Bcc Lattice Structures Research Articles

Study on rotary bending fatigue performance of TC4 lattice structure fabricated by selective laser melting

Prediction of the fatigue performance of lattice structures in additive manufacturing still lacks widely applicable methods. To address this issue, we investigated the effect of a BCC lattice structure combined with thin walls and ribs on the fatigue performance of TC4 alloy samples. The lattice-structured samples were fabricated by selective laser melting. In addition, we proposed a prediction model of fatigue performance that combined ABAQUS finite element analysis with FE-safe fatigue analysis. The simulation and experimental results verified the reliability of the model. Based on this method, the effects of lattice and ribbed plate structures on the bending fatigue performance were investigated. The experimental results showed that the stress concentration generated by lattice structures weakened the fatigue performance. On the contrary, ribbed plates can enhance fatigue performance, which also depends on the orientation of the rib structure. The simulation results showed that increasing the volume fraction of unit cells can mitigate the stress concentration, leading to improved fatigue performance. The lattice structure combined with the rib structure exhibited superior fatigue performance. In addition, the proposed models can also be applied to other metallic materials. The findings in this study can provide a theoretical basis for the design of lattice structures with better fatigue performance.

Improvement of manufacturing accuracy of graded Ti-6Al-4V BCC lattice structures by local laser power adaption

Additive Manufacturing by laser powder bed fusion (PBF-LB/M) enables the manufacturing of metallic implants with graded lattice structures, adapting the porosity and stiffness of the implant with cortical and trabecular bone for improved osseointegration. One drawback is the manufacturing accuracy of graded lattice structures due to deviating process strategies. Minimal structures with diameters < 150 µm require low energy input to avoid overmelting. Conversely, larger structures (> 200 µm) are then prone to insufficient melting and require higher energy input. This prevents a combination into one graded structure using standard strategies, which can result in deviations of up to 50%. Investigations show that adjusting the energy input at down-skin surfaces enables a more precise manufacturing for graded BCC lattice structures (ranging from 100 – 300 µm) without severe compromise for one size region. Furthermore, this approach also reduces the deviation for specific structure sizes to less than 2%.

Equivalent Elastic-Plastic Model of BCC Lattice Structures

Equivalent Elastic-Plastic Model of BCC Lattice Structures

Novel optimal design-making model of additive manufactured lattice structures based on mechanical physical model

Biostructure-inspired design methods play an important role in improving the mechanical properties of lattice structures with the same volume fraction. However, the current biostructure-inspired design methods mostly stay in the imitation of physical form/structure, and the natural evolution mechanism of biological structure is not clear in the optimization strategy of lattice structure. Combined with the fact that the zero-value average curvature of the minimal surface follows the Principle of Least Action (PLA), a new mechanical design strategy is proposed in this paper. Firstly, the mechanical model of BCC is solved. Furthermore, the physical model descripting the mechanical properties of lattice structures is solved equivalently, which shows that the regulation of mechanical properties of lattice structures can be more intuitively understood as the extreme motion for the pellet under various influencing factors. Moreover, the new design strategy for the mechanical properties of lattice structures is solved based on PLA. Finally, serials of BCC lattice structures are gained through node radius optimization. Then, the curvature characteristics and mechanical properties of optimized BCC structure are explored by means of simulation and experiment. The results show that the proposed design strategy has obvious effect in improving mechanical properties and provides a theoretical basis and technical route for the development of multiphysics applications of lattice structures.

Compressive Behavior of Various BCC Lattice Structure

The lattice structures are a particular type of structures made by the multiply of a unit cell. In addition, their structure is close to some physiological tissues and bone structure, which can allow their use to develop prostheses needed to the rehabilitation or replacement of a body part. Lattice structures are widely used in various engineering applications due to their high weight-to-strength ratio and exceptional energy absorbing performance. The feasibility of using different base materials to fabricate these cellular structures with complex geometries has been significantly widen with the development of additive manufacturing (AM) technology. Additive manufacturing in particular metal selective laser melting (SLM) processes are rapidly being industrialized. In this work, samples with different lattice structures were manufactured by SLM technique using CoCr powder alloy. Compression tests were carried out to characterize their mechanical behavior. Starting from a BCC lattice cell measuring 5x5x5mm and 1mm diameter of the strut, were designed using Catia V5 R19 software. The BCC lattice unit cell consists of 4 solid struts with circular cross-section by which they intersected at 45°angle and modify by adding radius at the intersection of all four struts, furthermore the empty space is filled with BCC cell to increase the stiffens of the structure. The BCC cell was duplicate in three directions (X, Y, Z) measuring 20mm in each direction. To obtain the final part the BCC structure ware intersected with a cylindrical part measuring 20mm in Z direction, 15mm diameter and 1mm wall thickness, resulting a cylindrical part with three different BCC lattice structure inside.

Performance prediction of different BCC lattice structures under static loading: an experimental approach

Performance prediction of different BCC lattice structures under static loading: an experimental approach

Experimental Comparison of the Energy Absorption Performance of Traditional Lattice and Novel Lattice Filled Tubes

In this study, β-Ti3Au lattice structure was proposed for the first time in the literature as a filling material to increase the energy absorption performance of thin-walled tubes. In this context, the energy absorption performances of conventional lattice structure (i.e., BCC and FCC) filled thin-walled tubes and proposed novel β-Ti3Au lattice structure filled thin-walled tubes with proposed were compared experimentally. BCC hybrid, FCC hybrid and β-Ti3Au hybrid structures produced by additive manufacturing technology using PA2200 powder were crushed and evaluated by considering various crashworthiness criteria such as EA and SEA. The results showed that the β-Ti3Au hybrid structures are better crashworthiness performance than that of traditional filling BCC and FCC lattice structure filled thin-walled tubes. In particular, the β-Ti3Au hybrid structure has 18.17% and 19.39% higher EA values than BCC hybrid and FCC hybrid, respectively. These values are 16.50% and 15.66% for SEA values, respectively. As a result, the current investigation showed that the suggested β-Ti3Au lattice structures as a filler material can be a significant alternative for applications where energy absorption performance is critical.

Modified beam modeling of powder bed fusion manufactured lattice structures

In this work a modified beam approach to model the compressive behavior of additively manufactured BCC and reinforced BCC lattice structures is proposed. Three-dimensional beam models are of interest because of their reduced computational time, with respect to numerical models that involves solid mesh elements, but they are not able to capture the behavior of lattice structures in proximity of the unit cell nodes, that presents higher stiffness due to the struts intersection and consequent material overlapping. In order to overcome this drawback when using beam finite elements, a modified beam approach is used in this work considering each lattice cell strut subdivided in a central flexible portion and two rigid extremities. A numerical procedure is implemented to tune the rigid extremities length of the strut by means of numerical simulations that aims to reproduce accurately the compressive behavior of the lattice cell solid model. The experimental campaign conducted on different powder bed fusion manufactured lattice structures is presented and experimental results are provided along with a numerical-experimental correlation that proves the accuracy of the method.

Experimental and FEM investigation of BCC lattice structure under compression test by using continuum damage mechanics with micro-defect closure effect

The failure of the cellular structures and the prediction of their limit load and type of failure are essential in their design and applications. The isotropic Continuum Damage Mechanics (CDM) model of Lemaitre with micro-defect closure effect was considered to simulate the mechanical response of the BCC lattice structure under a compression test. Defects caused during the manufacturing process is considered an initial damage. The simulation results of the compression tests on the 316L Stainless Steel (SS) lattice structures, which were manufactured by the Selective Laser Melting method (SLM), and the experimental results have been compared. The same study was conducted on the AlSi10Mg manufactured lattice structures. FE simulation showed that the CDM model can predict the elastic modulus and yield strength of the lattice structure with good accuracy. The stress–strain curve of the lattice structure, obtained from the FE simulation, agrees well with the experimental results before the condensation. According to the conducted experiments, the failure mechanism for the considered cases is bending dominated with high plastic deformation at the connection area of nodes and struts. The present model predicts the state of damage of the structure with good accuracy and it is in agreement with the experimental results.

Evaluation of mechanical properties of Ti–6Al–4V BCC lattice structure with different density gradient variations prepared by L-PBF

Based on the optimized pore size distribution and relative density, the functionally graded lattice structure is capable of achieving better mechanical properties than a uniform lattice structure with similar porosity. In this study, in order to investigate the effect of the strategy of density gradient variation on the lattice structure with similar porosity, three different density gradients were designed for the BCC-based lattice structure in parallel and perpendicular to the loading direction based on Ti–6Al–4V alloy powder and laser beam powder bed fusion technology, respectively. The results showed that the elastic modulus, yield strength and compressive strength of the lattice structure with a density varying as a logarithmic function perpendicular to the loading direction were 39.91%, 51.85% and 51.72% higher than the uniform lattice structure respectively. Moreover, the layer-by-layer collapse phenomenon was the primary aspect impacting the energy absorption in the lattice structures with density gradient parallel to the loading direction. By observing the fracture morphology of the lattice structures, it was found that all specimens exhibited dimple and smooth plane morphological features for a mixed failure mechanism of cleavage and dimple rupture, indicating that the failure mode of the lattice structures are a combination of brittle and ductile deformation. Therefore, a reasonable density gradient design can significantly improve the mechanical properties of the lattice structure with similar porosity. This work provides valuable inspiration for the design of lattice structures in engineering applications.

Multi-objective crashworthiness optimization of square aluminum tubes with functionally graded BCC lattice structure filler

The objective of this study is to find the optimum design configurations for the crashworthiness of functionally graded lattice structure filled aluminum tubes under multiple impact loading conditions. Base strut diameter, draft angle and aspect ratio are considered as filler material design parameters, and the optimal design configurations are sought for maximizing the specific energy absorption and minimizing the peak crush force. The finite element simulations are performed to establish the sample design space; linear and non-linear least square regression meta-models are developed to estimate the objective function values; the weighted superposition attraction-repulsion algorithm is employed to create design alternatives and seek their optimum combinations. The compromise programming technique is also adapted for combining multiple objectives and generating different optimum design options. The results revealed that the proper selection of design parameters can effectively enhance the crashworthiness performance of hybrid structures under multiple impact loading conditions. In particular, the results showed that the specific energy absorption value of square tubes can be improved up to 76% with the selection of appropriate lattice filler parameters. The present study provides a guideline for the optimum design of functionally graded lattice structure filled thin-walled structures under multiple impact loading conditions.

Geometry effect on mechanical properties and elastic isotropy optimization of bamboo-inspired lattice structures

Inspired by the geometry of bamboo, this study proposes a novel bamboo-inspired body-centered cubic (B-BCC) lattice structure consisting of tapered and hollow struts. Using representative volume elements applied with periodic boundary conditions, the mechanical properties and deformation behaviors of the B-BCC lattice structures are thoroughly evaluated by considering a large number of combinations of geometric parameters and volume fractions. Results reveal that the geometric parameters highly influence the deformation behavior of the B-BCC lattice structures under uniaxial compression (e.g, from bending- to stretching-dominated) but little under shear load. For this reason, tunable elastic modulus across a broad range can be realized via adjusting the geometric parameters and elastic isotropy can be obtained across all volume fractions. On this basis, a combination of artificial neural network and elastic isotropy optimization is proposed to obtain the isotropic B-BCC lattice structures with superior elastic modulus. The optimization results show that the elastic modulus of the isotropic B-BCC lattice structures increased by 271.24–1335 % and 17.72–43.63 %, as compared to the original BCC and isotropic hollow BCC lattice structures, respectively. Finally, the multi-layer simulation and compression experiments are applied to validate the optimization results. Good agreements are observed comparing the numerical and experimental results, demonstrating the effectiveness of the proposed bamboo-inspired design and optimization method for lightweight applications with desired properties.

Influence of Density Gradient on the Compression of Functionally Graded BCC Lattice Structure.

In this paper, five grading functional gradient lattice structures with a different density perpendicular to the loading direction were proposed, and the surface morphology, deformation behavior, and compression properties of the functional gradient lattice structures prepared by selective laser melting (SLM) with Ti-6Al-4V as the building material were investigated. The results show that the characteristics of the laser energy distribution of the SLM molding process make the spherical metal powder adhere to the surface of the lattice structure struts, resulting in the actual relative density of the lattice structure being higher than the designed theoretical relative density, but the maximum error does not exceed 3.33%. With the same relative density, all lattice structures with density gradients perpendicular to the loading direction have better mechanical properties than the uniform lattice structure, in particular, the elastic modulus of LF, the yield strength of LINEAR, and the first maximum compression strength of INDEX are 28.99%, 16.77%, and 14.46% higher than that of the UNIFORM. In addition, the energy absorption per unit volume of the INDEX and LINEAR is 38.38% and 48.29% higher, respectively, than that of the UNIFORM. Fracture morphology analysis shows that the fracture morphology of these lattice structures shows dimples and smooth planes, indicating that the lattice structure exhibits a mixed brittle and ductile failure mechanism under compressive loading. Finite element analysis results show that when the loading direction is perpendicular to the density gradient-forming direction, the higher density part of the lattice structure is the main bearing part, and the greater the density difference between the two ends of the lattice structure, the greater the elastic modulus.

Elastic axial stiffness properties of lattice structures: Analytical approach and experimental validation for bcc and f2cc,z unit cells

Additive manufacturing (AM) is a key technology for the individualized and resource-efficient production of structural components. Recent developments in manufacturing technologies enable improved quality of additively manufactured components and therefore they become more and more important in lightweight constructions. An example is the substitution of solid material by porous lattice structures. Those embedded lattice structures lead to highly weight-efficient structures. Most recent investigations focus on numerical and experimental studies to describe the mechanical behavior of lattice structures. In this paper, a method to determine analytical expressions for the axial stiffness properties of lattice structures is presented. The displacement method and direct stiffness method are used to derive symbolic parameter-dependent formulas for the axial stiffnesses and effective Young’s moduli for f2cc,z, and bcc unit cells. Furthermore, an empirical approach based on Finite Element simulations is presented to describe the stiffness reduction for non-embedded or rather free lattice structures. The results are further validated by physical experiments. Stereolithography is used for specimen production. f2cc,z, and bcc lattice structures are embedded in thin-walled rectangular aluminum tubes and tested under compression load. Furthermore, lattices without a surrounding tube are tested. The analytical and empirical solutions are in good agreement with the experimental and numerical results.

Developing scaling laws to predict compressive mechanical properties and determine geometrical parameters of modified BCC lattice structures

AbstractThe objective of this study is to develop generalized empirical closed‐form equations to predict the compressive mechanical properties and determine geometrical parameters. To achieve that, 117 models are built and analyzed using ABAQUS/CAE 2016 to provide two types of reliable data: one for lattice mechanical properties based on finite element method and the other for geometrical parameters using the measurements of ABAQUS diagnostic tool. All the models are created by modifying the basic feature of body‐centered cubic lattice structure based on a range of strut angles, a set of relative densities, and two design sets. Also, the influence of lattice cell tessellations and material distribution at strut intersections are considered within these models to provide accurate results. The first data set is fitted with the scaling laws, relating relative elastic modulus and stress with the relative density, to determine Gibson and Ashby's coefficients. The second type of data regarding lattice geometries is correlated with the relative density to estimate actual lattice volume, strut radius, aspect ratio, and overall lattice volume. By this way, these equations can be used to predict directly the lattice characteristics and geometrical parameters without the need for ABAQUS. The results show that the generalized empirical closed‐form equations can predict well both the lattice characteristics and geometries. In addition, the relative stresses and elastic modulus increase with increasing the strut angles since the main deformation mechanisms move toward stretch‐dominated rather than bending. Besides, Gibson and Ashby's coefficients along with the geometrical factors of aspect ratios are found to be approximately similar for both generations. This study contributes to developing efficient equations to provide the researchers with a preliminary insight about the best lattice design and its compatibility in a certain application before starting the fabrication process.

Topological and Mechanical Properties of Different Lattice Structures Based on Additive Manufacturing.

The appearance and development of additive manufacturing technology promotes the production and manufacture of parts with more complex designs and smaller sizes and realizes the complex topology that cannot be made by equal-material manufacturing and submanufacturing. Nowadays, the application of tri-periodic minimal surface (TPMS) in topology optimization design has become a new choice, and, because of its excellent structure and properties, has gradually become mainstream. In this paper, the mechanical properties of four different topologies prepared by selective laser melting (SLM) using 316L stainless steel powder were investigated, including two TPMS sheet structures (Primitive surface, Gyroid surface) and two common lattice structures (Bcc lattice, truss lattice). The mechanical properties (Young’s modulus, yield stress, plateau stress, and toughness) were compared by numerical simulation and compression experiment. It can be concluded from the results that the mechanical properties and deformation mechanism of the specimen are mainly related to the type of lattice, though have little relationship with unit thickness at the same relative density. The Gyroid curved structure showed the best mechanical properties and energy absorption capacity, followed by the truss lattice structure. By comparison, the mechanical properties of the traditional Bcc lattice structure and the Primitive surface structure are poor, and the deformation mechanism of these two structures is uncertain and difficult to control.

Compressive properties and energy absorption of BCC lattice structures with bio-inspired gradient design

Compressive properties and energy absorption of BCC lattice structures with bio-inspired gradient design

Lattice structure design parameters optimization for the structural integrity of passive vibration isolator

Passive vibration isolator with lower natural frequency has always been a challenge due to structural integrity issues. This study presents the use of RSM statistical tool to analyze and optimize the mechan-ical responses of BCC lattice structure for structural integrity in a passive vibration isolator application. The optimization was done to obtain low stiffness for low natural frequency but high yield stress for optimum load-bearing capability with unit cell size and strut diameter design parameters tweak. From the results, the significance and contribution of each design parameter on each mechanical response through compression test can be understood. Results indicated changes in strut diameter produced lin-ear growth while changes in the unit cell size produced inverse exponential responses. From optimiza-tion, a combination of 3.9 mm strut diameter with 10 mm unit cell size produced the optimum result. Therefore, it was demonstrated that RSM can provide statistical importance and contribution between input factors and their influence on each mechanical response with minimal test and cost.

Atomic Simulations for Packing Changes of Nano-Sized Cu Clusters Embedded in the Febulk on Heating

Understanding of the defect evolution mechanism under irradiation is very important for the research of pressure vessel steel embrittlement. In this paper, the embedded atom method (EAM) based canonical ensemble molecular dynamics (MD) method was used to study the evolution of the stacking structure of different nano-sized Cun (n = 13, 43 and 87) clusters in an Febulk embedded with BCC lattice structure during continuous heating. The mean square displacement, pair distribution functions and atomic structures of Cu atom clusters at the nanometer scale were calculated at different temperatures. The structural changes present apparent differences, for the Febulks contain nano-sized Cu clusters with different atom numbers during heating. For the Febulk–Cu13 system, since the ability to accommodate the atomic Cu in the Fe substrate is lesser, a small number of Cu atoms in BCC lattice positions cannot influence the whole structure of the Fe-Cu system. For the Febulk–Cu43 system, with an increase in temperature, a Cu atomic pile structural change happened, and the strain areas decreased significantly in the Febulk, but a single strain area grew large. For the Febulk–Cu87 system, when the Cu atoms are constrained by the Fe atoms in bulk, only a few of the Cu atoms adjust their positions. With the increase in temperature, strain in the Fe eased.

Theoretical Predictions of the Structural and Mechanical Properties of Tungsten-Rare Earth Element Alloys.

Tungsten (W) is considered as the potential plasma facing material of the divertor and the first wall material in fusion. To further improve the ductility of W, the structural and mechanical properties of W–M (M = rare earth element Y, La, Ce and Lu) alloys are systematically investigated by first-principles calculations. Our results reveal that all the W1−xMx (x = 0.0625, 0.125, 0.1875, 0.25) alloys can form binary solid solution at the atomic level, and the alloys keep bcc lattice structures until the concentration of M increases to a certain value. Although the moduli of the alloys are reduced compared to that of pure W metal, the characteristic B/G ratio and Poisson’s ratio significantly increase, implying all the four rare earth elements can efficiently improve the ductility of W metal. Considering both factors of mechanical strength and ductility, La and Ce are better alloying elements than Y and Lu.