Stress wave effects and influencing mechanisms on stress-strain curves in the elastic compression stage of SHPB tests based on generalized wave impedance theory
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摘要: 定量研究分离式霍普金森压杆（split Hopkinson pressure bar，SHPB）试验中弹性压缩阶段试件中的应力波效应是解耦准确材料弹性曲线的基础。在满足平面波假设的基础上，基于广义波阻抗理论，对杆与试件面积不匹配时试件弹性压缩阶段应力波演化造成的结构效应开展了定量理论研究，分析了不同情况下弹性阶段内试件唯象工程及实际材料应力-应变曲线的偏差特征与主要因素，并揭示了影响这种偏差的影响规律及其机理。研究表明：对于线性入射加载波，当无量纲时间为0.5的倍数时，即使其他参数改变，试件唯象与材料实际的应力-应变曲线仍对应相等；试件两端的应力差较大时，若应力差的变化趋于稳定，则试件唯象与材料实际的应力-应变曲线差异较小。计算了不同波动区间内试件的最大应力偏离值及其变化趋势和对应的无量纲时间，研究了入射波是双线性组合波时试件的应力-应变曲线。研究表明：双线性波入射时，2个线性区间可以独立分析，无论如何组合线性区间或应力差如何变化，只要试件两端应力差为近似恒定曲线，对应的试件唯象工程应力-应变曲线都是相对准确的。Abstract: Quantitative investigation of stress wave effects during the elastic compression stage of split Hopkinson pressure bar (SHPB) tests is fundamental for decoupling accurate elastic curve of material. Based on the assumption of plane waves and utilizing the generalized wave impedance theory, a quantitative theoretical analysis of the structural effects caused by the evolution of stress waves during the elastic compression stage of specimens with mismatched bar/specimen cross-sectional areas is conducted. The characteristics and main influencing factors of the deviation between engineering stress-strain curves of specimens during the elastic stage and the actual material stress-strain curves under different conditions are explored. It further reveals the governing rules and mechanisms influencing these deviations. The analysis indicates that for linearly incident loading waves, when the dimensionless time is a multiple of 0.5, even if other parameters change, the engineering stress-strain values of the specimen correspond approximately to the actual material stress-strain values. Even when there is a significant stress difference at both ends of the specimen, if the variation of stress difference tends to stabilize, the difference between the engineering stress-strain curve of the specimen and the actual material stress-strain curve is relatively small. The study calculates the maximum stress deviation value of the specimen and its corresponding dimensionless time, as well as the trend of the maximum stress deviation value of the specimen within different fluctuation intervals. Moreover, the study investigates the scenario where the incident wave is a bilinear combination wave. The results show that when a bilinear incident wave is present, the two linear intervals can be independently analyzed. Regardless of the combination or the variation of stress difference, only when the stress difference at both ends of the specimen reaches an approximately constant curve, the corresponding engineering stress-strain curve of the specimen is relatively accurate. This study provides theoretical references for the refined design of SHPB tests and the accurate data processing.
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图 2 初始时刻单增量波入射对应的物理平面示意图
Figure 2. Physical plane diagram corresponding to the initial moment of single incremental wave incidence
图 3 非线性加载时入射杆中的入射波示意图
Figure 3. Schematic diagram of nonlinear incident wave in incident rod
图 4 线性加载时入射杆中的入射波示意图
Figure 4. Schematic diagram of linear loading incident waveform in incident rod
图 5 理论计算与数值仿真的反射波与透射波应力对比
Figure 5. Comparison of theoretical calculation and numerical simulation of reflected and transmitted waves
图 7 线性入射波斜率不同时试件的平均应力无量纲时程曲线
Figure 7. Dimensionless time history curves of average stress in specimen at different slopes of incident wave
图 8 线性入射波斜率不同时试件两端的应力差时程曲线
Figure 8. Time history curves of stress difference at both ends of specimen at different slopes of incident wave
图 9 不同线性入射波斜率时试件两端的应力不均匀度时程曲线
Figure 9. Time history curve of dimensionless stress difference in specimen at different slopes of incident wave
图 10 线性入射波斜率不同时试件的应变率时程曲线
Figure 10. Time history curves of strain rate in specimen at different slopes of incident wave
图 11 线性入射波斜率不同时试件的应变时程曲线
Figure 11. Time history curves of strain in specimen at different slopes of incident wave
图 12 入射波上升沿宽度为8 μs时试件与材料的应力-应变曲线
Figure 12. Stress-strain curves of specimen and material with incident wave width of 8 μs
图 13 线性入射波斜率不同时试件的应力-应变曲线
Figure 13. Stress-strain curve of specimen under different incident wave slopes
图 14 截面积比不同时试件与材料的应力-应变曲线
Figure 14. Stress-strain curves of specimen and material with different area ratios
图 15 截面积比不同时试件的应变时程曲线
Figure 15. Time history curves of strain in specimen at different area ratios
图 16 截面积比不同时试件的应变率时程曲线
Figure 16. Time history curves of strain rate in specimen at different area ratios
图 17 截面积比不同时试件两端的应力差时程曲线
Figure 17. Time history curves of stress difference at both ends of specimen at different area ratios
图 18 实际弹性加载曲线示意图
Figure 18. Simplified schematic diagram of actual elastic loading curve
图 19 试件的轴向平均应力和应变时程曲线
Figure 19. Time history curves of stress-strain under bilinear incident wave and comparison with single linear
图 20 双线性入射时试件两端的应力差时程曲线
Figure 20. Time history curves of stress difference at both ends of specimen under bilinear incident
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