Study on plastic yield strength of Gyroid lattice structures based on functional principleson
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摘要: 点阵结构与密实结构存在的力学性能差异之一表现在塑性屈服响应上，因此，研究其屈服行为可为点阵结构的设计和应用提供重要的理论依据。首先，对Gyroid点阵结构进行简化，并基于变形体功能原理建立其力学模型，得到Gyroid点阵结构塑性屈服强度与体积分数之间的映射关系；然后，基于有限元分析软件Abaqus对Gyroid点阵结构准静态压缩过程开展仿真实验，初步验证理论模型的准确性；最后，通过选择性激光熔化(SLM)制备不同体积分数316L不锈钢Gyroid点阵结构，进行单轴压缩实验，分析其变形机制与力学性能。结果表明：理论推导、有限元仿真结果与实验结果相比，误差在25%以内，且根据3种方法结果拟合得到的Gibson-Ashby模型系数具有较好的一致性，表明本文基于理论推导建立的Gyroid点阵结构塑性屈服强度预测模型的有效性。理论模型的构建方法可以转化到其他复杂类型点阵结构中，为快速核算点阵结构力学性能，并将其应用在工程装备中提供理论依据。Abstract: One of the differences in mechanical properties between lattice structures and dense structures lies in the plastic yield response. Therefore, studying their yield behavior can provide important theoretical basis for the design and application of lattice structures. Firstly, The Gyroid lattice structure was simplified and its mechanical model was established based on the principle of deformable body function, obtaining the mapping relationship between the plastic yield strength and volume fraction of the Gyroid lattice structure. Then, based on the finite element analysis software Abaqus, simulation experiments were conducted on the quasi-static compression process of Gyroid lattice structures to preliminarily verify the accuracy of the theoretical model. Finally, different volume fractions of 316L stainless steel Gyroid lattice structures were prepared by selective laser melting (SLM), and uniaxial compression experiments were conducted to analyze their deformation mechanism and mechanical properties. The results show that the error between theoretical derivation, finite element simulation results and experimental results is within 25%, and the coefficients of the Gibson-Ashby model fitted based on the results of the three methods have good consistency, indicating the effectiveness of the Gyroid lattice structure plastic yield strength prediction model established based on theoretical derivation. The construction method of theoretical models can be transformed into other complex types of lattice structures, providing a theoretical basis for quickly calculating the mechanical properties of lattice structures and applying them in engineering equipment.
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图 1 Gyroid点阵结构设计与制造示意图
Figure 1. Schematic diagram of Gyroid lattice structure design and manufacturing
图 2 Gyroid点阵结构晶胞简化示意图
Figure 2. Simplified schematic diagram of Gyroid lattice structure cell
d—Diameter; l—Branching rod length; a—Spatial length of a cell
图 3 Gyroid晶胞受力分析
Figure 3. Analysis of Gyroid crystal cell stress
σ—Stress; F—Force; θ—Angle between pole and horizontal plane; M1—Torque at the node
图 5 压缩模拟载荷与边界条件
Figure 5. Compression simulation load and boundary conditions
A—Cross sectional area of lattice structure; L—Side length of the lattice structure; u—Displacement of upper plane nodes
图 6 不同单元尺寸的模型收敛性分析
Figure 6. Convergence analysis of models with different element sizes
图 7 有限元模拟获得的Gyroid点阵结构应力-应变曲线
Figure 7. Stress-strain curves of Gyroid lattice structure obtained from finite element simulation
图 8 Gyroid点阵结构应力/应变云图
Figure 8. Stress/strain distribution of Gyroid lattice structure
图 11 Gyroid点阵结构理论与实测尺寸对比
Figure 11. Comparison of theoretical and actual dimensions of Gyroid lattice structure
图 12 Gyroid点阵结构理论与实测质量对比
Figure 12. Comparison of theoretical and actual mass of Gyroid lattice structure
图 13 Gyroid点阵结构表面微观形貌
Figure 13. Microscopic morphologies of Gyroid lattice structure surface
图 14 Gyroid点阵结构压缩实验过程
Figure 14. Experimental process of Gyroid lattice structure compression
图 15 Gyroid点阵结构压缩变形机制
Figure 15. Compression deformation mechanism of Gyroid lattice structure
图 16 压缩实验获到的Gyroid点阵结构应力-应变曲线
Figure 16. Stress-strain curves of Gyroid lattice structure obtained from compression experiments
图 17 简化前后Gyroid点阵结构体积分数对比
Figure 17. Comparison of volume fractions of Gyroid lattice structures before and after simplification
图 18 Gyroid点阵结构塑性屈服强度Gibson-Ashby拟合
Figure 18. Gibson-Ashby fitting of plastic yield strength of Gyroid lattice structure
σG—Plastic yield strength of lattice structure; σs—Yield strength of base metal; Vv—Volume fraction
表 1 Gyroid点阵结构理论推导、有限元和实验结果对比
Table 1. Comparison of theoretical derivation, finite element and experimental results of Gyroid lattice structure
Volume fraction/vol% Plastic yield strength/MPa Theoretical derivation Finite element analysis Experimental 5 1.48 1.78 1.83 7.5 2.72 3.40 3.48 10 4.19 4.72 4.97 12.5 5.85 6.71 6.86 15 7.69 8.36 9.18 
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