XFEM and Its Application to Fatigue Crack Extension of Orthotropic Steel Bridge Deck

doi:10.3969/j.issn.1674-0696.2018.04.04

Abstract

Abstract: In order to study the cause of crack occurred at the orthotropic steel bridge deck test model of a long span flat steel box girder，the 3-D segment model was established and calculated by extended finite element method(XFEM) on the basis of the experiment model，and the crack propagation simulation was carried out by the discontinuous Galerkin finite element method(DG-XFEM).The results show that the places near the weld tip of connection of U rib and the curved opening are the high stress zones.This high stresses superimposed on such unfavorable factors as stress concentration caused by geometrical discontinuity，weld defects and built-in stresses make the places near the connection of U rib and the curved opening as the most sensitive sites of fatigue，that is fatigue crack producing area.The initial stage of crack growth is perpendicular to the principal stress isocline and extends along the direction of the maximum principal stress.The position，propagation path and length of the crack are in good agreement with the test results，which is consistent with the position and shape of the cracks in the actual bridge，and is also consistent with the basic theory of crack propagation.

Key words: bridge engineering, extended finite element method(XFEM), discontinuous Galerkin extended finite element method(DG-XFEM), orthotropic steel bridge deck, fatigue crack extension, curved opening of diaphragm

摘要： 为了研究某大桥扁平钢箱梁正交异性钢桥面板模型试验中出现裂纹的原因，根据试验模型创建了三维扩展有限元(XFEM) 模型进行整节段数值计算，利用不连续伽辽金扩展有限元(DG- XFEM) 对裂纹扩展进行了模拟。结果表明：弧形开孔与U肋连接附近为高应力区，该高应力与几何不连续、焊接缺陷引起的应力集中及残余应力等不利因素叠加，使得弧形开孔与U肋连接附近成为疲劳最敏感的部位，即疲劳裂纹产生地；裂纹扩展的初始阶段与主应力等值线垂直，沿最大主应力方向扩展；裂纹出现的位置、扩展路径和长度与试验结果符合很好，与实际桥梁裂纹出现的位置和形态基本一致，也与裂纹扩展的基本理论一致。

关键词: 桥梁工程, 扩展有限元, 不连续伽辽金扩展有限元, 正交异性钢桥面板, 疲劳裂纹扩展, 横隔板弧形开孔

CLC Number:

QU Yu1，2，ZENG Yong1，2，GU Anbang1，2，DU Baisong1，2. XFEM and Its Application to Fatigue Crack Extension of Orthotropic Steel Bridge Deck[J]. Journal of Chongqing Jiaotong University(Natural Science), 2018, 37(04): 21-27.

渠昱1，2，曾勇1，2，顾安邦1，2，杜柏松1，2. XFEM及其在正交异性钢桥面板疲劳裂纹扩展中的应用[J]. 重庆交通大学学报（自然科学版）, 2018, 37(04): 21-27.

References

［1］ RABCZUK T.Computational methods for fracture in brittle and quasi-brittle solids：State-of-the-art review and future perspectives［J］.ISRN Applied Mathematics，
2013，2013：1-38.
［2］ ALVES M K，ROSSI R.An extension of the partition of unity finite element method［J］.Journal of the Brazilian Society of Mechanical Sciences and Engineering，
2005，27(3)：209-216.
［3］ BELYTSCHKO T，GRACIE R，VENTURA G.A review of extended/generalized finite element methods for material modeling［J/OL］. Modelling and Simulation in Materials
Science and Engineering，2009，17(4)：043001.doi：10.1088/0965-0393/17/4/043001.［2017-05-12］ http：//iopscience.iop.org/article/10.1088/0965-0393/17/4/043001/meta.
［4］ BELYTSCHKO T，MOS N，USUI S，et al.Arbitrary discontinuities in finite elements［J］.International Journal for Numerical Methods in Engineering，2001，50(4)：
993-1013.
［5］ MOS N，GRAVOUIL A，BELYTSCHKO T.Non-planar 3D crack growth by the extended finite element and level sets-Part I：Mechanical model［J］.International Journal
for Numerical Methods in Engineering，2002，53(11)：2549–2568.
［6］ ABDELAZIZ Y，HAMOUINE A.A survey of the extended finite element［J］.Computers & Structures，2008，86(11)：1141-1151.
［7］ CHESSA J，WANG Hongwu，BELYTSCHKO T.On the construction of blending elements for local partition of unity enriched finite elements［J/OL］.International Journal
for Numerical Methods in Engineering，2003，57(7)：1015-1038.http：//onlinelibrary.wiley.com/doi/10.1002/nme.777/full.
［8］ SUKUMAR N，CHOPP D L，MOS N，et al.Modeling holes and inclusions by level sets in the extended finite element method［J］.Computer Methods in Applied Mechanics
and Engineering，2001，190(46)：6183-6200.
［9］ FRIES T P.A corrected XFEM approximation without problems in blending elements［J/OL］.International Journal for Numerical Methods in Engineering，2008，75(5)：
503-532.http：//onlinelibrary.wiley.com/doi/10.1002/nme.2259/full.
［10］ ARNOLD D N.An interior penalty finite element method with discontinuous elements［J］.SIAM Journal on Numerical Analysis，1982，19(4)：742-760.
［11］ GRACIE R，WANG Hongwu，BELYTSCHKO T.Blending in the extended finite element method by discontinuous Galerkin and assumed strain methods［J/OL］.International
Journal for Numerical Methods in Engineering，2008，74(11)：1645-1669.http：//onlinelibrary.wiley.com/doi/10.1002/nme.2217/full.
［12］ Sanford R J.Principles of Fracture Mechanics［J］.Upper Saddle River Nj，2002，12：29-44.
［13］中交规划设计研究院有限公司.公路钢结构桥梁设计规范：JTG D64—2015［S］.北京：人民交通出版社股份有限公司，2015.
CCCC Highway Consultants CO.，Ltd.Specification for Design of Highway Steel Bridge：JTG D 64-2015［S］.Beijing：China Communications Press Co.，Ltd，2015.
［14］曾勇，渠昱，谭红梅，等.大跨悬索桥主缆-吊杆-钢箱梁一体模型疲劳试验研究［J］.四川大学学报(工程科学版)，2016，48(4)：78-84.
ZENG Yong，QU Yu，TAN Hongmei，et al.Fatigue experimental study on integration model including main cable，hangers and box main girder of long-span suspension bridge［
J］.Journal of Sichuan University：Engineering Science Edition，2016，48(4)：78-84.
［15］ The American Association of State Highway and Transportation Officials(AASHTO).LRFD Bridge Design Specifications［S］.4th Ed.Washington，D C：AASHTO，2007.
［16］ CHOWDHURY P，SEHITOGLU H.Mechanisms of fatigue crack growth-a critical digest of theoretical developments［J］.Fatigue & Fracture of Engineering Materials &
Structures，2016，39(6)：652-674.
［17］ EL-HADDAD M H，TOPPER T H，SMITH K N.Prediction of non-propagating cracks［J］.Engineering Fracture Mechanics，1979，11(3)：573-584.
［18］刘艳萍，陈传尧，李建兵，等.14MnNbq焊接桥梁钢的疲劳裂纹扩展行为研究［J］.工程力学，2008，25(4)：209-213.
LIU Yanping，CHEN Chuanyao，LI Jianbing，et al.Fatigue crack growth behavior for the weld heat-affected zone of 14MnNBQ bridge steel［J］.Engineering Mechanics，2008，
25(4)：209-213.
［19］ NIEMI E，FRICKE W，MADDOX S J，et al.Fatigue Analysis of Welded Components——Designer’s Guide to the Structural Hot-Spot Stress Approach：IIW-1430-00
［S］.Cambridge：Woodhead Publishing Limited，2006.
［20］李传习，李游，陈卓异，等.钢箱梁横隔板疲劳开裂原因及补强细节研究［J］.中国公路学报，2017，30(3)：121-131.
LI Chuanxi，LI You，CHEN Zhuoyi，et al.Fatigue cracking reason and detail dimension of reinforcement about transverse diaphragm of steel box bridge［J］.China Journal
of Highway and Transport，2017，30(3)：121-131.

[1]	ZHOU Jianting1,2, LI Ya2, ZHANG Hong2, XIA Runchuan2, YANG Wenqi2. Two Point Corrosion Test Study of Steel Strands Based on Spontaneous Magnetic Flux Leakage Detection [J]. Journal of Chongqing Jiaotong University(Natural Science), 2021, 40(07): 74-81.
[2]	ZHANG Hua1, ZHANG Zhengqi2, CHENG Gao3,4, TIAN Boke1. Rational Distance of Pile Foundation in Precipitous Cliff Section of Loess Area [J]. Journal of Chongqing Jiaotong University(Natural Science), 2021, 40(07): 93-98.
[3]	LIU Jinchun, SONG Zixuan, LIANG Dong. Spatial Effect Analysis of Single Box Three Chambers Continuous Girder Bridge under Transverse Temperature Gradient and Eccentric Vehicle Load [J]. Journal of Chongqing Jiaotong University(Natural Science), 2021, 40(06): 80-86.
[4]	ZHENG Zhi1,2, GENG Bo2, YUAN Pei2, LI Songlin2, HU Zhengtao3. Experimental Study on a New Connection Structure of Anti-collision Device for Pier Composite Materials [J]. Journal of Chongqing Jiaotong University(Natural Science), 2021, 40(05): 66-73.
[5]	ZHANG Yang1, QU Shaoqin1, LU Jiuzhang2, HUO Wenbing3. Method of Fiber Aligning in UHPC and Its Influence on the Tensile Performance [J]. Journal of Chongqing Jiaotong University(Natural Science), 2021, 40(05): 74-80.
[6]	FU Lilei. Correlation Function Method for Parameter Identification Based on Random Excitation Response [J]. Journal of Chongqing Jiaotong University(Natural Science), 2021, 40(04): 70-75.
[7]	SU Xiaobo1, XIAO Lin2. Model Test and Numerical Simulation Research on Reasonable Structure of Steel-Concrete Composite Section in Space Rigid Frame [J]. Journal of Chongqing Jiaotong University(Natural Science), 2021, 40(04): 76-82.
[8]	LIANG Zongbao 1, CHAI Jie1, NA Shouyong2, MA Tianli1, TANG Yu1. Validity Analysis of Bridge Health Monitoring Data Based on Deep Learning [J]. Journal of Chongqing Jiaotong University(Natural Science), 2021, 40(03): 78-83.
[9]	TANG Qizhi1, XIN Jingzhou1,2, ZHOU Jianting1, FU Lei1,3, ZHANG Jun4. Damage Identification of Corroded RC Arch Based on Time Series Analysis:Simulation and Verification [J]. Journal of Chongqing Jiaotong University(Natural Science), 2021, 40(02): 69-77.
[10]	RONG Xian1, 2, YANG Hongwei1, ZHANG Jianxin1, 2. Experimental Research on Hysteresis Behavior of Prefabricated Concrete Beam-Column Joint with Steel End Connector [J]. Journal of Chongqing Jiaotong University(Natural Science), 2021, 40(02): 78-82.
[11]	LIU Xiaohui, XU Yang, CHEN Sitian, XU Lueqin. Seismic Response Analysis of Pedestrian Suspension Bridge [J]. Journal of Chongqing Jiaotong University(Natural Science), 2021, 40(01): 65-71.
[12]	JU Liping1, WANG Yinhui2, LU Xiaohong3, SHAN Jidong4. Failure Mode Analysis of Reinforced Concrete Box Girder under Impact of a Falling Cargo from Passing Truck [J]. Journal of Chongqing Jiaotong University(Natural Science), 2021, 40(01): 72-78.
[13]	WANG Zhen1,2, ZHOU Jianting1,3, ZHANG Jinquan1,4, WU Haijun1, WU Yuexing1. Influence Analysis of Cast-in-Situ Segment Length on Mechanical Behavior of Ten-Thousand-Ton Horizontal Swivel Cable-Stayed Bridge [J]. Journal of Chongqing Jiaotong University(Natural Science), 2020, 39(12): 44-52.
[14]	HAO Xianwu, SHU Peng, HAO Jianming. Static Wind Stability of Long-Span Asymmetric Suspension Bridge [J]. Journal of Chongqing Jiaotong University(Natural Science), 2020, 39(12): 53-59.
[15]	CHEN Sitian, PENG Qing, YANG Min. Human-Induced Vibration Response Analysis of Long-Span Pedestrian Suspension Glass Bridge in Kanggu Parkland [J]. Journal of Chongqing Jiaotong University(Natural Science), 2020, 39(12): 60-66.