Analysis of Energy Characteristics and Failure Mode of Pegmatite Gabbro under Confining Pressure
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摘要: 为探究围压条件下伟晶辉长岩的能量释放与破坏模式的关系，利用霍普金森压杆和LS-DYNA数值模拟软件对伟晶辉长岩开展了不同围压和不同冲击速度下的动态力学性能测试，分析其在不同围压和应变率下的能量释放特征及破坏规律。结果表明：高围压下，试样无明显塑性变形阶段，且围压状态对高应变率下的动态抗压强度有抑制作用，当冲击气压高于0.4 MPa时，动态抗压强度的增长趋势放缓；应变率和围压对伟晶辉长岩的能量与破坏模式有显著影响。随着围压的升高，试样的反射能占比增大，而透射能占比减小；能耗密度随应变率的增加而增大，当应变率为95 s–1时（对应的冲击气压为0.4 MPa）出现拐点，同时高围压下的能耗密度大于低围压下的能耗密度。对于处于围压下的试样，其破坏断面多带有一定的角度，通过LS-DYNA有限元软件模拟了试样在围压下的动态破坏过程，发现中低围压下试样多呈剪切破坏，而高围压下试样有多条剪切裂纹发育贯通，呈复合破坏模式。Abstract: To explore the relationship between energy release and failure mode of pegmatite gabbro under confining pressure, the dynamic mechanical properties under different confining pressures and different impact velocities were studied using split Hopkinson pressure bar and LS-DYNA simulation software, and the energy release characteristics and the failure laws under different confining pressures and strain rates were analyzed. The results show that there is no obvious plastic deformation stage under high confining pressure, and the confining pressure restrains the dynamic compressive strength under high strain rate, and the growth trend of the dynamic compressive strength slows down when the impact pressure is greater than 0.4 MPa in the specimen. The strain rate and the confining pressure have great significance for the energy and the failure mode of the specimen. With the increment of the confining pressure, the proportion of the reflected energy of the specimen gradually increases, while the proportion of the transmitted energy decreases. The energy consumption density increases with the increment of the strain rate, and there is an inflection point at the strain rate of 95 s–1 (corresponding to 0.4 MPa of impact pressure). The energy consumption density under high confining pressure is greater than that under low confining pressure. The specimen under confining pressure usually has a certain angle on the failure section. LS-DYNA simulations showed the dynamic failure process of the specimen under confining pressure from microscopic point of view. The specimen is mostly shear failure under medium and low confining pressures, while under high confining pressure, the specimen has multiple shear cracks developed and penetrated, showing a composite failure mode.
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Key words:
- Hopkinson pressure bar /
- pegmatite gabbro /
- energy dissipation /
- dynamic failure process
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图 2 (a) 典型试样的入射、反射和透射信号；(b) 典型试样的应力平衡
Figure 2. (a) Incident, reflected and transmitted signals of typical specimen; (b) stress balance of typical specimen
图 3 不同冲击载荷以及不同围压下试样的应力-应变曲线
Figure 3. Stress-strain curves of specimens under different confining pressures and impact loads
图 4 不同冲击载荷下围压与动态抗压强度的关系
Figure 4. Relation between confining pressure and dynamic compressive strength under different impact loads
图 5 不同围压下冲击载荷与动态强度因子的关系
Figure 5. Relation between impact load and dynamic increase factor under different confining pressures
图 6 不同冲击气压下能量占比随围压的变化
Figure 6. Ratios of energies versus confining pressures under different impact pressures
图 7 不同冲击气压下反射能占比随围压的变化
Figure 7. Reflection energy ratios versus confining pressures under different impact pressures
图 8 不同冲击气压下透射能占比随围压的变化
Figure 8. Transmitted energy ratios versus confining pressures under different impact pressures
图 9 不同围压下应变率与能耗密度的关系
Figure 9. Relationship between strain rate and energy consumption density under different confining pressures
图 10 中低围压下试样的破坏形态
Figure 10. Failure modes of the specimens under low and medium confining pressures
图 11 高围压下试样的破坏形态
Figure 11. Failure modes of the specimens under high confining pressures
图 14 模拟得到的入射杆和透射杆上的应力波形
Figure 14. Stress waveform of the incident bar and transmitted bar obtained by simulation
图 15 应力-应变曲线的数值模拟与试验结果对比
Figure 15. Comparison of the stress-strain curves between the simulated and tested results
图 16 围压为5 MPa、冲击速度为16.18 m/s时试样的破坏云图
Figure 16. Cloud charts of specimen failure under confining pressure of 5 MPa and impact velocity of 16.18 m/s
图 17 围压为25 MPa、冲击速度为16.39 m/s时试样的破坏云图
Figure 17. Cloud charts of specimen failure under confining pressure of 25 MPa and impact velocity of 16.39 m/s
表 1 伟晶辉长岩的静态力学参数
Table 1. Static mechanical parameters of pegmatite gabbro
ρ/(kg·m−3) fcu/MPa ft/MPa E/GPa μ 3340 62.2 4.57 8.96 0.26 
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表 2 冲击载荷下岩样的试验参数
Table 2. Test parameters of rock specimens under impact load
pa/MPa Specimen No. v/(m·s−1) pc/MPa $\dot \varepsilon$/s−1 ${\sigma _{\rm d}}$/MPa WI/J WR/J WT/J WS/J ${\psi {_{ {\text{DIF} } } } }$ 0.2 1 4.51 5 26.41 50.51 67.36 8.21 42.64 16.51 2 4.28 10 27.39 58.28 64.31 7.21 39.22 17.88 3 4.85 15 29.52 66.05 68.62 7.89 39.36 21.37 1.06 4 4.29 20 30.32 67.34 64.71 6.62 35.37 22.72 1.08 5 4.46 25 30.81 70.81 61.64 8.50 30.28 22.86 1.14 0.3 6 8.32 5 69.75 97.55 89.34 11.39 49.04 28.91 1.57 7 8.24 10 66.61 111.72 85.75 7.89 50.31 27.55 1.80 8 8.29 15 67.98 120.33 86.16 7.50 48.74 29.92 1.93 9 7.92 20 63.58 138.65 82.01 8.91 42.89 30.21 2.23 10 8.07 25 62.82 144.26 84.11 10.86 39.87 33.38 2.32 0.4 11 11.19 5 90.97 153.01 118.21 10.99 72.84 34.38 2.46 12 11.05 10 97.28 159.45 113.53 8.33 65.25 39.95 2.56 13 11.28 15 92.48 175.79 121.55 13.28 56.77 51.50 2.83 14 11.67 20 93.58 189.73 123.42 22.62 45.35 55.45 3.05 15 11.52 25 93.09 197.17 119.47 26.05 33.90 59.52 3.17 0.5 16 14.48 5 108.31 160.44 146.45 15.86 79.39 51.20 2.58 17 14.26 10 110.04 164.89 148.38 17.15 78.21 53.02 2.65 18 14.32 15 116.35 181.23 141.88 19.35 69.87 52.66 2.91 19 14.56 20 107.82 194.11 140.60 15.85 69.90 54.85 3.12 20 14.17 25 109.20 203.02 158.39 24.96 53.44 79.99 3.26 0.6 21 16.18 5 132.33 170.09 219.44 17.59 113.40 88.45 2.73 22 16.47 10 131.52 174.30 228.78 25.39 109.17 94.22 2.80 23 16.80 15 136.14 188.17 218.56 26.88 93.52 98.16 3.03 24 16.53 20 134.50 206.18 217.69 37.96 81.15 98.58 3.31 25 16.39 25 129.29 225.17 224.31 46.74 74.49 103.08 3.62
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表 3 伟晶辉长岩HJC模型参数
Table 3. HJC model parameters of pegmatite gabbro
ρ/(kg·m–3) G/GPa Fc/MPa A B C N Smax T/MPa pc/MPa μc 3340 3.55 62.2 0.52 0.79 0.007 0.61 7 4.57 20.73 3.33×10–3 pL/GPa μL K1/GPa K2/GPa K3/GPa D1 D2 ${\dot \varepsilon {_0} }$/s−1 fs ${\varepsilon {_{\rm {fmin} } } }$ 1.2 0.1 77 −169 206 0.04 1.0 1 2.0 0.004
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