Introduction

Three-dimensional printing (3-D printing), also known as additive manufacturing (AM)1 or rapid prototyping, has proved to be a novel digital fabrication technology capable of creating physical objects from a geometrical representation by successive addition of material2,3,4. The growing consensus of introducing the 3D fabricating system over traditional techniques is attributed to a series of advantages including fabrication of complex geometry with high precision, maximum material savings, flexibility in design, and personal customization5,6,7,8,9,10,11,12. Therefore, the developments in AM and material production characteristics are driving the rapid evolution towards smart and lightweight structures with high stiffness-to-weight and high strength-to weight ratios13,14. Porous structures have also been developed by AM, which can withstand the impulsive energy of impact or blast2,15,16.

Recently, porous structures have been widely used in several fields, such as bone implant applications17,18,19,20,21,22, energy absorption23,24,25,26,27, heat dissipating problem or thermal transport28,29,30, and lightweight applications31,32,33,34. For example, Ammar Alsheghri et al., provide an iterative network topology optimization approach based on modification of the number of abstract connections of the graph/network for designing and manufacturing lightweight and stiff bone-like structures. And, the biomimetic networks were compared to each other, and to the reference network derived from mature trabecular bone. Due to the superior structural, mechanical, and biological properties, six types of composite porous structures with differ strut radius are introduced to enhance the mechanical and biological properties further35. Furthermore, the FE approach is used to explore the mechanical properties, and the results show that the CP-Ti with CB composite porous structure presents similar strength and compressive modulus to the cortical bone and therefore can be considered for use as subchondral restorations. In addition, the recent study progress has shown that porous structures based on triply periodic minimal surface topologies presented excellent heat transfer performance than the traditional metal foam in latent heat thermal energy storage systems. Qureshi et al. explored the effect of porous structural porosity and functional grading of triply periodic minimal surface based phase change material on heat transfer performance36. And the results show that both porosity and functional grading have a significant effect on both conductive and convective heat transfer enhancement, which may be serve as a guideline for design and selection of a suitable triply periodic minimal surface candidate according to the applied boundary conditions of the respective latent heat thermal energy storage systems.

Generally, porous structures are characterized by large densification strains, high specific strength and possibility to have a smooth plateau stress during loading15,37,38. It is note that that AM porous structures are characterized by freedom design, multi-functional, and uniformity and repeatability in the response. In particular, AM allows for manufacturing extremely complex geometries from beam-based porous structures, such as body-centered cubic (BCC)39,40, face-center cubic (FCC)41, to surface-based porous structures, such as triply periodic minimal surface (TPMS) structures42,43,44,45,46. Additionally, nature-inspired porous structures47,48,49,50,51,52 have been deeply developed with AM, such as honeycomb structures53,54,55. Series of mechanical response can be induced, from conventional stretching- and bending-dominated responses to snap-through mechanisms. For instinct, a curving porous structure design strategy was introduced to obtain new forms of curving porous structures, the compressive deformations, mechanical properties, and energy absorption characteristic of the as-designed porous structures were compared and explored through theoretical models and quasi-static compression experiments and FEA. The results show that the mechanical properties of all the curving structures are significantly than the original due to the excellent properties of high specific elastic modulus, high compressive strength, and low weight56. Geometric arrangements such as topological configuration and gradient strategy have been shown to be the main factors affecting the mechanical properties of porous structures38,42,57. In this paper, the BCC configuration was selected to verify the influence of the evolution of the classical configuration on the mechanical properties. Furthermore, we design a porous structure with central junction shift, and discuss its equivalent elastic modulus, yield strength, peak strength, deformation behavior and energy absorption by finite element analysis and quasi-static compression experiments.

Methods

Porous structures design

As a regularly arranged crystalline material, the mechanical properties of BCC porous structures have been widely studied, such as gradient porous structures and TPMS porous structures. Due to the deformation of solids during the forming process or the different heat treatment methods, there are defects such as points, lines, and surfaces, which seriously affect the mechanical properties of porous materials56. Therefore, this paper discusses the mechanical properties of a single point defect in crystalline materials and the evolution of porous structures near their original positions. Herein, the deformation design of the porous structure based on BCC configuration is carried out here, as shown in Fig. 1. From the Fig. 1, it is clear that the central node of the TrBCC is located at the center of the cube, that is, the coordinates (2,2,2). Based on the configuration of TrBCC, the central node of the deformed BCC configuration shifts up or down, i.e. coordinates (2,2,3) and (2,2,1), and the rest of the cube remains unchanged. Furthermore, the CDBCC structure with node offset is designed by combination, as shown in Fig. 2.

Fig. 1
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Design of the lattice structure: (a) Porous structural framework; (b) BCC topological configuration; (c) center up; (d) Center down.

Fig. 2
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Porous structures of TrBCC and CDBCC.

To avoid accidents in structural performance, we designed three different volume fractions, including 5%, 10%, and 20%. Furthermore, the design parameters of porous structures are shown in Table 1. And the side diagram of the porous structure of TrBCC and CDBCC is provided, as shown in Fig. 2, to present the configuration characteristics of the proposed porous structure.

Table 1 Junction variation design parameters for BCC porous structures.
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Materials and manufacture

To gain the designed porous structure, Ti-6Al-4 V, is used in this paper, which has been widely applied in automotive, aerospace, and medical implants. The powder material is provided by AVIC Maite Additive Technology (Beijing) Co., Ltd. And its chemical composition is shown in Table 2. Moreover, the scanning electron microscope (SEM) micrographs of TC4 is presented in Fig. 3. It can be found from Fig. 3 that the SEM micrograph presents a nearly spherical shape with smooth surfaces, which provides better flowability for SLM process. And the experimental samples of the designed porous structure were printed by SLM machine (XDM 250, supplied by XDM Co., 1td, China) equipped with IPG fiber laser 500 w and a wavelength of 1064 nm. Furthermore, the built porous structure was removed from the base plate with wire electrical discharge machining, and the structural samples are shown in Fig. 4. As shown in Fig. 4, the designed porous structure is well formed and manufactured.

Fig. 3
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SEM micrograph of TC4: (a) 500×; (b) 1000×.

Fig. 4
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Porous structure samples with junction deformation.

Table 2 Chemical composition of Ti-6Al-4 V.
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FEM analysis and compressive test

Simulation analysis and computer-aided related methods have shown strong application potential in many fields such as mechanical calculation, dynamic analysis, and fluid analysis due to their advantages of speed, simplicity, low cost and high efficiency58,59,60,61,62,63. At present, commonly used analysis tools mainly include commercial software, such as ANASYS, ABAQUS, Fluent, and software that can customize the analysis, such as MATLAB, Python, etc. To explore the trend of mechanical properties of porous structures under compressive force, the finite element analysis method is used to simulate and calculate the constructed porous structures. Among them, the meshed finite element model was subjected to quasi-static compression test in Abaqus, the meshing was divided by a 0.2 mm C3D4 tetrahedral mesh, and the damage failure model for simulation analysis was based on the Johnson-Cook model64. Furthermore, the BCC meshing model and simulation analysis boundary settings are shown in Fig. 5. And HyperMesh software is used to mesh the porous structures with different volume fractions, and the finite element analysis model based on J-C damage model for Abaqus failure simulation is obtained.

Fig. 5
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Meshing and compression boundary condition.

The mechanical properties of the porous structure were tested using the Shenzhen Universal Testing Machine (CMT5105), equipped with a maximum loading unit of 100 KN, and a constant loading rate of 1.5 mm/min. The test standard ISO 13314:2011 (mechanical testing of metals-ductility testing-compression test for porous and cellular metals) is used to test the performance of prepared metal samples. Furthermore, The boundary condition of the compression test is set so that the lower surface of the porous structure is fixed on the base, and the upper surface follows the downward movement of the indenter of the compression testing machine. The mechanical properties of porous structures are obtained by structural strain and pressure calculations. And the compressed sample is cut from the molded substrate using a wire EDM.

Results and discussion

Compressive deformation behavior

As shown in Fig. 6, the microscopic features of the upper surface of the molded sample are obtained. It is intuitive to see that the quality of the samples formed by SLM is good, and there are no obvious pores and cracks.

Fig. 6
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Characterization of manufacturing samples.

As shown in Fig. 7, we compare the uniaxial compression test data of the test specimen and the simulation results. It can be seen from the figure that the evolution trend of experimental data and simulation data is consistent. From that, the right figure of Fig. 7 shows that the stress drop of the porous structure during the simulation process is mainly due to the flying out of the member in Step8, which is consistent with the previous research42. On the other hand, the stage of compacting the stress-strain curve of the experimental data is due to the accumulation of the broken structure in the undamaged structure, and with the increase of crushing and crushing structure, the structure is compacted successively, and then the stage of dense stress curve occurs. Based on these, the performance of the porous structure with the remaining volume fractions was explored by simulation approach, as shown in Fig. 8; Table 3.

Fig. 7
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Comparison of stress-strain curves in simulation and experiment(V = 5%).

Fig. 8
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Stress-strain relationship curves of porous structures under different volume fractions: (a) V = 5% (b) V = 10% (c) V = 15% (d) Comparison of equivalent elastic modulus.

As shown in Fig. 9, we describe the deformation behavior of porous structures under compression, including TrBCC and CDBCC. It can be seen from the figure that the traditional configuration of BCC porous structure has shear failure in the direction of 45°, which is consistent with the previous research42. Furthermore, the porous structure of CDBCC showed the phenomenon of layer-by-layer destruction, which was consistent with the experimental results. Specifically, the porous structure of CDBCC was destroyed at Step 4, while TrBCC was destroyed at Step 5. Moreover, the porous structure of the TrBCC configuration exhibits better mechanical properties as shown in Fig. 8, which can be explained by the different stress states in Step 3 in Fig. 10, at the same analysis step3.

Fig. 9
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Deformation behavior of compressed porous structure.

Fig. 10
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Prediction curves of the two structures.

Mechanical properties

Based on the compressive deformation behavior, the stress-strain curves under each volume fraction are further obtained, as shown in Fig. 8. It can be seen from the figure that the CDBCC structure has a high equivalent elastic modulus and a curve relationship between a higher stress plateau, mainly due to the failure behavior of the CDBCC structure, as shown the Step4 on the right in Fig. 7. Specifically, the maximum stress of CDBCC porous structure appears in the bottom layer under the same strain, and the degree of structural failure is low, which provides an indication that CDBCC porous structure has a better stress platform. Based on the stress-strain relationship, the equivalent elastic modulus under each volume fraction was obtained by linear fitting, as shown in Fig. 8(d). Specifically, under the condition of volume fraction of 5%, the equivalent elastic modulus of the CDBCC was 44.35% higher than that of TrBCC structures. Moreover, the porous structure of CDBCC under 10% and 15% volume fraction was 63.40% and 66.08% higher than that of the traditional BCC structure, compared with the TrBCC structure. With the increase of volume fraction, the equivalent elastic modules of the CDBCC structure gradually increases compared with the TrBCC structure, which is due to the increase of the material and the increase of the porous structure’s ability to resist deformation, as shown in Fig. 6.

Table 3 Compressed properties of the designed structures.
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Energy absorption

Porous structures usually exhibit a certain stage of stress platform when subjected to compressive loads, with a long strain rate, which is very conducive to energy absorption, so it is widely used in buffer energy absorption, protection devices and other fields. Therefore, the energy absorption characteristics of CDBCC structures are further analyzed, as shown in Fig. 10. It can be seen from the figure that the energy absorption characteristics of the CDBCC structure under 5%, 10% and 15% volume fraction increase by 31.57%, 72.42% and 27.23%, respectively, compared with the TrBCC structure. Among them, the energy absorption characteristics of CDBCC porous structures under 10% volume fractions were better than those of BCC porous structures under TPMS optimization65. This provides a new perspective for improving the energy absorption characteristics of porous structures under BCC configuration.

Based on the energy absorption, the evolution of the energy absorption characteristics as the volume fraction increases is predicted. It is found that the structure with the designed junction offset has better energy absorption characteristics than that of TrBCC. The results provide more options for the lightweight application of high specific stiffness and high energy absorption characteristics for porous structures, and present research basis and experimental data for the design of porous structures.

Conclusion

In this paper, the influence of lattice topological configuration changes on the mechanical properties of porous structures was discussed. Furthermore, the computer-aided design method was used to design the porous structures under the same volume fraction, and the mechanical properties of the designed porous structures was carried out by means of simulation analysis and experiments, and the following main conclusions were obtained.

(1) The porous structure of CDBCC has a high equivalent elastic modulus and a curve relationship between a higher stress plateau, mainly due to the failure behavior of CDBCC structures under compression. Furthermore, the equivalent modulus of elasticity under each volume fraction is obtained by linear fitting. Under the condition of volume fraction of 5%, the porous structure of CDBCC was 44.35% higher than that of TrBCC. Compared with the TrBCC structure, the CDBCC structures under 10% and 15% volume fraction was 63.40% and 66.08% higher than that of the TrBCC structure.

(2) Compared with the TrBCC structures, the energy absorption characteristics of the CDBCC structures under 5%, 10% and 15% volume fraction increased by 31.57%, 72.42% and 27.23%, respectively. Based on the energy absorption, the evolution of the energy absorption characteristics is fit and predicted as the volume fraction increases. It is found that the porous configuration with the designed junction offset has better energy absorption characteristics. And the designed structure provides more options for the lightweight application of porous structures with high specific stiffness and high energy absorption characteristics and presents research basis and experimental data for the design of porous structures.