Lattice structure performance characterization and optimization design method based on laser powder bed melting

Abstract

The invention relates to a lattice structure performance characterization and optimization design method based on laser powder bed melting, and belongs to the technical field of additive manufacturing and structural design. The method aims at improving the mechanical property of a traditional BCC lattice structure under complex loads. The equivalent Young modulus of the lattice structure can be effectively represented by providing a lattice performance characterization method based on large unit cell hypothesis and establishing an analytic relationship between the equivalent Young modulus and the relative density of the lattice. In addition, topological optimization design of the BCC dot matrix is carried out by adopting an SIMP method, and redundant struts are removed and the structural shape is optimized by taking maximization of the equivalent Young modulus of the dot matrix as an optimization target. Finally, compared with a traditional BCC dot matrix, the T-BCC dot matrix structure manufactured through the LPBF process shows higher rigidity and strength. According to the optimization design method, the compression resistance of the lattice structure can be improved on the premise that the light weight of the lattice structure is kept, and the method has wide application prospects in the field of high-end equipment such as aerospace and automobiles.

Description

Technical Field

[0001] This invention relates to a method for characterizing and optimizing the performance of lattice structures based on laser powder bed melting, belonging to the field of additive manufacturing and structural design technology. Background Technology

[0002] Lattice structures are widely used in high-end equipment fields such as aerospace and automotive due to their excellent mechanical properties, lightweight characteristics, and ease of fabrication. Traditional BCC (body-centered cubic) lattice structures possess good compressive strength; however, under complex service conditions, stress concentration and nodal fatigue cracking lead to a decrease in their mechanical properties and stability. Therefore, how to efficiently design and characterize the mechanical properties of these structures is a pressing technical challenge. Summary of the Invention

[0003] This invention aims to provide a performance characterization and optimization design method for lattice structures based on laser powder bed melting (LPBF) to address the problems of stress concentration and insufficient compressive strength in traditional BCC lattice structures under complex conditions. A performance characterization method for T-BCC (topology-optimized body-centered cubic) lattice structures based on the large unit cell assumption is proposed, quantitatively describing the core parameter of the lattice structure—Young's modulus. Based on this, an optimization design method for BCC lattices based on SIMP (Solid Isotropic Material Penalty Model) is proposed. This method aims to improve the equivalent Young's modulus of the lattice by removing redundant beam structures and optimizing the unit beams of the lattice using the intrinsic SIMP method for solid isotropic materials, resulting in an optimized T-BCC lattice structure.

[0004] The method for performance characterization and optimization design of lattice structures based on LPBF in this invention includes the following steps:

[0005] 1. A method for characterizing the equivalent Young's modulus of a truss lattice structure based on the large unit cell assumption is proposed, wherein the truss lattice structure includes at least a BCC lattice and a T-BCC lattice obtained based on BCC lattice topology optimization. The method includes:

[0006] T1. During the elastic working phase, the multi-layer lattice structure is equivalent to an isotropic homogeneous body. A representative volume unit containing several layers of periodic unit cells is selected as the large unit cell. The node region and support geometry are explicitly modeled in the large unit cell, and the relative density ρ* of the lattice is calculated based on the support radius, support length and unit cell side length.

[0007] T2. At the large unit cell level, based on the Euler-Bernoulli beam theory, the compression and bending modes of the representative support under uniaxial compressive load are mechanically analyzed, and the deflection, axial displacement and internal force distribution of the support are derived to obtain the axial equivalent stiffness of a single support.

[0008] T3. Decompose the large unit cell into several basic substructures, superimpose the axial compression deformation and bending deformation of each basic substructure, construct the overall force-displacement relationship of the large unit cell in the loading direction, and apply periodic boundary conditions to the two opposite end faces of the large unit cell to simulate the actual constraints of the multilayer lattice, and obtain the equivalent modulus of the large unit cell.

[0009] T4. Based on the equivalent modulus of large unit cell and the macroscopic stress-strain relationship of lattice, establish the analytical characterization relationship between the equivalent Young's modulus E* of lattice, the Young's modulus E of the parent material, and the relative density ρ* of lattice. Express the relationship between E* / E and ρ* in the form of a power function, and determine the power function coefficients through data fitting.

[0010] T5. For BCC lattices and T-BCC lattices formed by laser powder bed melting process, rectangular cross-section compression specimens are prepared according to ISO 13314 standard for compression testing of porous metallic materials. Stress-strain curves are obtained by uniaxial compression test. The equivalent Young's modulus is extracted by stress-strain slope in the elastic segment. The power function analytical characterization relationship is experimentally calibrated and its accuracy is verified.

[0011] According to the present invention, as a further preferred embodiment, the proposed equivalent Young's modulus characterization method wherein the large unit cell is composed of n periodically stacked along the x, y, and z directions. x ×n y ×n z It consists of n lattice units, where n x n y n z All values ​​are greater than or equal to 3, to explicitly introduce the boundary constraint effect caused by multi-level stacking; and by changing n x n y n z By taking the value of , we can obtain the influence relationship between the number of multilayer stacks and the decay law of the equivalent Young's modulus of the lattice.

[0012] According to the present invention, as a further preferred embodiment, the proposed equivalent Young's modulus characterization method wherein the analytical characterization relation in the form of the power function is: C and t are constants determined by the structural parameters and experimental data through least squares fitting, and different parameter combinations are given for BCC lattice and T-BCC lattice respectively, so as to uniformly characterize the equivalent Young's modulus of different lattice configurations under the same large unit cell theoretical framework.

[0013] According to the present invention, as a further preferred embodiment, the proposed equivalent Young's modulus characterization method wherein the uniaxial compression test uses Ti-6Al-4V alloy as the base material, the cross-section of the sample is rectangular, the side length of the cross-section is more than 10 times the average pore diameter of the lattice and greater than 10 mm, the ratio of the sample height to the side length is in the range of 1 to 2, and the loading rate is 1 mm / min, so as to ensure that stable elastic stage stress-strain data are obtained for calibration and verification of the analytical characterization relationship.

[0014] 2. A topology optimization design method for T-BCC lattice structures with equivalent Young's modulus as the optimization objective is proposed, which includes the following steps:

[0015] S1. Taking the struts in the BCC lattice unit cell as the topology optimization design object, establish a three-dimensional continuous design domain containing the entire length of the struts, set the end faces of the struts connected to the nodes as constraint surfaces, and apply boundary conditions corresponding to the macroscopic compression condition of the target lattice.

[0016] S2. A topology optimization mathematical model is constructed using the SIMP method. The design domain is discretized into finite element elements, with the element pseudo-density ρi as the topology optimization design variable, and the equivalent Young's modulus E of the i-th element is used as the topology optimization design variable. i Correlate with the Young's modulus E of the parent material through power interpolation. Under constraints of volume fraction, element density upper and lower limits, stress, empty element, and static equilibrium, the design objective of maximizing the equivalent Young's modulus is characterized by the objective function of minimizing the support rod compliance. The calculation formula is as follows:

[0017] Where F is the objective function, Compli is the overall compliance of the beam structure; μ i For variables; f i For volume force; t i Γ represents the boundary area force; Ω represents the computational domain, indicating the spatial region where optimization is performed; Γ represents the boundary of the spatial region where optimization is performed.

[0018] The model's constraints include volume constraints, upper and lower limits for element density, stress constraints, empty element constraints, and static equilibrium constraints, expressed as:

[0019]

[0020] Among them, υ i υi represents the volume of the i-th element; υ0 represents the volume of the entire beam structure; δ is the percentage of mass to be removed during optimization; ρ min This is a lower density limit to avoid singularities in the overall stiffness matrix; σ ij Let θε be the stress tensor. ij Indicates with σ ijThe corresponding virtual strain tensor; δμ i Represents virtual displacement; ∫ Ω σ ij δε ij dΩ-∫ Ω fδu i dΩ+∫ Γ t i δu i dΓ=0 is the static equilibrium equation.

[0021] S3. The topology optimization model is iteratively solved using a gradient-based mathematical programming method, and the pseudo-density ρ of the elements is adjusted according to the structural compliance. i Sensitivity update ρ i After convergence, the design domain is binarized according to a preset density threshold to obtain the topology-optimized support shape with thickened node regions and removal of redundant materials.

[0022] S4. Construct a corresponding CAD model based on the geometric shape of the topology-optimized support rod, and assemble the CAD model in three spatial directions according to the connection topology of the BCC lattice to obtain a T-BCC lattice unit cell containing spherical reinforced nodes and variable cross-section support rods.

[0023] S5. Under the same relative density conditions as the initial BCC lattice, a multi-layer T-BCC lattice structure is constructed by three-dimensional arraying of the unit cell of the T-BCC lattice. The equivalent Young's modulus of the obtained T-BCC lattice is evaluated using the aforementioned equivalent Young's modulus characterization method or compression experiment. When the equivalent Young's modulus of the T-BCC lattice is higher than that of the initial BCC lattice, the T-BCC lattice is output as the target optimized configuration.

[0024] According to the present invention, as a further preferred embodiment, the proposed T-BCC lattice structure topology optimization design method includes the following features: the penalty factor n in the power interpolation model is 3, so as to enhance the contribution of high-density elements in the equivalent stiffness and suppress the existence of intermediate-density elements, thereby improving the clarity and manufacturability of the topology optimization results.

[0025] According to the present invention, as a further preferred embodiment, the proposed T-BCC lattice structure topology optimization design method includes the following features: the boundary conditions for simulating the service conditions of the lattice in step S1 include two-stage load conditions: in the first stage, a uniformly distributed pressure is applied vertically downward on the upper constraint surface of the support rod, and a fixed constraint is applied on the lower constraint surface; in the second stage, a uniformly distributed pressure is applied vertically upward on the lower constraint surface of the support rod, and a fixed constraint is applied on the upper constraint surface; through the combination of two stages of compressive loads in opposite directions, the topology optimization result forms a spherical strengthening zone in the node region and weakens the redundant material at symmetrical positions, thereby optimizing the stress distribution at the node.

[0026] According to the present invention, as a further preferred embodiment, the proposed T-BCC lattice structure topology optimization design method includes the following features: the multidimensional structure of the lattice is obtained by periodically repeating T-BCC lattice unit cells in three-dimensional space, each T-BCC lattice unit cell includes: spherical reinforcing nodes located at the vertices and body center of the cube; a plurality of variable cross-section supports connecting adjacent spherical reinforcing nodes along the diagonal direction of the cube; wherein, the cross-sectional area of ​​each variable cross-section support increases near the spherical reinforcing node and decreases at the mid-span, so as to weaken stress concentration at the node and improve the overall equivalent Young's modulus of the lattice.

[0027] Preferred embodiment: In a preferred embodiment of the present invention, Ti-6Al-4V titanium alloy is used as the material and manufactured by laser powder bed melting (LPBF) technology.

[0028] Beneficial effects of the present invention: Experimental results show that the T-BCC lattice structure designed using the method of the present invention has a yield strength and Young's modulus that are 37.2% and 36% higher than those of the traditional BCC lattice structure, respectively, under the same relative density. Attached Figure Description

[0029] Figure 1 This is a simulation setup diagram for the topology optimization of the T-BCC lattice structure of the present invention.

[0030] Figure 2 This is a schematic diagram of the topology optimization design of the T-BCC lattice structure of the present invention, showing the changes in the lattice structure before and after optimization.

[0031] Figure 3 This is a diagram showing the overall displacement of the T-BCC lattice structure under pressure at the top, illustrating the displacement changes at different locations of the structure.

[0032] Figure 4 The image shows the Von Mises equivalent stress diagram under pressure at the top of the T-BCC lattice structure of this invention, illustrating the variation of equivalent stress at different locations of the structure.

[0033] Figure 5 This is a topographic image of the T-BCC lattice formed according to the present invention.

[0034] Figure 6 This is a diagram showing the compression deformation failure of the T-BCC lattice of the present invention.

[0035] Figure 7 This is a stress-strain curve obtained from the T-BCC lattice compression experiment of this invention.

[0036] Figure 8 This is a comparison chart of the theoretical and experimental values ​​of the Young's modulus of the T-BCC lattice of this invention.

[0037] Figure 9 This is a comparison chart of the Young's modulus of the T-BCC lattice of the present invention with other lattice structures. Detailed Implementation

[0038] The preferred embodiments of the present invention are described in detail below with reference to the accompanying drawings and specific examples. However, it should be understood that the scope of protection of the present invention is not limited to the specific embodiments.

[0039] In the attached diagram:

[0040] Figure 1 This paper demonstrates the topology optimization simulation setup for a T-BCC lattice structure. To achieve lightweight and efficient lattice structures, the SIMP method was used for topology optimization of the lattice beam structure. In this simulation, the boundary conditions of the structure were first defined, including fixed supports and applied load conditions. The simulation gradually removed redundant parts by calculating the stress and displacement of the element beams to maximize the stiffness of the structure. The advantage of the SIMP method is that it can achieve a smooth transition of material density, making the generated structure more suitable for practical additive manufacturing. Through topology optimization, an optimized T-BCC element structure was finally obtained, which has higher load-bearing capacity and lighter weight.

[0041] Figure 2 This paper illustrates the structural changes of T-BCC lattice elements before and after topology optimization. The original lattice structure consisted of traditional BCC elements, containing numerous redundant beams, resulting in high weight and low load-bearing efficiency. Topology optimization removed these unnecessary beams, generating the optimized T-BCC elements. The figure clearly shows that the optimized structure eliminates components that contribute less to the overall load-bearing capacity, thus improving material utilization. This optimized structure significantly improves stiffness and strength by reducing stress concentration and improving load transfer paths. This design process fully leverages the advantages of topology optimization algorithms, enabling the structure to achieve lightweight design while maintaining necessary strength.

[0042] Figure 3 This figure illustrates the overall displacement distribution of a T-BCC lattice structure after a vertical compressive force is applied at its top. This diagram is used to analyze the deformation mode of the structure under load. It shows significant differences in displacement at different locations within the structure. The top and bottom regions, in particular, experience the largest displacements due to the greater bending moments and axial forces, while the central region remains relatively stable. This displacement distribution can help identify weak points in the structure, providing a basis for further optimization. For example, by locally reinforcing high-displacement areas or redesigning the shape and dimensions of beams, the overall deformation resistance of the structure can be effectively improved.

[0043] Figure 4The Von Mises equivalent stress distribution of the T-BCC lattice structure after applying a vertical compressive force at its top is shown. The equivalent stress plot reflects the stress concentration of the structure during loading. It can be seen from the figure that the maximum stress is mainly concentrated at the intersections of nodes and beams, which are often the starting points of structural failure. The T-BCC structure, through topology optimization, achieves a more uniform stress distribution and reduces stress concentration at the nodes. This optimization significantly reduces the risk of local failure and improves the compressive strength and reliability of the entire lattice structure. The Von Mises stress distribution also provides theoretical support for subsequent experiments, enabling effective comparison between experimental data and simulation results.

[0044] Figure 5 The actual morphology of the T-BCC lattice structure prepared using LPBF technology is shown. It can be seen that the overall shape of the formed structure is highly consistent with the designed CAD model. Although there is some surface roughness, the overall structure is intact, and there are no obvious cracks or holes on the surface. These minor surface defects are usually caused by localized over-melting of the powder or uneven cooling during the LPBF process. Morphology analysis shows that LPBF technology can manufacture complex T-BCC lattice structures with high precision, providing a good foundation for subsequent mechanical property testing.

[0045] Figure 6 The deformation and failure process of the T-BCC lattice structure under compressive load is illustrated. As the compressive load gradually increases, the lattice structure undergoes different deformation stages: first, elastic deformation, then plastic deformation, and finally brittle failure under high load. The optimized T-BCC structure, by removing redundant beams, improves the load transfer path and exhibits better compressive resistance. The failure mode shown in the figure mainly occurs at the nodes because these areas experience significant stress concentration. Further optimization of the node design can improve the structure's resistance to failure.

[0046] Figure 7 The stress-strain curves of the T-BCC lattice structure obtained in compression experiments are presented. These curves reflect the mechanical behavior of the structure during compression and can be divided into four regions: the linear elastic region, the plastic deformation region, the brittle failure region, and the densification region. In the initial stage of compression (linear elastic region), stress and strain show a linear relationship, indicating that the structure is in an elastic working state. As strain increases, the structure enters the plastic deformation region, where the beams gradually yield and deform, exhibiting a high energy absorption capacity. Upon entering the brittle failure region, the beams fracture, leading to a rapid decrease in stress. Finally, in the densification region, the structure gradually compacts, showing a renewed increase in stress. By comparing the stress-strain curves of lattice structures with different optimized ratios, it can be concluded that the optimized structure has higher load-bearing capacity and better plasticity.

[0047] Figure 8 This paper presents a comparison between the theoretically calculated and experimentally measured Young's modulus of the T-BCC lattice structure. Young's modulus is an important parameter for measuring a material's resistance to deformation. Experimental results show that, under the same relative density, the Young's modulus of the topology-optimized T-BCC lattice is significantly higher than that of the traditional BCC lattice structure, and the error between the experimental and theoretical predictions is within an acceptable range (average error less than 7%). This indicates that the topology optimization method can effectively improve the stiffness of the lattice structure and verifies the accuracy of the Young's modulus prediction model based on the large element assumption. These results demonstrate that the T-BCC lattice structure can significantly improve its mechanical properties while achieving lightweight design, making it a strong candidate for high-performance structural materials.

[0048] Figure 9 This paper demonstrates the variation of the equivalent Young's modulus of the T-BCC lattice structure proposed in this invention under different relative densities, and compares it with various typical lattice configurations (including H2O2, FCC, Diamond, and Schwartz Diamond). The figure uses relative density as the x-axis and equivalent Young's modulus as the y-axis. It can be seen that in the lower relative density region, the T-BCC lattice has a higher equivalent stiffness than the H2O2 lattice, indicating that it can maintain or even improve the overall load-bearing capacity while achieving lightweighting. Compared with traditional lattices such as FCC and Diamond, the T-BCC lattice can achieve a weight reduction of over 50% with a lower relative density under the same equivalent Young's modulus, demonstrating the significant advantage of "achieving the target stiffness with the least amount of material." When compared with the Schwartz Diamond lattice, the equivalent Young's modulus of the T-BCC lattice is approximately twice as high at the same relative density, further illustrating its superiority in the synergistic optimization of lightweighting and high stiffness. The figure also shows the theoretical prediction curve and experimental data points based on the large element assumption. The comparison results show that the average deviation between the two in the prediction of the equivalent Young's modulus of BCC lattice is about 6.9%, which verifies the applicability and reliability of the theoretical model for evaluating the mechanical properties of T-BCC lattice.

[0049] Through the detailed explanation of the accompanying drawings, the specific embodiments of the present invention systematically demonstrate the design, manufacturing, and mechanical performance advantages of the T-BCC lattice structure. Through topology optimization, LPBF additive manufacturing, and experimental verification, the present invention provides a lattice structure that achieves a good balance between lightweight and high strength, and is expected to be widely used in high-end equipment fields such as aerospace and automotive.

[0050] The overall technical solution of this invention is a method for characterizing and optimizing the performance of lattice structures based on laser powder bed melting, comprising the following steps:

[0051] Step 1: Propose a method for characterizing the equivalent Young's modulus of truss lattice structures based on the large unit cell assumption, and quantitatively describe the core parameter of the lattice structure - Young's modulus.

[0052] Step 2: Based on this, a topology optimization design method for T-BCC lattice structures with equivalent Young's modulus as the optimization objective is proposed. With the goal of improving the equivalent Young's modulus of the lattice, redundant beam structures are removed, and the intrinsic SIMP method of solid isotropic materials is used to optimize the element beams of the lattice, thereby obtaining the optimized T-BCC lattice structure.

[0053] Example 1:

[0054] In this embodiment, a T-BCC lattice structure was prepared using Ti-6Al-4V titanium alloy as the base material through the LPBF process. Its load-bearing capacity and equivalent Young's modulus under compressive load were characterized. Based on the large unit cell assumption, an analytical relationship of the equivalent Young's modulus of the T-BCC lattice was established, thereby verifying the effectiveness of the method of the present invention in optimizing the performance of lattice structures.

[0055] I. Topology Optimization Design of T-BCC Lattice Structure

[0056] First, addressing the issues of redundant supports and stress concentration in traditional BCC lattices, the SIMP method is employed for topology optimization of individual BCC beams, establishing a design process based on T-BCC lattice topology optimization, such as... Figure 1 As shown.

[0057] In the topology optimization process, a single BCC (Body-Chip-Chip) column is discretized into solid elements under given boundary conditions and load cases. Volume fraction constraints are set, and the SIMP (Structured Simulation Method) is used to penalize element density. While maximizing structural stiffness, elements with smaller load-bearing contributions are gradually removed, resulting in an optimized I-shaped variable cross-section beam. Then, the optimized single-beam CAD model is assembled according to the topological relationship of the BCC unit cell to construct a T-BCC unit cell, which is then periodically arranged into a T-BCC lattice array structure in three-dimensional space, such as... Figure 2 As shown.

[0058] To compare the mechanical properties of T-BCC lattices under different degrees of topology optimization, this embodiment selects four unit cell types: unoptimized BCC lattices (optimization ratio 0%) and three types of T-BCC lattices (Type-A, Type-B, and Type-C), with beam volume fraction optimization ratios of 10%, 30%, and 50%, respectively. During the topology optimization process, as the optimization ratio increases, excess material on both sides of the single beam that does not participate in the effective load transfer is gradually reduced, and the beam cross-section evolves from an approximately cylindrical shape to an "I" shape. Spherical reinforcement regions are naturally formed at the nodes, thereby reducing stress concentration at the nodes and improving overall stiffness and stability.

[0059] II. Characterization of the equivalent Young's modulus of the large unit cell in the T-BCC lattice

[0060] After completing the T-BCC lattice topology design, this embodiment employs a characterization method based on the large unit cell assumption to characterize its equivalent Young's modulus at multiple lattice levels. Specifically, it includes the following steps:

[0061] 1. Select a representative volume element consisting of 3*3*3 periodic unit cells as the large unit cell. Explicitly model the geometric features of the spherical reinforcement nodes and variable cross-section supports within this large unit cell. Calculate the relative density ρ of the lattice based on the support radius, support length, and unit cell side length. * In this embodiment, the relative density is taken as ρ. * Three typical working conditions, namely 10%, 15%, and 20%, are used to represent T-BCC lattice samples with different wall thicknesses and cross-sectional dimensions.

[0062] 2. At the large unit cell level, the axial compression and bending modes of representative supports under uniaxial compressive loads are analyzed based on Euler-Bernoulli beam theory. Expressions for support deflection and axial displacement are derived, yielding the equivalent stiffness of a single support along the loading direction. The large unit cell is then divided into several basic substructures. By superimposing the axial compression and bending deformations of these substructures, the overall force-displacement relationship of the large unit cell is constructed. Periodic boundary conditions are applied to the upper and lower end faces of the large unit cell to obtain the equivalent modulus of the multilayer T-BCC lattice within its elastic working range. The above derivation process is consistent with the derivation of the equivalent modulus of the BCC lattice based on the large unit cell, only replacing the geometric parameters with the spherical nodes and variable cross-section beam dimensions of the T-BCC element.

[0063] 3. By combining the equivalent modulus of the large unit cell with the macroscopic stress-strain relationship of the lattice, the equivalent Young's modulus E of the lattice is established. * Young's modulus E and lattice relative density ρ of the parent material * The power function analytical relationship between them: Where C T-BCC and t T-BCC These are the coefficients of the power function corresponding to the T-BCC lattice.

[0064] In the specific calculations, this embodiment uses the discrete data of the equivalent Young's modulus of the T-BCC lattice obtained from the experiments in Chapter 3 of the thesis to fit and calibrate the above power function model. The relative density ρ... * Taking the Type-C T-BCC lattice at 0.20 as an example, its experimental equivalent Young's modulus is: The Young's modulus of the base material Ti-6Al-4V is E≈110 GPa; substituting this into the power function relationship above, similarly, ρ... *Substituting the experimental equivalent Young's moduli of the Type-A / B / C lattice of T-BCC at 10%, 15%, and 20% respectively, we can obtain a set of... Data points, C is determined by least squares fitting. T-BCC and t T-BCC The optimal value of is used to achieve analytical characterization of the equivalent Young's modulus of the T-BCC lattice.

[0065] Comparing the theoretical predictions of the large unit cell with the experimentally measured equivalent Young's modulus of the T-BCC lattice, the average deviation between the two is approximately 6.9%, indicating that the equivalent modulus characterization method based on the large unit cell assumption can accurately predict the elastic response of the T-BCC lattice, providing a reliable theoretical basis for subsequent topology optimization design.

[0066] III. LPBF Forming and Sample Parameters of T-BCC Lattice

[0067] In this embodiment, T-BCC lattice samples were prepared on a BLT-S210 laser selective melting equipment using LPBF process parameters optimized in the previous process. The forming material was Ti-6Al-4V alloy powder.

[0068] To ensure statistical reliability, this embodiment used nine T-BCC lattice configurations with three relative densities (10%, 15%, and 20%) and three topology optimization types (Type-A / B / C). Three cubic specimens with nominal dimensions of approximately 30mm × 30mm × 30mm were repeatedly formed for each configuration. The specimen whose geometric dimensions were closest to the theoretical model was selected for subsequent compression testing. The results showed that the measured dimensions of all specimens were close to 30mm, and the relative error between the measured density and the theoretical value was controlled within 10%. The forming quality met the requirements for mechanical property testing. The morphology of a typical formed specimen is shown below. Figure 5 As shown.

[0069] IV. Compression Test and Stress-Strain Behavior

[0070] According to ISO 13314-2011 "Metallic properties testing - Ductility testing - Compression testing of porous foamed metals", the above nine types of T-BCC lattice specimens were subjected to uniaxial compression tests at room temperature. The specimen cross-section was rectangular, with a cross-sectional dimension greater than 10 times the average pore diameter and not less than 10 mm, and the aspect ratio was controlled within the range of 1-2. The compression test was carried out on a QT-6105S servo universal testing machine with a loading rate of 1 mm / min. The indenter applied a normal load from the top of the specimen until the nominal strain exceeded 75% or the specimen showed obvious instability and failure.

[0071] Typical compression deformation and failure morphology, such as Figure 6As shown, it can be observed that the low-optimization ratio specimens experience more severe buckling and fracture near the nodes, while the high-optimization ratio Type-C T-BCC lattice exhibits a more uniform stress distribution and a milder failure mode under the same load. This is consistent with the design goal of topology optimization to enhance the node region and reduce stress concentration.

[0072] The testing machine automatically records the displacement and load data during the loading process and converts them into stress-strain curves. Stress-strain curves for various lattice specimens are shown below. Figure 7 As shown, the process can be divided into four stages: linear elasticity, plastic deformation, brittle failure, and densification. In the linear elastic region where the strain is less than about 5%, the curve is basically linear, and the lattice support mainly undergoes slight axial compression and minor bending deformation. Subsequently, it enters the plastic deformation region, where local members undergo significant bending and buckling. As the strain continues to increase, local units become unstable, and the load-bearing capacity is significantly reduced, corresponding to the brittle failure stage. Finally, under high strain, the pores are compacted, and the structure enters the densification stage.

[0073] V. Comparison of Yield Strength and Equivalent Young's Modulus

[0074] With relative density ρ * Taking a yield strength of 20% as an example, the yield strength of a traditional BCC lattice is approximately 32.38 MPa, while the yield strength of a Type-CT-BCC lattice is approximately 44.43 MPa, representing an increase of approximately 37.2% compared to the BCC lattice; in ρ * Under conditions of 15% and 10%, the yield strength of Type-C increases by approximately 33.9% and 31.2%, respectively. Under the same relative density conditions, the yield strength of the T-BCC lattice increases significantly with the increase of the beam optimization ratio, showing the order of C-type > B-type > A-type; and the combination of high density and high optimization ratio can significantly improve the ultimate bearing capacity of the lattice, demonstrating the beneficial effect of the T-BCC structural design of this invention on bearing performance.

[0075] Figure 8 The paper presents a comparison between the theoretically predicted and experimentally measured equivalent Young's modulus of the T-BCC lattice large unit cell, as well as the distribution of the equivalent Young's modulus of the T-BCC lattice under different relative densities and topology optimization ratios. The results show that, at ρ... * When the ρ = 10%, the equivalent Young's modulus of the Type-C T-BCC lattice is approximately 0.34 GPa, while that of the BCC lattice is only approximately 0.23 GPa, representing a modulus increase of approximately 36%; at ρ * At ρ = 15%, the equivalent modulus of Type-C is approximately 0.78 GPa, an increase of about 23.8% compared to 0.56 GPa of BCC; at ρ * When the modulus is 20%, the equivalent modulus of Type-C is approximately 1.55 GPa, while that of BCC is 1.21 GPa, representing an increase of approximately 26.0%.

[0076] Overall, the T-BCC lattice exhibits a higher equivalent Young's modulus than the BCC lattice at all relative density levels, and the modulus shows a significant upward trend with the increase of the beam optimization ratio. This further verifies the effectiveness of the topology optimization design method with the equivalent Young's modulus as the optimization target. Combining the yield strength and equivalent Young's modulus, it can be seen that at the same relative density, the yield strength of the T-BCC lattice is increased by up to approximately 37.2%, and the equivalent Young's modulus is increased by up to approximately 36%, which is consistent with the improvement range described in the "Beneficial Effects of the Invention" section of the specification.

[0077] The above preferred embodiments are only for illustrating the technical concept and features of the present invention, and are intended to enable those skilled in the art to understand the content of the present invention and implement it. They should not be used to limit the scope of protection of the present invention. All equivalent changes or modifications made in accordance with the essence of the present invention shall fall within the scope of protection of the present invention.

Claims

1. A method for performance characterization and optimization design of lattice structures based on laser powder bed melting, characterized in that, Includes the following steps: Step 1: Propose a method for characterizing the equivalent Young's modulus of truss lattice structures based on the large unit cell assumption, and quantitatively describe the core parameter of the lattice structure - Young's modulus. Step 2: Based on this, a topology optimization design method for T-BCC lattice structures with equivalent Young's modulus as the optimization objective is proposed. With the goal of improving the equivalent Young's modulus of the lattice, redundant beam structures are removed, and the intrinsic SIMP method of solid isotropic materials is used to optimize the element beams of the lattice, thereby obtaining the optimized T-BCC lattice structure.

2. The method for performance characterization and optimization design of lattice structures based on laser powder bed melting according to claim 1, characterized in that, In step 1, in the method for characterizing the equivalent Young's modulus of the truss lattice structure based on the large unit cell assumption, the truss lattice structure includes at least a body-centered cubic (BCC) lattice and a T-BCC lattice obtained based on BCC lattice topology optimization, including: T1. During the elastic working phase, the multi-layer lattice structure is equivalent to an isotropic homogeneous body. A representative volume unit containing several layers of periodic unit cells is selected as the large unit cell. The node region and support geometry are explicitly modeled in the large unit cell, and the relative density ρ* of the lattice is calculated based on the support radius, support length and unit cell side length. T2. At the large unit cell level, based on the Euler-Bernoulli beam theory, the compression and bending modes of representative struts under uniaxial compressive loads are mechanically analyzed. The strut deflection, axial displacement and internal force distribution are derived, and the axial equivalent stiffness of a single strut is obtained. T3. Decompose the large unit cell into several basic substructures, superimpose the axial compression deformation and bending deformation of each basic substructure, construct the overall force-displacement relationship of the large unit cell in the loading direction, and apply periodic boundary conditions to the two opposite end faces of the large unit cell to simulate the actual constraints of the multilayer lattice, and obtain the equivalent modulus of the large unit cell. T4. Based on the equivalent modulus of large unit cell and the macroscopic stress-strain relationship of lattice, establish the analytical characterization relationship between the equivalent Young's modulus E* of lattice, the Young's modulus E of the parent material, and the relative density ρ* of lattice. Express the relationship between E* / E and ρ* in the form of a power function, and determine the power function coefficients through data fitting. T5. For BCC lattices and T-BCC lattices formed by laser powder bed melting process, rectangular cross-section compression specimens are prepared according to ISO 13314 standard for compression testing of porous metallic materials. Stress-strain curves are obtained by uniaxial compression test. The equivalent Young's modulus is extracted by stress-strain slope in the elastic segment. The power function analytical characterization relationship is experimentally calibrated and its accuracy is verified.

3. The method for performance characterization and optimization design of lattice structures based on laser powder bed melting according to claim 1 or 2, characterized in that, The large unit cell consists of n cells periodically stacked along the x, y, and z directions. x ×n y ×n z It consists of n lattice units, where n x n y n z All values ​​are greater than or equal to 3, to explicitly introduce the boundary constraint effect caused by multi-level stacking; and by changing n x n y n z By taking the value of , we can obtain the influence relationship between the number of multilayer stacks and the decay law of the equivalent Young's modulus of the lattice.

4. The method for performance characterization and optimization design of lattice structures based on laser powder bed melting according to claim 3, characterized in that, The analytical representation of the power function form is as follows: C and t are constants determined by the structural parameters and experimental data through least squares fitting, and different parameter combinations are given for BCC lattice and T-BCC lattice respectively, so as to uniformly characterize the equivalent Young's modulus of different lattice configurations under the same large unit cell theoretical framework.

5. The method for performance characterization and optimization design of lattice structures based on laser powder bed melting according to claim 4, characterized in that, The uniaxial compression test used Ti-6Al-4V alloy as the base material. The cross-section of the specimen was rectangular, with a side length that was more than 10 times the average pore size of the lattice and greater than 10 mm. The ratio of the specimen height to the side length was in the range of 1 to 2. The loading rate was 1 mm / min to ensure that stable elastic stress-strain data were obtained for calibration and verification of the analytical characterization relationship.

6. The method for performance characterization and optimization design of lattice structures based on laser powder bed melting according to claim 5, characterized in that, In step 2, the T-BCC lattice structure topology optimization design method with the equivalent Young's modulus as the optimization objective, with the maximization of the lattice's equivalent Young's modulus as the optimization objective, includes: S1. Taking the struts in the BCC lattice unit cell as the topology optimization design object, establish a three-dimensional continuous design domain containing the entire length of the struts, set the end faces of the struts connected to the nodes as constraint surfaces, and apply boundary conditions corresponding to the macroscopic compression condition of the target lattice. S2. A topology optimization mathematical model is constructed using the SIMP method. The design domain is discretized into finite element elements, with the element pseudo-density ρi as the topology optimization design variable, and the equivalent Young's modulus E of the i-th element is used as the topology optimization design variable. i Correlate with the Young's modulus E of the parent material through power interpolation. Under constraints of volume fraction, element density upper and lower limits, stress, empty element, and static equilibrium, the design objective of maximizing the equivalent Young's modulus is characterized by the objective function of minimizing the support rod compliance. The calculation formula is as follows: Where F is the objective function, Compli is the overall compliance of the beam structure; μ i For variables; f i For volume force; t i Γ represents the boundary area force; Ω represents the computational domain, indicating the spatial region where optimization is performed; Γ represents the boundary of the spatial region where optimization is performed. The model's constraints include volume constraints, upper and lower limits for element density, stress constraints, empty element constraints, and static equilibrium constraints, expressed as: Among them, υ i υi represents the volume of the i-th element; υ0 represents the volume of the entire beam structure; δ is the percentage of mass to be removed during optimization; ρ min This is a lower density limit to avoid singularities in the overall stiffness matrix; σ ij Let θε be the stress tensor. ij Indicates with σ ij The corresponding virtual strain tensor; δμ i Represents virtual displacement; ∫ Ω σ ij δε ij dΩ-∫ Ω fδu i dΩ+∫ Γ t i δu i dΓ=0 is the static equilibrium equation; S3. The topology optimization model is iteratively solved using a gradient-based mathematical programming method, and the pseudo-density ρ of the elements is adjusted according to the structural compliance. i Sensitivity update ρ i After convergence, the design domain is binarized according to a preset density threshold to obtain the topology-optimized support shape with thickened node regions and removal of redundant materials. S4. Construct a corresponding CAD model based on the geometric shape of the topology-optimized support rod, and assemble the CAD model in three spatial directions according to the connection topology of the BCC lattice to obtain a T-BCC lattice unit cell containing spherical reinforced nodes and variable cross-section support rods. S5. Under the same relative density conditions as the initial BCC lattice, a multilayer T-BCC lattice structure is constructed by three-dimensional arraying of the unit cell of the T-BCC lattice. The equivalent Young's modulus of the obtained T-BCC lattice is evaluated using the equivalent Young's modulus characterization method or compression experiment. When the equivalent Young's modulus of the T-BCC lattice is higher than that of the initial BCC lattice, the T-BCC lattice is output as the target optimized configuration.

7. The method for performance characterization and optimization design of lattice structures based on laser powder bed melting according to claim 6, characterized in that, The penalty factor n in the power interpolation model is set to 3 to enhance the contribution of high-density elements to the equivalent stiffness and suppress the existence of intermediate-density elements, thereby improving the clarity and manufacturability of the topology optimization results.

8. The method for performance characterization and optimization design of lattice structures based on laser powder bed melting according to claim 7, characterized in that, The boundary conditions for simulating the service conditions of the lattice in step S1 include two stages of load conditions: in the first stage, a uniformly distributed pressure is applied vertically downward on the upper constraint surface of the support rod, and a fixed constraint is applied on the lower constraint surface; in the second stage, a uniformly distributed pressure is applied vertically upward on the lower constraint surface of the support rod, and a fixed constraint is applied on the upper constraint surface. By combining the two stages of compressive loads in opposite directions, the topology optimization results form a spherical strengthening zone in the node region and weaken the redundant material at symmetrical positions, thereby optimizing the stress distribution at the node.

9. The method for performance characterization and optimization design of lattice structures based on laser powder bed melting according to claim 8, characterized in that, The T-BCC lattice structure is obtained by periodically repeating T-BCC lattice unit cells in three-dimensional space. Each T-BCC lattice unit cell includes: spherical reinforcing nodes located at the vertices and body center of the cube; and several variable cross-section struts connecting adjacent spherical reinforcing nodes along the diagonal of the cube. The cross-sectional area of ​​each variable cross-section strut increases near the spherical reinforcing node and decreases at the mid-span, so as to reduce stress concentration at the node and improve the overall equivalent Young's modulus of the lattice.

Images