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Failure study of honeycomb sandwich structure with embedded part under axial pullout loading
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Failure study of honeycomb sandwich structure with embedded part under axial pullout loading Ruixiang Bai a, Hongqi Ou b, Kewang Peng a, Wen Wu a, Zhenkun Lei a, *, Tao Liu b, Mingliang Chen b, Linyu Song b, Renbang Lin b a b
State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, 116024, China Aerospace System Engineering Shanghai, Shanghai, 201109, China
A R T I C L E I N F O
A B S T R A C T
Keywords: Honeycomb structure Equivalent method Embedded part Digital image correlation Finite element method
The deformation and failure behavior of a regular hexagonal honeycomb sandwich structure with an embedded part under axial pullout loading are studied. The deformation process of the honeycomb sandwich structure was recorded using a noncontact full-field optical measurement method based on three-dimensional digital image correlation. A corresponding finite element numerical model of the honeycomb sandwich structure with embedded parts is established. A cohesive zone model is used to simulate the interface failure of the honeycomb sandwich structure with the embedded part. The four groups of interface parameters were characterized by standard testing procedures including the flatwise tensile test, single-lap test, double cantilever beam test and three-point bending test. The numerical results accurately predicted the ultimate load of the structure. The failure process and failure mechanism of the honeycomb sandwich structure with the embedded part are ob tained. The combination of an experiment and numerical methods effectively revealed the deformation and failure behavior of honeycomb sandwich structures with an embedded part under axial pullout loading.
1. Introduction A sandwich structure is composed of two thin high-strength sheets and a thick low-density core. Commonly, the core thickness is often larger than that of the sheet to reduce the weight of the sandwich structure as much as possible. Therefore, not only the high strength and high modulus of the sheet can be fully utilized, but also the designed strength and rigidity can be achieved [1]. By selecting a reasonably designed core, the bearing capacity of a sandwich structure can be effectively improved. The core is usually composed of a low-density material such as porous foam and aluminum honeycomb, which is commonly used when the skins are constructed from aluminum alloy or composite laminates. Different types of sand wich structures can be selected according to the actual requirements of different fields. The world’s first honeycomb sandwich structure (HSS) was produced in 1930. By the 1950s and 1960s, high-performance HSS had achieved maturity and was widely used in aviation, aerospace, marine, and other fields. At present, the honeycomb core possesses multiple configurations from squares to irregular shapes. The most widely used honeycomb core is the hexagonal honeycomb, which
possesses excellent mechanical properties [2]. The HSS frequently is required to be connected to other components by an embedded part such as a metal fastener, which embeds inside sandwich panels and bears the main load when the sandwich panel is connected to an external instrument. There is a complex failure behavior in the embedded honeycomb sandwich structure (EHSS), including interface debonding of the honeycomb core/skin, and fracture of filled foam and skin [3]. At present, the study of damage mechanism of EHSS primarily relies on pullout tests [4]. The EHSS are primarily subjected to axial tension and shear loading. There are two primary failure modes of the embedded honeycomb structure under an axial tensile load: these are debonding between the honeycomb core and skin, and shear failure of the honeycomb core around the embedded part. Interface debonding between the skin and the honeycomb core is the most common form of damage and causes a significant decline in the carrying capacity of the structure. Considering the economical and cyclical requirements of structural design, it is appropriate and necessary to determine the failure mode and carrying capacity of an embedded structure by experimen tation during the structural selection and verification. Moreover, numerical simulations are also a powerful method for
* Corresponding author. E-mail address: [email protected] (Z. Lei). https://doi.org/10.1016/j.tws.2019.106489 Received 24 February 2019; Received in revised form 22 October 2019; Accepted 6 November 2019 0263-8231/© 2019 Elsevier Ltd. All rights reserved.
Please cite this article as: Ruixiang Bai, Thin–Walled Structures, https://doi.org/10.1016/j.tws.2019.106489
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and numerical methods. The study is divided into three parts. First, the theoretical basis of the equivalent parameters of the HSS is introduced to determine a reasonable equivalent model. Then, an axial pullout experiment on the EHSS is performed and the full-field displacement is measured by the digital image correlation (DIC) technique. Finally, using the ABAQUS software package, a precise FE numerical model is established for predicting the failure mode and load capacity consid ering interface failure of the EHSS. The rationality of the FE model calculation is compared by experiment results. 2. FE simulation 2.1. Equivalent model Allen proposed an original honeycomb equivalent model, which assumed that the honeycomb core was extremely soft and only resistant to transverse shear stress, additionally, the skin was very thin and only resistant to the in-plane load [13]. Gibson proposed a new cell equiva lence theory that simplified the cell to a Bernoulli-Eulerian beam, and deduced an analytical formula that ignored the inconsistency of the cell wall thickness in the x and y directions [14]. Subsequently, multiple scholars considered the orthogonal anisotropy due to different thick nesses in the two directions of the cell wall, and derived some equivalent models [15–17]. A schematic view of a hexagonal HSS is shown in Fig. 1. The equivalent plate theory considers the HSS as an isotropic plate with different thickness. The parameters necessary for the FE method, such as the equivalent thickness, can be derived according to the stiff ness; however, the theory cannot reflect the influence of the core shape on the overall performance of the sandwich panel. In the honeycomb plate theory, the HHS is equivalent to an aniso tropic plate of equal stiffness and size when considering the in-plane and out-of-plane mechanical properties of the sandwich structure. Then, the mechanical parameters of the equivalent plate are derived. This model cannot be used to study problems, such as fiber fractures and interlayer debonding between the skin and core [18,19]. The sandwich plate theory considers the honeycomb core and skin separately. This theory assumes that the upper and lower plates obey Kirchhoff’s hypothesis, ignores the resistance to lateral shear forces, and are still isotropic homogeneous thin plates. Moreover, the honeycomb core is resistant to lateral shear loads and possesses certain in-plane stiffness rendering the honeycomb core is equivalent to an anisotropic plate. The sandwich plate theory is used in conjunction with the equivalent the honeycomb structure to study interfacial fractures of the adhesive layer between the skin and the honeycomb core. The model parameters are described as [20]. 8 8 � � pffiffi � > � > > > 4 t 2 t3 4 3 12 t2 t3 > > > > p ffi ffi E E ¼ 1 3 Es 1 ¼ G > cx s > cxy 2 3 > > 2 > > l l 5 5 l l3 3 > > > > > > � pffiffi < < 2� 3 4 3t t ; (1) and Gcxz ¼ 3 tGs Ecy ¼ pffiffi Es 1 2 3 > > 5 l l > 3 > 3 l > > > > pffiffi > > pffiffi > > > > 2 3t > > 8 3 t > > > : Gcyz ¼ Gs E E ¼ cz s > : 3 l 9 l
Fig. 1. Hexagonal honeycomb sandwich structure.
designing an improved optimized embedded structure; additionally, these simulations are vital in obtaining a comprehensive understanding of the failure process of the EHSS [5,6]. In the initial stage of structural design, particularly in the optimization design stage, it is extremely desirable for structural designers to predict the failure mode and bearing capacity of embedded structures with different design parameters by an accurate and effective numerical simulation method [7]. A pullout test is generally used to evaluate the failure behavior. Demelio et al. [8] experimentally verified the fatigue stress of Kevlar composite skin with embedded joints and an aramid honeycomb core sandwich layer in two load forms. Cao et al. [9] designed experiments to test composite sandwich panels containing steel hybrid joints. However, few researchers have been concerned with the influence of the bonding interface on the failure load of EHSS. Because of the existence of the skin, it is difficult to observe the failure process in the interface during the loading process using traditional experimental methods. Therefore, it is necessary to establish an effective honeycomb structure model by numerical simulation to simulate the interface damage when the embedded parts are pulled out. Owing to the complexity of the HSS, there is no line element suitable for the interface in the existing finite element (FE) software that can accurately simulate the honeycomb cell, this is especially true when studying the problem of interface cracking between the skin and the sandwich core. Therefore, the HSS is frequently simplified to an isotropic panel with equal thickness or an anisotropic panel with un equal thickness in theoretical analysis and numerical calculation ac cording to the equivalent plate theory, honeycomb plate theory, and sandwich plate theory [10–12]. The first two methods are equivalent to the entire honeycomb sandwich plate, while the third is equivalent only to the honeycomb core. The primary work of this study is to analyze the deformation and failure behavior of the EHSS under an axial pullout load by experimental
where Ecx, Ecy, and Ecz are the equivalent moduli in three directions. Gcxy, Gcxz, and Gcyz are the equivalent shear moduli of the three coor dinate planes. Es is Young’s modulus of the honeycomb structure ma terial. Here, t and l are the thickness and the length of the cell wall, respectively. 2.2. Cohesive zone model Certain methods have been applied to simulate the debonding damage propagation behavior of the adhesive layer between the skin and the honeycomb core, such as the virtual crack closure technique
Fig. 2. Bilinear model of CZM. 2
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Fig. 3. Four typical tests for characterizing interfacial parameters, (a) FT, (b) SL, (c) DCB and (d) TPB.
(VCCT), extended finite element method (EFEM), and element-free method (EFM) [21–23]. The VCCT method has problems with grid correlation and low computational efficiency. The EFEM is more suit able for simulating discontinuous materials; however, it is still limited to fractures of bi-material. Moreover, the computational efficiency of the EFM is lower. The cohesive zone model (CZM) can define different fracture criteria according to different materials, thus it is robustly applicable. In this study, the cohesive element is used to simulate the debonding process between the skin and the honeycomb core. The CZM is a simplified method that characterizes the interaction between molecules and atoms. The crack tip is assumed as a small cohesive zone composed of two in terfaces. As shown in Fig. 2, a typical bilinear model of the crack-tip cohesive zone is a linear relationship between the interfacial traction force T and the relative displacement U between two faces of the crack. When the relative displacement is δ0, the cohesive interface begins to debond and the traction force achieves its maximum, σ0. When the relative displacement is δf, the cohesive interface separates completely. The matrix form of the constitutive equation can be expressed as
respectively. Here, t0 is the original thickness of the cohesive element. In this study, the response of the cohesive elements is based on a tractionseparation approach, the default constitutive thickness is equal to 1 in ABAQUS software. This choice ensures that nominal strains are equal to the relative separation displacements. When the stress or strain satisfies the defined critical damage initi ation criterion, the damage initiates and the stiffness begins to degrade. In this study, a quadratic stress criterion is used as the criterion of damage initiation, namely � �2 � �2 � �2 σn σs σt þ 0 þ 0 ¼ 1; (4) 0
σn
where GIC, and GIIC represent the energy release rates in two directions. Here, Gshear ¼ GIIþ GIII,GT ¼ GIþ Gshear. and GII, and GIII are the mode-II and mode-III fracture strain energies, respectively. Here, η is the frac ture toughness coefficient. When the above formula is satisfied, the cohesive element is invalid, and the interface is debonded and failed.
where K is the stiffness matrix. The stress matrix, σ consists of three stress components (σn, σs, σt), which represent the normal and two tangential stresses, respectively. Correspondingly, the strain matrix, ε, consists of three components (εn, εs, εt), which defined as δ t0
δ t0
δ t0
εn ¼ n ; εs ¼ s ; εt ¼ t ;
σt
where σ 0n, σ 0s , and σ 0t are the peak stresses in each direction. When the sum of the squares of the stress ratio in Eq. (4) achieves 1, the damage is initiated and then enters the damage evolution stage. In this study, the BK criterion is used to describe the damage evolution law, namely � �n Gshear GIC þ ðGIIC GIC Þ ¼ GTC ; (5) GT
(2)
½σ � ¼ ½K�⋅½ε�;
σs
(3)
2.3. Cohesive interface parameters
where δn, δs, and δt are the corresponding relative displacements,
In this study, we assume that the cohesive layer is isotropic material 3
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Fig. 4. Experimental photos of (a) FT test, (b) SL test, (c) DCB test and (d) TPB test.
in the ns-plane, with the interface parameters in Eq. (4) and Eq. (5) satisfying σ 0t ¼ σ0s and GIIC ¼ GIIIC. Therefore, the determination of four interface parameters of the cohesive layer is required; these are the interface normal strength σ0n, the tangential strength σ 0t , the mode-I fracture toughness, GIC, and the mode-II fracture toughness, GIIC. There are three types of interfaces in this study: the interface between the honeycomb core and skin, between the skin and the embedded parts, and between the honeycomb core and the embedded parts. Therefore, it is required that the four interface parameters for each interface be ob tained from experiments. The skin-embedded interface is selected as an example to illustrate the experimental method for each parameter. Four experimental types are adopted to obtain the four groups of interface parameters. As shown in Fig. 3, there are the flatwise tension (FT), single lap (SL), double cantilever beam (DCB), and three-point bending (TPB) tests. Then, the specimen was designed and manufac tured based on the corresponding standards. The experimental photos are shown in Fig. 4. For the FT and SL tests, the interface strengths are equal to the ratio of the failure load and the bonding area [24,25]. For fracture toughness tests, Nettles [26] measured the fracture toughness of a honeycomb sandwich structure by referring to the DCB test method in the American Society for Testing Materials (ASTM D5528) standard. Pradeep et al. [27] used the climbing drum peel test to determine mode-I fracture toughness of a honeycomb sandwich inter face. In this study, the DCB and TPB tests were used to determine the interface fracture parameters used in a cohesive zone model. The frac ture toughness for mode-I and mode-II fracture tests is calculated ac cording to the ASTM standards [28,29]. Three samples for every type of
Table 1 Summary of interface parameters. Interface type
σ0n
σ0s
(MPa)
GIC (N/ mm)
GIIC (N/ mm)
Honeycomb core/skin Honeycomb core/embedded part Skin/embedded part
2.2588 3.3170
0.9950 1.7085
0.7272 0.5185
2.4583 1.7528
20.150
30.0
1.040
3.980
(MPa)
test were conducted to obtain an average value. The fracture toughness and strength parameters of each interface can be obtained through the above tests, as listed in Table 1. The test data for these interface pa rameters are obtained in Appendix A. 2.4. FE model A finite element model of the EHSS is established in the study using the commercial FE software ABAQUS. The skin and the embedded part are composed of isotropic aluminum alloy metal, whose constitutive relationship is a linear elastic-perfectly plastic model. The material Table 2 Mechanical properties of skin and embedded part.
4
Material
Elastic modulus (GPa)
Ultimate strength (MPa)
Poisson’s ratio
7A09
68
405
0.33
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cohesive layer between the skin and the core is simulated as a COH3D8 cohesive element. The entire structure is modeled using an integrated method, and the cohesive element is inserted at the bonding interface. This reduces the nonconvergence problem caused by contact and im proves the accuracy of the model. Both sides of the sandwich structure are clamped, and the off-plane displacement in the z-direction is coupled in the center of the embedded part to simulate the axial pullout load. The applied boundary condition is shown in Fig. 5(b).
Table 3 Equivalent material parameters of honeycomb core. Elastic modulus (MPa)
Shear modulus (MPa)
T/LDR
Ecx
Ecy
Ecz
Gcxy
Gcxz
Gcyz
μxy
0.31
0.31
1308.7
0.184
184.5
184.5
0.99
parameters of the skin and embedded part are listed in Table 2. The honeycomb core layer is equivalent to an anisotropic plate; the material parameters of the honeycomb core are calculated by Eq. (1), as listed in Table 3. The transverse/longitudinal deformation ratio (T/LDR) in this study is an equivalent one, which was originally derived from Gibson [30], and then modified by Hu [31]. The FE model of the EHSS is shown in Fig. 5(a). The equivalent anisotropic plate of the HSS is modeled as a C3D8S 3D solid element; the
3. Experiments 3.1. Specimen description The EHSS is a primary bearing component for linking an exposed
Fig. 5. (a) FEM model and (b) boundary conditions.
Fig. 6. (a) Scheme of the EHSS, (b) scheme of cross section near the embedded part, (c) front view and (d) lateral view of the specimen. 5
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Fig. 7. (a) Experimental setup photo and (b) local enlargement.
Fig. 8. (a) AOI for deformation measurement by 3D-DIC and (b) out-of-plane displacement of honeycomb sandwich panel under the load of 4.34 kN.
platform to aircraft structure, as shown in Fig. 6. The size of the spec imen is 200 � 200 mm, and the total thickness is 30 mm. The skin is made of a 0.3-mm 7A09 aluminum alloy panel, the size of the honey comb core is 0.05 � 4 mm. The mechanical properties of the primary materials are listed in Table 2. The HSS has the advantages of being light-weight, possessing high specific strength, and high specific stiffness, however, the honeycomb core is too soft to achieve the strength and durability requirements when connected to external equipment. Therefore, it is necessary to place potting materials and an embedded part (bolt or rivet) in the honeycomb core to reinforce the HSS. The center hole of the EHSS is used to connect the external bolt (Fig. 6(a)). The center is the embedded part with a radius of 11 mm; the loading hole screw radius is 8 mm. The outside of the embedded part is filled with J78D foam-bonded honeycomb to alleviate the stress
concentration in the honeycomb core connection area (Fig. 6(b)). The foam is required to be uniformly filled around the embedded part with a size of two or three honeycomb holes. A front view and lateral view of the specimen are shown in Fig. 6(c) and (d), respectively. 3.2. Axial pullout test The axial pullout experiment of the EHSS was conducted using a universal testing machine (CSS-2250, Changchun Testing Machine Research Institute). Its maximum loading capacity is 50 kN. The spec imen is installed as shown in Fig. 7(a). It is necessary to fasten the specimen to the clamp plate with bolts to ensure that the tensile load acts in the axial direction of the embedded part, as shown in Fig. 7(b). The loading rate of the pullout experiment was 1.0 mm/min. The three-dimensional digital image correlation (3D-DIC) technique was used to measure the deformation during the loading process. Cold lights were installed on both sides of the specimen to reduce image shadows caused by uneven indoor light during image acquisition. A camera was installed on a tripod to capture images with an acquisition frequency of 0.5 fps. Before the experiment, a random speckle pattern was prepared on the specimen surface using acrylic paints of titanium white and carbon black. 4. Results and discussion 4.1. Full-field deformation The acquired images were processed by the PMLAB package to obtain the displacement and strain fields at different times. The spatial resolution was 2 pixels/mm. The three-dimensional coordinate, XYZ, of the displacement field measured by 3D-DIC method is shown in Fig. 8 (a). The tension direction of the embedded part is parallel to the Z-axis. The area of interest (AOI) for the displacement measurement is in the XY-plane. A local image coordinate x1oy1, is set on the left corner of the AOI.
Fig. 9. Out-of-plane displacement and load curves of points of A, B, and C. 6
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Fig. 10. (a) εx and (b) εy distributions under the load of 4.34 kN, (c) εx and (d) εy distribution under the ultimate load of 6.23 kN.
A full-field out-of-plane displacement of the honeycomb sandwich panel under the load of 4.34 kN is shown in Fig. 8(b). It is clear that the out-of-plane displacement is circularly distributed around the loading bolt, the maximum value is a circle with radius identical to that of the embedded part. It is inferred that the load drives the embedded part to move axially, the shear force is applied to the honeycomb core through the adhesive layer. The skin has a maximum value in the range of the connection radius with the embedded part owing to the low bending stiffness. Three positions are relabeled as points of A, B, and C in Fig. 8(b), which are located on the arc with the radius R ¼ 11 mm and the angle, α, of 0� , 90� , and 180� in the image coordinate x1oy1, respectively. The corresponding pixel coordinates are A(92, 54) pixel, B(70, 350) pixel, and C(48, 53) pixel. The out-of-plane displacement and load curves of three points of A, B and C are plotted in Fig. 9 to observe the variation trend of the out-of-plane displacement near the embedded part. It is clear in Fig. 9 that the trend is identical; however, the out-ofplane displacement of the three points is slightly different. When the load is identical, the displacement of point A is the largest, the one of point B is the second, and the one of point C is the smallest. The dif ference is caused by the local debonding on the interface of the skin/ embedded part. Furthermore, the full-field xy-plane strains of εx and εy under the load of 4.34 kN and the ultimate load are shown in Fig. 10. It is clear that the strains are almost centrosymmetric within the radius of the embedded part; the closer to the loading point, the larger the strain. The strain distribution area indicates that the load is transferred from the embedded part to the skin, causing the skin to bulge. Accordingly, the full-field strains of εx and εy under the ultimate load of 6.24 kN are shown in Fig. 10(c) and (d). It is clear that the maximal strain areas gradually approach the loading point during the loading process, the maximum transverse strain is εx ¼ 0.0196, and the longi tudinal strain is εy ¼ 0.0624. It can be inferred that the maximum strain of the embedded honeycomb sandwich panel is always extended from the outside to the inside with the loading point as the center of the circle. The structural damages occur when the maximum strain radius achieves the loading point.
Fig. 11. Load-displacement curves of experiment.
4.2. Load-displacement curve The load-displacement curves of the EHSS are shown in Fig. 11. It can be seen that the stiffness decreases when the load steadily increases to a certain value. It indicates that the interfaces among foam, honey comb core and skin begin to fail. Then, the stiffness decreases again when the contact failure between the embedded part and the skin oc curs. The bearing capacity of the EHSS decreases dramatically until the load achieves 6.23 kN. 4.3. Failure analysis The failure mode of the EHSS is shown in Fig. 12(a). It is clear that a bulging phenomenon occurs in the upper skin around the embedded part. The plastic deformation of the skin near the embedded part results in cracking failure due to excessive tensile stress. The internal honey comb structure after manual peeling is shown in Fig. 12(b). It is clear that the local honeycomb cell around the embedded part is folded, and 7
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Fig. 12. Failure mode of the EHSS, (a) failure photo and (b) internal honeycomb structure after manual peeling.
Fig. 13. Result of numerical simulation, (a) Von Mises stress of the EHSS and (b) strain distribution of skin.
Fig. 14. Failure modes of the EHSS, (a) skin/honeycomb core interface and (b) embedded part/skin interface.
the foam filled in the honeycomb cell is broken, displaying the rough fracture cross-sections. In this structure, both the interface of the skin/honeycomb core and that interface of the skin/embedded part are bonded by a J78B adhesive layer. However, these two interfaces would appear to exhibit different failure behavior owing to the difference in the interface properties, as provided in Table 1. It is necessary to study the progressive failure behavior of the interfaces of EHSS under axial pullout load. A cohesive element is used to simulate the bonding interface; the interface damage is considered simultaneously. The failure condition and damage initia tion criterion of the cohesive layer are explained in detail in sections 2.2 and 2.3. The stress and skin strain obtained by FE simulation are shown in Fig. 13. It is clear that the stress around the loading point of the EHSS is always at the maximum value [Fig. 13(a)]; the strain field distribution on the skin is similar to the DIC results [Fig. 8(b)]. The skin bulges
around the embedded part and the maximum strain around the loading point is 0.0183, which is a 6.78% difference from the DIC result. The interface failure mode of the EHSS under the ultimate load is shown in Fig. 14, where SDEG represents the interface stiffness degra dation factor. The stiffness degradation is completed and the cohesive element is invalid when the value of SDEG achieves 1. As shown in Fig. 14(a), the damage to the interface of the skin and the honeycomb core distributes in a circle centered on the loading point whose radius is about 21 mm. By comparison, the interface of the embedded-part and the skin is almost completely destroyed. These interface damages cause the stiffness reduction. The FE simulated load vs. displacement curve is also shown in Fig. 15. The ultimate load of the numerical simulation is 5.9 kN, which possesses a of 5.35% difference from that of the experimental one (Fig. 11). This shows that the new calculation model is a good illustra tion of the mechanism of structural interface debonding and material 8
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Gibson, Cellular Solids: Structure and Properties, Cambridge university press, 1999. [31] Yuqin Hu, Equivalent Models Research and Numerical Analysis of Aluminum Honeycomb Sandwich Plates, Nanjing University of Aeronautics and Astronautics, 2008.
Fig. 15. Load-displacement curve of FE simulation.
failure of the honeycomb sandwich structure with embedded part. However, compared with the experimental results, the current calcula tion results still have differences. In addition to the experimental factors, the following aspects in the FE calculation could cause the differences. First, the honeycomb core is filled with foam in the specimen with a small area. Although the foam portion is not considered in the FE modeling, the effect of the foam is reflected in the interface parameters, which is determined by the above interface tests. Therefore, there is a relative large stiffness of structure in the simulated load-displacement curve. Besides, the stress singularity appeared in the honeycomb core due to the hexagonal geometric sharp corner, the honeycomb core in this study is equivalent to an orthotropic material, and the instability and bending deformation caused by the hexagonal thin wall are neglected. The equivalent mode of the honeycomb core also causes a relative small displacement. Last, there are many interfaces in the honeycomb sandwich struc ture, which shows the complexity of material nonlinear, geometric nonlinear and contact nonlinear. This study combines experiments and numerical methods to simplify the above complex problems, which is a useful attempt. Through the combing of the above problems, in the future numerical research, the author will further study the effect of the filled foam on the honeycomb sandwich structure. 5. Conclusions In this study, experimental and numerical studies of the EHSS under an axial pullout load were performed. Compared with the experiment, the FE simulation well predicted the deformation failure behavior and ultimate load of the EHSS under an axial tensile load. The FE simulated strain field is in accordance with the 3D-DIC results. The FE simulation verifies that the interface debonding and the skin damage are primary influences on the stiffness decrease. The predicted ultimate load main tains a smaller error within 5.35% of the experimental result. Acknowledgments The authors thank the National Natural Science Foundation of China (11572070, 11772081, 11635004), and Fundamental Research Funds for the Central Universities of China (DUT18ZD209). Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.
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Full length article
Failure study of honeycomb sandwich structure with embedded part under axial pullout loading Ruixiang Bai a, Hongqi Ou b, Kewang Peng a, Wen Wu a, Zhenkun Lei a, *, Tao Liu b, Mingliang Chen b, Linyu Song b, Renbang Lin b a b
State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, 116024, China Aerospace System Engineering Shanghai, Shanghai, 201109, China
A R T I C L E I N F O
A B S T R A C T
Keywords: Honeycomb structure Equivalent method Embedded part Digital image correlation Finite element method
The deformation and failure behavior of a regular hexagonal honeycomb sandwich structure with an embedded part under axial pullout loading are studied. The deformation process of the honeycomb sandwich structure was recorded using a noncontact full-field optical measurement method based on three-dimensional digital image correlation. A corresponding finite element numerical model of the honeycomb sandwich structure with embedded parts is established. A cohesive zone model is used to simulate the interface failure of the honeycomb sandwich structure with the embedded part. The four groups of interface parameters were characterized by standard testing procedures including the flatwise tensile test, single-lap test, double cantilever beam test and three-point bending test. The numerical results accurately predicted the ultimate load of the structure. The failure process and failure mechanism of the honeycomb sandwich structure with the embedded part are ob tained. The combination of an experiment and numerical methods effectively revealed the deformation and failure behavior of honeycomb sandwich structures with an embedded part under axial pullout loading.
1. Introduction A sandwich structure is composed of two thin high-strength sheets and a thick low-density core. Commonly, the core thickness is often larger than that of the sheet to reduce the weight of the sandwich structure as much as possible. Therefore, not only the high strength and high modulus of the sheet can be fully utilized, but also the designed strength and rigidity can be achieved [1]. By selecting a reasonably designed core, the bearing capacity of a sandwich structure can be effectively improved. The core is usually composed of a low-density material such as porous foam and aluminum honeycomb, which is commonly used when the skins are constructed from aluminum alloy or composite laminates. Different types of sand wich structures can be selected according to the actual requirements of different fields. The world’s first honeycomb sandwich structure (HSS) was produced in 1930. By the 1950s and 1960s, high-performance HSS had achieved maturity and was widely used in aviation, aerospace, marine, and other fields. At present, the honeycomb core possesses multiple configurations from squares to irregular shapes. The most widely used honeycomb core is the hexagonal honeycomb, which
possesses excellent mechanical properties [2]. The HSS frequently is required to be connected to other components by an embedded part such as a metal fastener, which embeds inside sandwich panels and bears the main load when the sandwich panel is connected to an external instrument. There is a complex failure behavior in the embedded honeycomb sandwich structure (EHSS), including interface debonding of the honeycomb core/skin, and fracture of filled foam and skin [3]. At present, the study of damage mechanism of EHSS primarily relies on pullout tests [4]. The EHSS are primarily subjected to axial tension and shear loading. There are two primary failure modes of the embedded honeycomb structure under an axial tensile load: these are debonding between the honeycomb core and skin, and shear failure of the honeycomb core around the embedded part. Interface debonding between the skin and the honeycomb core is the most common form of damage and causes a significant decline in the carrying capacity of the structure. Considering the economical and cyclical requirements of structural design, it is appropriate and necessary to determine the failure mode and carrying capacity of an embedded structure by experimen tation during the structural selection and verification. Moreover, numerical simulations are also a powerful method for
* Corresponding author. E-mail address: [email protected] (Z. Lei). https://doi.org/10.1016/j.tws.2019.106489 Received 24 February 2019; Received in revised form 22 October 2019; Accepted 6 November 2019 0263-8231/© 2019 Elsevier Ltd. All rights reserved.
Please cite this article as: Ruixiang Bai, Thin–Walled Structures, https://doi.org/10.1016/j.tws.2019.106489
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and numerical methods. The study is divided into three parts. First, the theoretical basis of the equivalent parameters of the HSS is introduced to determine a reasonable equivalent model. Then, an axial pullout experiment on the EHSS is performed and the full-field displacement is measured by the digital image correlation (DIC) technique. Finally, using the ABAQUS software package, a precise FE numerical model is established for predicting the failure mode and load capacity consid ering interface failure of the EHSS. The rationality of the FE model calculation is compared by experiment results. 2. FE simulation 2.1. Equivalent model Allen proposed an original honeycomb equivalent model, which assumed that the honeycomb core was extremely soft and only resistant to transverse shear stress, additionally, the skin was very thin and only resistant to the in-plane load [13]. Gibson proposed a new cell equiva lence theory that simplified the cell to a Bernoulli-Eulerian beam, and deduced an analytical formula that ignored the inconsistency of the cell wall thickness in the x and y directions [14]. Subsequently, multiple scholars considered the orthogonal anisotropy due to different thick nesses in the two directions of the cell wall, and derived some equivalent models [15–17]. A schematic view of a hexagonal HSS is shown in Fig. 1. The equivalent plate theory considers the HSS as an isotropic plate with different thickness. The parameters necessary for the FE method, such as the equivalent thickness, can be derived according to the stiff ness; however, the theory cannot reflect the influence of the core shape on the overall performance of the sandwich panel. In the honeycomb plate theory, the HHS is equivalent to an aniso tropic plate of equal stiffness and size when considering the in-plane and out-of-plane mechanical properties of the sandwich structure. Then, the mechanical parameters of the equivalent plate are derived. This model cannot be used to study problems, such as fiber fractures and interlayer debonding between the skin and core [18,19]. The sandwich plate theory considers the honeycomb core and skin separately. This theory assumes that the upper and lower plates obey Kirchhoff’s hypothesis, ignores the resistance to lateral shear forces, and are still isotropic homogeneous thin plates. Moreover, the honeycomb core is resistant to lateral shear loads and possesses certain in-plane stiffness rendering the honeycomb core is equivalent to an anisotropic plate. The sandwich plate theory is used in conjunction with the equivalent the honeycomb structure to study interfacial fractures of the adhesive layer between the skin and the honeycomb core. The model parameters are described as [20]. 8 8 � � pffiffi � > � > > > 4 t 2 t3 4 3 12 t2 t3 > > > > p ffi ffi E E ¼ 1 3 Es 1 ¼ G > cx s > cxy 2 3 > > 2 > > l l 5 5 l l3 3 > > > > > > � pffiffi < < 2� 3 4 3t t ; (1) and Gcxz ¼ 3 tGs Ecy ¼ pffiffi Es 1 2 3 > > 5 l l > 3 > 3 l > > > > pffiffi > > pffiffi > > > > 2 3t > > 8 3 t > > > : Gcyz ¼ Gs E E ¼ cz s > : 3 l 9 l
Fig. 1. Hexagonal honeycomb sandwich structure.
designing an improved optimized embedded structure; additionally, these simulations are vital in obtaining a comprehensive understanding of the failure process of the EHSS [5,6]. In the initial stage of structural design, particularly in the optimization design stage, it is extremely desirable for structural designers to predict the failure mode and bearing capacity of embedded structures with different design parameters by an accurate and effective numerical simulation method [7]. A pullout test is generally used to evaluate the failure behavior. Demelio et al. [8] experimentally verified the fatigue stress of Kevlar composite skin with embedded joints and an aramid honeycomb core sandwich layer in two load forms. Cao et al. [9] designed experiments to test composite sandwich panels containing steel hybrid joints. However, few researchers have been concerned with the influence of the bonding interface on the failure load of EHSS. Because of the existence of the skin, it is difficult to observe the failure process in the interface during the loading process using traditional experimental methods. Therefore, it is necessary to establish an effective honeycomb structure model by numerical simulation to simulate the interface damage when the embedded parts are pulled out. Owing to the complexity of the HSS, there is no line element suitable for the interface in the existing finite element (FE) software that can accurately simulate the honeycomb cell, this is especially true when studying the problem of interface cracking between the skin and the sandwich core. Therefore, the HSS is frequently simplified to an isotropic panel with equal thickness or an anisotropic panel with un equal thickness in theoretical analysis and numerical calculation ac cording to the equivalent plate theory, honeycomb plate theory, and sandwich plate theory [10–12]. The first two methods are equivalent to the entire honeycomb sandwich plate, while the third is equivalent only to the honeycomb core. The primary work of this study is to analyze the deformation and failure behavior of the EHSS under an axial pullout load by experimental
where Ecx, Ecy, and Ecz are the equivalent moduli in three directions. Gcxy, Gcxz, and Gcyz are the equivalent shear moduli of the three coor dinate planes. Es is Young’s modulus of the honeycomb structure ma terial. Here, t and l are the thickness and the length of the cell wall, respectively. 2.2. Cohesive zone model Certain methods have been applied to simulate the debonding damage propagation behavior of the adhesive layer between the skin and the honeycomb core, such as the virtual crack closure technique
Fig. 2. Bilinear model of CZM. 2
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Fig. 3. Four typical tests for characterizing interfacial parameters, (a) FT, (b) SL, (c) DCB and (d) TPB.
(VCCT), extended finite element method (EFEM), and element-free method (EFM) [21–23]. The VCCT method has problems with grid correlation and low computational efficiency. The EFEM is more suit able for simulating discontinuous materials; however, it is still limited to fractures of bi-material. Moreover, the computational efficiency of the EFM is lower. The cohesive zone model (CZM) can define different fracture criteria according to different materials, thus it is robustly applicable. In this study, the cohesive element is used to simulate the debonding process between the skin and the honeycomb core. The CZM is a simplified method that characterizes the interaction between molecules and atoms. The crack tip is assumed as a small cohesive zone composed of two in terfaces. As shown in Fig. 2, a typical bilinear model of the crack-tip cohesive zone is a linear relationship between the interfacial traction force T and the relative displacement U between two faces of the crack. When the relative displacement is δ0, the cohesive interface begins to debond and the traction force achieves its maximum, σ0. When the relative displacement is δf, the cohesive interface separates completely. The matrix form of the constitutive equation can be expressed as
respectively. Here, t0 is the original thickness of the cohesive element. In this study, the response of the cohesive elements is based on a tractionseparation approach, the default constitutive thickness is equal to 1 in ABAQUS software. This choice ensures that nominal strains are equal to the relative separation displacements. When the stress or strain satisfies the defined critical damage initi ation criterion, the damage initiates and the stiffness begins to degrade. In this study, a quadratic stress criterion is used as the criterion of damage initiation, namely � �2 � �2 � �2 σn σs σt þ 0 þ 0 ¼ 1; (4) 0
σn
where GIC, and GIIC represent the energy release rates in two directions. Here, Gshear ¼ GIIþ GIII,GT ¼ GIþ Gshear. and GII, and GIII are the mode-II and mode-III fracture strain energies, respectively. Here, η is the frac ture toughness coefficient. When the above formula is satisfied, the cohesive element is invalid, and the interface is debonded and failed.
where K is the stiffness matrix. The stress matrix, σ consists of three stress components (σn, σs, σt), which represent the normal and two tangential stresses, respectively. Correspondingly, the strain matrix, ε, consists of three components (εn, εs, εt), which defined as δ t0
δ t0
δ t0
εn ¼ n ; εs ¼ s ; εt ¼ t ;
σt
where σ 0n, σ 0s , and σ 0t are the peak stresses in each direction. When the sum of the squares of the stress ratio in Eq. (4) achieves 1, the damage is initiated and then enters the damage evolution stage. In this study, the BK criterion is used to describe the damage evolution law, namely � �n Gshear GIC þ ðGIIC GIC Þ ¼ GTC ; (5) GT
(2)
½σ � ¼ ½K�⋅½ε�;
σs
(3)
2.3. Cohesive interface parameters
where δn, δs, and δt are the corresponding relative displacements,
In this study, we assume that the cohesive layer is isotropic material 3
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Fig. 4. Experimental photos of (a) FT test, (b) SL test, (c) DCB test and (d) TPB test.
in the ns-plane, with the interface parameters in Eq. (4) and Eq. (5) satisfying σ 0t ¼ σ0s and GIIC ¼ GIIIC. Therefore, the determination of four interface parameters of the cohesive layer is required; these are the interface normal strength σ0n, the tangential strength σ 0t , the mode-I fracture toughness, GIC, and the mode-II fracture toughness, GIIC. There are three types of interfaces in this study: the interface between the honeycomb core and skin, between the skin and the embedded parts, and between the honeycomb core and the embedded parts. Therefore, it is required that the four interface parameters for each interface be ob tained from experiments. The skin-embedded interface is selected as an example to illustrate the experimental method for each parameter. Four experimental types are adopted to obtain the four groups of interface parameters. As shown in Fig. 3, there are the flatwise tension (FT), single lap (SL), double cantilever beam (DCB), and three-point bending (TPB) tests. Then, the specimen was designed and manufac tured based on the corresponding standards. The experimental photos are shown in Fig. 4. For the FT and SL tests, the interface strengths are equal to the ratio of the failure load and the bonding area [24,25]. For fracture toughness tests, Nettles [26] measured the fracture toughness of a honeycomb sandwich structure by referring to the DCB test method in the American Society for Testing Materials (ASTM D5528) standard. Pradeep et al. [27] used the climbing drum peel test to determine mode-I fracture toughness of a honeycomb sandwich inter face. In this study, the DCB and TPB tests were used to determine the interface fracture parameters used in a cohesive zone model. The frac ture toughness for mode-I and mode-II fracture tests is calculated ac cording to the ASTM standards [28,29]. Three samples for every type of
Table 1 Summary of interface parameters. Interface type
σ0n
σ0s
(MPa)
GIC (N/ mm)
GIIC (N/ mm)
Honeycomb core/skin Honeycomb core/embedded part Skin/embedded part
2.2588 3.3170
0.9950 1.7085
0.7272 0.5185
2.4583 1.7528
20.150
30.0
1.040
3.980
(MPa)
test were conducted to obtain an average value. The fracture toughness and strength parameters of each interface can be obtained through the above tests, as listed in Table 1. The test data for these interface pa rameters are obtained in Appendix A. 2.4. FE model A finite element model of the EHSS is established in the study using the commercial FE software ABAQUS. The skin and the embedded part are composed of isotropic aluminum alloy metal, whose constitutive relationship is a linear elastic-perfectly plastic model. The material Table 2 Mechanical properties of skin and embedded part.
4
Material
Elastic modulus (GPa)
Ultimate strength (MPa)
Poisson’s ratio
7A09
68
405
0.33
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cohesive layer between the skin and the core is simulated as a COH3D8 cohesive element. The entire structure is modeled using an integrated method, and the cohesive element is inserted at the bonding interface. This reduces the nonconvergence problem caused by contact and im proves the accuracy of the model. Both sides of the sandwich structure are clamped, and the off-plane displacement in the z-direction is coupled in the center of the embedded part to simulate the axial pullout load. The applied boundary condition is shown in Fig. 5(b).
Table 3 Equivalent material parameters of honeycomb core. Elastic modulus (MPa)
Shear modulus (MPa)
T/LDR
Ecx
Ecy
Ecz
Gcxy
Gcxz
Gcyz
μxy
0.31
0.31
1308.7
0.184
184.5
184.5
0.99
parameters of the skin and embedded part are listed in Table 2. The honeycomb core layer is equivalent to an anisotropic plate; the material parameters of the honeycomb core are calculated by Eq. (1), as listed in Table 3. The transverse/longitudinal deformation ratio (T/LDR) in this study is an equivalent one, which was originally derived from Gibson [30], and then modified by Hu [31]. The FE model of the EHSS is shown in Fig. 5(a). The equivalent anisotropic plate of the HSS is modeled as a C3D8S 3D solid element; the
3. Experiments 3.1. Specimen description The EHSS is a primary bearing component for linking an exposed
Fig. 5. (a) FEM model and (b) boundary conditions.
Fig. 6. (a) Scheme of the EHSS, (b) scheme of cross section near the embedded part, (c) front view and (d) lateral view of the specimen. 5
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Fig. 7. (a) Experimental setup photo and (b) local enlargement.
Fig. 8. (a) AOI for deformation measurement by 3D-DIC and (b) out-of-plane displacement of honeycomb sandwich panel under the load of 4.34 kN.
platform to aircraft structure, as shown in Fig. 6. The size of the spec imen is 200 � 200 mm, and the total thickness is 30 mm. The skin is made of a 0.3-mm 7A09 aluminum alloy panel, the size of the honey comb core is 0.05 � 4 mm. The mechanical properties of the primary materials are listed in Table 2. The HSS has the advantages of being light-weight, possessing high specific strength, and high specific stiffness, however, the honeycomb core is too soft to achieve the strength and durability requirements when connected to external equipment. Therefore, it is necessary to place potting materials and an embedded part (bolt or rivet) in the honeycomb core to reinforce the HSS. The center hole of the EHSS is used to connect the external bolt (Fig. 6(a)). The center is the embedded part with a radius of 11 mm; the loading hole screw radius is 8 mm. The outside of the embedded part is filled with J78D foam-bonded honeycomb to alleviate the stress
concentration in the honeycomb core connection area (Fig. 6(b)). The foam is required to be uniformly filled around the embedded part with a size of two or three honeycomb holes. A front view and lateral view of the specimen are shown in Fig. 6(c) and (d), respectively. 3.2. Axial pullout test The axial pullout experiment of the EHSS was conducted using a universal testing machine (CSS-2250, Changchun Testing Machine Research Institute). Its maximum loading capacity is 50 kN. The spec imen is installed as shown in Fig. 7(a). It is necessary to fasten the specimen to the clamp plate with bolts to ensure that the tensile load acts in the axial direction of the embedded part, as shown in Fig. 7(b). The loading rate of the pullout experiment was 1.0 mm/min. The three-dimensional digital image correlation (3D-DIC) technique was used to measure the deformation during the loading process. Cold lights were installed on both sides of the specimen to reduce image shadows caused by uneven indoor light during image acquisition. A camera was installed on a tripod to capture images with an acquisition frequency of 0.5 fps. Before the experiment, a random speckle pattern was prepared on the specimen surface using acrylic paints of titanium white and carbon black. 4. Results and discussion 4.1. Full-field deformation The acquired images were processed by the PMLAB package to obtain the displacement and strain fields at different times. The spatial resolution was 2 pixels/mm. The three-dimensional coordinate, XYZ, of the displacement field measured by 3D-DIC method is shown in Fig. 8 (a). The tension direction of the embedded part is parallel to the Z-axis. The area of interest (AOI) for the displacement measurement is in the XY-plane. A local image coordinate x1oy1, is set on the left corner of the AOI.
Fig. 9. Out-of-plane displacement and load curves of points of A, B, and C. 6
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Fig. 10. (a) εx and (b) εy distributions under the load of 4.34 kN, (c) εx and (d) εy distribution under the ultimate load of 6.23 kN.
A full-field out-of-plane displacement of the honeycomb sandwich panel under the load of 4.34 kN is shown in Fig. 8(b). It is clear that the out-of-plane displacement is circularly distributed around the loading bolt, the maximum value is a circle with radius identical to that of the embedded part. It is inferred that the load drives the embedded part to move axially, the shear force is applied to the honeycomb core through the adhesive layer. The skin has a maximum value in the range of the connection radius with the embedded part owing to the low bending stiffness. Three positions are relabeled as points of A, B, and C in Fig. 8(b), which are located on the arc with the radius R ¼ 11 mm and the angle, α, of 0� , 90� , and 180� in the image coordinate x1oy1, respectively. The corresponding pixel coordinates are A(92, 54) pixel, B(70, 350) pixel, and C(48, 53) pixel. The out-of-plane displacement and load curves of three points of A, B and C are plotted in Fig. 9 to observe the variation trend of the out-of-plane displacement near the embedded part. It is clear in Fig. 9 that the trend is identical; however, the out-ofplane displacement of the three points is slightly different. When the load is identical, the displacement of point A is the largest, the one of point B is the second, and the one of point C is the smallest. The dif ference is caused by the local debonding on the interface of the skin/ embedded part. Furthermore, the full-field xy-plane strains of εx and εy under the load of 4.34 kN and the ultimate load are shown in Fig. 10. It is clear that the strains are almost centrosymmetric within the radius of the embedded part; the closer to the loading point, the larger the strain. The strain distribution area indicates that the load is transferred from the embedded part to the skin, causing the skin to bulge. Accordingly, the full-field strains of εx and εy under the ultimate load of 6.24 kN are shown in Fig. 10(c) and (d). It is clear that the maximal strain areas gradually approach the loading point during the loading process, the maximum transverse strain is εx ¼ 0.0196, and the longi tudinal strain is εy ¼ 0.0624. It can be inferred that the maximum strain of the embedded honeycomb sandwich panel is always extended from the outside to the inside with the loading point as the center of the circle. The structural damages occur when the maximum strain radius achieves the loading point.
Fig. 11. Load-displacement curves of experiment.
4.2. Load-displacement curve The load-displacement curves of the EHSS are shown in Fig. 11. It can be seen that the stiffness decreases when the load steadily increases to a certain value. It indicates that the interfaces among foam, honey comb core and skin begin to fail. Then, the stiffness decreases again when the contact failure between the embedded part and the skin oc curs. The bearing capacity of the EHSS decreases dramatically until the load achieves 6.23 kN. 4.3. Failure analysis The failure mode of the EHSS is shown in Fig. 12(a). It is clear that a bulging phenomenon occurs in the upper skin around the embedded part. The plastic deformation of the skin near the embedded part results in cracking failure due to excessive tensile stress. The internal honey comb structure after manual peeling is shown in Fig. 12(b). It is clear that the local honeycomb cell around the embedded part is folded, and 7
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Fig. 12. Failure mode of the EHSS, (a) failure photo and (b) internal honeycomb structure after manual peeling.
Fig. 13. Result of numerical simulation, (a) Von Mises stress of the EHSS and (b) strain distribution of skin.
Fig. 14. Failure modes of the EHSS, (a) skin/honeycomb core interface and (b) embedded part/skin interface.
the foam filled in the honeycomb cell is broken, displaying the rough fracture cross-sections. In this structure, both the interface of the skin/honeycomb core and that interface of the skin/embedded part are bonded by a J78B adhesive layer. However, these two interfaces would appear to exhibit different failure behavior owing to the difference in the interface properties, as provided in Table 1. It is necessary to study the progressive failure behavior of the interfaces of EHSS under axial pullout load. A cohesive element is used to simulate the bonding interface; the interface damage is considered simultaneously. The failure condition and damage initia tion criterion of the cohesive layer are explained in detail in sections 2.2 and 2.3. The stress and skin strain obtained by FE simulation are shown in Fig. 13. It is clear that the stress around the loading point of the EHSS is always at the maximum value [Fig. 13(a)]; the strain field distribution on the skin is similar to the DIC results [Fig. 8(b)]. The skin bulges
around the embedded part and the maximum strain around the loading point is 0.0183, which is a 6.78% difference from the DIC result. The interface failure mode of the EHSS under the ultimate load is shown in Fig. 14, where SDEG represents the interface stiffness degra dation factor. The stiffness degradation is completed and the cohesive element is invalid when the value of SDEG achieves 1. As shown in Fig. 14(a), the damage to the interface of the skin and the honeycomb core distributes in a circle centered on the loading point whose radius is about 21 mm. By comparison, the interface of the embedded-part and the skin is almost completely destroyed. These interface damages cause the stiffness reduction. The FE simulated load vs. displacement curve is also shown in Fig. 15. The ultimate load of the numerical simulation is 5.9 kN, which possesses a of 5.35% difference from that of the experimental one (Fig. 11). This shows that the new calculation model is a good illustra tion of the mechanism of structural interface debonding and material 8
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Fig. 15. Load-displacement curve of FE simulation.
failure of the honeycomb sandwich structure with embedded part. However, compared with the experimental results, the current calcula tion results still have differences. In addition to the experimental factors, the following aspects in the FE calculation could cause the differences. First, the honeycomb core is filled with foam in the specimen with a small area. Although the foam portion is not considered in the FE modeling, the effect of the foam is reflected in the interface parameters, which is determined by the above interface tests. Therefore, there is a relative large stiffness of structure in the simulated load-displacement curve. Besides, the stress singularity appeared in the honeycomb core due to the hexagonal geometric sharp corner, the honeycomb core in this study is equivalent to an orthotropic material, and the instability and bending deformation caused by the hexagonal thin wall are neglected. The equivalent mode of the honeycomb core also causes a relative small displacement. Last, there are many interfaces in the honeycomb sandwich struc ture, which shows the complexity of material nonlinear, geometric nonlinear and contact nonlinear. This study combines experiments and numerical methods to simplify the above complex problems, which is a useful attempt. Through the combing of the above problems, in the future numerical research, the author will further study the effect of the filled foam on the honeycomb sandwich structure. 5. Conclusions In this study, experimental and numerical studies of the EHSS under an axial pullout load were performed. Compared with the experiment, the FE simulation well predicted the deformation failure behavior and ultimate load of the EHSS under an axial tensile load. The FE simulated strain field is in accordance with the 3D-DIC results. The FE simulation verifies that the interface debonding and the skin damage are primary influences on the stiffness decrease. The predicted ultimate load main tains a smaller error within 5.35% of the experimental result. Acknowledgments The authors thank the National Natural Science Foundation of China (11572070, 11772081, 11635004), and Fundamental Research Funds for the Central Universities of China (DUT18ZD209). Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.
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