Tensile Fracture Characteristics and Dynamic Crack Evolution Law of Concrete
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摘要: 为探究混凝土的拉伸断裂特性和裂纹演化规律，开展了巴西圆盘的准静态劈裂试验和落锤冲击动态劈裂试验，结合有限元-黏聚单元耦合法（finite-cohesive element method，FCEM）模拟分析裂纹扩展过程及力学响应。试验结果表明：准静态加载时，混凝土圆盘试件发生拉伸断裂，圆盘中心形成一条沿加载方向贯穿的主裂纹和少量与其平行的次裂纹，裂纹主要在砂浆内部及骨料-砂浆界面扩展；三维圆盘试件的拉伸性能随厚径比的增大而增强。在动态冲击载荷作用下，试件仍为中心起裂模式，即圆盘中心形成一条沿加载方向的主裂纹，边缘则产生三角状破碎区域。随着落锤释放高度的增加，试件的破坏形态依次表现为：未起裂、起裂未贯穿、起裂贯穿和严重破碎。通过高速摄影获得的不同时刻裂纹长度的结果表明，随着落锤释放高度的降低，裂纹扩展时间延长。数值模拟结果显示，试件的起裂时间随落锤释放高度的增加呈非线性递减，并给出了起裂时间与落锤释放高度关系的经验公式。Abstract: To investigate the tensile fracture characteristics and crack evolution mechanisms of concrete, Brazilian disc quasi-static splitting tests and falling weight impact tests were conducted. The crack propagation and mechanical responses were analyzed using the finite cohesive-element method (FCEM). Test results demonstrated that under quasi-static loading, concrete discs exhibited tensile fracture with a primary crack penetrating along the loading direction at the disc center, accompanied by minor parallel secondary cracks. Crack propagation primarily occurred within the mortar matrix and along aggregate-mortar interfaces. The tensile performance of three-dimensional concrete discs exhibited significant enhancement with increasing thickness-diameter ratio. Under dynamic impact loading, specimens maintained a center-initiated fracture pattern, where the main crack propagated along the loading diameter, while triangular crushing zones formed at the edges in contact with testing apparatus. With increasing drop height, the specimens sequentially exhibited four distinct failure modes: no crack initiation, crack initiation without penetration, complete crack penetration, and severe fragmentation. High-speed photography quantified time-dependent crack lengths, demonstrating prolonged crack propagation durations at reduced drop heights. Numerical simulations revealed a nonlinear decreasing trend in crack initiation time versus drop height, with an empirical formula established to describe their relationship.
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Key words:
- dynamic loading /
- Brazilian disc /
- cohesive zone model /
- tensile fracture /
- crack evolution /
- crack initiation time
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图 4 不同厚度圆盘试件的载荷-位移曲线
Figure 4. Load-displacement curves of specimens with different thicknesses
图 5 圆盘试件厚径比与抗拉强度的关系曲线
Figure 5. Relationship curve between thickness-diameter ratio and tensile strength of disc specimens
图 6 试件H1裂纹扩展的高速摄影图像
Figure 6. High-speed photographic images of crack propagation in the specimen H1
图 7 试件H1～试件H6的起裂时间与裂纹扩展时间
Figure 7. Crack initiation time and crack propagation time of specimens H1–H6
图 14 数值模拟和试验得到的载荷-位移曲线
Figure 14. Load-displacement curves obtained from numerical simulation and test
图 15 落锤冲击下混凝土试件中裂纹的萌生和扩展
Figure 15. Initiation and propagation of cracks in concrete specimens under falling weight impact
图 16 不同释放高度下落锤的加速度时程曲线
Figure 16. Acceleration-time curves of the falling weight under different release heights
图 17 不同释放高度下接触力的变化情况
Figure 17. Variation of contact forceunder different release heights
图 18 圆盘的起裂时间随落锤释放高度的变化
Figure 18. Variation of crack initiation timewith release height
表 1 混凝土试件的力学性能参数
Table 1. Mechanical property parameters of concrete specimens
ν ρ/(g·cm–3) E/GPa fc/MPa 0.19 2.32 25.5 32 
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表 2 不同厚径比试件的极限载荷与抗拉强度
Table 2. Ultimate load and tensile strength of specimens with different thickness-diameter ratio
Thickness/mm Thickness-diameter ratio Ultimate load/kN Tensile strength/MPa 15.0 0.30 2.99 2.54 21.2 0.42 4.58 2.75 25.6 0.51 5.94 2.95 30.8 0.62 7.54 3.12
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表 3 不同释放高度下巴西圆盘试件的落锤冲击试验工况
Table 3. Conditions for the falling weight impact test on Brazilian disc specimens at different release heights
Specimen No. Falling weight mass/kg Height/mm Velocity/(m·s–1) Impact energy/J H1 10 300 2.42 29.40 H2 10 200 1.98 19.60 H3 10 100 1.40 9.80 H4 10 50 0.99 4.90 H5 10 20 0.63 1.96 H6 10 15 0.54 1.47
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表 4 落锤冲击试验得到的圆盘起裂时间与裂纹扩展时间
Table 4. Crack initiation time and crack propagation time of disc specimens obtained from the falling weight impact tests
Specimen No. Height/mm Test results Crack initiation time/μs Crack propagation time/μs H1 300 100−150 150 H2 200 100−150 250 H3 100 150−200 400 H4 50 200−250 450 H5 20 300−350 50 H6 15 0 0
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表 5 混凝土的HJC模型参数
Table 5. Parameters of the HJC model for concrete
ρ/(g·cm–3) fc/MPa A B N C D1 D2 2.32 32 0.79 1.62 0.61 0.008 0.04 1.00 K1/GPa K2/GPa K3/GPa pc/MPa μc $ {\dot{\varepsilon }}_{0} $/s–1 εf,min Smax 0.85 −1.71 2.08 10.7 7.8×10–4 1.00 0.01 7.00
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ρ/(g·cm–3) $ \eta $ GⅠ/(N·m–1) GⅡ/(N·m–1) ET/(N·m–3) EN/(N·m–3) 2.32 −2 56.42 282.13 8.3×1010 8.3×1010
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表 7 不同释放高度下圆盘试件的起裂时间
Table 7. Crack initiation time of specimens under different release heights
Specimen No. Height/mm Crack initiation time/μs Test results Simulation results H1 300 100–150 108 H2 200 100–150 120 H3 100 150–200 156 H4 50 200–250 276 H5 20 300–350 300 H6 15 0 0
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