Simulation on fatigue crack initiation at U rib-cover plate welded joints of steel bridge decks
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摘要:
为建立适用于钢桥面板U肋-盖板焊缝疲劳裂纹萌生分析方法，以Roe-Siegmund循环内聚力模型为基础，考虑混合加载模式下的内聚力参数转换，对ABAQUS进行二次开发，形成反映疲劳累计损伤的VUMAT子程序；通过试验数据获得了Q345钢材对应的焊接区域材料内聚力参数，基于Voronoi图法、焊接区域晶粒微观形态与力学特性建立了U肋-盖板焊缝焊趾处微观晶粒组织，并与宏观二维平面应变模型合并，模拟了多尺度疲劳裂纹萌生；结合等效结构应力法和线弹性断裂力学裂纹扩展理论，考虑初始缺陷形态和疲劳断裂临界标准反推了不同应力水平下的累积内聚力长度，进而得到疲劳裂纹萌生寿命的计算方法。分析结果表明：采用提出的方法模拟U肋-盖板焊缝焊趾裂纹萌生行为时，裂纹在焊趾处萌生并垂直于顶板表面进行扩展，形成了穿晶断裂模式，微观晶粒组织应力分布随裂纹萌生及短裂纹扩展而不断变化，且随着微观晶粒组织分布和力学特性的随机性变化，仿真结果中的短裂纹扩展路径细节与临界循环次数均不相同；反推得到的累积内聚力长度随初始缺陷形状比、长裂纹扩展临界深度、微观晶粒组织分布及其力学特性以及所处应力幅值的不同产生变化，考虑上述因素获取的累积内聚力长度-等效结构应力幅拟合曲线能够获取对应的裂纹萌生寿命。由此可知，建立的多尺度疲劳裂纹萌生仿真分析方法可为钢桥面板疲劳裂纹萌生寿命的获取提供新的解决路径。
Abstract:To establish the fatigue crack initiation analysis method for U rib-cover plate welded joints of steel bridge decks, the conversion of cohesive parameters in the mixed loading mode was considered based on the Roe-Siegmund cyclic cohesive zone model, the secondary development of ABAQUS was carried out, and the VUMAT subroutine reflecting the cumulative fatigue damage was formed. The cohesive parameters of the material in the welding zone corresponding to the Q345 steel were obtained from the experimental data. Based on the Voronoi diagram method and the grain microstructure and mechanical characteristics of the welding zone, the microscopic grain structure at the U rib-cover plate weld toe was established. In addition, combined with the macroscopic 2D plane strain model, the multi-scale fatigue crack initiation was simulated. Combined with the equivalent structural stress method and the crack propagation theory of linear elastic fracture mechanics, the accumulated cohesive lengths under different stress levels were backpropagated considering the initial defect morphology and critical criterion of fatigue fracture, and then the calculation method for the crack initiation life was obtained. Analysis results show that when using the proposed method to simulate the crack initiation behavior at the weld toe of U rib-cover plate welded joint, the cracks initiate at the weld toe and propagate perpendicular to the top plate surface, forming a transcrystalline fracture mode. The stress distribution of the microscopic grain structure changes with crack initiation and short crack propagations, and as the microscopic grain structure distribution and mechanical characteristics change randomly, the details of short crack propagation paths and critical cycle numbers in the simulation results are not the same. The backpropagated accumulated cohesive length varies with the initial defect morphology ratio, the critical depth of long crack propagation, the distribution and mechanical characteristics of microscopic grain structure, and the stress amplitude. The fitted curves of accumulated cohesive length and equivalent structural stress amplitude obtained by considering the above factors are capable of obtaining the corresponding crack initiation lifes. Therefore, the established multi-scale fatigue crack initiation simulation analysis method can provide a new solution to obtain the fatigue crack initiation lifes of steel bridge decks.
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图 6 热影响区和焊缝的法向临界应力
Figure 6. Normal critical stresses of heat affected zone and welded joint
图 8 焊趾处多尺度裂纹萌生仿真模型
Figure 8. Multi-scale crack initiation simulation model of weld toe
图 10 微观晶粒组织x方向主应力变化
Figure 10. Variations of principal stresses in x direction of microscopic grain structures
图 11 焊趾微观晶粒短裂纹扩展路径
Figure 11. Short crack propagation paths of microscopic grains at weld toe
图 12 不同仿真组的裂纹萌生与短裂纹扩展仿真结果
Figure 12. Simulation results of crack initiations and short crack propagations for different simulation groups
图 13 不同仿真组裂纹扩展至0.3 mm时的循环加载次数及其分布
Figure 13. Cyclic loading numbers and their distributions for different simulation groups when cracks propagate to 0.3 mm
图 16 不同仿真结果在1.5 MPa均布荷载作用下的n
Figure 16. n of different simulation results under uniformly distributed load of 1.5 MPa
表 1 等效结构应力和全阶段寿命
Table 1. Equivalent structural stresses and full stage lives
荷载/MPa 膜应力/MPa 弯曲应力/MPa 等效结构应力幅值/MPa 全阶段寿命/万次 1.0 -1.11×10-3 68.55 94.09 1 901.70 1.5 -1.04×10-3 102.83 141.14 534.50 2.0 -2.23×10-3 137.11 188.19 217.22 2.5 -2.79×10-3 171.38 235.23 108.04 3.0 -3.34×10-3 205.66 282.28 61.06 3.5 -3.90×10-3 239.94 329.32 37.69 4.0 -4.46×10-3 274.21 376.37 24.81 4.5 -5.01×10-3 308.49 423.41 17.16 5.0 -5.57×10-3 342.76 470.46 12.34 5.5 -6.13×10-3 377.04 517.51 9.16 6.0 -6.68×10-3 411.32 564.55 6.97 
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表 2 不同荷载作用下的剩余疲劳寿命
Table 2. Residual fatigue lives under different loads
形状比 临界破坏深度/mm 不同荷载(MPa)作用下的剩余疲劳寿命/万次 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 0.2 8.0 319.33 97.80 45.65 25.32 14.54 9.95 6.66 4.56 3.38 2.68 1.96 10.8 457.38 133.43 66.52 33.22 19.04 13.53 9.48 6.42 4.45 3.75 2.81 0.3 8.0 345.46 103.39 47.15 26.43 15.73 10.72 7.05 5.05 3.76 2.87 2.20 10.8 477.93 135.11 65.78 34.96 21.93 14.58 9.99 7.20 4.94 3.84 2.93 0.4 8.0 361.21 113.60 50.26 27.49 16.12 10.63 7.25 5.13 3.73 2.97 2.26 10.8 487.30 157.35 65.28 35.95 22.38 13.54 10.20 6.56 5.15 3.93 3.06 0.5 8.0 362.23 115.26 51.07 28.55 16.47 11.05 7.61 5.20 4.07 3.12 2.42 10.8 502.06 161.06 70.10 37.33 22.02 14.72 10.30 6.96 5.45 4.25 3.39
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表 3 1.5 MPa均布荷载作用下的n
Table 3. n under uniformly distributed load of 1.5 MPa
形状比 临界深度/mm 全阶段寿命/万次 剩余疲劳寿命/万次 裂纹萌生寿命/万次 n 0.2 8.0 534.50 97.80 436.70 94 955 10.8 133.43 401.07 87 209 0.3 8.0 103.39 431.11 93 741 10.8 135.11 399.39 86 843 0.4 8.0 113.60 420.90 91 520 10.8 157.35 377.16 82 008 0.5 8.0 115.26 419.25 91 160 10.8 161.06 373.44 81 201
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