Identification of stress thresholds for crack propagation of rock under quasi-static and dynamic loadings
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摘要: 压缩荷载作用下岩石裂纹扩展应力阈值的识别是理解岩石渐进破坏过程和分析岩石宏观破坏机制的重要基础。对大理岩、粗花岗岩和细花岗岩开展了单轴压缩和动态冲击试验，引入岩石裂纹轴向应变和裂纹径向面积应变两个参数，根据岩石单轴压缩破坏时裂纹径向面积应变曲线斜率的不同，把以上三种岩石分成类型Ⅰ（大理岩）和类型Ⅱ（粗花岗岩和细花岗岩）岩石。研究表明，对于类型Ⅰ和类型Ⅱ岩石，分别利用其裂纹轴向应变和裂纹轴向应变刚度曲线特征点能准确识别出岩石在静态压缩荷载下裂纹稳定扩展应力σsd、裂纹不稳定扩展应力σusd以及裂纹相互贯通应力σct，证明了仅利用轴向应变数据就可对类型Ⅰ和类型Ⅱ岩石静荷载下应力阈值进行识别。而后将裂纹轴向应变法推广至动态冲击荷载下岩石的应力阈值识别，解决了动态冲击压缩载荷作用下试样难以进行裂纹扩展应力阈值识别的问题。与静态荷载下岩石的裂纹扩展应力阈值不同，在动态冲击荷载下，岩石裂纹稳定扩展应力与峰值强度的比值有所减小，裂纹不稳定扩展应力和裂纹相互贯通应力阈值相等，且与峰值强度的比值也有所减小，岩石产生更多的贯通裂纹，试样破坏时破碎程度更高。Abstract: The identification of stress threshold for crack propagation of rock under compressive loading is an important issue for understanding the progressive damage process and analyzing the macroscopic damage mechanism of rocks. In order to accurately identify the stress threshold of brittle hard rock under quasi-static and dynamic compressive loads, uniaxial and dynamic compression tests were carried out for three kinds of rock specimens (including marble, coarse granite and fine granite) by using an INSTRON 1346 and a split Hopkinson pressure bar (SHPB) system. Two deformation parameters were introduced in the paper, including crack axial strain and crack radial area strain. According to the slope difference of the crack radial area strain curves at the failure point, the three kinds of rocks were classified into type Ⅰ (marble) and type Ⅱ (coarse granite and fine granite) rocks. The testing results indicate that the crack axial strain curves and crack axial strain stiffness curves can be used to accurately identify the crack stability propagation stress σsd, crack instability propagation stress σusd and the crack connectivity stress σct under quasi-static compressive loading for type Ⅰ and type Ⅱ rocks respectively. It is proved that the stress thresholds of type Ⅰ and type Ⅱ rocks can be identified only by using the axial strain data. The method based on crack axial strain is extended to identify the stress threshold of rock under dynamic impact loading. It solves the problem to identify the stress threshold of rock specimens under dynamic compressive loading. Different from the stress threshold of rock under quasi static loading, it is found that the ratio of the crack stability propagation stress to the peak strength of the rock decreases under dynamic loading. The crack instability propagation stress and the crack connectivity stress coincide with each other, and the ratio to the peak strength also decreases. When the specimen is failed under dynamic loading, it usually generates more penetrating cracks and more fragments than that under quasi-static loading.
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1. 麻省理工学院研究人员发现金属在极端冲击下愈热愈强的反常规现象[1]
材料的强度依赖于加载测试时的速率，这是因为位错等缺陷的变形移动具有内在的动力学限制。随着变形应变率的增加，更多的强化机制被激发以增加其强度。麻省理工学院研究人员发现，在应变率大于 106 s−1 的微弹道冲击测试中，当温度升高至157 ℃时，铜的强度会增加约30%，纯钛和金中也观察到了这种效应。这种现象是违反直觉的，因为几乎所有材料在正常条件下加热时都会变软。纯金属的这种异常热强化是由于控制变形机制从热激活强化转变为位错的类弹道传输引起的，位错通过声子相互作用受到阻力。这些认识为从高速加工操作到高超音速运输中更准确地模拟和预测材料在各种极端应变率条件下的性能提供了新的思路。
2. 耶路撒冷希伯来大学研究人员实验证实拉伸裂纹速度可突破经典速度限制[2-3]
脆性材料会因快速裂纹而失效。经典断裂力学描述了拉伸裂纹的运动，这些裂纹在尖端的点状区域内将耗散掉被释放的弹性能。在这一框架内，“经典”拉伸裂纹并不能超过瑞利波速度。耶路撒冷希伯来大学研究人员实验利用水凝胶材料，通过实验证明了“超剪切”拉伸裂纹的存在。虽然水凝胶是一种柔性材料，但它的裂纹扩展特性完全遵循脆性材料断裂理论的预测。当水凝胶的拉伸状态超过极限时，拉伸裂纹的扩展速度明显地超过了瑞利波波速。超剪切动力学遵循的原理与指导“经典”裂纹的原理不同；这种断裂模式在临界（与材料相关）施加应变下被激发。这种非经典的拉伸断裂模式颠覆了对断裂力学的传统认知，亟需从理论层面揭示其存在的物理机制。
3. 北京大学等研究人员开发了一种动态强度高达14 GPa的碳纳米管纤维[4]
北京大学、北京石墨烯研究院、中国科学院力学研究所、武汉大学、中国科学院苏州纳米技术与纳米仿生研究所等研究人员提出了一种高强碳纳米管纤维的多尺度结构优化策略，系统提高了碳纳米管管间作用、纤维取向性、致密性和动态强度。在动态冲击性能的研究中，研究人员利用微尺度高速冲击拉伸实验装置，发现纤维随着拉伸速度的提高发生韧脆失效模式的转变，具有显著的应变率强化效应。当应变率约
1400 s−1时，纤维的动态强度达到14 GPa，突破了现有高性能纤维强度。运用强激光诱导的高速横向冲击实验方法，揭示了微米直径纤维单丝在模拟弹道冲击加载下的动力学响应规律，发现由于冲击能量的快速非局域耗散而展现出优异的防护性能，纤维比能量耗散功率远高于凯夫拉等传统防弹纤维。这些发现表明碳纳米管纤维在冲击防护领域具有巨大的应用潜力。 -
图 6 动态压缩试样裂纹轴向应变曲线
Figure 6. Crack axial strain curves of dynamic compression specimens
图 7 动态冲击荷载作用下岩石试样应力阈值识别分析
Figure 7. Stress threshold identification of rock specimens under dynamic compression loading
图 9 动态冲击压缩下岩石试样体积刚度曲线
Figure 9. Volume stiffness curves of rock specimens under dynamic compression loading
表 1 岩石基本物理力学参数
Table 1. Basic physical and mechanical parameters of rock samples
试样编号 波速/(m·s−1) 密度/(g·cm−3) 抗压强度/MPa 弹性模量/GPa 泊松比 DL-S-1 3996.80 2.83 104.01 35.04 0.29 DL-S-2 4167.08 2.83 143.03 41.92 0.34 DL-S-3 3998.00 2.83 142.53 − − CHG-S-1 4175.42 2.64 139.40 30.70 0.17 CHG-S-2 4179.17 2.64 137.69 30.26 0.15 CHG-S-3 4181.67 2.63 145.05 31.60 0.26 XHG-S-1 5483.89 2.79 164.64 39.89 0.20 XHG-S-2 5824.12 2.78 165.75 39.14 0.23 XHG-S-3 5538.89 2.80 161.98 38.99 0.30 
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表 2 岩石动态力学参数
Table 2. Dynamic mechanical parameters of rock samples
试样 应变率/s−1 动态抗压强度/MPa 动态弹性模量/GPa DL-D-1 36.43 247.70 93.15 DL-D-2 44.83 238.37 75.28 DL-D-3 37.58 240.92 75.61 CHG-D-1 38.26 302.84 87.64 CHG-D-2 36.50 337.62 76.73 CHG-D-3 37.95 250.25 91.16 XHG-D-1 未达到平衡条件 XHG-D-2 44.92 386.83 110.62 XHG-D-3 44.28 391.92 156.32
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表 3 体积刚度识别的类型Ⅱ岩石静态应力阈值
Table 3. Stress thresholds of type Ⅱ samples under quasi-static identified loading by volume stiffness
试样 σf/MPa σcc/MPa σcc/σf σci/MPa σci/σf σcd/MPa σcd/σf CHG.S-1 139.40 28.76 0.21 69.22 0.50 139.40 1 CHG-S-2 137.69 20.17 0.15 53.03 0.39 137.69 1 CHG-S-3 145.05 29.84 0.21 46.78 0.32 83.60 0.58 XHG-S-1 164.64 − − − − 164.64 1 XHG-S-2 165.75 − − − − 165.75 1 XHG-S-3 161.98 23.27 0.14 60.57 0.37 114.24 0.71
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表 4 声发射识别的类型Ⅱ岩石静态应力阈值
Table 4. Stress thresholds of type Ⅱ samples under quasi-static identified loading by acoustic emission
试样 σf/MPa σsd/MPa σsd/σf σusd/MPa σusd/σf σct/MPa σct/σf CHG-S-1 139.40 26.03 0.19 95.00 0.68 112.26 0.80 CHG-S-2 137.69 − − 88.30 0.64 97.29 0.71 CHG-S-3 145.05 30.77 0.21 97.62 0.67 111.73 0.77 XHG-S-1 164.64 26.30 0.16 123.68 0.75 147.13 0.89 XHG-S-2 165.75 − − 111.54 0.67 133.85 0.81 XHG-S-3 161.98 − − 86.53 0.53 102.09 0.63
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表 5 裂纹轴向应变刚度识别的类型Ⅱ岩石静态应力阈值
Table 5. Stress thresholds of type Ⅱ samples under quasi-static identified loading by axial strain stiffness of crack
试样 σf/MPa σsd/MPa σsd/σf σusd/MPa σusd/σf σct/MPa σct/σf CHG-S-1 139.40 43.91 0.31 94.08 0.67 116.01 0.83 CHG-S-2 137.69 36.11 0.26 97.50 0.71 117.31 0.85 CHG-S-3 145.05 34.64 0.24 94.36 0.65 118.43 0.82 XHG-S-1 164.64 25.92 0.16 137.35 0.83 152.80 0.93 XHG-S-2 165.75 39.67 0.23 118.06 0.71 140.99 0.85 XHG-S-3 161.98 28.27 0.17 100.09 0.62 132.20 0.82
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表 6 体积刚度法对岩石动态裂纹扩展应力阈值识别结果
Table 6. Stress thresholds for rock crack propagation under dynamic loading identified by volume stiffness
试样 σf/MPa σci/MPa σci/σf σcd/MPa σcd/σf DL-D-1 247.70 − − − − DL-D-2 238.37 27.74 0.12 54.82 0.23 DL-D-3 240.92 42.06 0.17 142.41 0.59 CHG-D-1 302.84 52.68 0.17 164.36 0.54 CHG-D-2 337.62 45.23 0.13 135.77 0.40 CHG-D-3 250.25 44.49 0.18 173.84 0.69 XHG-D-1 − − − − − XHG-D-2 386.83 177.21 0.46 277.93 0.72 XHG-D-3 391.92 133.20 0.34 267.83 0.68
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表 7 裂纹轴向应变法对岩石动态裂纹扩展应力阈值识别结果
Table 7. Stress thresholds for rock crack propagation under dynamic loading identified by axial strain of crack
试样 σf/MPa σsd/MPa σsd/σf σusd, σct/MPa σusd/σf DL-D-1 247.70 49.20 0.20 139.12 0.56 DL-D-2 238.37 35.63 0.15 131.49 0.55 DL-D-3 240.92 50.90 0.21 151.85 0.63 CHG-D-1 302.84 64.47 0.21 222.25 0.74 CHG-D-2 337.62 44.96 0.13 174.75 0.52 CHG-D-3 250.25 38.17 0.15 129.79 0.52 XHG-D-1 − − − − − XHG-D-2 386.83 43.26 0.11 232.43 0.60 XHG-D-3 391.92 60.23 0.15 226.50 0.58
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表 8 静载下大理岩裂纹扩展应力阈值识别结果
Table 8. Identification results of stress threshold for marble crack propagation under quasi-static loading
岩石类别 加载条件 σf/MPa σsd/σf σusd/σf σct/σf σsd/σct 大理岩 静载 123.52 − 0.78 0.90 0.27 动载 242.33 0.18 0.58 0.58 0.32 粗花岗岩 静载 140.71 0.27 0.72 0.83 0.33 动载 296.90 0.16 0.59 0.59 0.28 细花岗岩 静载 164.12 0.19 0.72 0.87 0.22 动载 389.38 0.13 0.59 0.59 0.23
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表 9 动静载下岩石裂纹扩展应力阈值识别结果
Table 9. Identification results of stress threshold for rock crack propagation under quasi-static and dynamic loading
试样编号 σf/MPa σsd/MPa σsd/σf σusd/MPa σusd/σf σct/MPa σct/σf DL-1 104.01 − − 81.47 0.78 86.65 0.83 DL-2 143.03 9.51 0.07 112.00 0.78 137.54 0.96
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