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The edgewise compressive behavior and failure mechanism of the composite Y-frame core sandwich column
Polymer Testing xxx (xxxx) xxx
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Test Method
The edgewise compressive behavior and failure mechanism of the composite Y-frame core sandwich column Jialin Liu a, Can Li a, Sihua Deng a, Jiayi Liu a, b, c, d, *, Wei Huang a, b, c a
School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology, Wuhan, 430074, PR China Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration (CISSE), Shanghai, 200240, PR China c Hubei Key Laboratory of Naval Architecture and Ocean Engineering Hydrodynamics (HUST), Wuhan, 430074, PR China d Department of Mechanical Engineering, University College London, Torrington Place, London, WC1E 7JE, UK b
A R T I C L E I N F O
A B S T R A C T
Keywords: Sandwich column Y-frame core Edgewise compression Mechanical behavior
A novel fabrication method was developed to fabricate the composite Y-frame core sandwich columns by hotpress molding method. The Y-frame core sandwich columns with different relative densities were obtained by hot-press molding method. The edgewise compressive tests were conducted. From the edgewise compressive tests, the mechanical behavior of the Y-frame core sandwich columns was recorded and analyzed. The effects of relative density on the failure modes, failure load and load-displacement curves were investigated. The dominant failure modes of the Y-frame core sandwich columns were macro buckling. The analytical prediction on the failure load of the Y-frame core sandwich column was presented, which was based on the macro buckling. The failure loads of the Y-frame core sandwich column at different relative densities were predicted with proposed method and compared with the experimental results.
1. Introduction The composite sandwich structures have been widely used in ship structures [1,2]. The ship structures made of composites exhibited high property of resisting to salt and alkali in seawater. The composite sandwich structures were good at ship collision protection [3,4]. Moreover, the composite sandwich structures also had superior perfor mance in the dynamic response and blast resistance [5–9]. Matsagar [10] examined the blast response reduction of the non-composite panels and composite sandwich panels. The numerical results implied that the alloy syntactic foam composite sandwich panels showed better blast response reduction ability than non-composite panel made of steel plates and concrete slabs. Kishore et al. [11] fabricated cylindrical bonded composite sandwich shell. The high-speed photography with Digital Image Correlation was employed to measure the displacements of the composite sandwich structure underwater implosion. The exper imental investigation revealed that the critical collapse pressure of the composite sandwich structure increases with the shear modulus of the core. Zhou et al. [12] numerically investigate the dynamic response of carbon fiber reinforced composite sandwich structure with honeycomb cores under water blast. By comparing the protection properties of the composite sandwich structure with honeycomb cores and the
mass-equal laminate, it indicated that the composite sandwich structure performed better in protection from water blast than the mass-equal laminate. Researchers also made deep investigations on composite sandwich structures with different core types, including lattice core [13–17], corrugated core [18,19] and honeycomb core [20,21]. Liu et al. [22] proposed a 3D printing method to fabricate carbon fiber reinforced lattice truss core sandwich structure. The cross sectional morphology was analyzed. The effects of relative density, fiber volume content and truss angle on the compressive properties of composite lattice truss sandwich structure were investigated by experiments, which indicated that the experimental results was close to the theoretical results. Xu et al. [23] designed and fabricated a novel composite corrugated core sand wich panel by auto-cutting process. The mechanical behavior and failure mechanism were revealed by experiments. The analytical estimates of the strength and stiffness were obtained, which were in good agreement with the experimental results. Rodriguez-Ramirez et al. [24] made a contribution to understand the postbuckling behavior of the composite honeycomb cores under bending load. The influence of the boundary conditions on the buckling of the cores was revealed via experiments and numerical simulation. Investigations on the static mechanical behavior of composite sandwich structures with different cell types were
* Corresponding author. School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology, Wuhan, 430074, PR China. E-mail address: [email protected] (J. Liu). https://doi.org/10.1016/j.polymertesting.2019.106188 Received 24 June 2019; Received in revised form 20 September 2019; Accepted 21 October 2019 Available online 23 October 2019 0142-9418/© 2019 Elsevier Ltd. All rights reserved.
Please cite this article as: Jialin Liu, Polymer Testing, https://doi.org/10.1016/j.polymertesting.2019.106188
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made up of three constituent members, which were the Y-flange, the web and the leg. The inclination of the Y-flange was 45� and is denoted by α. The size of the web was 2 mm and was denoted by e. The height of the leg was 18 mm and was denoted by h. The thickness of the Y-frame core and facesheets was denoted by t. The height of the Y-frame core was 27 mm and was denoted by H. The geometric parameters of a unit cell is shown in Fig. 1b. The size of the unit cell in 2-direction was denoted by L1 . The width of the unit cell is given by
conducted under different load conditions, including compressive load [25–27], shear load [28–30] and bending load [31–33]. With regard to the mechanical behavior of the composite sandwich structures under edgewise compressive load, many research results were obtained. Lei et al. [34] investigated the mechanical behavior of the foam-filled glass-fiber reinforced composite sandwich column under edgewise compressive load by experiments, analytical prediction and numerical simulation. The analytical prediction and numerical results were close to the experimental results. The experimental results revealed that the critical collapse load reduced as the ratio of slender ness increased. Xiong et al. [35] used hot-press molding method to fabricate composite sandwich structures with pyramidal truss cores. The analytical models were derived to predict failure load associated with the failure modes under edgewise compressive load. The analytical predictions showed good agreement with the measured load. Mamalis et al. [36] conducted a series of edgewise compressive tests to investi gate the mechanical properties, failure modes of the composite sand wich panels with various types of cores. The influence of the material properties and geometric parameters on the edgewise compressive properties, failure modes and energy absorption was presented and analyzed. However, the edgewise compressive behavior of the com posite Y-frame core sandwich column was limited. Thus, it is necessary to understand the failure modes and mechanical properties of the Y-frame core sandwich column, which could contribute to the applica tion of this composite sandwich structure in ship industry. In this paper, the composite Y-frame core sandwich column was fabricated by hot-press molding method. The mechanical behavior of the Y-frame core sandwich column was investigated by experiments under edgewise compressive load. The influence of relative density on the mechanical properties and failure modes was revealed. The analyt ical model was presented to estimate the failure load of the Y-frame core sandwich column.
L1 ¼ 4e þ t þ 2ðH
(1)
hÞcot α
The length of the Y-frame core in 3-direction is 90 mm and is denoted by L2 as shown in Fig. 1a. Hence, the relative density (RD) of the Y-frame core sandwich column is
ρ¼
h þ t þ 2e þ 2ðH HL1
hÞsin
1
α
(2)
t
Equation (2) implies that the relative density is dependent on the geometric parameters of the Y-frame core. The width of the web e, the height of the leg h and the inclination of the Y-flange α were designed to be constant. The relative density of the Y-frame core increases with the thickness t, which is shown in Table 1. Three different thicknesses are considered. Thus, the Y-frame core sandwich columns with three different relative densities can be obtained. 2.2. Manufacturing process Fig. 2 presents the manufacturing process of the Y-frame core sandwich columns through hot-press molding method. This process consists of four major steps. Firstly, the molds are assembled together and the Y-frame cores were clamped as shown in Fig. 2a. Secondly, the Table 1 The relative density and shear stiffness of the Y-frame core sandwich column fabricated from different layers of prepreg.
2. Geometry and fabrication 2.1. Geometry The geometry of the Y-frame core sandwich column is shown in Fig. 1. Fig. 1a shows that the Y-frame core sandwich column consists nine unit cells. A unit cell of the Y-frame core sandwich column was
Number of layers
Thickness t
Relative density
Shear stiffness GC [38]
8 12 16
0.8 mm 1.2 mm 1.6 mm
5.34% 7.95% 10.53%
1.679 MPa 5.768 MPa 13.528 MPa
Fig. 1. (a) Geometry of the Y-frame core sandwich column; (b) The unit cell of the Y-frame core. 2
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ends of the Y-frame cores are dispersed and embedded into the top and bottom facesheets as shown in Fig. 2b. Thirdly, the Y-frame core sand wich column was cured at 125 � C for 1.5 h as shown in Fig. 2c. Fourthly, the molds were removed from the Y-frame core sandwich column after curing and cooling as shown in Fig. 2d. During the fabrication of the composite Y-frame core sandwich col umns, the stacking sequence of the top and bottom facesheets and Yframe cores were designed to be [0� /90� ]2s, [0� /90� ]3s and [0� /90� ]4s, which were made of 8, 12 and 16 layers of unidirectional prepreg, respectively. The ends of the Y-flange and the leg are embedded into the top and bottom facesheet, respectively, which is shown in Fig. 3. After curing at 125 � C for 1.5 h, the top and bottom facesheets would be compressed and the stacking sequences of the facesheets, Y-flange, web and leg would be [0� /90� ]2s for the Y-frame core sandwich column with RD ¼ 5.34%. The Y-frame core sandwich columns were fabricated by the hot-press molding method as shown in Fig. 2. For each relative density, there were three Y-frame core sandwich columns fabricated. The spec imens with different relative densities are shown in Fig. 4, which are prepared for the edgewise compression tests.
compressive load on the Y-frame core sandwich column. The edgewise compression tests of the Y-frame core sandwich column were conducted according to ASTM C364 [37]. With respect to one relative density, we have prepared three Y-frame core sandwich columns. The tests were conducted three times with respect to one relative density. 4. Results and discussion 4.1. Experimental results and discussion The composite Y-frame core sandwich columns were tested under edgewise compressive load. The relative densities of the Y-frame core sandwich columns ranged from 5.34% to 10.53%. The effects of the relative density on the edgewise compressive load-displacement curves, failure modes and failure load were investigated. 4.1.1. Edgewise compression response Fig. 6 presents the edgewise compressive load-displacement curve of the Y-frame core sandwich column with RD ¼ 5.34%, which is followed by the deformation of the Y-frame core sandwich column in three typical loading stages. The three typical stages were labeled by I, II and III, respectively. In the first stage I, the load-displacement curve increased linearly as shown in Fig. 6a. In this stage, there is no failure in the Yframe core sandwich column as shown in Fig. 6b. In the second stage II, the load-displacement curve begin to drop as shown in Fig. 6a. The macro buckling is observed as shown in Fig. 6b. In the third stage III, the load decreases increasingly as shown in Fig. 6a, which implied that the Y-frame core sandwich column lost load-bearing capacity. In the third stage, the failure modes of the Y-frame core sandwich column includes the fracture in the top facesheet and the delamination in the web of the
3. The edgewise compression test Fig. 5 shows the edgewise compression test setup for the Y-frame core sandwich column. The test setup consists of three parts: the moveable part, the Y-frame core sandwich column and the stationary part. The moveable part consists of the test fixture and moveable head. The stationary part consists of the rest fixture and stationary head as shown in Fig. 5. Two ends of the Y-frame core sandwich column were clamped by the test fixtures of the moveable part and the stationary part. The moveable head moved at a speed of 0.5 mm/min to exert edgewise
Fig. 2. Manufacturing process of the composite Y-frame core sandwich column: (a) The molds were assembled together; (b) The ends of the molds were clamped. The ends of the Y-frame cores were embedded into the top and bottom facesheets; (c) The Y-frame core sandwich column was cured at 25 � C for 1.5 h; (d) The molds were removed after curing, and obtained the composite Y-frame core sandwich column. 3
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Fig. 3. Schematic of the stacking sequence [0� /90� /0� /90� ]s of the Y-frame core sandwich column.
Fig. 4. The composite Y-frame core sandwich columns with relative densities 5.34%, 7.95% and 10.53%.
Y-frame core as shown in Fig. 6b. Fig. 7 depicts the edgewise compres sive load-displacement curve and the failure images of the Y-frame core sandwich column with RD ¼ 7.95% in three typical loading stages. In the first stage I, the load increases linearly with the displacement, which indicates that no structural damage occurs as shown in Fig. 7a. In the second stage II, the load-displacement curve dropped rapidly. The macro buckling and delamination in the web occur in this stage as shown in Fig. 7b. In the third stage III, the delamination in the web and the facesheet-core interface in observed as shown in Fig. 7b. The fracture in the top facesheet is also observed. The failure modes of the Y-frame core sandwich column with RD ¼ 5.34% and RD ¼ 7.95% were not identical. The delamination failure is observed in the facesheet-core interface of the sandwich column with RD ¼ 7.95%. However, there is no delami nation and fracture observed in the second stage II as shown in Fig. 6b. This is due to the Y-frame core sandwich column with RD ¼ 5.34% has less manufacturing imperfections in the facesheet-core interface than that of the Y-frame core sandwich column with RD ¼ 7.95%. Hence, the dominant failure mode of the Y-frame core sandwich column with
RD ¼ 5.34% is macro buckling. Fig. 8 shows the load-displacement curve and failure process of the Y-frame core sandwich column with RD ¼ 10.53%. In the first stage I, the edgewise compressive load increased linearly with displacement as shown in Fig. 8a. In the second stage II, the load-displacement curve drops sharply. The macro buckling, delamination and fracture in the facesheet-core interface occurred as shown in Fig. 8b. In the third stage III, the delamination and fracture extended, which was similar to the Y-frame core sandwich column with RD ¼ 7.95% and 10.53%. 4.1.2. Failure mode For the Y-frame core sandwich column with different relative den sities, the dominant failure mode related to the drop of the peak load was macro buckling. The failure load was determined by the peak load in the first stage. Fig. 9 shows the failure load of the Y-frame core sandwich column with different relative densities. It implies that the failure load increases with the relative density. The average failure load of the Yframe core sandwich column varied from 2710.3 N to 18639.5 N as 4
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Fig. 5. Edgewise compression test setup of the Y-frame core sandwich column.
relative density changed from 5.34% to 10.53%. Moreover, the relative density had great influence on the failure mode of the Y-frame core sandwich column after attaining the peak load. For the Y-frame core sandwich column with RD ¼ 5.34%, macro buckling is the competing failure mode after the peak load drop in the second stage II as shown in Fig. 6b. For the Y-frame core sandwich column with RD ¼ 7.95%, the macro buckling and delamination are both observed after attaining the peak load in the second stage as shown in Fig. 7b. For the Y-frame core sandwich column with RD ¼ 10.53%, the macro buckling, delamination and fracture are observed after attaining the peak load in the second stage II as shown in Fig. 8b. The peak load of the Y-frame core sandwich column decreased more rapidly as the relative density increased. Furthermore, as the relative density increased, the Y-frame core sand wich column damaged more and more seriously after attaining the peak load. After the edgewise compression tests were finished, the Y-frame core sandwich columns were unloaded. Fig. 10 shows the deformation of the Y-frame core sandwich columns with different relative densities after unloading. It can be seen that the residual deformation of the Y-frame core sandwich column with RD ¼ 5.34% is smaller that of the Y-frame core sandwich columns with RD ¼ 7.95% and 10.53%. This was because the Y-frame core sandwich column with RD ¼ 7.95% and 10.53% had more serious damage than the Y-frame core sandwich column with RD ¼ 5.34% after attaining the peak load. Therefore, the elastic defor mation is easier to recover for the Y-frame core sandwich column with RD ¼ 5.34% than that for the Y-frame core sandwich column with RD ¼ 7.95% and 10.53% after unloading.
Fig. 6. (a) Load-displacement curve of the Y-frame core sandwich column with RD ¼ 5.34%; (b) Deformation of the Y-frame core sandwich column with RD ¼ 5.34% in three typical stages.
column subjected to edgewise compressive load. L ¼ nL1 is the length of the Y-frame core sandwich column. The number of the unit cell is denoted by n. The equivalent flexural rigidity Deq of the Y-frame core sandwich column can be given by Deq ¼ D0eq þ 2Dfeq þ DCeq ¼ Ef
L2 tðH þ tÞ2 L2 t3 L2 H 3 þ Ef þ EC 2 6 12
(3)
where Ef is the elastic modulus of the facesheets as shown in Table 2. EC is the elastic moduli of the Y-frame core. EC ¼ 0 for the Y-frame core. Hence, the equivalent flexural rigidity Deq is given by Deq ¼ Ef
L2 tðH þ tÞ2 L2 t3 þ Ef 2 6
(4)
As thickness t ranges from 0.8 mm to 1.6 mm, the following condi tion is satisfied 2
Ef L2 tðHþtÞ 2 t3
Ef L26
� �2 H ¼3 1 þ > 100 t
(5)
Therefore, the equivalent flexural rigidity Deq can given by
4.2. Theoretical analysis and discussion According to the experimental results of the Y-frame core sandwich column under edgewise compressive load, the peak load drop was due to the macro buckling. There were two types of buckling associated with the macro buckling, which were the Euler buckling and the core shear buckling [35]. Fig. 11 shows the schematic of the Y-frame core sandwich
Deq � Ef
L2 tðH þ tÞ2 2
(6)
Fig. 12a shows the schematic of the macro buckling of the endclamped Y-frame core sandwich column. The deformation v is super imposed by two displacements, which are the bending displacement w1 5
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Fig. 7. (a) Load-displacement curve of the Y-frame core sandwich column with RD ¼ 7.95%; (b) Deformation of the Y-frame core sandwich column with RD ¼ 7.95% in three typical stages.
Fig. 8. (a) Load-displacement curve of the Y-frame core sandwich column with RD ¼ 10.53%; (b) Deformation of the Y-frame core sandwich column with RD ¼ 10.53% in three typical stages.
and the additional displacement w2 . The additional displacement w2 is associated with the shear deformation of the Y-frame core. The bending moment M can be given by M ¼ Pv ¼ Pðw1 þ w2 Þ ¼ Deq
d2 w1 dx2
The differentiation of Equation (7) gives � � d3 w1 dw1 dw2 Deq 3 ¼ P þ dx dx dx
(7)
(8)
Fig. 12b shows the schematic of the typical segment deformation of the Y-frame core sandwich column. The angle θ denotes the slope of the Y-frame core sandwich column, which can be given by θ¼
dv dðw1 þ w2 Þ ¼ dx dx
(9)
The component FS of the force P at the cross section of the Y-frame core sandwich column is perpendicular to the axis of the Y-frame core sandwich column, which can be given by FS ¼ P sin θ
Fig. 9. The failure load of the Y-frame core sandwich column with different relative densities.
(10)
Under the consideration that the slope θ of the Y-frame core sand wich column is small in the elastic-linear stage, the component FS of the force P is
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Fig. 10. The deformation of the Y-frame core sandwich columns with different relative densities after unloading. Table 2 The elastic modulus of the composite laminates made from different layers of prepreg. Number of layers
Elastic modulus Ef [39]
8 12 16
27.53 GPa 29.68 GPa 30.91 GPa
where GC is the measured shear stiffness of the Y-frame core as shown in Table 1. Combination of Equations (11) and (12) gives dw2 P dðw1 þ w2 Þ ¼ dx dx AGC
(13)
Substituting Equation (13) into Equation (8) yields Deq
d3 w1 dw1 ¼ β2 dx3 dx
where β2 ¼ Deq ½1
(14) P P=ðAGC Þ�.
The solution w1 to Equation (14) is in the form of
w1 ¼ C1 sin βx þ C2 cos βx þ C3
(15)
Differentiating Equation (15) twice gives 2
d w1 ¼ dx2
C1 β2 sin βx
C2 β2 cosβx
(16)
Inserting Equation (16) in Equation (7) yields w1 þ w2 ¼
dðw1 þ w2 Þ dx
(11)
The boundary condition w1 þ w2 ¼ 0 at the cross section x ¼ 0 re quires that C2 ¼ 0; the boundary condition w1 þ w2 ¼ 0 at the cross section x ¼ L requires that αL ¼ kπ, which gives � �2 kπ P � � � β2 ¼ (19) ¼ L Deq 1 P ðAGC Þeq
According to Allen’s work [40], the component FS of the force P can be given by FS ¼ AGC
dw2 dx
(17)
The boundary condition of the end-clamped Y-frame core sandwich column is � w1 þ w2 ¼ 0; x ¼ 0 (18) w1 þ w2 ¼ 0; x ¼ L
Fig. 11. Schematic of the Y-frame core sandwich column subjected to edgewise compressive load.
FS ¼ P
Deq d2 w1 P dx2 Deq 2 ¼ β ð C1 sin βx C2 cos βxÞ P 1 ¼ ð C1 sin βx C2 cos βxÞ 1 P=ðAGC Þ
(12)
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Fig. 12. (a) The schematic of the macro buckling of the end-clamped Y-frame core sandwich column; (b) The schematic of the typical segment deformation of the Yframe core sandwich column.
According to Equation (19), the edgewise compressive load P P¼
PE PS PE þ PS
Table 3 The failure load of the composite Y-frame core sandwich columns with different relative densities.
(20) k2 π 2 D
where PE ¼ L2 eq is the Euler buckling load; k ¼ 2 for a column with built-in ends; PS ¼ ðAGC Þeq is the shear buckling load; A ¼ HL2 for a sandwich column [41]. Equation (20) is usually expressed in the following form 1 1 1 ¼ þ P PE PS
Relative density
Measurements
Predictions
5.34% 7.95% 10.53%
2710.3 N 11781.9 N 18639.5 N
4048.2 N 13786.1 N 31970.7 N
Data availability
(21)
The raw/processed data required to reproduce these findings cannot be shared at this time due to technical or time limitations. All relevant data supporting the findings of this study are included within the paper or are available from the corresponding author upon reasonable request.
The macro buckling failure load of the Y-frame core sandwich col umn can be predicted by Equation (21). A summary of analytical results and measured results for failure load of the Y-frame core sandwich column at different relative densities is presented in Table 3. There are some differences between the analytical results and measured results. The reasons for this difference are mainly due to the manufacture de fects. The ends of the Y-frame core were embedded into the top and bottom facesheets in the manufacturing process. As a result, the me chanical properties of the top and bottom facesheets were weakened. However, the effects of the manufacture defects on the mechanical properties were not considered in the analytical model, which led to the failure load of the analytical results are larger than that of the measured results.
Declaration of competing interest The authors declared that they have no conflict of interest to this work. We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted. Acknowledgement The present work is supported by National Science Foundation of China under Grant Nos. 11402094 and 11802100.
5. Conclusions The composite Y-frame core sandwich columns with different rela tive densities were fabricated by hot-press molding method. The influ ence of the relative density on the failure load, the feature of the loaddisplacement curve and the failure mode was investigated. The edge wise compressive tests revealed that the failure load increased as the relative density increased. As relative density increased from 5.34% to 10.53%, the average failure load of the Y-frame core sandwich column varied from 2710.3 N to 18639.5 N. The dominant failure mode of Yframe core sandwich columns with different relative densities was macro buckling. The analytical model was presented to predict the failure load based on the dominant failure mode. The peak load of the Yframe core sandwich column dropped more rapidly in the second stage as the relative density increased. Moreover, as the relative density increased, the failure mode was more sophisticated and the Y-frame core sandwich column damaged more seriously after attaining the peak load.
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V. Chalivendra, B. Song, D. Casem (Eds.), Dynamic Behavior of Materials, New York, 2013, pp. 275–286. H. Arora, P.A. Hooper, J.P. Dear, Blast loading of sandwich structures and composite tubes, in: S. Abrate, B. Castani�e, Y. Rajapakse (Eds.), Dynamic Failure of Composite and Sandwich Structures, Dordrecht, 2013, pp. 47–92. V.A. Matsagar, Comparative performance of composite sandwich panels and noncomposite panels under blast loading 49 (2015) 611–629. S. Kishore, P.N. Parrikar, N. Denardo, A. Shukla, Underwater dynamic collapse of sandwich composite structures, Exp. Mech. (2019), https://doi.org/10.1007/ s11340-019-00470-x. H. Zhou, T. Liu, R. Guo, R.Z. Liu, P. Song, Numerical investigation on water blast response of freestanding carbon fiber reinforced composite sandwich plates with square honeycomb cores, Appl. Compos. Mater. (2019) 605–625. J. Smardzewski, K.W. Wojciechowski, Response of wood-based sandwich beams with three-dimensional lattice core, Compos. Struct. 216 (2019) 340–349. Y. Hu, W.X. Li, X.Y. An, H.L. Fan, Fabrication and mechanical behaviors of corrugated lattice truss composite sandwich panels, Compos. Sci. Technol. 125 (2016) 114–122. B. Wang, L.Z. Wu, L. Ma, Y.G. Sun, S.Y. Du, Mechanical behavior of the sandwich structures with carbon fiber-reinforced pyramidal lattice truss core, Mater. Des. 31 (2010) 2659–2663. B. Wang, L.Z. Wu, L. Ma, J.C. Feng, Low-velocity impact characteristics and residual tensile strength of carbon fiber composite lattice core sandwich structures, Compos. B Eng. 42 (2011) 891–897. J. Xiong, L. Ma, L.Z. Wu, B. Wang, A. Vaziri, Fabrication and crushing behavior of low density carbon fiber composite pyramidal truss structures, Compos. Struct. 92 (2010) 2695–2702. F.N. Jin, H.L. Chen, L. Zhao, H.L. Fan, C.G. Cai, N. Kuang, Failure mechanisms of sandwich composites with orthotropic integrated woven corrugated cores: experiments, Compos. Struct. 98 (2013) 53–58. S.W. Kavermann, D. Bhattacharyya, Experimental investigation of the static behavior of a corrugated plywood sandwich core, Compos. Struct. 207 (2019) 836–844. M. Tauhiduzzaman, L.A. Carlsson, Influence of constraints on the effective inplane extensional properties of honeycomb core, Compos. Struct. 209 (2018) 616–624. S.S. Shi, Z. Sun, X.Z. Hu, H.R. Chen, Carbon-fiber and aluminum-honeycomb sandwich composites with and without Kevlar-fiber interfacial toughening, Compos. Appl. Sci. Manuf. 67 (2014) 102–110. S.T. Liu, Y.G. Li, N.Y. Li, A novel free-hanging 3D printing method for continuous carbon fiber reinforced thermoplastic lattice truss core structures, Mater. Des. 137 (2018) 235–244. G.D. Xu, Z.H. Wang, T. Zeng, S. Cheng, D.N. Fang, Mechanical response of carbon/ epoxy composite sandwich structures with three-dimensional corrugated cores, Compos. Sci. Technol. 156 (2018) 296–304. J.D.D. Rodriguez-Ramirez, B. Castanie, C. Bouvet, Experimental and numerical analysis of the shear nonlinear behaviour of Nomex honeycomb core: application to insert sizing, Compos. Struct. 193 (2018) 121–139.
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Polymer Testing journal homepage: http://www.elsevier.com/locate/polytest
Test Method
The edgewise compressive behavior and failure mechanism of the composite Y-frame core sandwich column Jialin Liu a, Can Li a, Sihua Deng a, Jiayi Liu a, b, c, d, *, Wei Huang a, b, c a
School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology, Wuhan, 430074, PR China Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration (CISSE), Shanghai, 200240, PR China c Hubei Key Laboratory of Naval Architecture and Ocean Engineering Hydrodynamics (HUST), Wuhan, 430074, PR China d Department of Mechanical Engineering, University College London, Torrington Place, London, WC1E 7JE, UK b
A R T I C L E I N F O
A B S T R A C T
Keywords: Sandwich column Y-frame core Edgewise compression Mechanical behavior
A novel fabrication method was developed to fabricate the composite Y-frame core sandwich columns by hotpress molding method. The Y-frame core sandwich columns with different relative densities were obtained by hot-press molding method. The edgewise compressive tests were conducted. From the edgewise compressive tests, the mechanical behavior of the Y-frame core sandwich columns was recorded and analyzed. The effects of relative density on the failure modes, failure load and load-displacement curves were investigated. The dominant failure modes of the Y-frame core sandwich columns were macro buckling. The analytical prediction on the failure load of the Y-frame core sandwich column was presented, which was based on the macro buckling. The failure loads of the Y-frame core sandwich column at different relative densities were predicted with proposed method and compared with the experimental results.
1. Introduction The composite sandwich structures have been widely used in ship structures [1,2]. The ship structures made of composites exhibited high property of resisting to salt and alkali in seawater. The composite sandwich structures were good at ship collision protection [3,4]. Moreover, the composite sandwich structures also had superior perfor mance in the dynamic response and blast resistance [5–9]. Matsagar [10] examined the blast response reduction of the non-composite panels and composite sandwich panels. The numerical results implied that the alloy syntactic foam composite sandwich panels showed better blast response reduction ability than non-composite panel made of steel plates and concrete slabs. Kishore et al. [11] fabricated cylindrical bonded composite sandwich shell. The high-speed photography with Digital Image Correlation was employed to measure the displacements of the composite sandwich structure underwater implosion. The exper imental investigation revealed that the critical collapse pressure of the composite sandwich structure increases with the shear modulus of the core. Zhou et al. [12] numerically investigate the dynamic response of carbon fiber reinforced composite sandwich structure with honeycomb cores under water blast. By comparing the protection properties of the composite sandwich structure with honeycomb cores and the
mass-equal laminate, it indicated that the composite sandwich structure performed better in protection from water blast than the mass-equal laminate. Researchers also made deep investigations on composite sandwich structures with different core types, including lattice core [13–17], corrugated core [18,19] and honeycomb core [20,21]. Liu et al. [22] proposed a 3D printing method to fabricate carbon fiber reinforced lattice truss core sandwich structure. The cross sectional morphology was analyzed. The effects of relative density, fiber volume content and truss angle on the compressive properties of composite lattice truss sandwich structure were investigated by experiments, which indicated that the experimental results was close to the theoretical results. Xu et al. [23] designed and fabricated a novel composite corrugated core sand wich panel by auto-cutting process. The mechanical behavior and failure mechanism were revealed by experiments. The analytical estimates of the strength and stiffness were obtained, which were in good agreement with the experimental results. Rodriguez-Ramirez et al. [24] made a contribution to understand the postbuckling behavior of the composite honeycomb cores under bending load. The influence of the boundary conditions on the buckling of the cores was revealed via experiments and numerical simulation. Investigations on the static mechanical behavior of composite sandwich structures with different cell types were
* Corresponding author. School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology, Wuhan, 430074, PR China. E-mail address: [email protected] (J. Liu). https://doi.org/10.1016/j.polymertesting.2019.106188 Received 24 June 2019; Received in revised form 20 September 2019; Accepted 21 October 2019 Available online 23 October 2019 0142-9418/© 2019 Elsevier Ltd. All rights reserved.
Please cite this article as: Jialin Liu, Polymer Testing, https://doi.org/10.1016/j.polymertesting.2019.106188
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made up of three constituent members, which were the Y-flange, the web and the leg. The inclination of the Y-flange was 45� and is denoted by α. The size of the web was 2 mm and was denoted by e. The height of the leg was 18 mm and was denoted by h. The thickness of the Y-frame core and facesheets was denoted by t. The height of the Y-frame core was 27 mm and was denoted by H. The geometric parameters of a unit cell is shown in Fig. 1b. The size of the unit cell in 2-direction was denoted by L1 . The width of the unit cell is given by
conducted under different load conditions, including compressive load [25–27], shear load [28–30] and bending load [31–33]. With regard to the mechanical behavior of the composite sandwich structures under edgewise compressive load, many research results were obtained. Lei et al. [34] investigated the mechanical behavior of the foam-filled glass-fiber reinforced composite sandwich column under edgewise compressive load by experiments, analytical prediction and numerical simulation. The analytical prediction and numerical results were close to the experimental results. The experimental results revealed that the critical collapse load reduced as the ratio of slender ness increased. Xiong et al. [35] used hot-press molding method to fabricate composite sandwich structures with pyramidal truss cores. The analytical models were derived to predict failure load associated with the failure modes under edgewise compressive load. The analytical predictions showed good agreement with the measured load. Mamalis et al. [36] conducted a series of edgewise compressive tests to investi gate the mechanical properties, failure modes of the composite sand wich panels with various types of cores. The influence of the material properties and geometric parameters on the edgewise compressive properties, failure modes and energy absorption was presented and analyzed. However, the edgewise compressive behavior of the com posite Y-frame core sandwich column was limited. Thus, it is necessary to understand the failure modes and mechanical properties of the Y-frame core sandwich column, which could contribute to the applica tion of this composite sandwich structure in ship industry. In this paper, the composite Y-frame core sandwich column was fabricated by hot-press molding method. The mechanical behavior of the Y-frame core sandwich column was investigated by experiments under edgewise compressive load. The influence of relative density on the mechanical properties and failure modes was revealed. The analyt ical model was presented to estimate the failure load of the Y-frame core sandwich column.
L1 ¼ 4e þ t þ 2ðH
(1)
hÞcot α
The length of the Y-frame core in 3-direction is 90 mm and is denoted by L2 as shown in Fig. 1a. Hence, the relative density (RD) of the Y-frame core sandwich column is
ρ¼
h þ t þ 2e þ 2ðH HL1
hÞsin
1
α
(2)
t
Equation (2) implies that the relative density is dependent on the geometric parameters of the Y-frame core. The width of the web e, the height of the leg h and the inclination of the Y-flange α were designed to be constant. The relative density of the Y-frame core increases with the thickness t, which is shown in Table 1. Three different thicknesses are considered. Thus, the Y-frame core sandwich columns with three different relative densities can be obtained. 2.2. Manufacturing process Fig. 2 presents the manufacturing process of the Y-frame core sandwich columns through hot-press molding method. This process consists of four major steps. Firstly, the molds are assembled together and the Y-frame cores were clamped as shown in Fig. 2a. Secondly, the Table 1 The relative density and shear stiffness of the Y-frame core sandwich column fabricated from different layers of prepreg.
2. Geometry and fabrication 2.1. Geometry The geometry of the Y-frame core sandwich column is shown in Fig. 1. Fig. 1a shows that the Y-frame core sandwich column consists nine unit cells. A unit cell of the Y-frame core sandwich column was
Number of layers
Thickness t
Relative density
Shear stiffness GC [38]
8 12 16
0.8 mm 1.2 mm 1.6 mm
5.34% 7.95% 10.53%
1.679 MPa 5.768 MPa 13.528 MPa
Fig. 1. (a) Geometry of the Y-frame core sandwich column; (b) The unit cell of the Y-frame core. 2
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ends of the Y-frame cores are dispersed and embedded into the top and bottom facesheets as shown in Fig. 2b. Thirdly, the Y-frame core sand wich column was cured at 125 � C for 1.5 h as shown in Fig. 2c. Fourthly, the molds were removed from the Y-frame core sandwich column after curing and cooling as shown in Fig. 2d. During the fabrication of the composite Y-frame core sandwich col umns, the stacking sequence of the top and bottom facesheets and Yframe cores were designed to be [0� /90� ]2s, [0� /90� ]3s and [0� /90� ]4s, which were made of 8, 12 and 16 layers of unidirectional prepreg, respectively. The ends of the Y-flange and the leg are embedded into the top and bottom facesheet, respectively, which is shown in Fig. 3. After curing at 125 � C for 1.5 h, the top and bottom facesheets would be compressed and the stacking sequences of the facesheets, Y-flange, web and leg would be [0� /90� ]2s for the Y-frame core sandwich column with RD ¼ 5.34%. The Y-frame core sandwich columns were fabricated by the hot-press molding method as shown in Fig. 2. For each relative density, there were three Y-frame core sandwich columns fabricated. The spec imens with different relative densities are shown in Fig. 4, which are prepared for the edgewise compression tests.
compressive load on the Y-frame core sandwich column. The edgewise compression tests of the Y-frame core sandwich column were conducted according to ASTM C364 [37]. With respect to one relative density, we have prepared three Y-frame core sandwich columns. The tests were conducted three times with respect to one relative density. 4. Results and discussion 4.1. Experimental results and discussion The composite Y-frame core sandwich columns were tested under edgewise compressive load. The relative densities of the Y-frame core sandwich columns ranged from 5.34% to 10.53%. The effects of the relative density on the edgewise compressive load-displacement curves, failure modes and failure load were investigated. 4.1.1. Edgewise compression response Fig. 6 presents the edgewise compressive load-displacement curve of the Y-frame core sandwich column with RD ¼ 5.34%, which is followed by the deformation of the Y-frame core sandwich column in three typical loading stages. The three typical stages were labeled by I, II and III, respectively. In the first stage I, the load-displacement curve increased linearly as shown in Fig. 6a. In this stage, there is no failure in the Yframe core sandwich column as shown in Fig. 6b. In the second stage II, the load-displacement curve begin to drop as shown in Fig. 6a. The macro buckling is observed as shown in Fig. 6b. In the third stage III, the load decreases increasingly as shown in Fig. 6a, which implied that the Y-frame core sandwich column lost load-bearing capacity. In the third stage, the failure modes of the Y-frame core sandwich column includes the fracture in the top facesheet and the delamination in the web of the
3. The edgewise compression test Fig. 5 shows the edgewise compression test setup for the Y-frame core sandwich column. The test setup consists of three parts: the moveable part, the Y-frame core sandwich column and the stationary part. The moveable part consists of the test fixture and moveable head. The stationary part consists of the rest fixture and stationary head as shown in Fig. 5. Two ends of the Y-frame core sandwich column were clamped by the test fixtures of the moveable part and the stationary part. The moveable head moved at a speed of 0.5 mm/min to exert edgewise
Fig. 2. Manufacturing process of the composite Y-frame core sandwich column: (a) The molds were assembled together; (b) The ends of the molds were clamped. The ends of the Y-frame cores were embedded into the top and bottom facesheets; (c) The Y-frame core sandwich column was cured at 25 � C for 1.5 h; (d) The molds were removed after curing, and obtained the composite Y-frame core sandwich column. 3
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Fig. 3. Schematic of the stacking sequence [0� /90� /0� /90� ]s of the Y-frame core sandwich column.
Fig. 4. The composite Y-frame core sandwich columns with relative densities 5.34%, 7.95% and 10.53%.
Y-frame core as shown in Fig. 6b. Fig. 7 depicts the edgewise compres sive load-displacement curve and the failure images of the Y-frame core sandwich column with RD ¼ 7.95% in three typical loading stages. In the first stage I, the load increases linearly with the displacement, which indicates that no structural damage occurs as shown in Fig. 7a. In the second stage II, the load-displacement curve dropped rapidly. The macro buckling and delamination in the web occur in this stage as shown in Fig. 7b. In the third stage III, the delamination in the web and the facesheet-core interface in observed as shown in Fig. 7b. The fracture in the top facesheet is also observed. The failure modes of the Y-frame core sandwich column with RD ¼ 5.34% and RD ¼ 7.95% were not identical. The delamination failure is observed in the facesheet-core interface of the sandwich column with RD ¼ 7.95%. However, there is no delami nation and fracture observed in the second stage II as shown in Fig. 6b. This is due to the Y-frame core sandwich column with RD ¼ 5.34% has less manufacturing imperfections in the facesheet-core interface than that of the Y-frame core sandwich column with RD ¼ 7.95%. Hence, the dominant failure mode of the Y-frame core sandwich column with
RD ¼ 5.34% is macro buckling. Fig. 8 shows the load-displacement curve and failure process of the Y-frame core sandwich column with RD ¼ 10.53%. In the first stage I, the edgewise compressive load increased linearly with displacement as shown in Fig. 8a. In the second stage II, the load-displacement curve drops sharply. The macro buckling, delamination and fracture in the facesheet-core interface occurred as shown in Fig. 8b. In the third stage III, the delamination and fracture extended, which was similar to the Y-frame core sandwich column with RD ¼ 7.95% and 10.53%. 4.1.2. Failure mode For the Y-frame core sandwich column with different relative den sities, the dominant failure mode related to the drop of the peak load was macro buckling. The failure load was determined by the peak load in the first stage. Fig. 9 shows the failure load of the Y-frame core sandwich column with different relative densities. It implies that the failure load increases with the relative density. The average failure load of the Yframe core sandwich column varied from 2710.3 N to 18639.5 N as 4
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Fig. 5. Edgewise compression test setup of the Y-frame core sandwich column.
relative density changed from 5.34% to 10.53%. Moreover, the relative density had great influence on the failure mode of the Y-frame core sandwich column after attaining the peak load. For the Y-frame core sandwich column with RD ¼ 5.34%, macro buckling is the competing failure mode after the peak load drop in the second stage II as shown in Fig. 6b. For the Y-frame core sandwich column with RD ¼ 7.95%, the macro buckling and delamination are both observed after attaining the peak load in the second stage as shown in Fig. 7b. For the Y-frame core sandwich column with RD ¼ 10.53%, the macro buckling, delamination and fracture are observed after attaining the peak load in the second stage II as shown in Fig. 8b. The peak load of the Y-frame core sandwich column decreased more rapidly as the relative density increased. Furthermore, as the relative density increased, the Y-frame core sand wich column damaged more and more seriously after attaining the peak load. After the edgewise compression tests were finished, the Y-frame core sandwich columns were unloaded. Fig. 10 shows the deformation of the Y-frame core sandwich columns with different relative densities after unloading. It can be seen that the residual deformation of the Y-frame core sandwich column with RD ¼ 5.34% is smaller that of the Y-frame core sandwich columns with RD ¼ 7.95% and 10.53%. This was because the Y-frame core sandwich column with RD ¼ 7.95% and 10.53% had more serious damage than the Y-frame core sandwich column with RD ¼ 5.34% after attaining the peak load. Therefore, the elastic defor mation is easier to recover for the Y-frame core sandwich column with RD ¼ 5.34% than that for the Y-frame core sandwich column with RD ¼ 7.95% and 10.53% after unloading.
Fig. 6. (a) Load-displacement curve of the Y-frame core sandwich column with RD ¼ 5.34%; (b) Deformation of the Y-frame core sandwich column with RD ¼ 5.34% in three typical stages.
column subjected to edgewise compressive load. L ¼ nL1 is the length of the Y-frame core sandwich column. The number of the unit cell is denoted by n. The equivalent flexural rigidity Deq of the Y-frame core sandwich column can be given by Deq ¼ D0eq þ 2Dfeq þ DCeq ¼ Ef
L2 tðH þ tÞ2 L2 t3 L2 H 3 þ Ef þ EC 2 6 12
(3)
where Ef is the elastic modulus of the facesheets as shown in Table 2. EC is the elastic moduli of the Y-frame core. EC ¼ 0 for the Y-frame core. Hence, the equivalent flexural rigidity Deq is given by Deq ¼ Ef
L2 tðH þ tÞ2 L2 t3 þ Ef 2 6
(4)
As thickness t ranges from 0.8 mm to 1.6 mm, the following condi tion is satisfied 2
Ef L2 tðHþtÞ 2 t3
Ef L26
� �2 H ¼3 1 þ > 100 t
(5)
Therefore, the equivalent flexural rigidity Deq can given by
4.2. Theoretical analysis and discussion According to the experimental results of the Y-frame core sandwich column under edgewise compressive load, the peak load drop was due to the macro buckling. There were two types of buckling associated with the macro buckling, which were the Euler buckling and the core shear buckling [35]. Fig. 11 shows the schematic of the Y-frame core sandwich
Deq � Ef
L2 tðH þ tÞ2 2
(6)
Fig. 12a shows the schematic of the macro buckling of the endclamped Y-frame core sandwich column. The deformation v is super imposed by two displacements, which are the bending displacement w1 5
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Fig. 7. (a) Load-displacement curve of the Y-frame core sandwich column with RD ¼ 7.95%; (b) Deformation of the Y-frame core sandwich column with RD ¼ 7.95% in three typical stages.
Fig. 8. (a) Load-displacement curve of the Y-frame core sandwich column with RD ¼ 10.53%; (b) Deformation of the Y-frame core sandwich column with RD ¼ 10.53% in three typical stages.
and the additional displacement w2 . The additional displacement w2 is associated with the shear deformation of the Y-frame core. The bending moment M can be given by M ¼ Pv ¼ Pðw1 þ w2 Þ ¼ Deq
d2 w1 dx2
The differentiation of Equation (7) gives � � d3 w1 dw1 dw2 Deq 3 ¼ P þ dx dx dx
(7)
(8)
Fig. 12b shows the schematic of the typical segment deformation of the Y-frame core sandwich column. The angle θ denotes the slope of the Y-frame core sandwich column, which can be given by θ¼
dv dðw1 þ w2 Þ ¼ dx dx
(9)
The component FS of the force P at the cross section of the Y-frame core sandwich column is perpendicular to the axis of the Y-frame core sandwich column, which can be given by FS ¼ P sin θ
Fig. 9. The failure load of the Y-frame core sandwich column with different relative densities.
(10)
Under the consideration that the slope θ of the Y-frame core sand wich column is small in the elastic-linear stage, the component FS of the force P is
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Fig. 10. The deformation of the Y-frame core sandwich columns with different relative densities after unloading. Table 2 The elastic modulus of the composite laminates made from different layers of prepreg. Number of layers
Elastic modulus Ef [39]
8 12 16
27.53 GPa 29.68 GPa 30.91 GPa
where GC is the measured shear stiffness of the Y-frame core as shown in Table 1. Combination of Equations (11) and (12) gives dw2 P dðw1 þ w2 Þ ¼ dx dx AGC
(13)
Substituting Equation (13) into Equation (8) yields Deq
d3 w1 dw1 ¼ β2 dx3 dx
where β2 ¼ Deq ½1
(14) P P=ðAGC Þ�.
The solution w1 to Equation (14) is in the form of
w1 ¼ C1 sin βx þ C2 cos βx þ C3
(15)
Differentiating Equation (15) twice gives 2
d w1 ¼ dx2
C1 β2 sin βx
C2 β2 cosβx
(16)
Inserting Equation (16) in Equation (7) yields w1 þ w2 ¼
dðw1 þ w2 Þ dx
(11)
The boundary condition w1 þ w2 ¼ 0 at the cross section x ¼ 0 re quires that C2 ¼ 0; the boundary condition w1 þ w2 ¼ 0 at the cross section x ¼ L requires that αL ¼ kπ, which gives � �2 kπ P � � � β2 ¼ (19) ¼ L Deq 1 P ðAGC Þeq
According to Allen’s work [40], the component FS of the force P can be given by FS ¼ AGC
dw2 dx
(17)
The boundary condition of the end-clamped Y-frame core sandwich column is � w1 þ w2 ¼ 0; x ¼ 0 (18) w1 þ w2 ¼ 0; x ¼ L
Fig. 11. Schematic of the Y-frame core sandwich column subjected to edgewise compressive load.
FS ¼ P
Deq d2 w1 P dx2 Deq 2 ¼ β ð C1 sin βx C2 cos βxÞ P 1 ¼ ð C1 sin βx C2 cos βxÞ 1 P=ðAGC Þ
(12)
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Fig. 12. (a) The schematic of the macro buckling of the end-clamped Y-frame core sandwich column; (b) The schematic of the typical segment deformation of the Yframe core sandwich column.
According to Equation (19), the edgewise compressive load P P¼
PE PS PE þ PS
Table 3 The failure load of the composite Y-frame core sandwich columns with different relative densities.
(20) k2 π 2 D
where PE ¼ L2 eq is the Euler buckling load; k ¼ 2 for a column with built-in ends; PS ¼ ðAGC Þeq is the shear buckling load; A ¼ HL2 for a sandwich column [41]. Equation (20) is usually expressed in the following form 1 1 1 ¼ þ P PE PS
Relative density
Measurements
Predictions
5.34% 7.95% 10.53%
2710.3 N 11781.9 N 18639.5 N
4048.2 N 13786.1 N 31970.7 N
Data availability
(21)
The raw/processed data required to reproduce these findings cannot be shared at this time due to technical or time limitations. All relevant data supporting the findings of this study are included within the paper or are available from the corresponding author upon reasonable request.
The macro buckling failure load of the Y-frame core sandwich col umn can be predicted by Equation (21). A summary of analytical results and measured results for failure load of the Y-frame core sandwich column at different relative densities is presented in Table 3. There are some differences between the analytical results and measured results. The reasons for this difference are mainly due to the manufacture de fects. The ends of the Y-frame core were embedded into the top and bottom facesheets in the manufacturing process. As a result, the me chanical properties of the top and bottom facesheets were weakened. However, the effects of the manufacture defects on the mechanical properties were not considered in the analytical model, which led to the failure load of the analytical results are larger than that of the measured results.
Declaration of competing interest The authors declared that they have no conflict of interest to this work. We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted. Acknowledgement The present work is supported by National Science Foundation of China under Grant Nos. 11402094 and 11802100.
5. Conclusions The composite Y-frame core sandwich columns with different rela tive densities were fabricated by hot-press molding method. The influ ence of the relative density on the failure load, the feature of the loaddisplacement curve and the failure mode was investigated. The edge wise compressive tests revealed that the failure load increased as the relative density increased. As relative density increased from 5.34% to 10.53%, the average failure load of the Y-frame core sandwich column varied from 2710.3 N to 18639.5 N. The dominant failure mode of Yframe core sandwich columns with different relative densities was macro buckling. The analytical model was presented to predict the failure load based on the dominant failure mode. The peak load of the Yframe core sandwich column dropped more rapidly in the second stage as the relative density increased. Moreover, as the relative density increased, the failure mode was more sophisticated and the Y-frame core sandwich column damaged more seriously after attaining the peak load.
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