Accepted Manuscript Performance enhancement of sandwich panels with honeycomb-corrugation hybrid core Bin Han, Wenbin Wang, Zhijia Zhang, Qiancheng Zhang, Feng Jin, Tianjian Lu PII: DOI: Reference:
S2095-0349(16)00004-0 http://dx.doi.org/10.1016/j.taml.2016.01.001 TAML 65
To appear in:
Theoretical and Applied Mechanics Letters
Received date: 29 September 2015 Revised date: 30 December 2015 Accepted date: 2 January 2016 Please cite this article as: B. Han, W. Wang, Z. Zhang, Q. Zhang, F. Jin, T. Lu, Performance enhancement of sandwich panels with honeycomb-corrugation hybrid core, Theoretical and Applied Mechanics Letters (2016), http://dx.doi.org/10.1016/j.taml.2016.01.001 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
*Manuscript
Manuscript submitted to Theoretical & Applied Mechanics Letters
Performance enhancement of sandwich panels with honeycomb-corrugation hybrid core Bin Han,1 1) School 2) MOE
,2,3
,3
Wenbin Wang,2 Zhijia Zhang,2,3 Qiancheng Zhang,2 Feng Jin,2,3 Tianjian Lu2,3,
a
of Mechanical Engineering, Xi'an Jiaotong University, Xi'an 710049, PR China
Key Laboratory for Multifunctional Materials and Structures, Xi’an Jiaotong University, Xi’an 710049, China
3)
State Key Laboratory for Mechanical Structure Strength and Vibration, Xi’an Jiaotong University, Xi’an 710049, China
a)
Corresponding author. E-mail:
[email protected]
Abstract The concept of combining metallic honeycomb with folded thin metallic sheets (corrugation) to construct a novel core type for lightweight sandwich structures is proposed. The honeycomb-corrugation hybrid core is manufactured by filling the interstices of aluminum corrugations with precision-cut trapezoidal aluminum honeycomb blocks, bonded together using epoxy glue. The performance of such hybrid-cored sandwich panels subjected to out-of-plane compression, transverse shear, and three-point bending is investigated, both experimentally and numerically. The strength and energy absorption of the sandwich are dramatically enhanced, compared to those of a sandwich with either empty corrugation or honeycomb core. The enhancement is induced by the beneficial interaction effects of honeycomb blocks and folded panels on improved buckling resistance as well as altered crushing modes at large plastic deformation. The present approach provides an effective method to further improve the mechanical properties of conventional honeycomb-cored sandwich constructions with low relative densities. Keywords Honeycomb-corrugation, compression, shear, bending, performance enhancement Honeycombs are available in a wide range of base materials, from beeswax and propolis (a kind of plant resin), paper, metal, ceramic to composite [1]. Especially, due to their high stiffness, strength, and energy absorption as well as great saving in weight, hexagonal honeycombs fabricated from aluminum (Al) alloys by an in-plane expansion process with two of the six cell walls having double thickness are widely employed in aerospace and other industries. The mechanical response of hexagonal honeycombs under out-of-plane compression and shear has been extensively studied, both experimentally and theoretically [2-6]. In out-of-plane compression, these honeycombs exhibit a stress peak followed by a series of stress oscillations associated with progressive formation of plastic folds in the cell walls. Most experimental studies about honeycombs are restricted to low relative density ( 0.03 ), as debonding of honeycombs from the faceplates has been observed at higher relative densities. This deficiency limits the load-bearing and energy absorbing capability of traditional honeycombs for heavy-duty applications. Like honeycombs, corrugations (folded plates) also have fairly high specific stiffness and specific strength. Unlike honeycombs, however, the energy absorption capacity of corrugations is typically low. Under quasi-static compression, for instance, a metallic corrugated sandwich core deforms by stretching of its struts (core webs) and collapses by Euler or plastic buckling, with a sharp softening after the peak load. Metallic corrugations are thus less attractive for energy absorption applications because large forces are transferred while limited amount of energy is absorbed [7]. Recently, to increase further the specific strength and specific absorbed energy (SAE) of either 1
2
honeycombs or corrugations, the concept of foam filling to construct hybrid-cellular materials has been exploited. The performance benefits of foam filling to sandwiches having honeycomb or corrugated cores derive mainly from the stabilizing effects of foam insertion on the buckling of constituent members (e.g., cell walls). For sandwich plates with foam-filled Al honeycomb cores subjected to uniform out-of-plane compression [8-10], foam filling increases both the mean crushing strength and energy absorption capability due to increased number and regularity of folds of honeycomb cell walls. Similarly, in the case of corrugated cores [11-14], foam filling stabilizes buckling and post-buckling of core webs, leading to synergistic benefits in strength and energy absorption. Inspired by the beneficial effect of foam filling, this study proposes to combine honeycombs and corrugations to construct a hybrid sandwich core as shown in Fig. 1(a). The performance of the honeycomb-corrugation hybrid sandwich is investigated under out-of-plane compression, transverse shear and three-point bending, both experimentally and numerically. As shown in Fig. 1(a), the honeycomb-corrugation hybrid core is composed of folded plates (corrugations) and trapezoidal honeycomb blocks, which is manufactured by filling the interstices of Al corrugations with precision-cut Al honeycomb blocks, bonded together using epoxy glue. Folded plates made of Al-3003-H24 and honeycomb blocks made of Al-3003-H18 are employed. The geometric parameters of the hybrid-cored sandwich specimens are: honeycomb cell length lH = 2 mm, single wall thickness tH = 0.05 mm, corrugated plate length lC = 17 mm, corrugation angle α = 63.5o, width of corrugation platform d = 4 mm, core height h = 15.3 mm, corrugated plate thickness tC = 0.2 mm, and faceplate thickness tf = 1.1 mm. Thus, the relative density of the hybrid core is: C H (1 C )
(1)
where H and C denote the relative density of honeycomb and empty corrugation, respectively, given by: H
C
8tH 3( 3lH 2t H )
8 tH 3 3 lH
tC (d lC ) (d lC cos )(tC lC sin )
(2)
(3)
Firstly, quasi-static out-of-plane compression tests are performed for sandwich specimens having empty corrugated core, honeycomb core and hybrid core. The measured compressive stress versus strain curves are presented in Fig. 2(a). The flow stress of the hybrid-cored sandwich is seen to be significantly higher than that obtained from summing the constituent contributions, i.e., curve ‘Sum’ in Fig. 2(a). The interaction effect between the curves of ‘Honeycomb–corrugation hybrid’ and ‘Sum’, represented by the shaded area in Fig. 2(a), is strong. This implies that the compressive stiffness, strength and energy absorption of both constituents (i.e., honeycomb and corrugation) are significantly enhanced. It is further seen from Fig. 2(a) that, different from the honeycomb core, the stress versus strain curve of the honeycomb-corrugation core beyond the initial peak strength exhibits little fluctuations. It then enters gradually a stress strengthening region at εn ≈ 0.25, much smaller than the densification strain of honeycomb. From representative deformation images of both empty corrugation and hybrid cores at εn = 0.25 acquired using a video camera that are also included 2
Manuscript submitted to Theoretical & Applied Mechanics Letters
in Fig. 2(a), it is seen that the corrugated-core sandwich collapses by Euler buckling with asymmetric deformations, causing the formation of plastic hinges. In contrast, the hybrid-cored sandwich maintains approximately symmetric deformation during crushing, and the deformation mode is significantly different from that of either the empty corrugation [7] or honeycomb [15]. However, as it is difficult to clearly identify detailed deformation of honeycomb blocks in the hybrid, finite element (FE) analysis is needed to complement the digital images of Fig. 2(a) and to explore further the deformation mechanisms underlying the superior performance of the hybrid-cored sandwich. This is performed next.
Adhesive interfaces
(a)
(b) (c) (d) Fig. 1. (a) Schematic of honeycomb-corrugation hybrid sandwich; (b) half unit cell; (c) representative volume element (RVE) model for out-of-plane compression; and (d) RVE model for transverse shear. SB: symmetric boundary. PB: periodic boundary. FB: fixed boundary.
FE simulations are carried out using the explicit solver of commercial FE code ABAQUS (version 6.10). Under out-of-plane compression, due to deformation symmetry of both the honeycomb blocks and corrugated plates (see Fig. 2(a)), only half of a unit cell with symmetric boundaries (SB) is considered, as shown in Fig. 1(b). Further, in view of honeycomb periodicity along the 3-direction, the mechanical characteristics of interest may be simulated using a representative volume element (RVE) model (surrounded by dashed lines in Fig. 1(b); also see Fig. 1(c)) with additional periodic boundaries (PB). This approach not only enables better visualization of deformation but also saves computational cost. The honeycomb blocks and corrugated plates are discretized using linear quadrilateral shell elements with reduced integration (S4R), with the top and bottom faceplates both taken as rigid. The bottom faceplate is fixed, while the top one is loaded 3
4
with displacement δ along the 2-direction, with a sufficiently low loading rate to ensure quasi-static compression. Perfect bonding is assumed at all the interfaces, including honeycomb/faceplate, corrugation/faceplate and honeycomb/corrugation interfaces, with general contact employed during the crushing process. The present FE simulations are limited to the relatively early stage of deformation (compressive strain not exceeding 0.3), since at higher strains, debonding would occur at honeycomb/corrugation interfaces as observed experimentally.
n
Empty corrugation
(a)
(b) (c) Fig. 2. (a) Experimentally measured compressive stress versus strain curves of honeycomb, empty corrugation, and honeycomb-corrugation sandwiches, and typical deformation images of empty corrugation and hybrid cores captured at εn = 0.25; (b) meaured compressive response of hybrid core compared with numerical calculation; (c) numerically simulated deformation process in hybrid core at εn = 0.25, with two different deformation mechanisms amplified.
Figure 2(b) compares the FE simulated compressive response of the hybrid with that measured experimentally, while Fig. 2(c) presents typical deformation simulated for the case of εn = 0.25. The features calculated by the FE analysis appear to be in qualitative agreement with those observed from experiments, e.g., Fig. 2(a). From the simulation it is found that, at the early compressive stage, the empty corrugation core and the honeycomb core both collapse by elastic buckling. In contrast, the initial collapse of the hybrid core is dominated by material yielding of corrugated plates and buckling of honeycomb cell walls, but with much higher critical compressive stress than that of single honeycomb, resulting in significantly enhanced compressive strength (Fig. 2(b)). The enhancement is attributed to the mutual deformation constraints of corrugation and honeycomb, which stabilize the corrugated plates and honeycomb cell walls against elastic buckling, and thus greatly increase the critical stresses of both constituent components. At large compressive strains, complicated and localized plastic deformation dominates the crushing of the hybrid core, as evidenced in Fig. 2(c). Two distinctive deformation mechanisms are notable: (1) conventional progressive folding of honeycomb cell walls [2, 15] in Region I; (2) a novel defomation mechanism of coupling interaction between twisted folding of honeycomb cell walls and rotation of 4
Honeyc
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multi-plastic hinges on corrugated plate in Region II, where the deformation is quite different from that in either empty corrugation or single honeycomb. As εn exceeds 0.25, the interaction effects of corrugation and honeycomb in Region II play an increasingly important role, causing sustained strengthening of the hybrid structure as shwon in Figs. 2(a~b), which in turn leads to greatly enhanced energy absorption. Additionally, two more hybrid sandwich specimens having larger values of tc (i.e. tc=0.4 and 0.7) are also tested under out-of-plane compression. Figure 3 compares the compressive strength and energy absorption of the honeycomb-corrugation hybrid sandwich cores (HBC) with other competing cores, including 304 stainless steel square honeycomb (SH) [16], aluminum foam-filled 304 stainless steel corrugations (FC) [12], 304 stainless steel empty corrugations (EC) [12], Al hexagonal honeycombs (HH) and Al empty corrugations (EC). It is clear from Fig. 3 that the proposed hybrid structure has structural preponderance in both compressive strength and energy absorption, especially in the low density regime (less than 0.5 g/cm3).
(a) (b) Fig. 3. Comparison of (a) compressive strength and (b) energy absorption. Exp. denotes the experimentally measured data in present study.
For transverse shear of the hybrid core, only FE simulations are performed. Different from the case of out-of-plane compression, a representative volume element (RVE) model with prescribed boundary conditions is employed, as illustrated in Fig. 1(d). The bottom faceplate is fixed. While the rotation of the top faceplate is constrained, it can translate in direction 2, implying that the normal traction T2 = 0. To model pure transverse shear loading, a translational displacement δ along direction 1 is prescribed on the top faceplate. The geometric parameters, meshing and bonding conditions are identical as those employed for out-of-plane compression. Figure 3 presents the simulated shear stress versus strain curves and the corresponding shear deformation modes for empty corrugation, honeycomb and hybrid sandwich cores. Similar to out-of-plane compression, the shear stress of the hybrid structure is significantly larger than that obtained from summing constituent contributions, i.e., curve ‘Sum’ in Fig. 4(a). Also, the positive interaction effect between the curves of ‘Hybrid’ and ‘Sum’ is much stronger than that under out-of-plane compression. From Figs. 4(b~d) it can be seen that, the empty corrugation collapses by Euler elastic buckling of its member in compression, and the crushing is dominated by the rotation of only three plastic hinges. The honeycomb under shear collapses first by local buckling and, subsequently, post-buckling induces progressive shear folding during crushing [3]. As for the hybrid core, more plastic hinges form in the initially compressed corrugated member whereas shear buckling in honeycomb blocks dominates a much wider region, rather than a quite localized and narrow region. Again, the mutual deformation constraints of honeycomb and corrugation improve 5
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the buckling resistance of constituent members. This is the main reason why the shear strength of the hybrid core is significantly enhanced. At large shear strains, compared to both empty corrugation and honeycomb, the hybrid core experiences more serious plastic deformation, including rotation of more plastic hinges in corrugated members and more shear bands in honeycomb blocks, due again to the interaction of its constituent components. Hence, the hybrid core dissipates much more plastic deformation energy in shear.
(a)
(b) (c) (d) Fig. 4. Comparison of the numerical results of honeycomb, empty corrugation, and honeycomb-corrugation hybrid sandwiches subjected to transvers shear: (a) shear stress versus strain responses of honeycomb, empty corrugation, and honeycomb-corrugation sandwiches, (b)~(d) refer to the shear deformations of the hybrid, honeycomb, and empty corrugation at the shear strain of 0.25, respectively.
In addition to FE simulation, three-point bending experiments are carried out on honeycomb, empty corrugation, and honeycomb-corrugation sandwich beams with span length L = 300 mm, beam width b = 60 mm, and maximum loading deflection δ = 20 mm. For sandwich beams with empty corrugation and hybrid cores, the beam axis is perpendicular to the prismatic direction of corrugated plate. Figure 5 presents the experimentally measured load versus deflection curves and deformation processes. It can be seen that the peak force per mass (load capacity under bending) of the hybrid-cored sandwich is larger than that of empty corrugation or honeycomb cored sandwich, which is dominated by initial debonding at honeycomb/corrugation interfaces. Upon reaching the peak, the load decreases dramatically due to rapid expansion of debonding to honeycomb/faceplate and corrugation/faceplate interfaces. Differently, the corrugate-cored sandwich collapses by core shear failure with buckling of core webs [17], while the honeycomb-cored sandwich collapses by indentation failure with bucking of honeycomb cell walls underneath the loading punch [18, 19], both without obvious debonding. However, for the hybrid-cored sandwich, the measured loading capacity under bending is rather limited and below expectation, due mainly to premature debonding and little deformation in the hybrid core. This implies that, in the present experiments, the potential of the hybrid core is not effectively revealed. Consequently, to explore further the structural superiority of its bending resistance, FE simulations with perfect bonding assumed for all the interfaces are carried out. The results are presented in Fig. 6. It can be seen from Figs. 6(a-c) that, in terms of both load versus deflection curve and deformation mode, good agreement between FE calculations and experimental results is achieved 6
Manuscript submitted to Theoretical & Applied Mechanics Letters
for corrugated and honeycomb sandwiches, but not for the hybrid sandwich. As shown in Fig. 6(c), with debonding excluded due to perfect interfacial bonding assumed, the hybrid sandwich collapses by indentation failure, resulting in a much higher peak load and greatly improved post-peak softening than that experimentally measured. For the three sandwich beams considered, Fig. 6(d) compares the energy absorption per mass of constituent components up to δ = 20 mm. It can be concluded that, the corrugated plates and honeycomb blocks in the hybrid core, together with its bottom and top faceplates, all dissipate greater energy than that of the empty corrugated or honeycomb sandwich. This implies that the hybrid sandwich possesses greater bending resistance so long as its interfaces are well bonded. In other words, there is room for improvement of the present hybrid-cored sandwich specimens for three-point bending testing.
(a)
(b) Fig. 5. FE simulation results for honeycomb, empty corrugation, and honeycomb-corrugation sandwich beams subjected to three-point bending: (a) load versus deflection curves; (b) digital images of deformation history.
(a)
(b)
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(c) (d) Fig. 6. (a)~(c) Measured and simulated bending responses of empty corrugation, honycomb, and honeycomb-corrugation sandwich beams; (d) comparison of energy absorption of constituent components among the three sandwich beams subjected to three-point bending.
The performance of honeycomb-corrugated hybrid sandwich subjected to out-of-plane compression, transverse shear, and three-point bending is experimentally and numerically evaluated. Under out-of-plane compression and transverse shear, the strength and energy absorption of the hybrid core are both greatly improved, attributed to the positive interaction effects of corrugated plates and honeycomb cell walls on mutual deformation constraints against buckling as well as altered crushing modes at large plastic deformation. As for three-point bending, much improved peak load and post-peak softening can be achieved if good interfacial bonding in the hybrid-cored sandwich is ensured. Honeycomb-corrugation hybrid structures are promising candidates for ultralight load-bearing and energy absorbing applications. This work was supported by the National Natural Science Foundation of China (11472208) and the National 111 Project of China (B06024). [1]
Q.C. Zhang, X.H. Yang, P. Li, G.Y. Huang, S.S. Feng, C. Shen, B. Han, X.H. Zhang, F. Jin, F. Xu, T.J. Lu, Bioinspired engineering of honeycomb structure - using nature to inspire human innovation. Prog. Mater. Sci. 74 (2015) 332-400. [2] D. Mohr, M. Doyoyo, Nucleation and propagation of plastic collapse bands in aluminum honeycomb. J. Appl. Phys. 94 (2003) 2262-2270. [3] D. Mohr, M. Doyoyo, Deformation-induced folding systems in thin-walled monolithic hexagonal metallic honeycomb. Int. J. Solids Struct. 41 (2004) 3353-3377. [4] D. Mohr, M. Doyoyo, Experimental investigation on the plasticity of hexagonal aluminum honeycomb under multiaxial loading. J. Appl. Mech. 71 (2004) 375-385. [5] D. Mohr, Z.Y. Xue, A. Vaziri, Quasi-static punch indentation of a honeycomb sandwich plate: experiments and modelling. J. Mech. Mater. Struct. 1 (2006) 581-604. [6] M. Doyoyo, D. Mohr, Microstructural response of aluminum honeycomb to combined out-of-plane loading. Mech. Mater. 35 (2003) 865-876. [7] F. Cote, V.S. Deshpande, N.A. Fleck, A.G. Evans, The compressive and shear responses of corrugated and diamond lattice materials. Int. J. Solids Struct. 43 (2006) 6220-6242. [8] A.A. Nia, M.Z. Sadeghi, The effects of foam filling on compressive response of hexagonal cell aluminum honeycombs under axial loading - experimental study. Mater. Design 31 (2010) 1216-1230. [9] M.Z. Mahmoudabadi, M. Sadighi, A study on the static and dynamic loading of the foam filled metal hexagonal honeycomb - theoretical and experimental. Mat. Sci. Eng. A 530 (2011) 333-343. [10] T. Sadowski, J. Bec, Effective properties for sandwich plates with aluminium foil honeycomb core and polymer foam filling - static and dynamic response. Comp. Mater. Sci. 50 (2011) 1269-1275. 8
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[11] L.L. Yan, B. Yu, B. Han, C.Q. Chen, Q.C. Zhang, T.J. Lu, Compressive strength and energy absorption of sandwich panels with aluminum foam-filled corrugated cores. Compos. Sci. Technol. 86 (2013) 142-148.
[12] B. Han, L.L. Yan, B. Yu, Q.C. Zhang, C.Q. Chen, T.J. Lu, Collapse mechanisms of metallic sandwich structures with aluminum foam-filled corrugated cores. J. Mech. Mater. Struct. 9 (2014) 397-425.
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[14] B. Han, K.K. Qin, B. Yu, Q.C. Zhang, C.Q. Chen, T.J. Lu, Design optimization of foam-reinforced corrugated [15] [16] [17] [18] [19]
sandwich beams. Compos. Struct. 130 (2015) 51-62. A. Wilbert, W.Y. Jang, S. Kyriakides, J.F. Floccari, Buckling and progressive crushing of laterally loaded honeycomb. Int. J. Solids Struct. 48 (2011) 803-816. F. Côté, V.S. Deshpande, N.A. Fleck, A.G. Evans, The out-of-plane compressive behavior of metallic honeycombs. Mat. Sci. Eng. A-Struct. 380 (2004) 272-280. L. Valdevit, Z. Wei, C. Mercer, F.W. Zok, A.G. Evans, Structural performance of near-optimal sandwich panels with corrugated cores. Int. J. Solids Struct. 43 (2006) 4888-4905. J.K. Paik, A.K. Thayamballi, G.S. Kim, The strength characteristics of aluminum honeycomb sandwich panels. Thin Wall Struct. 35 (1999) 205-231. C.C. Foo, G.B. Chai, L.K. Seah, Quasi-static and low-velocity impact failure of aluminium honeycomb sandwich panels. P. I. Mech. Eng. L-J. Mat. 220 (2006) 53-66.
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Highlights y
Performance of a honeycomb-corrugated hybrid sandwich subjected to out-of-plane compression, transverse shear, and three-point bending is evaluated.
y
The strength and energy absorption of the sandwich are dramatically enhanced
y
The enhancement is attributed to the positive interaction effects of corrugated plates and honeycomb cell walls on mutual deformation constraints.
