Dynamic behaviors and energy dissipation characteristics of marble under cyclic impact loading
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摘要: 为了研究循环冲击荷载作用下大理岩的动态力学行为和能量耗散特性，首先采用分离式霍普金森压杆，通过试冲法确定出5种代表性的入射子弹速度，据此完成了大理岩试样的等幅循环冲击试验，并对试样的应力均匀性进行了检验。接着，从应变率时程曲线、应力-应变关系、冲击次数和能量耗散特性等方面对测试数据进行了系统分析。最后，基于能量演化定义损伤变量，探讨了能量耗散与岩样损伤发展之间的关联机制。结果表明：试样应变率时程曲线在低弹速下会出现变化率恒定的平台段，应力-应变曲线在峰后阶段均产生一定的回弹；随着循环次数的增加，试样峰值应力总体减小，而峰值应变、平均应变率和累积比能量吸收值则变化趋势相反，且在临近破坏或开裂前其变化速率呈现突增现象；峰值应力与平均应变率存在明显的线性关系，弹性模量随平均应变率的变化整体上符合指数衰减规律；试样的耗散比能与平均应变率之间呈线性正相关，基于能量耗散定义的损伤变量可以较好地表征该大理岩试样动载下的损伤破坏过程。Abstract: In order to study the dynamic behaviors and energy dissipation characteristics of marble under cyclic impact loading, a split Hopkinson pressure bar system was first adopted to determine the five representative incident velocities of striking projectile through the trial impact method. Based on this, constant amplitude cyclic impact tests of the marble samples were performed, and stress uniformity of the samples was examined. Then, a systematic analysis is conducted on the test data from the aspects of strain rate time history curve, stress-strain relationship, impact times and energy dissipation properties. Finally, a damage variable is defined based on the energy evolution, and the associated mechanism between energy dissipation and damage development of the rock samples is further explored. The results show that the time-history curves of the strain rate of the samples exhibit a plateau segment with a constant rate of change at low projectile velocities, and the stress-strain curve has a certain rebound at the post-peak stage. The peak stress of the rock samples decreases with the increase of the number of cycles, while the peak strain, average strain rate and cumulative absorption specific energy take on the opposite trend, and their change rates all show a sudden increase phenomenon before sample’s break or fracture. The peak stress has a linear relationship with the average strain rate, while the variation of sample elastic modulus with average strain rate generally follows an exponential decay law. There is a positive linear correlation between the dissipated specific energy and the average strain rate of the marble samples. The damage variable defined based on energy dissipation analysis can better characterize the break or fracture process of the marble samples under dynamic loading. The research results of this study have certain reference value for revealing the evolution mechanism of rock internal damage under cyclic load disturbance.
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Key words:
- marble /
- cyclic impact /
- dynamic characteristics /
- energy dissipation /
- damage evolution
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图 3 弹速为7.5 m/s时第1次冲击荷载下试样的动态应力平衡检验曲线
Figure 3. Dynamic stress balance test curves of the specimen under the first impact loading at the projectile velocity of 7.5 m/s
图 4 试样S18在弹速8.0 m/s循环冲击下的应力波形
Figure 4. Stress waveforms in specimen S18 under cyclic impact with the projectile velocity of 8.0 m/s
图 5 弹速为6.5 m/s时试样的应变率时程曲线
Figure 5. Strain-rate history curves of the specimen at the projectile velocity of 6.5 m/s
图 6 弹速为7.0 m/s时试样的应变率时程曲线
Figure 6. Strain-rate history curves of the specimen at the projectile velocity of 7.0 m/s
图 7 弹速为7.5 m/s时试样的应变率时程曲线
Figure 7. Strain-rate history curves of the specimen at the projectile velocity of 7.5 m/s
图 8 弹速为8.0 m/s时试样的应变率时程曲线
Figure 8. Strain-rate history curves of the specimen at the projectile velocity of 8.0 m/s
图 9 弹速为8.5 m/s时试样的应变率时程曲线
Figure 9. Strain-rate history curves of the specimen at the projectile velocity of 8.5 m/s
图 10 在6.5 m/s的弹速循环冲击下试样的应力-应变曲线
Figure 10. Stress-strain curves of the specimen under cyclical impact loading at the projectile velocity of 6.5 m/s
图 11 在7.0 m/s的弹速循环冲击下试样的应力-应变曲线
Figure 11. Stress-strain curves of the specimen under cyclical impact loading at the projectile velocity of 7.0 m/s
图 12 在7.5 m/s的弹速循环冲击下试样的应力-应变曲线
Figure 12. Stress-strain curves of the specimen under cyclical impact loading at the projectile velocity of 7.5 m/s
图 13 在8.0 m/s的弹速循环冲击下试样的应力-应变曲线
Figure 13. Stress-strain curves of the specimen under cyclical impact loading at the projectile velocity of 8.0 m/s
图 14 在8.5 m/s的弹速循环冲击下试样的应力-应变曲线
Figure 14. Stress-strain curves of the specimen under cyclical impact loading at the projectile velocity of 8.5 m/s
图 15 不同冲击速度下试样的破坏形态
Figure 15. Failure modes of specimens under different impact velocities
图 21 不同冲击速度下累积耗散比能与冲击次数的关系
Figure 21. Relation of cumulative specific dissipated energy with impact times under different impact velocities
图 22 耗散比能与平均应变率的关系
Figure 22. Relation of specific dissipated energy with average strain rate
图 24 损伤变量与累积耗散比能的关系
Figure 24. Relation of damage variable with cumulative specific dissipated energy
表 1 试样基本参数
Table 1. Basic physical parameters of the specimens
试样 高度/mm 直径/mm 密度/(g·cm−3) 声速/(m·s−1) 试样 高度/mm 直径/mm 密度/(g·cm−3) 声速/(m·s−1) S2 25.10 49.40 2.82 5390 S17 25.12 49.52 2.79 4850 S4 24.94 49.40 2.83 5390 S18 24.94 49.32 2.84 5110 S5 25.18 49.48 2.79 4970 S19 25.20 49.40 2.82 5110 S7 25.30 49.36 2.80 5180 S20 24.94 49.42 2.80 5110 S9 25.18 49.54 2.80 5390 S21 24.92 49.38 2.83 4970 S12 25.10 49.50 2.79 5390 S23 24.92 49.32 2.83 5240 S14 24.94 49.36 2.83 5240 S24 24.92 49.28 2.84 4970 S16 25.10 49.36 2.82 4970 
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表 2 循环冲击的基本参数
Table 2. Basic parameters of cyclic impacts
试样 平均弹速/(m·s−1) 最大循环冲击次数N 入射波幅值/MPa S21 8.51 4 75.25 S23 8.53 2 76.96 S24 8.52 2 77.03 S18 8.10 4 71.99 S19 8.09 4 70.12 S20 8.13 3 72.56 S2 7.53 4 64.98 S4 7.52 6 63.91 S5 7.50 6 63.76 S7 6.98 9 61.57 S9 7.14 12 60.88 S12 7.09 12 60.92 S14 6.55 10 51.88 S16 6.51 23 50.22 S17 6.52 21 50.74
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表 3 循环冲击后试样力学参数
Table 3. Mechanical parameters of specimens after cyclic impact
试样 总冲击次数 经历的冲击次数 峰值应力/MPa 峰值应变/10−3 弹性模量/GPa S4 6 1 68.73 2.36 41.83 6 58.26 7.90 9.62 S12 12 1 61.32 2.25 42.80 6 63.84 2.53 38.75 11 55.33 6.06 11.47 S17 21 1 52.79 2.16 37.53 6 49.92 2.12 26.94 11 51.78 1.85 23.7 16 51.95 3.31 21.63 21 44.05 6.36 8.52
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