Simulation of Ⅰ - Ⅱ Mixed Mode Cracking Behavior of Ultra-Dense Asphalt Concrete
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摘要: 为了研究低温地区超密实型沥青混凝土内部Ⅰ - Ⅱ复合型微裂纹扩展规律，基于Eshelby等效夹杂理论和最大周向应力断裂准则，建立了当复合型裂纹发生失稳型扩展时其内部微裂纹偏转角β与应力场之间的关系，并确定了扩展方向；建立沥青混凝土细观离散元模型，考虑沥青混凝土的黏弹性，分析了内部微裂纹β对复合裂纹扩展的影响规律. 研究结果表明：对二维平面问题，β的变化主要引起裂纹在沥青混凝土中分布状态的变化，在极大程度上造成了沥青混凝土的宏观有效弹性模量和剪切模量在时域内的减小；在常荷载作用下，β的增大造成了宏观裂纹孕育和扩展历程的缩短，还致使复合型裂纹由Ⅰ型裂纹逐渐转变为Ⅱ型裂纹；β的增大不仅使裂尖域内应力场发生一定偏转，而且导致裂尖域内应力场和衰坏区的减小.
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关键词:
- 道路工程 /
- 超密实型沥青混凝土 /
- Ⅰ - Ⅱ复合型裂纹 /
- Eshelby等效夹杂 /
- 离散元模型
Abstract: This work aims to study the propagation behavior of Ⅰ - Ⅱ mixed mode micro-cracks in the ultra-dense asphalt concrete in cold regions. Based on the Eshelby equivalent inclusion theory and the maximum circumferential stress fracture criterion, the relationship between the declination angle β and the stress field is established for the composite cracks propagating in unstable mode, and whereby the crack propagation direction is determined. Then, a two-dimensional mesoscopic discrete element model of asphalt concrete is built; taking the viscoelasticity of asphalt concrete into consideration, the model is used to simulate the mixed mode micromechanical fracture behavior of the ultra-dense asphalt concrete. The influence of declination angle β on the unstable crack growth is analyzed. Results are obtained as follows: For the two-dimensional plane problems, the change of declination angle β mainly causes the change of crack distribution in asphalt concrete, greatly reducing the effective modulus and shear modulus of asphalt concrete in the time domain. Under the action of constant load, the increase of declination angle β shortens the process of crack initiation and propagation in the ultra-dense asphalt concrete, causing the fracture mode gradually transformed from type Ⅰ cracking into type Ⅱ cracking. Meanwhile, the increase of declination angle β not only causes a certain deflection of the stress field near the crack tip, but also leads to a decrease of the stress field and failure zone in the crack tip region. -
图 1 RVE单元薄椭圆形裂纹缺陷示意
Figure 1. Schematic diagram of the RVE unit thin elliptica crack defect
图 3 E'/E与参数p、β的关系
Figure 3. Relationship between effective modulus and parameters p and β
图 7 含复合型裂纹沥青混合料的断裂韧度曲线
Figure 7. Fracture toughness curve of aspahlt mixture with composite crack
图 8 不同β对初始裂尖应力场的影响
Figure 8. Effect of different crack deflection angles β on stress and initial stress filed of crack tip
图 9 不同裂纹β对裂尖衰坏区影响
Figure 9. Effect of different crack deflection angles β on failure zone of crack tip
表 1 超密实型沥青混凝土级配
Table 1. Gradation of Ultra-dense asphalt concrete
筛孔尺寸/mm 16.0 13.2 9.5 4.75 2.36 1.18 0.60 0.30 0.15 0.075 通过率/% 100.0 97.5 84.0 62.5 42.5 32.0 24.0 15.5 11.0 6.0 
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表 2 Burgers模型宏观参数
Table 2. Macroscopic parameters of Burgers model
参数 E1/MPa E2/MPa η1/（MPa•s） η2/（MPa•s） 取值 0.586 0.368 108.112 28.135
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表 3 Burgers模型微观参数
Table 3. Microscopic parameters of Burgers model
参数 Kkn/（× 103 Pa•m） Ckn/（× 105 Pa•m•s） Kmn/（× 103 Pa•m） Cmn/（× 105 Pa•m•s） 取值 1.47 1.13 2.34 4.32 参数 Kks/（× 105 Pa•m） Cks/（× 104 Pa•m•s） Kms/（× 103 Pa•m） Cms/（× 105 Pa•m•s） 取值 5.89 4.50 1.56 1.73
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表 4 裂纹扩展过程中的相关参数
Table 4. Parameters related to crack propagation
β/（°） 阶段Ⅰ 阶段Ⅱ 阶段Ⅲ θ0/（°） 应力强度因子/（MPa•mm1/2） 裂纹数量/条 ΔλⅠ 裂纹数量/条 ΔλⅡ 裂纹数量/条 KⅠ KⅡ 0 1 4.389 87 16 0.264 13 593 0 2210.86 0.120 22.5 1 4.360 40 31 0.253 60 462 25.9 2129.32 415.130 45.0 1 4.358 98 37 0.250 02 446 44.2 1836.62 853.565 67.5 1 4.354 11 52 0.188 89 388 63.2 1454.09 1171.250 90.0 1 4.349 15 66 0.173 85 355 90.0 0.11 1928.300 注：ΔλⅠ为裂纹孕育阶段经历时间对数，即第一条微裂纹出现时间；ΔλⅡ为裂纹快速扩展阶段经历时间对数，即初始裂纹出现到裂纹发生快速增长经历的时间；KⅠ、KⅡ分别为Ⅰ、Ⅱ型裂纹的应力强度因子.
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