Dynamic crack propagation characteristics of media with bedding under an impact load
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摘要: 利用數字激光動態焦散線實驗系統（DLDC），對含不同層理角度（30°，45°和60°）的3組有機玻璃板（Polymethyl methacrylate, PMMA）試件進行三點彎落錘沖擊試驗，借助高速相機記錄了試件的斷裂過程和裂紋尖端的動態焦散斑形狀變化過程，得到了其Ⅰ、Ⅱ型動態應力強度因子的變化特征，并分析了其裂紋尖端位移及速度曲線。結合離散格子彈簧模型（DLSM），對比分析了試件的斷裂形態，得到了裂紋尖端的應力場和運動場的變化規律，研究了應力波在層理處的透射和反射特征，最后利用DLSM分析了層理參數對介質斷裂特性的影響。結果表明，試件的斷裂特征，裂紋的起裂時間等都隨層理角度的變化而不同，裂紋在不同角度層理內擴展速度不同；試件的斷裂表現出拉剪復合特征；裂紋在抵達層理前速度在某一數值上下波動；層理的彈性模量和厚度都會對試件的動態斷裂特性產生影響。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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Key words:
- caustics /
- bedding /
- impact load /
- crack propagation /
- stress intensity factor /
- numerical simulation
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圖 2 試件示意圖.（a）試件A；（b）試件B；（c）試件C
Figure 2. Diagram of a specimen: (a) specimen A; (b) specimen B; (c) specimen C
圖 4 模型建立及加載示意圖（層理角度30°）
Figure 4. Diagram of model establishment and loading (bedding angle, 30°)
圖 5 3組試件的破壞形態及數值計算結果.（a）試件A；（b）試件B；（c）試件C
Figure 5. Failure form and numerical results of the three groups of specimens: (a) specimen A; (b) specimen B; (c) specimen C
圖 6 3組試件裂紋擴展的動態焦散斑圖片.（a）試件A；（b）試件B；（c）試件C
Figure 6. Dynamic caustics spot image of crack propagation in three groups of specimens: (a) specimen A; (b) specimen B; (c) specimen C
圖 7 動態應力強度因子隨時間的變化曲線.（a）試件A；（b）試件B；（c）試件C
Figure 7. Variation curve of the dynamic stress intensity factor vs time: (a) specimen A; (b) specimen B; (c) specimen C
圖 8 應力波在試件A模型中傳遞的應力云圖
Figure 8. Stress cloud map transmitted by stress waves in the specimen A model
圖 9 應力波在預制層理處的傳播云圖.(a)試件B；(b)試件C
Figure 9. Propagation of stress waves at precast beddings: (a) specimen B; (b) specimen C
圖 10 參考點M處y方向應力的變化曲線
Figure 10. Variation curve of y-direction stress at reference point M
圖 11 裂紋擴展速度隨時間的變化曲線.（a）試件A；（b）試件B；（c）試件C
Figure 11. Variation curve of crack propagation velocity with time: (a) specimen A; (b) specimen B; (c) specimen C
圖 12 不同層理彈性模量條件下模型的開裂結果.（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
圖 13 不同層理彈性模量條件下的裂紋擴展位移(a)和速度對比曲線(b)
Figure 13. Contrast curves of crack propagation displacement (a) and velocity under different elastic moduli of bedding (b)
圖 14 不同層理厚度條件下模型的開裂結果.（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
久色视频
圖 15 不同層理厚度條件下裂紋擴展的位移（a）和速度對比（b）曲線
Figure 15. Displacement (a) and velocity contrast (b) curves of crack propagation under different bedding thicknesses
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