- Email: [email protected]
Mechanical behavior of carbon fiber reinforced polymer composite sandwich panels with 2-D lattice truss cores
Materials and Design 55 (2014) 591–596
Contents lists available at ScienceDirect
Materials and Design journal homepage: www.elsevier.com/locate/matdes
Technical Report
Mechanical behavior of carbon fiber reinforced polymer composite sandwich panels with 2-D lattice truss cores Bing Wang a,c,⇑, Guoqi Zhang a, Qilin He b, Li Ma a, Linzhi Wu a, Jicai Feng c a
Center for Composite Materials, Harbin Institute of Technology, Harbin 150001, PR China Beijing Institute of Astronautical Systems Engineering, Beijing 100076, PR China c School of Materials Science and Engineering, Harbin Institute of Technology, Harbin 150001, PR China b
a r t i c l e
i n f o
Article history: Received 11 October 2012 Accepted 10 October 2013 Available online 21 October 2013
a b s t r a c t Composite sandwich structures with lattice truss cores are attracting more and more attention due to their superior specific strength/stiffness and multi-functional applications. In the present study, the carbon fiber reinforced polymer (CFRP) composite sandwich panels with 2-D lattice truss core are manufactured based on the hot-pressing method using unidirectional carbon/epoxy prepregs. The facesheets are interconnected with lattice truss members by means of that both ends of the lattice truss members are embedded into the facesheets, without the bonding procedure commonly adopted by sandwich panels. The mechanical properties of the 2-D lattice truss sandwich panels are investigated under out-of-plane compression, shear and three-point bending tests. Delamination of the facesheets is observed in shear and bending tests while node failure mode does not occur. The tests demonstrate that delamination of the facesheet is the primary failure mode of this sandwich structure other than the debonding between the facesheets and core for conventional sandwiches. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Sandwich structures consisting of low density core and solid face sheets are widely used in naval and aeronautical applications due to their high stiffness/strength-to-weight ratio [1]. The conventional cores are honeycombs [2,3] and foams [4,5]. These sandwich panels have superior mechanical properties to their solid plate counterpart; however, these closed-cell configurations limit their multi-functional applications [6,7]. Recently, lattice truss cores have begun to be explored as a candidate core material because of their superior specific strength/stiffness and the large interconnected void space. The stiffness and strength of lattice materials scale linearly with the relative density q, which results that the lattice materials, at low relative densities, can therefore be more than an order of magnitude stronger and stiffer than equivalent mass per unit volume foams made from the same parent material. In order to explore the mechanical properties of lattices, the corresponding techniques to manufacture such sandwich structures have rapidly expanded during the past years. The investment casting, metal weaving and perforated wrought mental sheet folding methods have emerged to fabricate metal lattice structures [8–10]. For the design calculations, the mechanism maps based on beam theory have been given by
⇑ Corresponding author at: Center for Composite Materials, Harbin Institute of Technology, Harbin 150001, PR China. Tel./fax: +86 451 86402376. E-mail address: [email protected] (B. Wang). 0261-3069/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.matdes.2013.10.025
Desphande and Fleck [11]. Wicks and Hutchinson have optimally designed such panels subject to prescribed combinations of bending and transverse shear loads [12]. Besides, the quasi-static /dynamic mechanical response of the lattice sandwich structures has been investigated by numerous scholars [13–15]. The measurements have shown that the lattice sandwich structures have desirable mechanical properties such as specific strength/stiffness and impact energy absorption. In addition, such materials are also expected to find applications in lightweight, compact structural heat exchangers [16]. Their open-cell configuration allows heat exchange along the panel core, making them as attractive candidates for development of multi-function systems. Moreover, the Kagome core sandwich structures have been investigated as shape morphing structure by Symons et al. [17,18]. As we know, the behavior of sandwich structures primarily depends on the topology and the parent material. The optimized lattice topology and superior parent material properties can be combined to create new engineering materials, which expand the material property space. In view of this, the CFRP which can provide high uniaxial specific strength is used as the parent material of the lattice core sandwich structures. Fan et al. [19,20] have manufactured a carbon fiber-reinforced three-dimensional lattice core sandwich panel using an intertwining method. Finnegan et al. [21] manufactured CFRP pyramidal truss cores by slot-fitting method. In order to improve the shear performance of pyramidal lattice core sandwich structure, Yuguo Sun and Liang Gao presented an improved pyramidal lattice truss core sandwich structure by introducing a series of parallel
592
B. Wang et al. / Materials and Design 55 (2014) 591–596
distributed cross-bars to core members [22]. Compared with 3-D lattice sandwich structures, the preparation process of 2-D lattice sandwich structures is easier [23]. In contrast, the longitudinal shear performance of 2-D lattice sandwich structures is better, which may be used under shear loading in one direction. Thus, the aim of the present work is to develop a new method to manufacture the composite 2-D lattice sandwich structures. In addition, the mechanical properties of 2-D lattice truss core sandwich panels are tested under the out-of-plane compression, shear and threepoint bending loadings. Finally, the failure mechanism and mechanical properties of the new structure are also discussed.
The unit cell of 2-D lattice truss core is shown in Fig. 1. The relative density of the 2-D lattice truss cores depends on the diameter of the truss member d, inclination angle x, length l of truss member, width b of the unit cell, and the distance t between the adjacent truss members, which is as following
pd2 4b sin xðl cos x þ tÞ
ð1Þ
The geometrical parameters are taken as d = 3 mm, l = 17 mm, b = 20 mm, t = 3 mm, and x = 45° in the present study, so the relative density of the truss core, q, is 3.33%. The composite sandwich panels with 2-D lattice truss cores are manufactured based on the hot-pressing method. In order to configure the lattice core topology, many cuboid flat steel plates with semicircular grooves on the side face are used as molds, as shown in Fig. 2. In the manufacturing process, the molds are assembled after the surface is cleaned with acetone and coated with the mold release agent. Carbon fiber prepregs are cut to the required size, and then rolled into rods as truss members with fibers along the direction of truss members, whose radius coincides with that of the semicircular grooves on the side face of molds. Then, the composite rods are inserted into the holes of the assembled mold with about 0.5 cm outside the molds, as depicted in Fig. 3. After that, the unidirectional carbon/epoxy (T700/TDE85) prepregs are layered on the top surface of molds to configure the facesheets, with the stacking sequence [00/450/450/00]s, and both ends of truss members are dispersed and gradually embedded into the eight layers of facesheets. The preforms are then cured at 170 °C under pressure of 0.7 MPa for 3 h on the hot press. Finally, removing the molds and cutting out the panels to the required dimensions, we get the corresponding samples, as shown in Fig. 4. 3. Experiments 3.1. Out-of-plane compression of 2-D truss core sandwich panels Compression tests are performed with panels of 73 60 15 mm to determine their compressive stiffness and
Fig. 1. Schematic of 2-D lattice truss core unit cell.
strength in the out-of-plane direction in accordance with ASTM: C365/C365 M-11a A screw driven testing machine (Instron 5569) is used to test samples at a rate of 0.5 mm/min. At least three tests are conducted to confirm the repeatability of the measurements. 3.2. Shear behavior of 2-D truss core sandwich panels
2. Fabrication
q ¼
Fig. 2. Photograph of the molds.
As we know, sandwich structures are usually used in situations where they are subjected to significant bending loads. The applied bending moment is balanced by the bending stress in the facesheets. On the other hand, the traverse shear load is supported mainly by the core. Typically, cores are the weakest part of sandwich structures. Based on the work done by Deshpande and Fleck [11], we know that this 2-D lattice is anisotropic in bending and shearing loads. Along the orthogonal direction, the shear/bending strength must be much smaller. Thus, the core should be optimally designed to select the appropriate orientation to achieve a high load carrying capacity, and the case that the core along the orthogonal direction bears the load is not desirable. Therefore, it is instructive to explore the properties of this core along the wave direction. In this case, the shear or bending tests for this sandwich structure is also along this direction. Shear tests are performed in accordance with ASTM: C273/ C273 M-11. The test fixture used to obtain shear stress/strain of the core is shown in Fig. 5. The specimens are rigidly bonded to steel plates by adhesive, and the dimensions of the specimens are 150 60 15 mm. 3.3. Bending behavior of 2-D truss core sandwich panels Three-point bending tests are conducted using the Instron 5569 universal testing machine according to ASTM C393/C393 M-11e1 The specimens with the dimension of 200 60 15 mm, and the distance between the supports is 180 mm, as shown in Fig. 6. The column radius of the support and loading pins is 10 mm. 4. Results The typical compressive stress–strain response is shown in Fig. 7. Following an initial linear response, the compressive stress approaches the peak value. After that, the zigzag fluctuation appears due to the splitting occurring at the ends of truss members, and then the load suddenly decreases because of the buckling of the fibers, as shown in Fig. 8. Based on the compressive stress– strain curve, the compressive strength and the Young’s modulus, 2.64 and 210.2 MPa, respectively, are obtained for such sandwich structure. Considering the composite density of 1560 kg/m3, the specific strength (compressive strength/ density) of this 2-D lattice truss core is 51.28 103 N m/kg, which is compared well with other lightweight cores [24]. The shear stress–strain response is shown in Fig. 9. During the initial stage of loading, the response is fairly linear. Thus, based on this linear stage, we can obtain the shear modulus of 94.8 MPa. Thereafter, a small fluctuation emerges when the shear stress approaches 1.1 MPa while the load continues to increase as the shear stress arrives at the maximum value, 1.38 MPa. In the tests, delamination of facesheets is observed which is due to the defects such as fiber tangle or voids generated when the truss members are embedded into the facesheets, as shown in Fig. 10.
B. Wang et al. / Materials and Design 55 (2014) 591–596
593
Fig. 3. Fabrication of the CFRP 2-D lattice truss core sandwich structures. (a) The unidirectional carbon/epoxy prepregs; (b) the truss member rolled by the prepregs; (c) the assembled molds.
Fig. 4. The sandwich panel with carbon fiber-reinforced 2-D lattice truss core.
Fig. 6. The three-point bending test.
Fig. 7. The stress–strain curve of out-of-plane compression test.
Fig. 5. Schematic of the tension shear test fixture.
However, the debonding failure mode between the core and facesheets which is prone to occur for sandwich panels under shear tests is not observed [22]. This delamination failure in tests implies
that the future work will focus on improving the fabrication process to increase the interlayer property. The load–displacement curve for the three-bending tests depicted in Fig. 11 display two representative regions, referred to as the elastic region A and the delamination region B, C and D,
594
B. Wang et al. / Materials and Design 55 (2014) 591–596
Fig. 8. The failure mode of the 2-D lattice truss core sandwich panels during out-ofplane compression test.
Fig. 11. The load–displacement curve of 2-D lattice truss core sandwich panel during the three-point bending test.
member failure is not observed during the bending test. The three points in the load–displacement curve indicate that the interfacial delamination occurs for three times, as shown in Fig. 12(b–d). 5. Discussion Fig. 9. The shear stress–strain curve for 2-D truss core sandwich panels.
(a)
(b)
Analytical expressions for the compressive modulus E of the 2-D lattice truss cores are given by first analyzing the elastic deformations of a single strut of the 2-D lattice truss cores and then extending the results to evaluate the effective properties of the whole core. Considering a strut of length l and circle cross-section of diameter d as shown in Fig. 13, symmetry conditions indicate that the top end of the strut is only free to move along the x3-direction. For an imposed displacement d in the x3-direction, the axial and shear forces in the strut are given by elementary beam theory as
FA ¼ Fs ¼
1 2 d sin x pd Es 4 l 3Es Id cos x l
ð2Þ
ð3Þ
3 4
d where I ¼ p64 is the second moment of area of the strut cross-section. The total applied force F in the x3-direction then follows as
" # 2 2 Es pd d 3 d 2 2 F ¼ F A sin x þ F S cos x ¼ sin x þ cos x 4l 16 l
ð4Þ
Then, the through-thickness stress r and strain e applied to the 2-D cores are related to the force F and displacement d via:
2F b ð2l cos x þ 2tÞ " # 2 2 E s pd d 3 d 2 2 sin x þ cos x ¼ 4blðl cos x þ tÞ 16 l
r¼ Fig. 10. Photographs of the experimental shear test. (a) Initial loading; (b) delamination of facesheets.
ð5Þ
and respectively. The calculated bending rigidity is 6.32 kN/m2 based on the elastic region while the applied maximum load is 1887 N in the test. As we know, the applied bending moment is supported mainly by the facesheets and the top facesheet mainly carries the compressive load while the bottom facesheet mainly bears the tensile load. On the other hand, the traverse shear load is sustained mainly by the core. With the applied load increase, the top facesheet tends to buckle under compressive load which also induces delamination. The delamination of the top facesheet leads to a sudden drop of the load, as shown in Fig. 11, while the facesheets and the truss cores are still connected together. Node failure or truss
e¼
d l sin x
ð6Þ
respectively. Combining Eqs. (4)–(6) then gives the effective Young’s modulus of the 2-D cores:
" # 2 EC pd2 sin x 3 d 2 2 ¼ sin x þ cos x 16 l ES 4bðl cos x þ tÞ2 4
sin x þ Ec ¼ ES q
2 3 d 2 ES q sin x cos2 x 16 l
ð7Þ
ð8Þ
B. Wang et al. / Materials and Design 55 (2014) 591–596
595
(a)
(b)
(c)
(d)
(e)
Fig. 12. Deformation history of composite sandwich structure with inclined lattice truss cores in the three-point bending test. (a) Elastic deformation; (b) splitting of composite columns; (c–e) delamination of facesheet.
where ES = 33.2 GPa is the compressive Young’s modulus of unidirectional carbon fiber composite truss member measured by means of a single truss member under compressive load [22]. However, due to the intricate failure mode as mentioned earlier, analytical expressions for the prediction of compressive strength can not be derived. According to Eq. (9), the effective compressive Young’s modulus of the 2-D truss cores sandwich panel is 276.39 MPa, which is about 31.2% larger than the measured Young’s modulus. It is because that there may be many micro-defects in the truss members caused by the less pressure along the radial direction of fiber rods in the molding of composite structures. The shear stiffness of lattice truss cores is given by Deshpande [13] as
Gs ¼
Fig. 13. (a) Sketch of the deformation of a single strut of 2-D lattice truss core under out-of-plane compression. (b) The free-body diagram of a strut loaded in a combination of compression and shear.
2
¼ 4b sin xpðldcos xþtÞ is the relative density. where q The first and second terms in Eq. (8) represent the contributions to the stiffness of the 2-D cores due to the stretching and bending of the struts, respectively. Compared with the first term, the second term is a small quantity and can be neglected. 4
sin x Ec ¼ ES q
ð9Þ
1 2 Es sin 2x q 8
ð10Þ
where Es = 33.2 GPa is the compressive Young’s modulus of the carbon fiber composite truss members measured on the single truss member under compressive test. According to Eq. (10), the effective shear modulus of 2-D lattice truss cores is 138.2 MPa, about 47.87% larger than the tests. This discrepancy may be attributed to the sample misalignment as well as the small gaps in the fixture that may introduce excessive relative displacement during the tests. The large discrepancy can also be found by Deshpande and Fleck [13]. Although debonding between the cores and facesheet which always occurred for sandwiches under shear load did not emerge during the parent investigation, the shear strength was not desirable compared with the work done by Tochukwu George et al. [25]. It is that the lattice truss members were embedded in the cruciform shaped slots around the facesheets in their investigation.
596
B. Wang et al. / Materials and Design 55 (2014) 591–596
During the tests, only buckling and delamination of truss members occurred, which can efficiently take advantage of the material property of composites. For the shear tests of metal lattice truss members, the fracture, yielding and buckling of truss members were the main failure modes [8,13]. Therefore, the shear performance of this composite lattice truss cores was not fully presented owing to the delamination of facesheets. The shear performance of such sandwich structures can be better supposing the delamination of facesheets was restrained. For the bending tests, the bending rigidity is desirable considering the mass of such sandwich structures. However, also the delamination failure mode of facesheets governed the subsequent performance of such sandwich structures. Therefore, the future work will focus on improving the interface property of facesheets to prevent the early occurring of delamination.
6. Conclusions In the present study, CFRP 2-D truss core sandwich panels are manufactured based on the hot-pressing method. The 2-D truss cores and the facesheets are interconnected together by means of both ends of truss members embedded into the facesheets during the prepreg laying process. Out-of-plane compression, shear and three-point bending tests are carried out to study the mechanical behaviors of the 2-D truss core sandwich panels. According to the experiments, the mechanical behaviors of the CFRP 2-D truss core sandwich panels can be concluded as follows: Delamination of facesheets is the main weakness this composite 2-D truss core sandwich panel; The shear strength of the 2-D lattice truss core is higher than the interface strength of facesheets; The delamination always occurs around to the area where the truss members embedded into the facesheets. Therefore, the future work will focus on improving the fabrication process to increase the interface property.
Acknowledgements The present work is supported by National Science Foundation of China under Grant No. 11202059, Natural Science Foundation of Heilongjiang Province (No. A201204), the Major State Basic Research Development Program of China (973 Program) under Grant No. 2011CB600303, Key Laboratory Opening Funding of Advanced Composites in Special Environment(2011) and the fundamental research funds for the central Universities (Grant No. HIT.NSRIF.2010069).
References [1] Gibson LJ, Ashby MF. Cellular solids: structure and properties. Cambridge University Press; 1997. [2] Papka SD, Kyriakides S. In-plane compressive response and crushing of honeycomb. J Mech Phys Solids 1994;42:1499–532. [3] Klinworth JW, St ronge WJ. Plane punch indentation of a ductile honeycomb. Int J Mech Sci 1989;3:359–78. [4] Banhart J, Stanzick H, Helfen L, Baumbach T. Metal foam evolution studied by synchrotron radioscopy. Appl Phys Lett 2001;178:1152–4. [5] Evans AG, Hutchinson JW, Fleck NA, et al. The topological multifunctional cellular metals. Prog Mater Sci 2001;46:309–27. [6] Evans AG, Hutchinson JW, Ashby MF. Multifunctionality of cellular metal systems. Prog Mater Sci 1999;43:171–221. [7] Wadley HNG, Fleck NA, Evans AG. Fabrication and structural performance of periodic cellular metal. Composi Sci Technol 2003;63:2331–43. [8] Yuki Sugimura. Mechanical response of single-layer tetrahedral trusses under shear loading. Mech Mater 2004;36:715–21. [9] Lim Ji-Hyun, Kang Ki-Ju. Mechanical behavior of sandwich panels with tetrahedral and Kagome truss cores fabrication from wires. Int J Solids Struct 2006;43:5228–46. [10] Kooistra Gregory W, Deshpande Vikram S, Wadley Haydn NG. Compressive behavior of age hardenable tetrahedral lattice truss structures made from aluminum. Acta Mater 2004;52:4229–37. [11] Deshpande VS, Fleck NA. Collapse of truss core sandwich beams in 3pointbending. Int J Solids Struct 2001;38:6275–305. [12] Nathan Wicks, Hutchinson John W. Optimal truss plates. Int J Solids Struct 2001;38:5165–83. [13] Deshpande VS, Fleck NA, Ashby MF. Effective properties of the octet-truss lattice material. J Mech Phys Solids 2001;49:1747–69. [14] Yungwirth Christian J, Radford Darren D, Aronson Mark, Wadley Haydn NG. Experiment assessment of the ballistic response of composite pyramidal lattice truss structures. Composite: Part B 2008;39:556–69. [15] Cote F, Fleck NA, Deshpande VS. Fatigue performance of sandwich beams with a pyramidal core. Int J Fatigue 2007;29:1402–12. [16] Lu TJ, Valdevit L, Evans AG. Active cooling by metallic sandwich structures with periodic cores. Prog Mater Sci 2005;50:789–815. [17] Symons DD, Hutchinson RG, Fleck NA. Actuation of the Kagome Double-Layer Grid. Part 1: Prediction of performance of the perfect structure. J Mech Phys Solids 2005;53:1855–74. [18] Symons DD, Shieh J, Fleck NA. Actuation of the Kagome Double-Layer Grid. Part 2: Effect of imperfections on the measured and predicted actuation stiffness. J Mech Phys Solids 2005;53:1875–91. [19] Fan HL, Yang W, Yan Y, Fu Q, Fang DN, Zhuang Z. Design and manufacturing of a composite lattice structure reinforced by continuous carbon fibers. Stinghua Sci Technol 2006;11:515–22. [20] Fan HL, Meng FH, Yang W. Sandwich panels with kagome lattice cores reinforced by carbon fibers. Compos Struct 2007;81:533–9. [21] Finnegan K, Koositra G, Wadley HNG, Dshpande VS. The compressive response of carbon fiber composite pyramidal truss sandwich cores. Int J Mat Res 2007;98:1264–72. [22] Wang Bing, Linzhi Wu, Jin Xin, Shanyi Du, Sun Yuguo, Ma Li. Experimental investigation of 3D sandwich structure with core reinforced by composite struts. Mater Des 2010;31:158–65. [23] Sun Yuguo, Gao Liang. Structural responses of all-composite improvedpyramidal truss sandwich cores. Mater Des 2013;43:50–8. [24] Jingjing Zheng, Long Zhao, Hualin Fan. Energy absorption mechanisms of hierarchical woven lattice composites. Composite: Part B 2012;43:1516–22. [25] Tochukwu George, Deshpande SVikram, Wadley Haydn NG. Mechanical response of carbon fiber composite sandwich panels with pyramidal truss cores. Composite: Part A 2013;47:31–40.
Contents lists available at ScienceDirect
Materials and Design journal homepage: www.elsevier.com/locate/matdes
Technical Report
Mechanical behavior of carbon fiber reinforced polymer composite sandwich panels with 2-D lattice truss cores Bing Wang a,c,⇑, Guoqi Zhang a, Qilin He b, Li Ma a, Linzhi Wu a, Jicai Feng c a
Center for Composite Materials, Harbin Institute of Technology, Harbin 150001, PR China Beijing Institute of Astronautical Systems Engineering, Beijing 100076, PR China c School of Materials Science and Engineering, Harbin Institute of Technology, Harbin 150001, PR China b
a r t i c l e
i n f o
Article history: Received 11 October 2012 Accepted 10 October 2013 Available online 21 October 2013
a b s t r a c t Composite sandwich structures with lattice truss cores are attracting more and more attention due to their superior specific strength/stiffness and multi-functional applications. In the present study, the carbon fiber reinforced polymer (CFRP) composite sandwich panels with 2-D lattice truss core are manufactured based on the hot-pressing method using unidirectional carbon/epoxy prepregs. The facesheets are interconnected with lattice truss members by means of that both ends of the lattice truss members are embedded into the facesheets, without the bonding procedure commonly adopted by sandwich panels. The mechanical properties of the 2-D lattice truss sandwich panels are investigated under out-of-plane compression, shear and three-point bending tests. Delamination of the facesheets is observed in shear and bending tests while node failure mode does not occur. The tests demonstrate that delamination of the facesheet is the primary failure mode of this sandwich structure other than the debonding between the facesheets and core for conventional sandwiches. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Sandwich structures consisting of low density core and solid face sheets are widely used in naval and aeronautical applications due to their high stiffness/strength-to-weight ratio [1]. The conventional cores are honeycombs [2,3] and foams [4,5]. These sandwich panels have superior mechanical properties to their solid plate counterpart; however, these closed-cell configurations limit their multi-functional applications [6,7]. Recently, lattice truss cores have begun to be explored as a candidate core material because of their superior specific strength/stiffness and the large interconnected void space. The stiffness and strength of lattice materials scale linearly with the relative density q, which results that the lattice materials, at low relative densities, can therefore be more than an order of magnitude stronger and stiffer than equivalent mass per unit volume foams made from the same parent material. In order to explore the mechanical properties of lattices, the corresponding techniques to manufacture such sandwich structures have rapidly expanded during the past years. The investment casting, metal weaving and perforated wrought mental sheet folding methods have emerged to fabricate metal lattice structures [8–10]. For the design calculations, the mechanism maps based on beam theory have been given by
⇑ Corresponding author at: Center for Composite Materials, Harbin Institute of Technology, Harbin 150001, PR China. Tel./fax: +86 451 86402376. E-mail address: [email protected] (B. Wang). 0261-3069/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.matdes.2013.10.025
Desphande and Fleck [11]. Wicks and Hutchinson have optimally designed such panels subject to prescribed combinations of bending and transverse shear loads [12]. Besides, the quasi-static /dynamic mechanical response of the lattice sandwich structures has been investigated by numerous scholars [13–15]. The measurements have shown that the lattice sandwich structures have desirable mechanical properties such as specific strength/stiffness and impact energy absorption. In addition, such materials are also expected to find applications in lightweight, compact structural heat exchangers [16]. Their open-cell configuration allows heat exchange along the panel core, making them as attractive candidates for development of multi-function systems. Moreover, the Kagome core sandwich structures have been investigated as shape morphing structure by Symons et al. [17,18]. As we know, the behavior of sandwich structures primarily depends on the topology and the parent material. The optimized lattice topology and superior parent material properties can be combined to create new engineering materials, which expand the material property space. In view of this, the CFRP which can provide high uniaxial specific strength is used as the parent material of the lattice core sandwich structures. Fan et al. [19,20] have manufactured a carbon fiber-reinforced three-dimensional lattice core sandwich panel using an intertwining method. Finnegan et al. [21] manufactured CFRP pyramidal truss cores by slot-fitting method. In order to improve the shear performance of pyramidal lattice core sandwich structure, Yuguo Sun and Liang Gao presented an improved pyramidal lattice truss core sandwich structure by introducing a series of parallel
592
B. Wang et al. / Materials and Design 55 (2014) 591–596
distributed cross-bars to core members [22]. Compared with 3-D lattice sandwich structures, the preparation process of 2-D lattice sandwich structures is easier [23]. In contrast, the longitudinal shear performance of 2-D lattice sandwich structures is better, which may be used under shear loading in one direction. Thus, the aim of the present work is to develop a new method to manufacture the composite 2-D lattice sandwich structures. In addition, the mechanical properties of 2-D lattice truss core sandwich panels are tested under the out-of-plane compression, shear and threepoint bending loadings. Finally, the failure mechanism and mechanical properties of the new structure are also discussed.
The unit cell of 2-D lattice truss core is shown in Fig. 1. The relative density of the 2-D lattice truss cores depends on the diameter of the truss member d, inclination angle x, length l of truss member, width b of the unit cell, and the distance t between the adjacent truss members, which is as following
pd2 4b sin xðl cos x þ tÞ
ð1Þ
The geometrical parameters are taken as d = 3 mm, l = 17 mm, b = 20 mm, t = 3 mm, and x = 45° in the present study, so the relative density of the truss core, q, is 3.33%. The composite sandwich panels with 2-D lattice truss cores are manufactured based on the hot-pressing method. In order to configure the lattice core topology, many cuboid flat steel plates with semicircular grooves on the side face are used as molds, as shown in Fig. 2. In the manufacturing process, the molds are assembled after the surface is cleaned with acetone and coated with the mold release agent. Carbon fiber prepregs are cut to the required size, and then rolled into rods as truss members with fibers along the direction of truss members, whose radius coincides with that of the semicircular grooves on the side face of molds. Then, the composite rods are inserted into the holes of the assembled mold with about 0.5 cm outside the molds, as depicted in Fig. 3. After that, the unidirectional carbon/epoxy (T700/TDE85) prepregs are layered on the top surface of molds to configure the facesheets, with the stacking sequence [00/450/450/00]s, and both ends of truss members are dispersed and gradually embedded into the eight layers of facesheets. The preforms are then cured at 170 °C under pressure of 0.7 MPa for 3 h on the hot press. Finally, removing the molds and cutting out the panels to the required dimensions, we get the corresponding samples, as shown in Fig. 4. 3. Experiments 3.1. Out-of-plane compression of 2-D truss core sandwich panels Compression tests are performed with panels of 73 60 15 mm to determine their compressive stiffness and
Fig. 1. Schematic of 2-D lattice truss core unit cell.
strength in the out-of-plane direction in accordance with ASTM: C365/C365 M-11a A screw driven testing machine (Instron 5569) is used to test samples at a rate of 0.5 mm/min. At least three tests are conducted to confirm the repeatability of the measurements. 3.2. Shear behavior of 2-D truss core sandwich panels
2. Fabrication
q ¼
Fig. 2. Photograph of the molds.
As we know, sandwich structures are usually used in situations where they are subjected to significant bending loads. The applied bending moment is balanced by the bending stress in the facesheets. On the other hand, the traverse shear load is supported mainly by the core. Typically, cores are the weakest part of sandwich structures. Based on the work done by Deshpande and Fleck [11], we know that this 2-D lattice is anisotropic in bending and shearing loads. Along the orthogonal direction, the shear/bending strength must be much smaller. Thus, the core should be optimally designed to select the appropriate orientation to achieve a high load carrying capacity, and the case that the core along the orthogonal direction bears the load is not desirable. Therefore, it is instructive to explore the properties of this core along the wave direction. In this case, the shear or bending tests for this sandwich structure is also along this direction. Shear tests are performed in accordance with ASTM: C273/ C273 M-11. The test fixture used to obtain shear stress/strain of the core is shown in Fig. 5. The specimens are rigidly bonded to steel plates by adhesive, and the dimensions of the specimens are 150 60 15 mm. 3.3. Bending behavior of 2-D truss core sandwich panels Three-point bending tests are conducted using the Instron 5569 universal testing machine according to ASTM C393/C393 M-11e1 The specimens with the dimension of 200 60 15 mm, and the distance between the supports is 180 mm, as shown in Fig. 6. The column radius of the support and loading pins is 10 mm. 4. Results The typical compressive stress–strain response is shown in Fig. 7. Following an initial linear response, the compressive stress approaches the peak value. After that, the zigzag fluctuation appears due to the splitting occurring at the ends of truss members, and then the load suddenly decreases because of the buckling of the fibers, as shown in Fig. 8. Based on the compressive stress– strain curve, the compressive strength and the Young’s modulus, 2.64 and 210.2 MPa, respectively, are obtained for such sandwich structure. Considering the composite density of 1560 kg/m3, the specific strength (compressive strength/ density) of this 2-D lattice truss core is 51.28 103 N m/kg, which is compared well with other lightweight cores [24]. The shear stress–strain response is shown in Fig. 9. During the initial stage of loading, the response is fairly linear. Thus, based on this linear stage, we can obtain the shear modulus of 94.8 MPa. Thereafter, a small fluctuation emerges when the shear stress approaches 1.1 MPa while the load continues to increase as the shear stress arrives at the maximum value, 1.38 MPa. In the tests, delamination of facesheets is observed which is due to the defects such as fiber tangle or voids generated when the truss members are embedded into the facesheets, as shown in Fig. 10.
B. Wang et al. / Materials and Design 55 (2014) 591–596
593
Fig. 3. Fabrication of the CFRP 2-D lattice truss core sandwich structures. (a) The unidirectional carbon/epoxy prepregs; (b) the truss member rolled by the prepregs; (c) the assembled molds.
Fig. 4. The sandwich panel with carbon fiber-reinforced 2-D lattice truss core.
Fig. 6. The three-point bending test.
Fig. 7. The stress–strain curve of out-of-plane compression test.
Fig. 5. Schematic of the tension shear test fixture.
However, the debonding failure mode between the core and facesheets which is prone to occur for sandwich panels under shear tests is not observed [22]. This delamination failure in tests implies
that the future work will focus on improving the fabrication process to increase the interlayer property. The load–displacement curve for the three-bending tests depicted in Fig. 11 display two representative regions, referred to as the elastic region A and the delamination region B, C and D,
594
B. Wang et al. / Materials and Design 55 (2014) 591–596
Fig. 8. The failure mode of the 2-D lattice truss core sandwich panels during out-ofplane compression test.
Fig. 11. The load–displacement curve of 2-D lattice truss core sandwich panel during the three-point bending test.
member failure is not observed during the bending test. The three points in the load–displacement curve indicate that the interfacial delamination occurs for three times, as shown in Fig. 12(b–d). 5. Discussion Fig. 9. The shear stress–strain curve for 2-D truss core sandwich panels.
(a)
(b)
Analytical expressions for the compressive modulus E of the 2-D lattice truss cores are given by first analyzing the elastic deformations of a single strut of the 2-D lattice truss cores and then extending the results to evaluate the effective properties of the whole core. Considering a strut of length l and circle cross-section of diameter d as shown in Fig. 13, symmetry conditions indicate that the top end of the strut is only free to move along the x3-direction. For an imposed displacement d in the x3-direction, the axial and shear forces in the strut are given by elementary beam theory as
FA ¼ Fs ¼
1 2 d sin x pd Es 4 l 3Es Id cos x l
ð2Þ
ð3Þ
3 4
d where I ¼ p64 is the second moment of area of the strut cross-section. The total applied force F in the x3-direction then follows as
" # 2 2 Es pd d 3 d 2 2 F ¼ F A sin x þ F S cos x ¼ sin x þ cos x 4l 16 l
ð4Þ
Then, the through-thickness stress r and strain e applied to the 2-D cores are related to the force F and displacement d via:
2F b ð2l cos x þ 2tÞ " # 2 2 E s pd d 3 d 2 2 sin x þ cos x ¼ 4blðl cos x þ tÞ 16 l
r¼ Fig. 10. Photographs of the experimental shear test. (a) Initial loading; (b) delamination of facesheets.
ð5Þ
and respectively. The calculated bending rigidity is 6.32 kN/m2 based on the elastic region while the applied maximum load is 1887 N in the test. As we know, the applied bending moment is supported mainly by the facesheets and the top facesheet mainly carries the compressive load while the bottom facesheet mainly bears the tensile load. On the other hand, the traverse shear load is sustained mainly by the core. With the applied load increase, the top facesheet tends to buckle under compressive load which also induces delamination. The delamination of the top facesheet leads to a sudden drop of the load, as shown in Fig. 11, while the facesheets and the truss cores are still connected together. Node failure or truss
e¼
d l sin x
ð6Þ
respectively. Combining Eqs. (4)–(6) then gives the effective Young’s modulus of the 2-D cores:
" # 2 EC pd2 sin x 3 d 2 2 ¼ sin x þ cos x 16 l ES 4bðl cos x þ tÞ2 4
sin x þ Ec ¼ ES q
2 3 d 2 ES q sin x cos2 x 16 l
ð7Þ
ð8Þ
B. Wang et al. / Materials and Design 55 (2014) 591–596
595
(a)
(b)
(c)
(d)
(e)
Fig. 12. Deformation history of composite sandwich structure with inclined lattice truss cores in the three-point bending test. (a) Elastic deformation; (b) splitting of composite columns; (c–e) delamination of facesheet.
where ES = 33.2 GPa is the compressive Young’s modulus of unidirectional carbon fiber composite truss member measured by means of a single truss member under compressive load [22]. However, due to the intricate failure mode as mentioned earlier, analytical expressions for the prediction of compressive strength can not be derived. According to Eq. (9), the effective compressive Young’s modulus of the 2-D truss cores sandwich panel is 276.39 MPa, which is about 31.2% larger than the measured Young’s modulus. It is because that there may be many micro-defects in the truss members caused by the less pressure along the radial direction of fiber rods in the molding of composite structures. The shear stiffness of lattice truss cores is given by Deshpande [13] as
Gs ¼
Fig. 13. (a) Sketch of the deformation of a single strut of 2-D lattice truss core under out-of-plane compression. (b) The free-body diagram of a strut loaded in a combination of compression and shear.
2
¼ 4b sin xpðldcos xþtÞ is the relative density. where q The first and second terms in Eq. (8) represent the contributions to the stiffness of the 2-D cores due to the stretching and bending of the struts, respectively. Compared with the first term, the second term is a small quantity and can be neglected. 4
sin x Ec ¼ ES q
ð9Þ
1 2 Es sin 2x q 8
ð10Þ
where Es = 33.2 GPa is the compressive Young’s modulus of the carbon fiber composite truss members measured on the single truss member under compressive test. According to Eq. (10), the effective shear modulus of 2-D lattice truss cores is 138.2 MPa, about 47.87% larger than the tests. This discrepancy may be attributed to the sample misalignment as well as the small gaps in the fixture that may introduce excessive relative displacement during the tests. The large discrepancy can also be found by Deshpande and Fleck [13]. Although debonding between the cores and facesheet which always occurred for sandwiches under shear load did not emerge during the parent investigation, the shear strength was not desirable compared with the work done by Tochukwu George et al. [25]. It is that the lattice truss members were embedded in the cruciform shaped slots around the facesheets in their investigation.
596
B. Wang et al. / Materials and Design 55 (2014) 591–596
During the tests, only buckling and delamination of truss members occurred, which can efficiently take advantage of the material property of composites. For the shear tests of metal lattice truss members, the fracture, yielding and buckling of truss members were the main failure modes [8,13]. Therefore, the shear performance of this composite lattice truss cores was not fully presented owing to the delamination of facesheets. The shear performance of such sandwich structures can be better supposing the delamination of facesheets was restrained. For the bending tests, the bending rigidity is desirable considering the mass of such sandwich structures. However, also the delamination failure mode of facesheets governed the subsequent performance of such sandwich structures. Therefore, the future work will focus on improving the interface property of facesheets to prevent the early occurring of delamination.
6. Conclusions In the present study, CFRP 2-D truss core sandwich panels are manufactured based on the hot-pressing method. The 2-D truss cores and the facesheets are interconnected together by means of both ends of truss members embedded into the facesheets during the prepreg laying process. Out-of-plane compression, shear and three-point bending tests are carried out to study the mechanical behaviors of the 2-D truss core sandwich panels. According to the experiments, the mechanical behaviors of the CFRP 2-D truss core sandwich panels can be concluded as follows: Delamination of facesheets is the main weakness this composite 2-D truss core sandwich panel; The shear strength of the 2-D lattice truss core is higher than the interface strength of facesheets; The delamination always occurs around to the area where the truss members embedded into the facesheets. Therefore, the future work will focus on improving the fabrication process to increase the interface property.
Acknowledgements The present work is supported by National Science Foundation of China under Grant No. 11202059, Natural Science Foundation of Heilongjiang Province (No. A201204), the Major State Basic Research Development Program of China (973 Program) under Grant No. 2011CB600303, Key Laboratory Opening Funding of Advanced Composites in Special Environment(2011) and the fundamental research funds for the central Universities (Grant No. HIT.NSRIF.2010069).
References [1] Gibson LJ, Ashby MF. Cellular solids: structure and properties. Cambridge University Press; 1997. [2] Papka SD, Kyriakides S. In-plane compressive response and crushing of honeycomb. J Mech Phys Solids 1994;42:1499–532. [3] Klinworth JW, St ronge WJ. Plane punch indentation of a ductile honeycomb. Int J Mech Sci 1989;3:359–78. [4] Banhart J, Stanzick H, Helfen L, Baumbach T. Metal foam evolution studied by synchrotron radioscopy. Appl Phys Lett 2001;178:1152–4. [5] Evans AG, Hutchinson JW, Fleck NA, et al. The topological multifunctional cellular metals. Prog Mater Sci 2001;46:309–27. [6] Evans AG, Hutchinson JW, Ashby MF. Multifunctionality of cellular metal systems. Prog Mater Sci 1999;43:171–221. [7] Wadley HNG, Fleck NA, Evans AG. Fabrication and structural performance of periodic cellular metal. Composi Sci Technol 2003;63:2331–43. [8] Yuki Sugimura. Mechanical response of single-layer tetrahedral trusses under shear loading. Mech Mater 2004;36:715–21. [9] Lim Ji-Hyun, Kang Ki-Ju. Mechanical behavior of sandwich panels with tetrahedral and Kagome truss cores fabrication from wires. Int J Solids Struct 2006;43:5228–46. [10] Kooistra Gregory W, Deshpande Vikram S, Wadley Haydn NG. Compressive behavior of age hardenable tetrahedral lattice truss structures made from aluminum. Acta Mater 2004;52:4229–37. [11] Deshpande VS, Fleck NA. Collapse of truss core sandwich beams in 3pointbending. Int J Solids Struct 2001;38:6275–305. [12] Nathan Wicks, Hutchinson John W. Optimal truss plates. Int J Solids Struct 2001;38:5165–83. [13] Deshpande VS, Fleck NA, Ashby MF. Effective properties of the octet-truss lattice material. J Mech Phys Solids 2001;49:1747–69. [14] Yungwirth Christian J, Radford Darren D, Aronson Mark, Wadley Haydn NG. Experiment assessment of the ballistic response of composite pyramidal lattice truss structures. Composite: Part B 2008;39:556–69. [15] Cote F, Fleck NA, Deshpande VS. Fatigue performance of sandwich beams with a pyramidal core. Int J Fatigue 2007;29:1402–12. [16] Lu TJ, Valdevit L, Evans AG. Active cooling by metallic sandwich structures with periodic cores. Prog Mater Sci 2005;50:789–815. [17] Symons DD, Hutchinson RG, Fleck NA. Actuation of the Kagome Double-Layer Grid. Part 1: Prediction of performance of the perfect structure. J Mech Phys Solids 2005;53:1855–74. [18] Symons DD, Shieh J, Fleck NA. Actuation of the Kagome Double-Layer Grid. Part 2: Effect of imperfections on the measured and predicted actuation stiffness. J Mech Phys Solids 2005;53:1875–91. [19] Fan HL, Yang W, Yan Y, Fu Q, Fang DN, Zhuang Z. Design and manufacturing of a composite lattice structure reinforced by continuous carbon fibers. Stinghua Sci Technol 2006;11:515–22. [20] Fan HL, Meng FH, Yang W. Sandwich panels with kagome lattice cores reinforced by carbon fibers. Compos Struct 2007;81:533–9. [21] Finnegan K, Koositra G, Wadley HNG, Dshpande VS. The compressive response of carbon fiber composite pyramidal truss sandwich cores. Int J Mat Res 2007;98:1264–72. [22] Wang Bing, Linzhi Wu, Jin Xin, Shanyi Du, Sun Yuguo, Ma Li. Experimental investigation of 3D sandwich structure with core reinforced by composite struts. Mater Des 2010;31:158–65. [23] Sun Yuguo, Gao Liang. Structural responses of all-composite improvedpyramidal truss sandwich cores. Mater Des 2013;43:50–8. [24] Jingjing Zheng, Long Zhao, Hualin Fan. Energy absorption mechanisms of hierarchical woven lattice composites. Composite: Part B 2012;43:1516–22. [25] Tochukwu George, Deshpande SVikram, Wadley Haydn NG. Mechanical response of carbon fiber composite sandwich panels with pyramidal truss cores. Composite: Part A 2013;47:31–40.