A hybrid joining insert for sandwich panels with pyramidal lattice truss cores

Journal Pre-proofs A hybrid joining insert for sandwich panels with pyramidal lattice truss cores Ge Qi, Yun-Long Chen, Philip Richert, Li Ma, Kai-Uwe Schröder PII: DOI: Reference:

S0263-8223(19)34107-8 https://doi.org/10.1016/j.compstruct.2020.112123 COST 112123

To appear in:

Composite Structures

Received Date: Revised Date: Accepted Date:

29 October 2019 13 January 2020 22 February 2020

Please cite this article as: Qi, G., Chen, Y-L., Richert, P., Ma, L., Schröder, K-U., A hybrid joining insert for sandwich panels with pyramidal lattice truss cores, Composite Structures (2020), doi: https://doi.org/10.1016/ j.compstruct.2020.112123

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A hybrid joining insert for sandwich panels with pyramidal lattice truss cores Ge Qia, Yun-Long Chena, Philip Richertb, Li Maa*, Kai-Uwe Schröderb a Center

for Composite Materials, Harbin Institute of Technology, Harbin 150001, PR China

b Institute

of Structural Mechanics and Lightweight Design, RWTH Aachen University, Aachen 52062, Germany

Abstract Sophisticated and efficient technique of sandwich attachment for composite sandwich structure assembly is imperatively required by industries. Certain types of joining inserts are widely used to carry the localized loads, but little is known regarding to the joining method for composite lattice truss core sandwich structures. In this study, a novel hybrid insert fastener, which comprises a plurality of carbon-fiber-reinforced grid cells and a metallic part, is developed for pyramidal truss core sandwich structures. Finite element models are developed to predict the failure modes and the load capabilities of different insert locations. Static pull-out and shear experiments are carried out, and the failure behaviors for each load case are discussed. The results show that the shear performance is significantly improved, and the insert position greatly affects the static pull-out behavior. An optimization of the hybrid joining insert to enhance the pull-out characteristic is addressed and verified by the finite element analysis. Keywords: Sandwich panels; Pyramidal truss core; Hybrid inserts; Failure

*

Corresponding author, Tel./fax: +86 451 86402739.

E-mail address: [email protected] (Li Ma)

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behavior

1. Introduction In modern industrial engineering, when a structural design requires the highest attainable mechanical behavior with minimum weight, i.e., superior specific stiffness and strength, composite sandwich structure, formed from a cellular core and two covering face-sheets, is an attractive alternative by its very nature. Numerous materials, including alloys, papers, woods, carbon/glass fibers and polymers, have been successfully used for the covering face-sheets and cellular cores depending on the intended application, e.g., aircraft, aerospace, electronics, transportation, construction and even food industries [1]. Composite sandwich structures generally serve as the load support member based on their dramatic load-bearing capability. Other applications focus on the porous topological architecture of cores and explore the multi-functional integration [2]. Typically, lattice truss sandwich structures are dominant in both application potentials. On the one hand, the stretching-dominated solids have been shown to be more weight efficient than the conventional bending-dominated materials [3–5]. On the other hand, the cross-linked and open channels in the periodic cells can be designed to achieve multi-functionality to satisfy the demand of the mechanical and other characteristic indices [2,6–9]. Consequently, there is a growing trend towards applying composite sandwich structures, especially lattice materials, in industrial engineering. Basically, four logical steps might be included in sandwich applications, as shown in Fig. 1. The primary sandwich structure is applied in sheeting or flat panel protocols as the load-bearing members [2,10–12]. The second step of sandwich utilization is the monocoque design of shell, cylinder or other configurations with constant curvature [13–15], while a higher level means complex shapes with compound curves [16], which 2

requires advanced improvement in product and process techniques. The modular structural systems with multi-functional integration, which serve as both device or equipment and load support members, are the highest and most desirable step [17–20]. For the primary application level, e.g., the floors of cabins in the aerospace industry or curtain walls in the architecture industry, when external subcomponents and device are attached onto a sandwich panel, localized loads introduced by mechanical joints, such as bolts or rivets, for assembly might result in unexpected failure before the desired service capacity because the thin, weak, soft cellular core, by its very nature, cannot carry a concentrated loading. The earlier failure with a lower strength or a shorter service life of the joints nullifies the beneficial properties, which profit from the high specific strength of sandwich structures, so mechanically fastening panels with joints is one of the most important parts of the design [21]. Furthermore, more sophisticated and efficient joining and joint techniques are imperatively needed to facilitate the assembly of complicated structural systems for higher-level sandwich applications. Until now, the investigations on sandwich joints have been mainly studied for the flat panel, and the topological configuration of cellular cells has concentrated on the honeycomb or foam structure. The principal method of the sandwich joints is to reinforce the cores with a lightweight insert for fastener sustainability and to uniformly transmit the localized stress to the covering face-sheets and cores. Typical inserts in honeycomb sandwich panels are illustrated in Fig. 2. Initial attempts for joining resort to a monolithic but crude attachment (generally metallic or woody blocks) which substitutes plenty of cells, as shown in Fig. 2(a). Potting epoxy into cores to support the mechanical fasteners is also used to develop the expected properties, Fig. 2(b). However, the imprudent method without the design parameter optimization adds undue weight, which counteracts the advantages of the sandwich structures. Classically, the

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threaded inserts with potting compounds, Fig. 2(c), including partial and through-thethickness types, are widely employed due to their inherent benefits of workability and carrying capacity. In addition, hollow profiles are also utilized in some engineering fields (Fig. 2(d)). Some monographs are published on the standardized and systematized guidance on the insert design, manufacturing and evaluation criterion [22–24]. However, the available studies show a lack of theoretical analysis and numerical calculation methods, and most investigations concentrate on the experimental assessment. Thomsen et al. [25,26] proposed a high-order sandwich plate theory to analyze the stress distribution in honeycomb sandwich panels with inserts. The development of the mathematical model can be numerically solved with the multi-segment method of integration, which is convenient and cost-effective for the sandwich plate with inserts of fully potted and partial potted types, which are subjected to axisymmetric and non-axisymmetric external loadings. Bozhevolnaya et al.[27] and Frostig et al. [28] considered the stress concentration caused by material discontinuity induced in the vicinity of inserts for foam core sandwich panels. Smith and Banerjee [29] compared four different reliability analysis methods on the utility of reliability analysis in design based on the analytical Thomsen model. In a recent study by Seemann and Krause [30], a virtual testing framework on the building block approach (BBA) was described to predict the progressive failure behavior to conserve testing efforts. In addition, an analytical tool was developed by Wolff et al. [31,32] to predict the failure load of a separable insert using the simple sandwich theory. Furthermore, additional attempts have focused on experimental investigations of the variability in the honeycomb-sandwich-insert structure performance of various shapes [33,34], geometries [35,36], materials [37,38], manufacturing methods [39], circumstances [40], and applied loads [41–44].

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As mentioned above, few joints or junctions are exploited for lattice truss core sandwich panels, except in our previous work [45] as shown in Fig. 2(e). Despite the valid joining concept and good strength, deficiencies, including the restricted insert position and low shear stiffness, imply that more work is necessary to enhance the joining concept. Thus, the main objective of the present study is to develop a novel hybrid insert concept with carbon composite reinforced grid cells and to investigate the failure mechanism. Finite element analysis is carried out to predict the mechanical performance of the lattice-sandwich-insert structure, and the pull-out and shear behaviors are experimentally tested. Then, a design optimization is addressed to realize effective and reliable mechanical behaviors.

2. Design and fabrication When a random external device or facility is attached to the surface of the sandwich panel, the insert joints must be compatible with the load capabilities of the combined tests in various circumstances. Herein, pull-out loads normal to the sandwich surface and shear loads parallel to the panel are two primary forms of loads, and the materials comprising the sandwich play different roles when subjected to combinations of the two primary loads in multiple directions. The cores and covering face-sheets naturally act as major roles in the insert rigidity. For the strength, the interfacial properties between the materials provide the ultimate strength in the case of pull-out loading [25,26], while the covering face-sheet thickness dominates the strength in the shear condition [35]. Consequently, of prime importance to insert design is to spread the localized load over the largest possible area and to maintain the insert stability, for which the main methods range from increasing the bonding area between the covering face-sheets and the insert to distributing an adequate surrounding medium around the insert. 5

According to the analysis above, a novel hybrid insert concept comprising a plurality of carbon-fiber-reinforced grid cells and a metallic part is designed, as illustrated in Fig. 3. The carbon-fiber-reinforced grid cells are composed of juxtaposed elementary tubular cells, whose height is equal to the pyramidal lattices, to be bonded to the top and bottom covering face-sheets. In the cavity of the central cell, a metallic part with identical cross-sectional dimensions to the central cell is contained to fix the mechanical rivet or bolt. The shape and overall dimensions of the insert are designed to fit the pyramidal lattices of the core as shown in Fig. 3(c). Herein, the distance between the edge of horizonal projection of the struts (green dot line) and the lattice node is defined as a feature size R . And the size L of the grid cell wall patterns, which is twice as length as R , is adopted as shown in Fig. 3(d). Accordingly, the cross-sections of the elementary grid cells are generally not identical, i.e., some cells are squares on the diagonal but others are rectangles. To more efficiently introduce the stress and increase the pull-out strength, the metallic part is flanked by two tips to be tightly inserted into the corresponding square holes on the elementary grid cells for precise positioning and larger stress delivery. When an external device or equipment is attached to the surface of the panel, the pull-out load is supported by the whole insert structure with an expanded area, and the juxtaposed elementary grid cells can deliver most of the encountered load to the covering face-sheets at the top and bottom. The grid cells offer inherent rigidity to increase the stiffness of the sandwich panels, especially in the vicinity of the mechanical fastener. Since the unique lattice truss architecture can hardly connect sufficiently to the hard point joint, it is awkward to use the cores as a stabilizer. The perpendicular distribution of the elementary grid cells can offer continuous and wrapped constraints for stability, especially when encountered single-shear load with a relatively high turning-over moment.

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One major benefit of the new proposed hybrid insert concept is the lightweight mass without potting materials or other hulking monolith. The size of the metallic part in the center is minimal with sufficient fastening capability to reduce the redundant weight. Meanwhile, the elementary grid cells produced by carbon-fiber-reinforced composites are much more weight-efficient than conventional potting methods. Compared with the threaded insert with potting compounds, the new hybrid insert concept has significant mass advantage with weight reduction, which will facilitate a large weight reduction in industrial applications when a great amount of joints are used. Another major benefit of the developed hybrid insert concept in this paper is the convenient fabrication process because the insert structure is positioned and bonded to the covering face-sheets in the same process of the sandwich panel assembly, and the procedure is schematically summarized in Fig. 4. First, the grid cell wall patterns with the interlocking-slots are cut from composite laminates using computer numerical control milling, and a clearance of 0.1 mm is set at the slots for the sufficiently tight fit during assembly. Then, the juxtaposed elementary grid cells are fabricated in the interlocking procedure. These patterns are interlocked into each other and assembled, while the tips of the metallic part with surface treatment according to ASTM D393398(2010) [46] are inserted into the corresponding holes after deburring and redundant resin removal to form the hybrid insert structure. Finally, the hybrid insert structure is placed into the pre-position, where the nodes and struts are cut off within the pyramidal truss core sandwich panel; when the insert is fixed, the specimen is hot-bonded at 130°C for 2 hours at 0.3 MPa. In this investigation, the cross-section dimensions of pyramidal lattice struts are 2 mm × 2 mm (width × thickness) and the relative density of the cores is 2.75%. The average thickness of the sandwiches is 22 mm, within which, the height of the hybrid

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insert structure and lattice truss cores is 20 mm. Carbon-fiber-reinforced orthogonal weave prepregs (LS-3K, Shanghai Liso Composite Material Technology Co., Ltd, PR China) are used to manufacture the covering composite face-sheets and juxtaposed elementary grid cells. Pyramidal lattice cores and the metallic part of the insert structure are made by aluminum alloy 2A12-T4 (Harbin Dongqing Metals Manufacturing Co., Ltd, PR China). The film adhesive J-272-A, supplied by Institute of Petrochemistry Heilongjiang Academy of Science, PR China, is used as the bonding material. The properties of the materials and dimensions of the composite grid cell wall patterns in this study are listed in Table 1 and Table 2, respectively.

3. Finite element prediction Basically, an efficient and rational structural arrangement of the insert joints is desirable for industrial applications, which requires full consideration of typical design parameters. However, it is difficult to definitively investigate the effects of the design parameter on the mechanical performance of insert joints under external loads, ascribed to the complicated material combinations and various geometries. The static performance of the hybrid insert structure under pull-out loads is predicted using the general-purpose finite element code ABAQUS 6.14-6. Taking the typical topological architecture of pyramidal lattices into consideration, the proposed hybrid inserts are located at four representative positions, as illustrated in Fig. 5, for a comprehensive evaluation. Position A is defined at the bottom node of the lattices, which is evidently one of the typical geometrical points. Then, Position B is the midpoint of the strut, and the center-point of four adjacent nodes is selected as Position C. Position D is the top node of the pyramidal cell. Thus, different types of models based on the insert positions are developed in the current investigation and marked as P-A, P-B, P-C and P-D respectively. The nodes and struts in the insert area are removed 8

from the lattice cores. Herein, the amount of removed nodes with the corresponding struts is one for models P-A and P-D, two for P-B and four for P-C. The finite element model of sample P-A for the static pull-out test is illustrated in Fig. 6. For the cases of P-A, P-C and P-D, the sandwich panel with the hybrid insert can be simulated by a quarter model due to the symmetry. In contrast, a full model is addressed for case P-B ascribed to asymmetry of the pyramidal cell distribution. The composite covering face-sheets made from carbon-fiber-reinforced orthogonal weave laminates are modeled with 4-node shell elements (S4R), and composite layups are used to represent the 4 layers with the fabric stacking sequence of [0-90/0-90/0-90/090]. For the aluminum alloy struts, 2-node linear shear flexible beam elements (B31) are adopted. The metallic part and grid cells of the hybrid insert are simulated using 8node linear reduced-integration solid elements (C3D8R) and shell elements (S4R), respectively. A steel fixture is applied to the top surface of the sandwich panel and identified as a rigid body to supply a circular support with the diameter of 120 mm. The contact between the fixture and the panel is defined as a penalty friction formulation with a friction coefficient of 0.2. A fixed boundary condition is applied on the fixture, and a displacement condition normal to the sandwich surface is employed on the insert as the pull-out load. A mesh convergence study of different element sizes from 1.5 mm to 0.5 mm is carried out to ensure the mesh refinement is fine enough with reasonable accuracy and the resultant force-displacement and moment-displacement curves are represented in Fig. 7. It could be indicated that the results converge for element size of 0.67 mm and sufficient accuracy for the present structure can be obtained. The representative results from the finite element analysis are shown in Fig. 8, including the distribution of stress component in 1-direction of face-sheet (S11) and

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predictive failure load. Stress concentrations are distinctly observed at the top nodes of lattice cores of model P-D and corner of the hybrid insert of model P-A. The literature [45] confirms that the debonding failure mainly occurs at the top nodes and the bottom of the insert, where the peel effect is caused by deformation characteristics, see Fig. 8(b). Despite the stress concentration at the bottom node of lattice cores, no debonding failure will occur in this area, because the adhesive film is under compression. Thus, the peel moments of the two competing failure regions are calculated as critical parameters, and the climbing drum peel strength M of 86.1 N  m / m is used to predict the failure load of the insert, as shown in Fig. 8(c). When the moment at the top node of struts or the corner of the hybrid insert reaches the peel strength M , initial debonding failure is considered to occur and the corresponding force is treated as the failure strength. The predictive stiffness and strength of all four models are listed in Table 3. Since no particular method is used to simulate the bonding interaction property of the adhesive film between the face-sheets and pyramidal lattice cores and the insert, the complete failure progress and post-failure performance of the sandwich panel cannot be covered in this study. The developed finite element model remains effective because the major purpose of the finite element analysis is to predict the initiation of failure and general performance of the sandwich-insert structure.

4. Experimental procedure The static performance of the hybrid insert structure under pull-out and shear loads are experimentally investigated. Based on the insert positions shown in Fig. 9, four types of pull-out specimens labeled as P-A, P-B, P-C and P-D and three types of shear specimens labeled as S-A, S-B and S-C are fabricated in the current investigation. Thus,

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approximately 28 sandwich specimens in 7 different types are experimentally tested, and four repeated specimens (7  4  28) are measured to gauge the variability in each type. The dimensions of the pull-out and shear specimens are 200 mm  200 mm (5  5 cells) and 260 mm  170 mm (7  4 cells), respectively. Two inserts are embedded in the shear specimens, and the center-to-center distance is 99 mm, which corresponds to three pyramidal cells. Until now, no general experimental standards are established for these truss core sandwich and insert configurations in this study. The test recommendations for the honeycomb sandwich panel inserts from [22] and our investigation in [45] can be the references. In the case of pull-out tests, a circular bearing support with a diameter of 120 mm (3  3 cells) is employed, so special fixtures are used to hold the sandwich specimens as shown in Fig. 9(a) and Fig. 9(b). An M5 bolt is used to connect the test specimen and a U-shaped pull-out piece. The pull-out piece and fixture are mounted onto the testing machine with steel pins to avoid extra moments. In the shear test, a shear load is supplied by two steel jigs, which are also attached onto the sandwich surface using M5 bolts, as shown in Fig. 9(c) and Fig. 9(d). Similarly, the jigs and testing machine are connected using pins. Both pull-out and shear tests are performed using a screw-driven test machine Instron 5569 with a constant displacement rate of 1 mm/min until the ultimate failure at room temperature. During the experiments, the defection and force data are recorded from the machine output at a rate of 10 Hz, and the failure behaviors are described.

5. Experimental results Types P-B, P-C and P-D have similar experimental curves, but type P-A exhibits a different curve. Thus, the results of the static pull-out testing for specimens P-A and PD are depicted in terms of load-displacement and stiffness progression relationship in 11

Fig. 10, representatively. The test scatter of all the experimental curves is plotted by gray lines in the background to shown the variability, and a typical test curve is indicated by red lines to represent the characteristic progression. Additively, the stiffness progression corresponding to the typical test, calculated via the differential of the load-displacement, is represented by blue dash lines. In the case of type P-D in Fig. 10(a), three points can be identified from the curves, which reveals the deformation and failure process based on the consulting literatures [22,47]. In the beginning, the curves show an increasing stiffness after some initial bedding-in, which is attributed to the compaction of the clearances during fabrication. Loading the insert twice before any macro-damage occurs will lead to a stable stiffness behavior without crucial performance degradation, which is confirmed by reference [32]. Subsequently, a quasilinear region is observed due to elastic deformations. A critical point of maximal stiffness Fp ,ms is indicated, which might imply that some damages occur in the specimens. If in strict accordance with the standards [47], Fp ,ms must be used as the failure load of the proposed insert. However, when the pull-out load is beyond the point of Max. stiffness, no significant deviations from quasi-linearity are shown for the loaddeflection curves, and the stiffness responses present a slow decrease instead of a sharp drop. For the specimens, no macro-failure is observed. Therefore, the micro-damage in the constitute materials and local failure in the subcomponents might not affect the global behaviors of the specimens, and similar phenomena were found in the investigations on honeycomb inserts [29,32]. Then, another failure load Fp , fp , which is much higher than Fp ,ms , is identified at the point corresponding to the first peak of the load-displacement curves, which is caused by the debonding of the top face-sheet and lattice nodes adjacent to the insert, as shown in Fig. 10(b). Following a slight drop

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of the response, the hybrid insert continues to support the pull-out load, and the curves increase again until the third critical point of maximal load Fp ,ml , which denotes the debonding failure of the bottom face-sheet and the insert, as presented in Fig. 10(b). In the case of type P-A in Fig. 10(c), only two critical points, including the maximal stiffness Fp ,ms and maximal load Fp ,ml , can be defined from the curves because no debonding failure occurs at the top node in the maximal peak, which corresponds to the debonding failure between the hybrid insert and bottom face-sheet, as shown in Fig. 10(d). The measurements of the static pull-out testing are summarized in Table 3. In the case of stiffness, the average values of the quasi-linear region in the stiffnessdisplacement curves are addressed with standard deviations. The stiffness of the proposed insert is consistent with the predictive value, and the testing responses show a slightly higher level than the predictive results because of the negligence of the strengthening effect by the convex platforms at the lattice nodes in the finite element simulation. For the strength, good consistency of the failure loads is generally obtained, except specimen type P-B. The first reason explaining this phenomenon is that the asymmetrical distribution of the pyramidal lattices promotes the complex of the deformation characteristics and failure progression. The second reason is that sufficient adhesive is filled into the gap between the insert and the adjacent top nodes, which enhances the local peel strength. Thus, the lattice-sandwich-inserts mainly fail first at the predictive position; other debonding areas might be manifested at the same time for specimen P-B. Since the specimens do not represent an obvious decrease in stiffness at the point of maximal stiffness and macro-damage in the sandwich panels is not significantly observed at the points of the first peak, the characteristic interpretations mainly focus 13

on Fp , fp and Fp ,ml in the current study. This method of interpretation, which adopt

Fp , fp and Fp ,ml for the critical failure loads, are widely employed in investigations on honeycomb sandwiches [33–40]. To clarify the load capability of the proposed insert when it encounters a pull-out load, Fig. 11 shows the experimental results in comparison to the insert concept P-R1 in our previous work [45] as shown in Fig. 2(e) and conventional insert P-R2 in honeycomb panels [35]. Nearly all inserts obtain similar levels of pull-out stiffness, except specimen P-C shows a pull-out stiffness of less than half (42%), and type P-D exhibits the best stiffness performance (111%). For strength, type P-A exhibits the highest load bearing capacity, and the failure load is increased by 28%. Specimens P-B and P-D also increase in strength, but unfortunately,

Fp , fp and Fp ,ml of type P-C decrease in strength by 51% and 30%, respectively. Since the nodes and struts adjacent to the insert are cut off from the lattice cores, the specimens have diminishing load resistance and increasing local deformation. The experimental tests indicate that the failure mode of the hybrid insert in the current work is dominated by debonding, and the insert position affects both stiffness and strength properties under a pull-out load. Consequently, stronger interface bonding characteristics and optimized lattice distribution might enhance the performance of the insert. The representative load-displacement responses with corresponding failure modes for static shear testing are displayed in Fig. 12. Gray lines are plotted in the background for the test scatter, and a typical test curve (red line) is utilized for the detailed curve progression. The stiffness results are also provided through the differential of the typical load-displacement curves and shown by blue dash lines in Fig. 12(a). Some beddingin at the initial phase, which is ascribed to the experimental setup, is followed by a quasi-linear increase in all testing curves when shear loads are applied onto the inserts. 14

The first critical shear load Fs ,ms can be defined at the point with the maximal stiffness, beyond which the stiffness gradually decreases with increasing displacement. Similar to the pull-out tests, Fs ,ms stands for the local plastification within the structures but has a slight effect on the global properties. Thus, the critical load Fs ,ms is only used for characteristic progression but not as the failure load of the insert in this study. Because the amount of permanent deformation and micro-damage is acceptable, and only visible failure can generally result in a considerable decrease. With increasing load, critical loads Fs , fp and Fs ,ml are identified for the first peak and ultimate load, respectively. A significant degradation of stiffness is visible from the curves after the point of the first peak Fs , fp due to the bearing failure of the top face-sheet, as presented in Fig. 12(b). The final drop, which is defined as Fs ,ml , occurs and is ascribed to the crushing of the composite grid cells in front of the insert in the load direction. The experimental data for shear testing, including the stiffness and strength, are shown in Fig. 13 and compared with the investigations in the literature [35,45]. The shear performance is dramatically improved for this novel hybrid insert. The stiffness of all the types of inserts is approximately twice as high as that of S-R1 for the lattice sandwiches and higher than S-R2 for honeycomb structures. This implies that the carbon-fiber-reinforced grid cells provide continuous and wrapped supports to sufficiently bear the upsetting moment and maintain the continuity with the face-sheets. Based on the good stability, external shear loads can be fully transferred into face-sheets via the large bonding area. Thus, the inserts fail by crushing of composite grid cells instead of debonding of the face-sheets and inserts, achieving the improvement in strength. If compared to honeycomb inserts S-R2 in reference [35], the current hybrid insert denotes more than twice the load Fs , fp which is commonly regarded as the 15

relevant load [35,38,40,44]. No remarkable discrepancy has been gained in either stiffness or strength among types S-A, S-B and S-C; therefore, the position of the joining insert hardly affects that shear properties.

6. Design consideration In engineering applications, the relative joining positions to pyramidal lattices are in stochastic conditions, when an external device or equipment connected onto the surface of the sandwich panels, which include but are not limited to the investigated representative positions. Consequently, the analysis on the insert performance should be addressed to a more general case. The experiments indicate that the insert positions have little effect on the shear behaviors but have markedly impact on pull-out performance due to significant local effects. Thus, a more effective design concept of the hybrid insert for a stochastic joining location under static pull-out loading will be discussed. Two possible design principles are suggested by previous testing to relieve the local effects and increase the pull-out load capability. The first design principle is to reduce the number of removed nodes and struts because a greater absence of nodes or struts would decrease support for the covering face-sheets, as shown by specimens P-B and P-D. The other principle is that the edges of the inserts should be as close as possible to the reserved lattice nodes. The composite juxtaposed grid cells filled in the cut-out space can smoothen the core “discontinuity” and introduce the defection to a global deformation. The sketches in Fig. 14 present the lattices and insert with the design parameters for optimization. For the pyramidal lattice cores, the center-to-center distance D between two adjacent nodes is equal to 33 mm. The length bc and width

tc of the convex platform are 10 mm and 2 mm, respectively. Due to the periodicity

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and asymmetry of the lattices, the joining location, represented by the red circle, can be identified at a stochastic position in the blue triangle area. The edge size L of the insert, i.e., the length of the grid cells, is defined as a variable in this study to optimize the design configuration for a generalized joining case. A Cartesian coordinate system

 x, y 

is adopted with the origin at the center-point

of four adjacent nodes, and x  and y  axes are parallel and perpendicular to the struts, respectively, as illustrated in Fig. 14. The hybrid insert is shown using a red square, and the center position is represented by a red circle with the coordinate

 x0 , y0  . The position of the center reads  2D 0  y0   4 y  x  y 0 0  0

(2)

Based on the principle of “least removed nodes”, only the four nodes adjacent to the origin, including two top and two bottom nodes, can be cut off from the cores. Thus, the edge length L of the insert might be described in  L1  2  L2  2   L3 2   L4  2

3 2 D bc  4 2 3 2 D bc   4 2 3 2 D bc   4 2 3 2 D bc   4 2



 x0  x0

(3)  y0  y0

Combined with Eq. (1), edge length L of the insert is

L  min  L1 , L2 , L3 , L4  

3 2D  bc  2 y0 2

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(4)

The suggested edge length L of the insert is shown in Fig. 15. The value of the advised insert size ranges from 36 mm to 60 mm, and an obvious symmetry is observed. All values for coordinates (-11.6, 11.6), (0,11.6), (11.6, 11.6), which correspond to specimens P-A, P-B and P-D, respectively, are equal to 36 mm, as verified above. However, the preferred length for the origin (0, 0) is 60 mm, which is higher than the investigated size of specimen P-C. Thus, an finite element model with the suggested hybrid insert is developed, and the responses are obtained in Fig. 16(a). A dramatic improvement is achieved from 1.1 kN/mm to 3.5 kN/mm. In addition, the predictive debonding failure loads for the top node and insert corner are 4.0 kN and 4.7 kN, respectively. Despite the inevitable defect that the weight of the hybrid insert increases by 190% (from 15 g to 43.5 g), the thinner thickness of the grid wall patterns and larger size of the juxtaposed grid cells might relieve this issue. Additionally, a numerical model is performed for a more general case of joining at (0, 5.83), and the results are shown in Fig. 16(b). The stiffness is 1.8 kN/mm due to the local deformation of the face-sheets, and the strength levels corresponding to the top node debonding and insert debonding are 3.5 kN and 3.3 kN, respectively. Although the numerical models calculated in Fig. 16 cannot cover all joining cases, the improvements due to the optimization are directly observed, especially in strength. If in strict accordance with the proposed design principles, a rectangle-shape instead of a square-shape insert might contribute to the desired mechanical behaviors but increase the design work and extra weight. Thus, a tradeoff might be made between properties and consumption. Some characteristics can be obtained from the developed hybrid joining insert compared to our previous design [45] as shown in Fig. 2(e) and conventional insert within honeycomb sandwich plates as shown in Fig. 2(c). For comparison with our

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previous insert [45], this hybrid insert concept can be used when an external device is attached to a random position of the sandwich panel, while the insert in literature [45] can be only employed at the position of the truss nodes. Then, the weak capability to bear shear loads of our previous design is dramatically improved, especially shear stiffness. Despite a decreased behavior of specimen P-C under static pull-out load, the design optimization for the dimensions can solve this issue. As for comparison with conventional insert for honeycomb sandwiches, the carbon fiber reinforced composite grid cells can eliminate the potting compounds or other hulk monolith, reducing joining mass effectively. Meanwhile, a uniform load distribution could be realized via the grid cells, and increased mechanical performance are demonstrated by testing. In consequence, this developed hybrid insert concept provides an effective joining method for composite pyramidal lattice truss core sandwich panels, which offers an alternative for engineering applications.

7. Conclusions In this study, a novel hybrid insert comprising juxtaposed carbon-fiber-reinforced grid cells and a metallic part is proposed for pyramidal truss core sandwich structures to achieve reliable assembly. This novel hybrid concept increases the bonding area between inserts and covering face-sheets without significantly adding weights, which contributes to the effective transformation of the local loading to face-sheets. The failure behavior and load capability of the present hybrid insert are experimentally investigated, and the effect of the joining position is analyzed. When subjected to static pull-out, the lattice-sandwich-insert structures fail by debonding failure and the joining position significantly affects the load capability. However, the static shear testing shows that the juxtaposed grid cells provide sufficient supports to bear the upsetting moment and maintain the continuity with the face-sheets, which 19

achieve superior shear properties. A design optimization for the hybrid insert dimensions is performed, and an informed design configuration is offered, which aims at reliable pull-out performance.

Acknowledgements This present work is supported by the National Nature Science Foundation of China under Grant Nos. 11672085. GQ would also gratefully acknowledge the financial support from the China Scholarship Council (CSC) during the visit at RWTH Aachen University.

Data availability The raw/processed data required to reproduce these findings will be made available on email request.

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Figure Captions: Fig. 1. Logical steps in sandwich applications. 26

Fig. 2. Typical inserts in the sandwich panels [22]. The concepts of (a) through-panel tube, (b) blind hole in the potted area, (c) threaded insert, and (d) through-panel hollow profile are joining methods for honeycomb sandwiches. The concept of (e) quadrangular-prism is the joining configuration for lattice sandwiches. Fig. 3. Schematic illustration of the hybrid inserts. (a) Insert concept; (b) Top view of the hybrid insert; (c) Feature size for the design configuration; and (d) Geometries of the grid cell wall patterns. Fig. 4. Fabrication procedure of the hybrid insert. (a) Cutting the grid cell wall patterns with the interlocking-slots; (b) Interlock assembly method; (c) Photograph of the hybrid insert; (d) Lay-up with the insert. Fig. 5. Sketches of the insert positions. Fig. 6. Finite element model for the static pull-out test of model P-D. Fig. 7. Influence of element size on finite element results. (a) Pull-out forcedisplacement curves; (c) Moment of the top-node of struts. Fig. 8. Finite element results under a static pull-out load. Deformation and stress distribution (S11) of the sandwich panel (a) P-A and (b) P-D. (c) Predicted failure load of P-D. Fig. 9. Experimental setup for sandwich specimens with inserts. (a) Sketch of the fixture and load setup for the pull-out tests; (b) Specimen under the pull-out load; (c) Sketch of the jigs and load setup for the shear tests; (d) Specimen under the shear load. Fig. 10. Experimental result of specimens P-A and P-D for the pull-out tests and failure modes. (a) Load-displacement curves for specimen P-D; (b) Post-failure cross-sections of specimen P-D; (c) Load-displacement curves for specimen P-A; (d) Post-failure cross-sections of specimen P-A. Fig. 11. Stiffness and strength of different insert types under the pull-out load. P-R1

27

and P-R2 denote the insert types for lattice sandwich panels in reference [22] and honeycomb sandwiches in reference [36]. The percentages show the improvement (or degradation) compared to the results of P-R1. Fig. 12. Experimental results of specimen S-B for shear tests and failure modes. (a) Load-displacement curves; (b) Post-failure images. Fig. 13. Stiffness and strength of different insert types under shear load. S-R1 and SR2 denote insert types for lattice sandwich panels in reference [22] and honeycomb sandwiches in reference [36]. Percentages show the improvement (or degradation) compared to results of S-R1. Fig. 14. Illustrations of the design optimization of the hybrid insert. (a) A pyramidal cell with design parameters; (b) Top view of the lattices and insert. Fig. 15. Suggested edge length of the hybrid inserts. Fig. 16. Finite element results from the optimized insert under a static pull-out load. (a) Joining at the origin; (b) Joining at (0, 5.83).

28

Fig. 1. Logical steps in sandwich applications.

Fig. 2. Typical inserts in the sandwich panels [22]. The concepts of (a) through-panel tube, (b) blind hole in the potted area, (c) threaded insert, and (d) through-panel hollow profile are joining methods for honeycomb sandwiches. The concept of (e) quadrangular-prism is the joining configuration for lattice sandwiches.

29

Fig. 3. Schematic illustration of the hybrid inserts. (a) Insert concept; (b) Top view of the hybrid insert; (c) Feature size for the design configuration; and (d) Geometries of the grid cell wall patterns.

Fig. 4. Fabrication procedure of the hybrid insert. (a) Cutting the grid cell wall patterns with the interlocking-slots; (b) Interlock assembly method; (c) Photograph of the hybrid insert; (d) Lay-up with the insert.

30

Fig. 5. Sketches of the insert positions.

Fig. 6. Finite element model for the static pull-out test of model P-D.

31

(a)

(b)

Fig. 7. Influence of element size on finite element results. (a) Pull-out forcedisplacement curves; (c) Moment of the top-node of struts.

Fig. 8. Finite element results under a static pull-out load. Deformation and stress distribution (S11) of the sandwich panel (a) P-A and (b) P-D. (c) Predicted failure load of P-D.

32

Fig. 9. Experimental setup for sandwich specimens with inserts. (a) Sketch of the fixture and load setup for the pull-out tests; (b) Specimen under the pull-out load; (c) Sketch of the jigs and load setup for the shear tests; (d) Specimen under the shear load.

33

Fig. 10. Experimental result of specimens P-A and P-D for the pull-out tests and failure modes. (a) Load-displacement curves for specimen P-D; (b) Post-failure cross-sections of specimen P-D; (c) Load-displacement curves for specimen P-A; (d) Post-failure cross-sections of specimen P-A.

34

4.0

6

Stiffness

3.5

Fp,fp

2.0

0.0

P-R1

P-A

P-B

P-C

115%

111% 114%

70%

114%

107% 100%

128%

128%

97%

93%

94%

P-R2

42% 49%

0.5

70%

100%

1.0

100%

1.5

3 2

Strength (kN)

4

2.5

100%

Stiffness (kN/mm)

5

Fp,ml

3.0

1

P-D

0

Insert type

Fig. 11. Stiffness and strength of different insert types under the pull-out load. P-R1 and P-R2 denote the insert types for lattice sandwich panels in reference [22] and honeycomb sandwiches in reference [36]. The percentages show the improvement (or degradation) compared to the results of P-R1.

Fig. 12. Experimental results of specimen S-B for shear tests and failure modes. (a) Load-displacement curves; (b) Post-failure images.

35

10

3.0

Stiffness Fs,fp

2.0 6

0.0

S-R1

S-R2

S-A

S-B

133%

191%

112%

129%

215%

107%

131%

117%

218% 79%

180% 51%

0.5

100%

1.0

100%

1.5

S-C

4

Strength (kN)

8

Fs,ml

100%

Stiffness (kN/mm)

2.5

2

0

Insert type

Fig. 13. Stiffness and strength of different insert types under shear load. S-R1 and SR2 denote insert types for lattice sandwich panels in reference [22] and honeycomb sandwiches in reference [36]. Percentages show the improvement (or degradation) compared to results of S-R1.

Fig. 14. Illustrations of the design optimization of the hybrid insert. (a) A pyramidal cell with design parameters; (b) Top view of the lattices and insert.

36

60.00

10

57.08 54.15

Y coordinate

5

51.23

0

48.30 45.38

-5

42.45 39.52

-10

36.60

-10

-5

0

10 Insert size (mm)

5

X coordinate (mm)

Fig. 15. Suggested edge length of the hybrid inserts.

150 Predictive load

100

Peel strength of the adhesive film

75

2

50 Pull-out force Moment at top node Moment at insert corner

1 0 0.0

0.5

1.0

1.5

100 Peel strength of the adhesive film

4

80 Predictive load

Load (kN)

Predictive load

4 3

125

Peel moment (kNm/m)

Load (kN)

5

(b) 5

25

0 2.0

3

60

2

40

1

20 Pull-out force Moment at top node Moment at insert corner 0 1.0 1.5 2.0

0 0.0

Displacement (mm)

Predictive load

0.5

Peel moment (kNm/m)

(a) 6

Displacement (mm)

Fig. 16. Finite element results from the optimized insert under a static pull-out load. (a) Joining at the origin; (b) Joining at (0, 5.83).

Table Captions: Table 1 Mechanical properties of materials. 37

Table 2 Dimensions for the composite grid cell wall pattern (unit:). mm Table 3 Predictive and experimental performance of the hybrid insert under static pullout load.

38

Table 1 Mechanical properties of materials. Carbon fiber reinforced orthogonal weave laminates G f 12 f 1560 kg/m3 E f 11 , E f 22

LS-3K 3.6 GPa

46.7 GPa

Aluminum alloy

E Al

2A12-T4

Al

68.7 GPa

0.3

Film adhesive

J-272-A

 J 272

300 g/m2

 Jn

8.5 MPa

M

86.1 N  m / m

 Js ,  Jt

24.3 MPa

Table 2 Dimensions for the composite grid cell wall pattern (unit: mm ). L

b c

36.0 4.0 4.5

H

w t

39

20.0 8.0 1.0

Table 3 Predictive and experimental performance of the hybrid insert under static pull-out load. Stiffness ( kN / mm ) Type

FE Predictive

Test

P-A

2.35

2.58  0.11

P-B

2.23

2.86  0.23

P-C

1.10

1.11  0.09

P-D

2.38

2.96  0.08

Strength ( kN ) FE Predictive Position

Load

TN

2.10

IC

4.14

TN

2.27

IC

5.37

TN

2.08

IC

2.26

TN

3.70

IC

6.90

Test Position

Load

IC

3.91  0.06

TN/IC

3.05  0.34

TN

1.55  0.25

TN

3.46  0.27

Notes: The abbreviations TN and IC in the Position column denote that the first debonding failure occurs at top nodes and insert corner, respectively.

Statement of Author Contribution Paper Title: A hybrid joining insert for sandwich panels with pyramidal lattice truss cores Authors: Ge Qi, Yun-Long Chen, Philip Richert, Li Ma, Kai-Uwe Schröder Author Contributions: Ge Qi: Formal analyisis, Investigation, Methodology, Validation, Writing - original draft. Yun-Long Chen: Investigation, Validation. Philip Richert: Investigation, Validation.. Li Ma: Conceptualization, Formal analysis, Investigation, Methodology, Supervision, Validation, Writing - review & editing. Kai-Uwe Schröder: Methodology, Writing - review & editing.

40