency: cylindrical (with circular decks) and hexahedral (with square decks) structures. Both structures are made of three decks, which are connected together with 8 tubes. The configuration of the cylindrical structure is shown in Figure 5, and the configuration of the hexahedral structure is similar to that shown in Figure 1. For comparison purposes and simplicity all materials used in the structure are considered isotropic (material properties of aluminum were used). These are the

8 20 Advances in Composite Materials and Structures III configurations that were considered for comparison analysis only. Tubes are 25mm in diameter and 2mm in thickness. Circular decks of the cylindrical structure are 500mm in diameter and square decks of the hexahedral structure are 442mmx442mm. The dimensions of square decks were set to have the area of the deck equivalent to that of the circular deck. Similar finite element modeling methods as those described in previous section are used for the analyses. The results of the analyses are shown in Table 6. Figure 5. Configuration of cylindrical structure of the satellite. Table 6. Natural frequencies (Hz) and modes of vibration of cylindrical and hexahedral configuration. Hexah. conf. T'mode 72 (torsion) 2" mode (lateral bending) 98 Cylin. conf. l^mode 35 (lateral bending) 2 * mode (torsion) 47 In terms of stiffness, these results suggest the use of square decks rather than circular ones. These results are interesting in the sense that the stiffness of a single circular deck in torsion is higher than a square deck with the same area

9 Advances in Composite Materials and Structures VII (by about 12%, according to Sarafm el al [3] ); however, the stiffness of whole assembly seems to be more governed by other parameters. Tubes in the hexahedral structure are positioned farther from the center (or neutral axis of the structure) in comparison to the cylindrical configuration. This may justify the higher natural frequency of lateral mode for the hexahedral structure. Evaluation of modeling methods To check the effect of different ways of modeling the honeycomb structure of decks, three case analyses of a single circular deck were performed. These cases are: case 1) laminate representation using a single layer of shell elements, case 2) solid elements for core and two layers of shell elements for skins, case 3) all solid elements for core and skins. Skins and honeycomb core were assumed to be made of aluminum. A nonstructural mass of 20kg was employed. The frequencies for the first mode of three cases were obtained to be 87, 112, and 126 Hz for case 1 to 3 respectively. The difference is due to the averaging process in calculating properties of a composite laminate when the difference in material properties of constraint material is large. Since the frequencies given by the second and third method are acceptably close, either method may then be used for modeling sandwich decks. However, in terms of computer time and memory consumption, method of case 2 is preferred. When decks are integrated in the structure, these methods of modeling affect the overall predicted stiffness of the structure in an additional way. With method one, using shell elements to represent the panels, only a line of nodes around the tube is constrained by the shell elements of the deck. With method 2 and 3; however, nodes at two levels along the tube, distanced by the thickness of the deck, are constrained as shown in Figure 6. It is obvious that the method 2 and 3 are better representative of the actual structure and that a two-level constraint yields a stiffer structure. Therefore, the method one of modeling honeycomb panels underestimates the overall stiffness of the structure at two levels: at the component level and at the system level. 21 Tube (a) Deck Tube (b) Deck Figure 6. Connection between the deck and tube due to different modeling methods: a) shell element for deck, b) solid and shell elements for deck

10 22 Advances in Composite Materials and Structures VII Conclusions An analysis of frequency performance of a small satellite structure with regard to the material selection and structure configuration is performed. It was shown that the hexahedral configuration, which uses square decks, offers higher stiffness and natural frequency compared to cylindrical configuration. The study revealed that aluminum, used for tubular beams of the hexahedral configuration, yields better frequency performance compared to the unidirectional graphite-epoxy that has along-fiber elastic modulus of approximately twice as that of aluminum. These results were further supported by the results of analyses of tubular beams with varying lengths. It was shown, by later results, that the relative performance of aluminum and graphite-epoxy shifts at a certain length-to-depth ratio of the beam. Therefore, it is essential to identify this ratio for candidate materials, when one of them is a composite laminate or any material that has significantly different transverse shear and elastic modulus compared to the rest of targeted materials. This is due to the fact the shift in the performance of beams stems from the relative role of shear and normal deformation in compliance of the structure. It is therefore clear that material selection can not be carried out without consideration of geometry variables, as is the case when material indices are used to select optimum materials. For designers it can be said that to take full advantage of composite materials, which have low transverse shear modulus, the design should minimize the out-of-plane shear deformation. However, some quantitative guidelines, which are currently being studied by the authors, seem to be needed for designers. References: 1. Grastataro, C.I., T.A. Butler, E.G. Smith, and T.C. Thompson, Development of a Composite Satellite Structure for Forte, Proceedings of ICCM-10, Canada, Garvey, R.E., 1990, Potential for Advanced Thermoplastic Composites in Space Systems, 22^ International SAMPE Technical Conference, Sarafin, T. P. and Larson, W. J., Spacecraft structures and mechanisms : from concept to launch, Torrance, Calif. : Microcosm ; Dordrecht : Kluwer Academic, Larson, W. J. and Wertz, J. R., Space mission analysis and design, Torrance, Calif. : Microcosm ; Dordrecht: Kluwer Academic, 1992.