A new experimental technique of dynamic compression-shear combined loading based on metamaterials
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摘要: 材料或结构在动态压剪复合加载条件下的力学性能对于其工程应用具有重要影响。然而，现有的动态复合加载实验技术存在压缩波和剪切波难以同步施加到试件、实验设备昂贵等问题。本文中利用压扭超材料进行应力波转化，在一维分离式霍普金森压杆（split Hopkinson pressure bar，SHPB）上实现动态压剪同步复合加载。该实验技术具有荷载精准同步、剪压比可控、简单便捷、低成本等优点。针对当压扭超材料转化出来的扭转波幅值较大，透射杆惯性约束不足情况下出现的扭转信号三角波的问题进行详细讨论，并提出相应的解决方案。选用屈服应力各不相同的金属钛、304不锈钢和316L不锈钢等3种材料进行了实验测试，证实了动态压剪同步复合加载技术的有效性。借助有限元模型，深入分析压扭超材料的几何参数对其压扭系数及承载能力的影响，并结合实验结果讨论了该实验技术的适用范围，预测动态压剪同步复合加载技术能测试的材料强度可达约1 GPa，施加给试件的剪压比可达1.18。Abstract: The mechanical properties of materials or structures under dynamic compression-shear combined loading conditions significantly influence their engineering applications. However, existing experimental methodologies for dynamic combined loading confront challenges, such as the difficulty in synchronously applying compression and shear waves to test specimens, in addition to the high cost of experimental equipment. This study introduces a novel experimental technique that utilizes compression-torsion coupling metamaterials for the conversion of stress waves, enabling synchronous dynamic compression-shear combined loading on a one-dimensional Hopkinson pressure bar. This technique offers several advantages, including precise load synchronization, a controllable shear-compression ratio, simplicity, convenience, and low cost. A detailed discussion is presented on the issue of triangular torsion signals that arise when the amplitude of torsional waves converted from compression-torsion metamaterials reaches considerable levels, coupled with insufficient inertial confinement in the transmission bar of the split Hopkinson pressure bar system. Additionally, corresponding solutions to this issue are proposed. Experimental tests were conducted on three materials with distinct yield stresses: titanium, 304 stainless steel, and 316L stainless steel, validating the effectiveness of this experimental technique. Furthermore, leveraging finite element models, an in-depth analysis was conducted on the influence of the geometric parameters of the compression-torsion coupling metamaterials on their compression-torsion coefficients and load-bearing capacities. By integrating these findings with experimental results, the applicability of this experimental technique was discussed, predicting its capability to test materials with strengths up to approximately 1 GPa and to apply shear-compression ratios up to 1.18 to specimens, providing a reference for its application in a broader range of fields. This innovative integration of metamaterials with traditional experimental equipment opens up new avenues for realizing more complex dynamic loading experiments.
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图 2 压扭超材料的几何参数约束
Figure 2. Geometric parameter constraints of the compression-torsion metamaterials
图 3 压扭超材料的准静态有限元模型示例
Figure 3. Example of the quasi-static finite element model of the compression-torsion metamaterial
图 4 准静态有限元计算结果分析示例
Figure 4. Examples of quasi-static finite element calculation results analysis
图 5 承载能力和压扭系数与斜杆数量关系曲线
Figure 5. Relation of bearing capacity and compression-torsion coefficient with respect to the number of inclined rods
图 6 承载能力和压扭系数与斜杆倾斜角度关系
Figure 6. Relation of bearing capacity and compression-torsion coefficient with the tilt angle of inclined rods
图 7 承载能力和压扭系数与斜杆直径关系
Figure 7. Relation of bearing capacity and compression-torsion coefficient with respect to the diameter of inclined rods
图 8 承载能力和压扭系数与斜杆长度关系
Figure 8. Relation of bearing capacity and compression-torsion coefficient with respect to the length of inclined rods
图 9 不同斜杆倾斜角度下压扭系数与斜杆长度关系（d=2 mm）
Figure 9. Relationship curves between the compression-torsion coefficient and the length of inclined rods under different tilt angles of inclined rods (d=2 mm)
图 10 压扭超材料和SHPB有限元模型示例
Figure 10. Example of the finite element model of compression-torsion metamaterial and SHPB
图 11 Ti6Al4V钛合金的准静态拉伸实验曲线及其拟合曲线
Figure 11. Quasi-static tensile experiment curve and its fitting curve of Ti6Al4V titanium alloy
图 12 SHPB系统的有限元模拟与实验结果对比 （D=20 mm）
Figure 12. Comparison between FEM and experimental results in SHPB system (D=20 mm)
图 13 不同斜杆直径和透射杆直径的SHPB系统有限元分析结果
Figure 13. FEM results of SHPB systems with different diameters of inclined rods and different diameters of transmission bars
图 14 SHPB系统的有限元模拟与实验结果对比（D=50 mm）
Figure 14. Comparison between FEM and experimental results in SHPB system (D=50 mm)
图 16 动态压缩-扭转实验下弹性应变范围内（压缩应变0.002 8）薄壁圆筒钛试件的DIC压缩应变云图和剪切应变云图
Figure 16. Cloud maps of compression strain and shear strain obtained from DIC for a thin-walled cylinder titanium specimen in elastic strain range (compression strain 0.002 8) under dynamic compression-torsion experiments
图 17 动态压缩-扭转实验下塑性应变范围内（压缩应变0.004 9）薄壁圆筒钛试件的DIC压缩应变和剪切应变云图
Figure 17. Cloud maps of compression strain and shear strain obtained from DIC for a thin-walled cylinder titanium specimen in plastic strain range (compression strain 0.004 9) under dynamic compression-torsion experiments
图 18 钛动态压缩-扭转实验的应变率-应变曲线
Figure 18. Strain rate-strain curves of titanium under dynamic compression-torsion experiments
图 19 钛动态压缩-扭转实验的应力-应变曲线
Figure 19. Stress-strain curves of titanium under dynamic compression-torsion experiments
图 20 准静态条件下304不锈钢的压缩应力-应变曲线
Figure 20. Compressive stress-strain curves of 304 stainless steel under quasi-static conditions
图 21 304不锈钢动态压缩-扭转实验的应力-应变曲线
Figure 21. Stress-strain curves of 304 stainless steel under dynamic compression-torsion experiments
图 22 316L不锈钢动态压缩-扭转实验的应力-应变曲线
Figure 22. Stress-strain curves of 316L stainless steel under dynamic compression-torsion experiments
图 23 压扭超材料能提供的扭矩和轴向载荷范围
Figure 23. Range of torque and axial loads that compression-torsion metamaterials can provide
图 24 基于压扭超材料的动态复合加载技术应用范围
Figure 24. Application range of the dynamic combined loading technique based on the compression-torsion metamaterials
表 1 有限元模型采用的材料参数
Table 1. Material parameters used in the finite element model
材料 密度/
(g∙cm−3)弹性模量/
GPa屈服应力/
MPa泊松比 7075铝合金 2.85 71 0.33 Ti6Al4V钛合金 4.40 120 910 0.33 
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表 2 钛的动态压缩-扭转实验结果
Table 2. Dynamic compression-torsion experiment results of titanium
试件编号 $ \theta $/(°) $ {\sigma }_{\mathrm{s}} $/MPa $ {\tau }_{\mathrm{s}} $/MPa $ {\sigma }_{\mathrm{y}} $/MPa 1 70 453.58 117.01 496.80 2 70 429.49 126.49 482.15 3 60 374.31 174.72 481.34 4 60 382.43 180.40 493.84 5 50 346.23 198.34 487.74
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表 3 304不锈钢的动态压缩-扭转实验结果
Table 3. Dynamic compression-torsion experiment results of 304 stainless steel
试件编号 $ \theta $/(°) $ {\sigma }_{\mathrm{s}} $/MPa $ {\tau }_{\mathrm{s}} $/MPa $ {\sigma }_{\mathrm{y}} $/MPa 1 70 350.08 125.87 412.42 2 60 305.43 160.12 412.56
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表 4 316L不锈钢的动态压缩-扭转实验结果
Table 4. Dynamic compression-torsion experiment results of 316L stainless steel
试件编号 $ \theta $/(°) $ {\sigma }_{\mathrm{s}} $/MPa $ {\tau }_{\mathrm{s}} $/MPa $ {\sigma }_{\mathrm{y}} $/MPa 1 70 471.19 172.86 558.27 2 60 440.02 221.21 583.45 3 50 402.85 237.92 576.28
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