Body-centered Cubic Lattice Structures Research Articles

Impact of lattice structure on compressive performance and strength to weight ratio in continuous stereolithography

Lattice structures have emerged as a creative solution in additive manufacturing to achieve lightweight structures. Lattices offer the capability to reduce material usage, production costs, and weight while maintaining the structural integrity of a part. Due to its rise in popularity and excellent properties, lattice structures have been used in many applications, including but not limited to aerospace, bioengineering, and acoustics. This study aimed to explore the performance of different types of lattices on 3D additive manufactured parts by varying the type of unit cell. The three unit cells that were compared are body-centered cubic (BCC), face-centered cubic (FCC), and Fluorite. The lattice’s strength-to-weight ratio of different lattice unit cells when subjected to compression forces was evaluated. BCC and FCC have had considerable research while Fluorite has had far less research. This study aims to contribute new knowledge on the less studied Fluorite unit cell. The selected lattice structures were printed using continuous stereolithography (CSLA). This 3D printing process utilizes a photopolymerization reaction to solidify liquid resin layer by layer. Through this study, Fluorite demonstrated the highest strength-to-weight ratio among the three lattice structures examined, averaging 19,377 Nm/kg over five samples. Its potential for applications requiring high strength requirements is highlighted by this finding. Alternatively, BCC lattice structures had the weakest strength-to-weight ratio but exhibited remarkable structural resilience to deformation. The BCC lattice structures showed a more significant deformation before failure. Fluorite lattice structures are more suitable for high-strength applications, while BCC lattice structures can be used where high strength is not a primary parameter. This research aimed to determine the optimal lattice unit cell to implement in future choices in additive manufacturing applications.

Mechanical Properties and Energy Absorption Characteristics of Additively Manufactured Lattice Structures of a High‐Temperature Titanium Matrix Composite

Lightweight lattice structure is of great significance in the fields of aerospace thermal protection and energy absorption. In this study, compressive properties and energy‐absorbing characteristics of additively manufactured body‐centered cubic (BCC) lattice structures of a high‐temperature titanium matrix composite (TMC) are investigated systematically. It is found that compressive strength increases monotonically as either lattice strut diameter or temperature increases. With lattice strut diameter increasing from 1.0 to 1.5 and 2.0 mm, strength increases from 78 to 94 and 108 MPa at room temperature (RT) and from 71 to 104 and 123 MPa at 650 °C. Unexpectedly, specific energy absorption (SEA) capability increases as strut diameter decreases, although also increases as temperature increases. BCC lattice structure with a strut diameter of 1.0 mm presents the highest SEA being up to 13.7 MJ m−3 at RT and 142 MJ m−3 at 650 °C. And sphericizing the lattice nodes is found incapable of enhancing strength and SEA. Besides, numerical simulation is used to demonstrate the compressive stress and strain fields, in order to explain the fracture modes and SEA capability of individual BCC lattice structures. This study provides deep insights into the mechanical properties and energy absorption behavior of additively manufactured lattice structures of TMCs.

Design and mechanical performance analysis of T-BCC lattice structures

The Body-Centered Cubic (BCC) lattice structure is commonly used in high-end equipment fields, such as aerospace, due to its superior mechanical properties, lightweight characteristics, and ease of processing. However, there is a need to improve the performance-to-weight ratio of the traditional BCC lattice structure. This study utilizes topology optimization to design a T-BCC lattice structure based on the BCC unit cell, with the aim of maximizing stiffness. A model proposing the characterization of the Young's modulus of BCC lattice structures is presented. The model is based on calculations of cell porosity and beam stress analysis, assuming a large cell. This approach indirectly enables the calculation of the Young's modulus of T-BCC lattice arrays in multiple dimensions. Simulation and experimental comparison were used to analyze the compressive performance and load-bearing modes of T-BCC lattice structures, revealing the mechanisms of compressive deformation and failure modes. The accuracy of the characterization model for Young's modulus was found to be 93.1%. Compared to BCC lattice structures designed by traditional methods, T-BCC lattice structures designed via topology optimization can increase the Young's modulus by up to 36% and yield strength by 37.2%. This suggests that T-BCC lattice structures are a more lightweight and efficient solution for designing components in high-end equipment fields.

Shear deformation behavior of additively manufactured 316L stainless steel lattice structures

With the development of additive manufacturing, lattice structures have emerged as a disruptive technology across various fields, including aerospace, automotive, and defense. Lattice structures exhibit exceptional properties for lightweight and energy absorption capacities, especially under compressive loads. However, the lack of experimental data on complex loads, such as shear properties of lattice structures, poses challenges to their broader application across different load types. This study aims to analyze the shear deformation behavior of lattice structures and compare them with their compressive properties, enabling the safe design of lattice structures for various load applications. To achieve this, 316 L stainless steel lattice structures were fabricated using additive manufacturing in three different geometries: body-centered cubic (BCC), face-centered cubic (FCC), and octet truss (OCT), all at the same relative density. The lattice geometries were compared for their mechanical properties and deformation mechanisms under the two types of loading using DIC and FEM analyses, compression and shear tests. It was found that the mechanical properties of the lattice structures under compression and shear loads varied depending on the geometry, showing that each lattice geometry has a unique load-bearing capacity that exhibits superior mechanical properties. Furthermore, under shear loading, the struts of the BCC lattice structure showed a bending-dominated deformation mode due to the rotation of the nodes, whereas the struts of the FCC and OCT structures presented a compression and tension-dominated deformation mode. As a result, the BCC lattice specimens showed a higher shear energy absorption capacity than the other specimens and were capable of bearing higher loads. In addition, the FCC specimens showed lower shear energy absorption. The OCT specimens presented a uniform strain distribution under both compression and shear loading and showed compliant performance. The shear deformation behavior of various lattice structures has been evaluated by considering both geometrical and local strain distribution aspects. Implications for optimization guidelines and potential improvements were also discussed. These results can be used for research and development of the shear properties of lattice structures, the safe design of lattice structures, and industrial applications.

The extended scaling laws of the mechanical properties of additively manufactured body-centered cubic lattice structures under large compressive strains

Additively manufactured lattice structures are porous light-weight structures with mechanical properties that are dictated both from the topology and the parent material properties. When printed from metals, these structures can withstand large continuous plastic deformation. In this paper, we focus on body-centered cubic (BCC) lattice structures under compression up to large deformation strains, and we propose relations between the slenderness ratio of struts and the following mechanical properties: Young's modulus, yield strength, hardening rate of the structure and the densification strain. We perform a systematic study using finite element modelling (FEM) to find how both material properties and lattice structures are affecting the effective mechanical properties of BCC lattice structures under compression. Based on this analysis we propose the scaling laws of the mechanical properties. The scaling laws can be explained as an extension of the Gibson-Ashby power law relations for bend-dominated structures with non-slender beams. We also discuss how rounding the connections between the struts using fillets affects the scaling laws. We demonstrate the scaling laws in the analysis of experimental results, showing the accuracy and limitations of the scaling laws in predicting the mechanical properties, with an emphasis on large deformations. In the analysis, we use experimental values published in literature, and we also present here experimental results of lattice structures printed from Inconel 718.

Mechanical Properties of Selective Laser Melting‐Processed Multihierarchical Lattice Structure Based on Body‐Centered‐Cubic Unit Cell

Herein, three types of multihierarchical lattice structures (MHLSs) with different configurations are designed based on the body‐centered‐cubic (BCC) unit cell. The designed lattice structures are fabricated using Ti‐6Al‐4 V powder as feedstock material through selective laser melting (SLM) technology. The microstructure and surface morphology of the SLM‐formed samples are observed by optical microscopy and scanning electron microscopy, respectively. Theoretical calculation and quasistatic compression experiment are carried out to investigate their mechanical properties. The result shows that the size error of slave cell with small strut diameters is greater than that of master cell with larger strut diameters. All MHLSs exhibit superior mechanical properties compared to the BCC lattice structure. Moreover, the specific elastic modulus and specific yield strength of MHLSs with the best mechanical properties are 70.1% and 51.0% higher than that of BCC lattice structure, respectively. Meanwhile, theoretical calculation results of the elastic modulus and yield strength are consistent with the results of quasi‐static compression testing. The fracture morphology analysis indicates that the struts of the MHLSs samples exhibit a mixed brittle–plastic fracture mode, while the nodes exhibit a plastic fracture mode.

Biomimetic dual-phase ceramic lattice architectures with enhanced mechanical and vibration isolation performances

Ceramic materials have broad application prospects for impact/perforation protection purposes due to their high strength, high hardness, and other characteristics. Nevertheless, the high brittleness, susceptibility to fracture, and difficulty in processing and forming limit the popularization of ceramic components. This paper proposed a novel silica gel-filled dual-phase ceramic lattice meta-structure based on a biomimetic biphasic design method to achieve the improvement of mechanical properties. Two configurations of dual-phase body-centered cubic (BCC) and face-centered cubic (FCC) ceramic lattice structures were designed and fabricated through DLP-based additive manufacturing and simple filling technology. Quasi-static compression and dynamic vibration testing were conducted. Comparisons between single-phase and dual-phase ceramic lattices were performed from the perspective of compression strength, fracture toughness, and vibration level difference. It was demonstrated that the addition of soft silica gel reduced the stress concentration at the connection of the lattice rod and effectively inhibited the crack propagation. The dual-phase BCC lattice structure exhibited a 3 times increase in toughness and a 4.2 times increase in compressive strength relative to the single-phase design. The toughness and compressive strength of the dual-phase FCC ceramic lattice were increased by 1.4 times. The introduction of the soft silica gel achieved a significant vibration isolation in the pre-resonance frequency band between 1000 Hz to 3000 Hz. This study provides a reliable method for constructing biomimetic dual-phase meta-structures with both load-bearing capacity and low-frequency vibration isolation capacity.

Experimental study on the influence of abrasive flow machining on the surface quality and mechanical properties of BCC lattice structure manufactured by L-PBF

During the L-PBF process for preparing porous biomaterials, the "spheroidization effect" and the "stair-step effect" lead to defects such as pore clogging and rod diameter thickening in the actual components. These defects affect the part's dimensional accuracy, which in turn has the critical influence on the mechanical properties of the workpiece. Thus, suitable post treatment methods are required to improve the surface quality of porous biomaterials. This paper aims to investigate the effects of abrasive flow machining on the surface quality and mechanical properties of body-centered cubic (BCC) lattice-structured specimens molded by L-PBF at different pressures and abrasive concentrations and their mechanisms. Experimental results indicate that the number of powders adhering to the rod diameter of the member is significantly reduced after the abrasive grain flow process treatment. The roughness of the rod diameter surface is reduced from 17.48 μm to 6.82 μm, and the surface finishing is improved by 60.98%. The abrasive flow machining can effectively eliminate the "spheroidization effect" on the mechanical properties of the lattice structure. The maximum compressive strength of specimens subjected to abrasive flow machining have all been increased. Especially, with the abrasive flow machining under the pressure of 4 MPa and the abrasive grain concentration of 60%, the maximum compressive strength of the specimens was even been increased by 8.89%.

A partially hollow BCC lattice structure with capsule-shaped cavities for enhancing load-bearing and energy absorption properties

Lattice structures have gained larger design space and wider application in aerospace, automobile, civil and other engineering fields due to the advancements in additive manufacturing (AM) technology. Seeking the optimal lattice structure configuration for the purpose of enhancing mechanical performance holds paramount importance. The hollow lattice structure possesses high material utilization efficiency, but often suffers from premature failure at the node interconnections. In this paper we propose a partially hollow lattice structure (PHBCC) with solidified nodes and capsule-shaped cavities in the middle of truss components. Quasi-static compression tests were performed on the partially hollow body-centered cubic (BCC) lattices manufactured via selective laser melting technology (SLM). The effects of various geometric parameters were analyzed through finite element simulations. The findings demonstrate that the introduced PHBCC lattice exhibits enhanced mechanical properties. Specifically, there is an observed increase of 92%, 51.9%, and 22.8% in terms of specific stiffness, specific strength, and specific energy absorption, respectively, in comparison to the conventional BCC and hollow BCC (HBCC) structure. Notably, the proposed PHBCC lattice displays superior energy absorption capacity compared to a majority of existing lattice structures.

Effects of structure parameters on performances of laser powder bed fusion processed AlSi10Mg body-centered cubic lattices

The study aims to explore the impact of structural parameters on the formability, mechanical properties, and heat conductivity of body centered cubic (BCC) lattice structures produced through laser powder bed fusion (LPBF). The BCC lattice structures with varied cell diameters and cell sizes were fabricated using LPBF. Surface morphologies, compression properties, and numerical simulation of heat transfer were carried out. Results indicated that the relative density of the BCC structure was influenced by the diameter and size of the cell. An increase in the diameter or a decrease in the size of the cell led to an increase in the relative density of the BCC lattice structure. However, the surface forming quality decreased. On the other hand, the compressive strength of the structure increased, and the heat transfer property was also enhanced. The BCC lattice structure achieved its highest relative density and obtained a peak compressive strength of 320.66 MPa when the cell rod diameter was 1.5 mm and the cell size was 3 mm.

Eriyik Yığma Modelleme ile Üretilen PLA, ABS VE PETG Polimerlerinin Özellikleri Üzerinde Kafes Tasarımı ve Proses Parametrelerinin Etkisi

In this study, tensile strengths of different polymer-based materials PLA (Polylactic Acid), ABS (Acrylonitrile Butadiene Styrene), and PETG (Polyethylene Terephthalate Glycol) were investigated by applying BCC (Body-Centered Cubic), FCC (Face-Centered Cubic) and Gyroid lattice designs with FDM (Fused Deposition Modeling) method which one of the additive manufacturing methods. In addition, weight reduction was performed in the materials with the lattice designs applied. After the mechanical tests, it was determined that the lattice structure has an important role in tensile strengths. Especially in the gyroid lattice structure, which is one of the TPMS (Triply Periodic Minimal Surface) lattice types, it was determined that the maximum strength was obtained in PLA material. In terms of % deformation, the maximum elongation was obtained for PETG material in the gyroid lattice structure. In addition, weight reduction was aimed by using lattice structure patterns, and the maximum weight reduction was found in the BCC lattice structure.

An Analytical Method for Elastic Modulus of the Sandwich BCC Lattice Structure Based on Assumption of Linear Distribution.

An analytical method to predict the elastic modulus of the sandwich body-centered cubic (BCC) lattice structure is presented on the basis of the assumption of a linearly changing elastic modulus. In the constrained region, the maximum of elastic modulus used the elastic moduli of the BCC lattice element with plate constraints and is calculated with Timoshenko beam theory, the minimum used without plate constraints. In the rest of the constrained region, a linear function along the thickness direction is proposed to calculate elastic modulus. The elastic modulus of the unconstrained region is constant and it is the same as the minimum of the constrained region. The elastic modulus of the whole sandwich BCC lattice structure can be calculated theoretically with the elastic modulus of the constrained and unconstrained regions and a single-layer slice integration method. Six kinds of sandwich BCC lattice structures with different geometric parameters are designed and made by resin 3D printing technology, and the elastic moduli are measured. By comparing the predictions of the elastic modulus using the proposed analytical method and existing method with experimental results, the errors between the results of the existing method and the experimental results varied from 10.3% to 24.7%, and the errors between the results of the proposed method and the experimental results varied from 1.6% to 7.4%, proving that the proposed method is more accurate than the existing methods.

Mechanical performances of novel cosine function cell-based metallic lattice structures under quasi-static compressive loading

This study proposes a novel lattice structure named cosine function cell-based (CFCB) lattice, in which cell rods are designed in the shape of cosine function curve. Several quasi-static compression tests are conducted to explore their compression behaviors, and their advantages are explored by comparing with traditional body-centered cubic (BCC) lattice structure. Further, influences of several key parameters on mechanical performances are experimentally investigated for CFCB lattice structures. The experimental results indicate that CFCB lattice structures have distinct superiority in compressive stiffness and strength, and their energy absorption characteristics are more than twice as high as those of BCC lattice structure. Further, it is also found that their cell rod diameter and cosine function period length have larger influences on mechanical performances. Subsequently, association relationship between deformation modes and key parameters is numerically explored for CFCB lattice structures, and a distribution map is plotted for their deformation modes. The numerical results indicate that cell rod diameter is positively associated with their energy absorption characteristics, and negatively correlated with their densification strain. Besides, it is also found that the performance indicators exhibit a reducing trend firstly but increase with further raising period length on the whole. With increasing relative density, their energy absorption characteristics and plateau stress show a general upward trend, while a general downward trend is observed in their densification strain. Finally, based on collapse mechanisms of the typical unit cell, theoretical models are deduced to predict equivalent elastic modulus, Poisson’s ratio and plateau stress for the proposed CFCB lattice structures.

Specific Sensitivity Analysis and Imitative Full Stress Method for Optimal BCCZ Lattice Structure by Additive Manufacturing

Additive manufacturing (AM) can quickly and easily obtain lattice structures with light weight and excellent mechanical properties. Body-centered cubic (BCC) lattice structure is a basic type of lattice structure. BCC with Z strut (BCCZ) lattice structure is a derivative structure of BCC lattice structure, and it has good adaptability to AM. Generally, the thickness of each pillar in the BCCZ lattice structure is uniform, which results in the uneven stress distribution of each pillar. This makes the potential of light weight and high strength of the BCCZ lattice structure not fully played, and the utilization rate of materials can be further improved. This paper designs an optimization method. Through the structural analysis of a BCCZ lattice structure, an optimization method of a BCCZ lattice structure based on parametric modeling parameters is presented. The section radius of all pillars in the BCCZ lattice is taken as a design variable, and the specific sensitivity analysis method and simulated full stress optimization idea are successively used to determine the optimal section radius of each pillar. Finally, the corresponding model is designed and samples are manufactured by LPBF technology for simulation and experimental verification. The results of simulation and experiment show that the strength limit of the optimized parts increased by 18.77% and 18.43%, respectively, compared with that before optimization.

Compressive mechanical properties of layer hybrid lattice structures fabricated by laser powder bed fusion technique

A layered hybrid lattice structure consisting of a body-centered cubic (BCC) structure and an N-type structure with a negative Poisson's ratio effect is designed. In order to assess the effect of the position and number of N-type structure layers in the overall lattice structure on the mechanical properties, three kinds of hybrid lattice structures with different positions and numbers of N-structure layers are manufactured by using laser powder bed fusion (LPBF) technique. Compression experiments are carried out on the three kinds of layered hybrid lattice structures and the BCC lattice structure for comparisons. The entire loading process is recorded and the deformation pattern of the lattice structure is captured. The experimental results show that the presence of the N-type structure has a significant effect on the deformation pattern of the lattice structure. Comparing the mechanical response and energy absorption efficiency, it is found that the hybrid lattice structure performs better than the BCC structure when the structural strain is small. In addition, finite element models of the N-type structure unit-cell and hybrid lattice structures are established. Numerical simulations are conducted to verify the negative Poisson's ratio behavior of the N-structure and predict the deformation modes of the layered hybrid lattice structure.

HIGH COMPRESSIVE STRENGTH 3D PRINTED INFILL BASED ON STRUT-BASED LATTICE STRUCTURE

In an attempt to make Additive Manufacturing more material-efficient, researchers come across the idea of re-enforcing 3D printed objects by infill pattern modification. In line with this concept, this paper introduces a new innovative infill pattern inspired by a variety of strut-base lattice structures that is stronger and more material-efficient than conventional 3D printing infill. This research provides the design, analysis, and experimental results of the developed 3D printed infills, then compared with a benchmark infill. Three (3) strut-based lattice test samples, namely Body-Centered Cubic (BCC), Face-Centered Cubic (FCC), and Octet-Truss, were designed and 3D printed with an equal amount of material used, then undergo compressive test on Universal Testing Machine. Results showed that BCC, FCC, and Octet-truss infill pattern print has a compressive strength of 11.25 MPa, 8.47 MPa, 7.44 MPa consecutively, while benchmark infill has 9.73 MPa. This data proves that with the same amount of material consumed, the BCC lattice structure infill withstands a compressive load higher than the benchmark infill, which is offered in a 3D printing slicer.

A Novel Lattice Structure for Enhanced Crush Energy Absorption

the energy absorption capacity of a few common lattice structures printed out of PLA using fused deposition modeling and proposes an improved lattice structure. Simple cubic (SC), honeycomb (HC), body-centered cubic (BCC), and novel PeckGy80 (PG80) lattice structures were subjected to compressive tests. The quasi-static load-displacement behavior of lattice specimens was characterized in terms of specific energy absorption and crush load efficiency. The damage mechanisms were then related to energy absorption. Cracks and brittle fractures occurred in all lattice structures during the crush test. Different lattice structures induced different damage mechanisms, significantly affecting their energy absorption. SC lattice structure showed structural separation at a small displacement, rendering it an ineffective energy absorber. BCC and HC lattice structures demonstrated almost identical shear band failure modes. The PG80 lattice structure, although made of brittle PLA, displayed progressive failure from the bottom layer to the upper layers, exhibiting both a high peak load and stable post-yield behaviour. This damage mode enabled the PG80 lattice to be far superior in terms of specific energy absorption to HC, SC, and BCC lattice structures.

Abnormal hardening and amorphization in an FCC high entropy alloy under extreme uniaxial tension

Ever more extreme environments in advancing industrial applications motivate efforts to design new generation of alloys with excellent mechanical properties. High entropy alloys (HEAs) are considered as promising candidates for bearing extreme loadings. However, the reported results of correspondence between extremely mechanical behaviors and micromechanisms are still in infancy. Here we showed mechanical responses over wide strain rate and temperature ranges and microscopic observations recovered from dynamic uniaxial tension of face-centered cubic (FCC) HEA to reveal plasticity mechanisms transition under various loading conditions. In particular, with an increasing strain during the extreme dynamic tension a sequence of mechanisms, including twinning, detwinning-induced localization, nanoscale body-centered cubic (BCC) phase transformation and symbiotic amorphization, were progressively activated for continued plasticity. At strains over 35%, twin boundaries hindrance to localized band propagation and more dislocations emitting from BCC phases even collectively caused a second sharp rise in hardening. Additionally, the plasticity kept increasing during crystal to amorphization transition, which should be promoted by severe lattice distortion in super-dense dislocations areas. By combining large scale molecular dynamic simulations, the causes of phase transition to BCC lattice structure or even to amorphous bands were explained in depth. The thorough uncovering of these brand-new mechanisms can help understand the plasticity and amorphization of HEAs under the extreme loadings.

Design, mechanical properties and optimization of lattice structures with hollow prismatic struts

Lattice structures with hollow struts exhibit superior mechanical properties as compared to solid ones. In this study, we introduce a new type of body-centered cubic (BCC) lattice, consisting of hollow prismatic struts with mechanical properties defined by an inner hollow parameter. The mechanical properties and deformation behavior of the BCC lattice structures with different inner hollow parameters are investigated under periodic boundary conditions. It is shown that the elastic modulus of the hollow-strut BCC lattice structure improves significantly by 598%-1460% and their deformation mechanism gradually changes from bending-dominated to stretching-dominated, when the inner hollow size increases. In contrast, there are little influences on shear deformation. Interestingly, tunable Poisson's ratio and isotropic elasticity can be achieved by adjusting the inner hollow size. In addition, the BCC lattice structures with different inner hollow parameters are fabricated by digital light processing for compression tests, and the experimental results are in good agreement with the simulation with relative errors of less than 14.6%. Finally, a high-fidelity interpolation model is employed to describe the effective elastic matrix of lattice structures, and a new optimization framework is proposed to simultaneously optimize the distribution of the volume fraction and inner hollow size of hollow-strut lattice structures. This proposed approach significantly improves the stiffness (compliance decreased by 15.8% to 53.1%) of the cantilever beam as compared to traditional optimal designs, demonstrating the potential application of the proposed approach in lightweight designs.

Spatial Array Configuration Effect of Body‐Centered Cubic Lattice Structures with Finite Unit Cells

The mechanical properties lattice structures have been studied a lot due to the simple geometry. They all follow the assumption that the mechanical properties of lattice structures are identical with the corresponding unit cell. However, our experimental results show obvious boundary effect. In this paper, the spatial array configuration effect (n x , n y , n z ) of body centered cubic (BCC) lattice structures is pronounced to declare the difference. The multilayer BCC lattice structures are divided into three types which show three different deformation mechanism, and their equivalent stiffness will not converge on a unique solution. Then, the “large unit cell” assumption is proposed to theoretically predict the equivalent modulus with different array configuration. Furthermore, the failure modes of the three types are also discussed. The finding results show that the spatial array configuration also plays an important role in determining both the equivalent modulus and the failure modes for the multilayer BCC lattice structures. In addition, we conclude that the name “lattice structure” is more suitable for the current manufacturing level than the “lattice material.”