Abstract
This study investigates the mechanical responses in three-point bending and compression of body-centered cubic (BCC) for specific aerospace applications to achieve lightweight and improved mechanical properties. The mechanical characteristics of functionally graded BCC lattice structures were explored, resulting in enhanced mechanical features compared with uniform-graded BCC lattice structures. Due to the gradient lattice structure, the average bending load significantly increased to 62.5%. It was found that the BCC lattice structure only exhibits a dual failure model comprising buckling and fracture, compared with other lattice structures that often offer sole buckling or fracture failure. The buckling of the struts starts from the bottom and ends with a fracture. BCC lattice sandwiches provide an opportunity to balance strength and weight ratio effectively. The experimental findings showed close agreement with finite element results. Numerical modeling illustrates the stress–strain and force–deformation curves, and the failure mechanism is the strut buckling triggered from the plastic hinges with high-stress levels.
Keywords
Introduction
Additive manufacturing (AM) has allowed researchers to transform their concept into a functional model with customized and improved mechanical properties. In AM technologies, a structure is created, modeled, and designed using the computer-aided design (CAD) method. It is then divided into several thin layers. The material is added layer by layer, from bottom to top, utilizing an ultrasonicate, laser, or electron beam to melt and combine the materials. 1 A variety of technologies are currently utilized for metallic part AM; each of these procedures has perks and drawbacks in terms of print quality, mechanical properties, component performance, and limitations of materials that can be used for these procedures as follows: selective laser melting (SLM) is getting a lot of industry acceptance to create complex, high-value metal components that are customized for use in biomedical, automotive, aerospace, and other fields.2–5 SLM results in precision in creating complex geometry with good tolerance and built part layer by layer, forming firm, dense, and fully dense metal parts.6,7 AM techniques have been considered an alternative to traditional manufacturing techniques for decades. 8 The main advantage that encourages their implementation on a large scale is their ability to produce near-net form goods quickly from a variety of materials. 9 Most aerospace parts are manufactured using conventional methods, and the final work contains less than 5% of the source material. 10 In the case of AM, maximum material utilization is of net parts. 11 AM methods’ most common geometrical elements include thin-walled structures, complex curved designs, and lattice structures. 12
AM has enabled innovative methods to achieve lightweight, allowing for even higher bulk reduction. 13 This lightweight significantly lowers production costs and emissions, while enhancing ergonomics, performance, mechanical properties, and ergonomics aspects of design, and using AM to make items lighter results in more productive, as well as functionally improved, parts for a variety of sectors,5,14 that is, applications in the field of aerospace, 5 defense, 15 automotive, and medical. 16 The aerospace sector is one of the leading industries using AM technologies for manufacturing end-use components and prototypes. 17 According to a recent survey, aerospace applications occupy 12.3% of the worldwide AM market. 18 In addition, the analysis projects that the AM industry is predicted to grow from $1.5 to $100 billion in the next 20 years; with the aerospace industry driving the majority of this increase, Lockheed Martin Space Systems reduces cost, cycle time, and material waste using 3D printing technology to print satellite parts made of titanium. 18 Rolls-Royce 3D printed “front bearing housing” using titanium. In addition, they reduced manufacturing time by 30% using this AM approach instead of traditional manufacturing techniques. 19 In partnership with Monash University, the Australian Research Council (ARC) has utilized AM to advance Australia’s manufacturing sector. Nine million dollars (AUD) have been provided by ARC to support the promotion and development of Australia’s aerospace sector. The research team concentrated on additively manufactured tiny jet engine components of titanium alloy. The study team discovered that engine components might be made more quickly and cheaply with 3D printing technology, which would also reduce weight and carbon emissions. 15
In aerospace, especially aviation, reducing weight is directly related to improving fuel efficiency. For a specific range profile, a lighter aircraft or spacecraft requires less fuel to be carried. 20 Weight reduction is a conceptual challenge for engineers and designers, stimulating new developments in manufacturing processes, materials science, and overall vehicle design. 21 This is crucial for space exploration since carrying more people, cargo, or scientific equipment may be constrained by the spaceship’s weight. The weight of the spacecraft may be kept to a minimum, creating more room for valuable payloads. Lighter aircraft may travel longer or survive in flight for longer, which is vital for various aerospace applications. 22 Due to superior thrust-to-weight ratios, more lightweight aircraft can fly faster and at higher altitudes. During flight, a lighter aircraft experiences less stress on its structural parts, which might result in longer operating lifespans and fewer frequent maintenance requirements. 23 Lighter aerospace vehicles have less overall environmental effects since they use less fuel and emit fewer pollutants. 5 For aerospace manufacturing and research companies, achieving weight reduction can lead to a competitive advantage by offering more efficient and capable aerospace solutions.23,24 AM technology is getting more attention from researchers and manufacturers for aerospace applications because of the growing need for intricate and lightweight metal components. 25 Thus, this work aims to reduce the weight of aircraft fins by increasing strength to weight ratio. Compression testing and three-point bending were performed on BCC lattice sandwich and functionally graded samples manufactured using SLM with titanium alloy (TiAl6V4) to explore the mechanical responses of these structures. The presented research is composed of four sections. The first section is design, which describes the design process and details of software used to design specimens’ fin, material, and printing. At the same time, the second section discussed the mechanical findings, including strength and failure modes. The third section discusses the FEA, boundary conditions, and comparison of the experimental results with those of the FEA. Finally, the fourth section highlights the conclusions.
Designing
Cellular lattice structure has a significant role in aerospace and defense industry applications due to their high specific strength and stiffness. 26 The architecture and parent material impact the lattice structure’s mechanical performance. 27 The lightweight, highly stable, and energy-absorbing BCC lattice structure is perfect for bending because of its resistance to deformation. 28 BCC lattice structures perform well under bending loads and have lower per unit mass than other lattice structures, such as face-centered cubic or gyroid. 29 Fin design used it to minimize mass and sustain the bending load.
Model design
The model of the aeroplane fin was designed using SolidWorks® 30 to design solid geometry, as shown in Figure 1A. The CAD geometry was imported to nTopology©31 Software for further processing. The design of the fin was illustrated in the flowchart, as shown in Figure 1. The imported CAD body was converted into implicit and then shelled. The shelled part was subtracted from the main body, and a BCC lattice structure was inserted. Both shell and lattice bodies were Boolean to make a single body. A static structural simulation was performed on that single body.

The flowchart of fin design: (
First, a uniform lattice density structure (shown in Fig. 2A) was inserted into the Boolean subtract body and was combined to make a single body. Static structural analysis was performed on a uniform lattice density body. Second, the lattice structure was replaced with the functionally graded one (shown in Fig. 2B), which is a gradual change in structure along the volume of a structure. Functionally graded lattice structure 32 was designed, and static structural analysis was performed. Functionally graded lattice structure shows excellent bending load and displacement results compared with uniform density lattice structure. 33

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Specimen preparation
The unit cell is regarded as the representative volume element of the lattice structure because periodic lattice structures are composed of unit cells symbolically reproduced in the region. As shown in Figure 3A, a typical BCC unit cell has eight equal-length diagonal struts. To specify the topology of the BCC unit cell, the following parameters are required: unit cell length (lu), strut diameter (d), lattice angle (θ), and strut length (2l). 35 It is well known that compression and three-point bending stresses are the main ways in which lattice sandwich mechanical characteristics are achieved. 36 According to our fin functionally graded lattice model design shown in Figure 3B, two types of specimens were designed of three-point bending test samples named uniform density lattice and functionally graded lattice structures, as shown in Figure 3B and C. The specimens’ corresponding models have top and bottom plates with equal thickness (t), identical specimens’ height (H) and width (W), and different lengths for compression (LC) and three-point bending (LB).

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For compression testing
Compression test specimens for titanium alloy with a BCC lattice structure were designed using software tools, including nTopology. Three compression specimens were designed using topology with the geometry shown in Figure 4. Using ASTM C365 standard, the specimen was designed as per the parameters listed in Table 1.

CAD model of compression specimen.
The Dimensions of Body-Centered Cubic Test Specimens
d, strut diameter; H, height; LC, length for compression; LB, length for three-point bending; lu, unit cell length; t, thickness; W, width.
For bending testing
Flexural testing assessed the material’s mechanical properties, explicitly bending strength, and stiffness. The specimens typically consist of a rectangular bar with a specific geometry allowing controlled bending. As shown in Figure 3B, the three-point bending test specimen of uniform lattice density had a total length of 49.5 mm, width of 12.6 mm, and height of 9.7 mm as specified in ASTM C393 standard. Regarding comparing the mechanical efficiency of lattice structures with uniform and graded densities, a functionally graded lattice structure of a three-point bending specimen, as shown in Figure 3C, was designed using the same ASTM C393 standard with a varying strut diameter of 0.5 mm minimum and 1.5 mm maximum. The dimensions of all remaining parameters were kept the same as a three-point bending test specimen of uniform density lattice.
Materials and Methods
The SLM process fabricates metallic 3D BCC lattice sandwiches with titanium alloy. The process was realized using the Farsoon FS421M 37 machine. Ti6Al4V powder was repeatedly layered on a Ti6Al4V substrate, and then the powder was selectively melted in line with the data from the CAD model. The raw material used was gas-atomized Ti6Al4V powders with spherical diameters ranging from 0.015 to 0.050 mm. Argon was the protective gas utilized to protect against contamination and act as a coolant for printing. The process parameters are listed in Table 2. The scanning path used was zigzag. The fabricated 3D BCC lattice test specimens are presented in Figure 5.

As fabricated, all BCC lattice test specimens.
Selective Laser Melting Process Parameters for TiAl6V4
The lattice structures were subjected to abrasive blasting to eliminate the residual powders; however, polishing was not done because of the structure’s unique and intricate geometry. The build plate was heat treated to remove residual stresses before removing prints.
Mechanical testing
Regarding the mechanical response measurement, the mechanical response was tested experimentally using a universal testing machine (HAIDA HD-B607-S), 38 as shown in Figure 6 under tensile, compression, and bending loading cases. The tensile specimen of the Ti6Al4V fabricated by SLM was tested according to ASTM E8/8M. 39 The stress–strain curve of the tensile test is given in Figure 7. The yield strength was acquired as σs = 1300.0 MPa, and Young’s modulus was E = 95.0 GPa, less than 2% different from previously published research. 40 The obtained tensile properties exhibit a slight reduction compared with the Ti6Al4V generated by conventional forging, as SLM inherently introduces micro defects such as interlayer gaps and unmelted raw powders. According to ASTM C365, a compressive load was applied to the BCC lattice sandwiches using Instron 5985 at a 2 mm/min loading rate. The testing machine’s sensor recorded the deformation during the compression test.

Stress–strain curve.

An experimental setup shows the direction of application of the bending force.
To assess mechanical parameters, including strength, stiffness, and deformation behavior, the three-point bending test of Ti6Al4V involves applying a load to a standard specimen, measuring the resulting deflection, and analyzing the results. This test is essential for determining if the material is appropriate for a specific technical application and assuring the reliability of the final product. By ASTM C393, functional graded and three-point bending mechanical tests were carried out. 41 The force sensor detected the applied load, and the loading speed was 2 mm/min. A dial indicator mounted at the bottom measured the deflection under bending. A digital video camera (SONY DSC-RX100 M4) recorded the specimens’ failure models and deformation evolutions during the testing.
Results and Discussion
The outcomes are reported for the load-bearing capacity, failure mode, and deformation in the lattice sandwich structure in compression and three-point bending tests. FEA was performed for compression and three-point bending tests to relate the experimental and simulation results.
Compressive responses
A compression test was used to determine the effective stress–strain curves concerning the compressive responses of the BCC lattice sandwich compression specimen. Figure 8 illustrates the average stress–strain behavior of compression tests with experimental figures.

Stress–strain curve under compression for BCC lattice structure with experimental setup procedure from (
Figure 8A shows the downward compressive load applied on the compression specimen because stresses rise linearly until they reach their first peak. At this stage, the BCC lattice core sustains the load linearly up to the highest peak, and the yield stress is obtained. The buckling of the struts in the top and bottom face sheets region is the primary deformation mechanism. In the area shown in Figure 8B, the struts close to the face sheets start losing energy, and the curve drops rapidly to relatively low levels. The compressive specimen design shown in Figure 4 has multiple layers of BCC lattice structure, so due to those layers, the stresses increase again as these layers bear the compressive load further. The curve rises again from the region shown in Figure 8C to the next peak. The specimen holds this plateau region and resists compression up to maximum strain. As summarized in Figure 8C–E, finally, the BCC lattice structure ultimately fractures and loses the load capacity as the curve drops rapidly downward.
The stress–strain curves of the specimen obtained from compression tests are shown in Figure 9; all the curves show excellent consistency and follow the same trends, with sharp peaks and plateau regions. These patterns indicate the accuracy of the experiment design and fabrication.

Stress–strain curves of BCC lattice structure.
Bending responses
In this section, the three-point bending test is briefly explained as a mechanical test used to evaluate the flexural strength of materials. To determine their flexural strength, the test was performed on homogenous and functionally graded lattice structures. The specimens were positioned between two supports extending from the edges, and force was applied on the middle point of the upper surface as presented in Figure 6.
This depicts that both curves have different behaviors because of their unique lattice core design inside sandwich structures. As designed for robust, functionally graded force–displacement curves show excellent response to its strength and stiffness. However, homogenous structures have a lower value of force–displacement, but excellent behavior in energy absorption and buckling deformation.
Uniform lattice structure
ASTM C393 performed three-point bending mechanical tests regarding the bending reactions. The load–deflection curves of all three specimens under bending experiments are defined in Figure 10. All three curves have a linear sharp peak, a sinusoidal plateau region, and a sharp rise till fracture. Overall, the curves for repeated samples show great consistency for a homogeneous lattice, indicating the validity of the studies and the accuracy of the fabrication. The evolutions of bending deformation are illustrated in Figure 11A–D. At the initial stage, as shown in Figure 11A, the load is just applied on the top face sheet, which holds the load for a certain time with no deformation, but after a certain time, the face sheet starts deforming very slowly. The bending load linearly increases to the highest peak due to the strength of the top face of the uniform lattice structure specimen. As presented in Figure 11B, the graph suddenly drops to the lowest level due to the fracture of the face. Due to the layer-by-layer structure in the core of the specimen, the lattice sustains the load, and the curve holds a wide range of plateau regions. In Figure 11C, the plateau region shows sinusoidal behavior just because of different BCC lattice structures bearing the buckling load and after significant buckling deformation. Finally, the curved struts are fractured, and the load capacity of the core is lost. As shown in Figure 11, the core is completely compacted, and the bottom face sheets buckle simultaneously, causing the curves to only reach one peak. After large buckling deformation, the homogenous lattice structure specimen is completely fractured. Every specimen was fully damaged close to the area where the force was applied. Due to the specimens’ bending, the said location experiences the most compression force.

(

Load–deflection curve of homogenous lattice structure with experimental step-by-step pictures: (
Functionally graded lattice structure
The bending response of uniform and graded lattice, as shown in Figure 10, shows that an increase in strut thickness behaves rigidly. All the functionally graded lattice structure specimens have shallow buckling deformation compared with homogenous ones. As shown in Figure 10B, the curves linearly increase to the highest peak, and finally, the curved struts fracture. In Figure 12, the graph and figures show the outcomes of the three-point bending test on the functionally graded lattice structures. The result of the functionally graded structure looks different from the uniform lattice structure due to the change in lattice density in the core of the specimen. At the initial stage, as shown in Figure 12A, the top face bears the bending load and linearly rises to the first highest peak. Compared with homogenous lattice structures, this specimen shows more excellent load bearing due to variations in lattice density. The lattice density is higher at three points where the load is applied and two support points. These various lattice structures sustain the bending load, showing shallow deformation. The load gradually increases downward from the middle point of the top face sheet, and the functionally graded lattice structure specimen resists the bending load to the highest value of 16,000 N. In Figure 12B, the large bending force finally fractures the lower core portion of the specimen with bottom face sheet failure. This is due to the higher density lattice structure at the top and support points. It has been observed that homogenous lattice structure shows more significant buckling deformation, while functionally graded specimens show more rigid behavior. These fractures demonstrate that the crack follows the weakest struts and nodes. Variations in unit cell structure and strut thickness can cause different fracture behaviors. 42 The junction of struts and nodes, which are the locations where stress concentrations occur, is often where homogeneous and graded lattice specimens fail. 43

Load–deflection curve of functionally graded lattice structure with bending test experiment setup: (
The comparison of results (Figs. 11 and 12) shows that homogenous structures have a high buckling deformation due to their core lattice design. In contrast, functionally graded specimens show characteristically brittle behavior, with roughly linear stiffness until catastrophic collapse.
Validation
Finite element analysis was done to analyze the compression and three-point bending using ANSYS© 19.2 numerically. The geometrical parameters, boundary, and loading conditions were the same as the experimental conditions of the specimens. 3D models of the compression and three-point bending test specimens were designed using SolidWorks software. The model was then imported into ANSYS Workbench, where the simulation was performed. The elastic–plastic material model was constructed using plastic stress and strain data. The lower surface was modeled as fixed support for compression, and the upper surface was displaced downward to apply compression load. For bending, the supporting bodies were utterly restrained. 44 The rigid punch was then loaded vertically to apply the bending loads. Numerical modeling was used to obtain the evolution and variation of stress and the failure mechanism, which could not be achieved and explored through experimental measurements. The experimental and FEA of the compression test and bending test are presented in Figure 13.

Experimental and numerical test specimens.
The comparison between the experimental and simulation results is shown in Figure 14. The graph can be divided into three stages, the first stage (Fig. 14A) is an elastic region in which the results (experimental and simulation) are almost the same and have the same trend. The second region (Fig. 14B) has variation as the experimental result showed the higher peak, which represents the material’s properties rather than the structural properties, that is, densification,45,46 which cannot be incorporated during simulation. The third stage (Fig. 14C), in which the samples are fully deformed and fractured, is in close agreement with the simulation results and follows the same trend. Figure 15 represents the struts’ buckling behavior experimentally and numerically with time. Similarly, the location of the struts near face sheets always shows relatively high-stress levels and can be considered plastic hinges. These plastic hinges have the potential to cause buckling failure, which is consistent with experimental findings, as can be seen in Figures 8 and 11.

Experimental and FEA curves of compression test.

A comparison of the compression behavior of specimens experimentally (
The force–deflection curves of experimental and numerical simulation for three-point bending tests are plotted in Figure 16. The experimental outcomes show significant repeatability, and the curve obtained from the simulation agrees with experimental findings. The error percentage between simulation and experimental results has been calculated for both compression and three-point bending tests as 10.2% and 16.4%. As shown in Figure 17, a vertical load is applied at the middle of the top face sheet and gradually increases downwards at a 2 mm/min rate. The experiment results and the numerical analysis demonstrate that the struts under the punch buckle subsequently deform significantly. As presented in Figure 17, the experimental finding is that strut failure frequently happens under the punch where the stress of the struts is greater than everywhere else. These results demonstrate that the failure of the BCC lattice structures under compression starts at the connections between the struts and face sheets.

Experimental and FEA curves of three-point bending test.

From (
The behavior of specimens during experimental testing and FEA was compared and shown in Figure 17. The results of the experiment and numerical analysis demonstrated that the struts under the punch buckle deform significantly, which is the same as the experimental finding that strut failure frequently happens under the punch, where the stress of the struts is greater than everywhere else. In addition, the results showed that the failure of the BCC lattice structures under compression starts at the connections between the struts and face sheets.
A strong correlation was observed between the experimental findings and the functionally graded structure’s FEA of the three-point bending test. The experimental data and the FEA stress–strain graph closely matched, suggesting that the structure behaved rigidly under load in line with the results of the physical testing. As shown in Figure 18, the FEA graph was mostly linear during the bending phase, indicating that the structure mostly underwent elastic deformation and that plastic deformation was negligible. The percentage error between experimental and numerical results of functionally graded structure is 11.12%. Figure 19 represents that the graded density of the material is responsible for the notable fact that only the BCC lattice structure fractured at the bottom under the load point. The simulated and experimental findings closely match, confirming the FEA model’s correctness and dependability in forecasting functionally graded materials’ behavior under bending stress.

Experimental and numerical graph for functionally graded materials.

Experimental and numerical setup for functionally graded structure.
Conclusions
In this study, BCC lattice sandwich structures were designed and additively manufactured successfully using SLM technology aeroplane fin to enhance its mechanical properties, including stiffness and load-bearing capacity. Experimental and numerical simulations were performed to explore the mechanical outcomes from compression and three-point bending tests. The simulation results illustrate that the failure modes of the BCC lattice sandwich structures were mainly due to strut buckling and face sheet wrinkling. The numerical modeling also revealed that the SLM process introduced randomly distributed imperfections, which affected the compressive responses of the BCC lattice sandwich structures. The following are the key results.
(1) During compression, the primary deformation mode is strut buckling, followed by fracture failure, and deformed up to 6.2 mm, causing the core lattice to be completely damaged.
(2) While bending, the lattice sandwich’s struts under the punch are more likely to buckle, which causes the struts close to the upper face sheet to distort significantly and cause small deformation of the bottom face sheets.
(3) Due to the functionally graded lattice, the average bending load capacity significantly increases to 62.5%, and the lattice showed rigid behavior compared with a homogenous lattice structure. These results suggest that functionally graded lattice structures are suitable for widespread application in producing high-performance components for many industries.
(4) The experimental and numerical models for both compression and three-point bending show close agreement, as the failure modes of the BCC lattice structure were mainly due to strut buckling and face sheet wrinkling.
(5) In the present research, the solid geometry of the fin was constructed by introducing a BCC lattice structure, which can be uniform or functionally graded. In both cases, the mass of the fin was reduced, which clearly indicates that lightweight is achieved. In the future, more studies will be conducted by utilizing two different kinds of lattice structures to further reduce the weight/mass of the fin without altering its properties.
There is still potential to study the mechanical characteristics of BCC lattice structure by changing the geometrical specifications, including face sheet thickness, the struts’ slenderness ratio, the unit cell’s size, and the span length; a broad range of failure models, such as buckling and shrinking on the face sheets and buckling on the struts, will be considered. Besides, a new kind of functionally graded lattice structure can be created by combining materials or changing the shape of the struts. In addition, different types of periodic unit cells can be connected to form a hybrid structure that enhances the design’s multifunctionality and mechanical performance.
Authors’ Contributions
A.J.: Conceptualization, data curation, formal analysis, methodology, software, and writing—original draft. A.M.: Supervision, conceptualization, and visualization. M.R.H.: Revision of draft and editing, supervision, conceptualization, and software. M.S.K.: Revision of draft, formal analysis, and validation. A.K.: Utilization of resources and printing of samples. M.N.A.: Printing of samples and utilization of resources. A.A.K.: External supervision and conceptualization. M.K.: Simulation and validation.
Footnotes
Author Disclosure Statement
The authors have no personal/financial or any other conflict of interest to declare.
Funding Information
No funding was received for this article.
