Dynamic crack propagation characteristics of media with bedding under an impact load
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摘要: 利用数字激光动态焦散线实验系统（DLDC），对含不同层理角度（30°，45°和60°）的3组有机玻璃板（Polymethyl methacrylate, PMMA）试件进行三点弯落锤冲击试验，借助高速相机记录了试件的断裂过程和裂纹尖端的动态焦散斑形状变化过程，得到了其Ⅰ、Ⅱ型动态应力强度因子的变化特征，并分析了其裂纹尖端位移及速度曲线。结合离散格子弹簧模型（DLSM），对比分析了试件的断裂形态，得到了裂纹尖端的应力场和运动场的变化规律，研究了应力波在层理处的透射和反射特征，最后利用DLSM分析了层理参数对介质断裂特性的影响。结果表明，试件的断裂特征，裂纹的起裂时间等都随层理角度的变化而不同，裂纹在不同角度层理内扩展速度不同；试件的断裂表现出拉剪复合特征；裂纹在抵达层理前速度在某一数值上下波动；层理的弹性模量和厚度都会对试件的动态断裂特性产生影响。Abstract: With the gradual development of mines, tunnels, and other underground constructions, theoretical research on the influence of internal defects in rock structure on rock dynamic fracture behavior and related engineering practices are of great importance. In this paper, a digital laser dynamic caustics experimental system is used to conduct three-point bending drop hammer impact tests on three groups of polymethyl methacrylate specimens with different angles of bedding (30°, 45°, and 60°). The fracture process of the specimens and the shape change process of the dynamic caustic speckle at the crack tip were recorded using a high-speed camera. The characteristics of dynamic stress intensity factors Ⅰ and Ⅱ were obtained, and the crack tip displacement and velocity curves were analyzed. Combined with the discrete lattice spring model (DLSM), the fracture morphology of the specimens was analyzed, and the variation law of the stress field and field at the crack tip was obtained. The transmission and reflection characteristics of stress waves were studied at stratification. Finally, the impact of the fracture characteristic stratification parameters of the medium was analyzed using DLSM. The results show that the fracture characteristics of the specimens, the initiation time of the crack, and the propagation speed of the crack in the bedding plane vary with the bedding angle. With increasing bedding angle, the initiation time of the crack advances, the propagation speed of the crack increases along the weak bedding plane after extending to the bedding plane, and the crack is more inclined to extend along the weak bedding plane to complete specimen fracture. With the crack expansion, the type Ⅱ stress intensity factor appears, and the specimen fracture shows the characteristics of tension–shear composite failure. Before arriving at a particular bedding speed, cracks fluctuate up and down, and attenuation in the aftermath of the bedding generally has lower volatility change; the elastic modulus and bedding thickness affect the dynamic fracture characteristics of the specimens. If the bedding elastic modulus is less than 0.1 GPa, the crack extension in the bedding plane distance increases with the elastic modulus. If it is more than 0.1 GPa, when the bedding for the organic glass bonding effect increases, the crack goes directly through the bedding. The propagation distance of cracks along the weak plane of the bedding increases with the bedding thickness.
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Keywords:
- caustics /
- bedding /
- impact load /
- crack propagation /
- stress intensity factor /
- numerical simulation
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图 2 试件示意图.（a）试件A；（b）试件B；（c）试件C
Figure 2. Diagram of a specimen: (a) specimen A; (b) specimen B; (c) specimen C
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图 4 模型建立及加载示意图（层理角度30°）
Figure 4. Diagram of model establishment and loading (bedding angle, 30°)
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图 5 3组试件的破坏形态及数值计算结果.（a）试件A；（b）试件B；（c）试件C
Figure 5. Failure form and numerical results of the three groups of specimens: (a) specimen A; (b) specimen B; (c) specimen C
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图 6 3组试件裂纹扩展的动态焦散斑图片.（a）试件A；（b）试件B；（c）试件C
Figure 6. Dynamic caustics spot image of crack propagation in three groups of specimens: (a) specimen A; (b) specimen B; (c) specimen C
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图 7 动态应力强度因子随时间的变化曲线.（a）试件A；（b）试件B；（c）试件C
Figure 7. Variation curve of the dynamic stress intensity factor vs time: (a) specimen A; (b) specimen B; (c) specimen C
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图 8 应力波在试件A模型中传递的应力云图
Figure 8. Stress cloud map transmitted by stress waves in the specimen A model
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图 9 应力波在预制层理处的传播云图.(a)试件B；(b)试件C
Figure 9. Propagation of stress waves at precast beddings: (a) specimen B; (b) specimen C
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图 10 参考点M处y方向应力的变化曲线
Figure 10. Variation curve of y-direction stress at reference point M
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图 11 裂纹扩展速度随时间的变化曲线.（a）试件A；（b）试件B；（c）试件C
Figure 11. Variation curve of crack propagation velocity with time: (a) specimen A; (b) specimen B; (c) specimen C
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图 12 不同层理弹性模量条件下模型的开裂结果.（a）E=0.01 GPa；（b）E=0.04 GPa；（c）E=0.1 GPa；（d）E=0.13 GPa
Figure 12. Cracking results of the model under different elastic moduli of beds: （a）E=0.01 GPa；（b）E=0.04 GPa；（c）E=0.1 GPa；（d）E=0.13 GPa
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图 13 不同层理弹性模量条件下的裂纹扩展位移(a)和速度对比曲线(b)
Figure 13. Contrast curves of crack propagation displacement (a) and velocity under different elastic moduli of bedding (b)
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图 14 不同层理厚度条件下模型的开裂结果.（a）d=0.3 mm；（b）d=0.4 mm；（c）d=0.6 mm；（d）d=0.7 mm
Figure 14. Cracking results of the model under different bedding thicknesses: (a) d=0.3 mm; (b) d=0.4 mm; (c) d=0.6 mm; (d) d=0.7 mm
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