Research On Fatigue Crack Propagation Of Orthotropic Bridge Deck Based On Extended Finite Element Method

Due to the complex structure,dense welds,numerous internal defects and stress concentration of the orthotropic steel bridge deck,fatigue cracks are prone to occur in the weld joints of U-rib deck and U-rib diaphragm.Under the repeated action of vehicle wheel load,fatigue failure of the crack will be accelerated.In this paper,based on the summary of domestic and foreign research on fatigue cracks of orthotropic steel bridge deck and online within the framework of elastic fracture mechanics,a multi-scale finite element model of bridges containing initial fatigue cracks at typical weld details of steel box girder is established,and the stress characteristics of the crack tip and stress intensity factor influence line were studied based on extended finite element method.Then simulated the welding residual stress field by elastic-plastic finite element method,investigated the influence of residual stress on crack tip stress field and fatigue crack propagation.On this basis,the influence of the plastic zone at the crack tip on the fatigue crack propagation is further investigated and explored,and the crack mechanism and propagation rules of the fatigue crack in the typical welding details of orthotropic steel bridge are revealed based on the elastic-plastic finite element theory.The main work and achievements of this paper are as follows:(1)The stress characteristics of static cracks in typical welding details of orthotropic bridge deck were analyzed by extended finite element method.First of all,established a multi-scale finite element model of the long-span bridges,the model contains the characteristic scale 10²m of the whole bridge model respectively,and the characteristic scale for 10⁰ m of the orthotropic steel bridge deck refinement model that contain the top deck,the bottom deck,inclined web,U-rib-diaphragm,as well as the characteristic scale for 10^-3 m of solid model of welding details with an initial carck.The boundary displacement of the solid model is in harmony with the nodal displacement of the equivalent orthotropic steel bridge.Under the action of the standard fatigue,the stress intensity factor(SIF)at the crack tip of U-rib-deck weld,U-rib-diaphragm weld toe and opening of diaphragm in a series of typical fatigue welding details of a bridge was studied by method of static influence line loading.According to the influence lines of stress intensity factor at different details,the most unfavorable loading position of the individual vehicle load was determined,and based on the linear elastic fracture mechanics theory,it can be judged whether the stress field at the crack tip of typical fatigue details could drive the initial crack growth under the most unfavorable loading conditions.It is found that under the most unfavorable loading conditions,the stress field of the fatigue crack tip at the U-rib welding toe and diaphragm welding toe of the U-rib-diaphragm connection can drive the initial crack to expand.(2)Analyzed the dynamic propagation behavior of the fatigue crack at the connection site of U rib-diaphragm by using the extended finite element method.The most unfavorable loading positions of various fatigue cracks were obtained by the influence lines of stress intensity factor of each typical crack under different loading conditions.Under the action of moving vehicle load,U-rib-diaphragm connection parts can drive the crack tip stress field of crack propagation and material yield has not been achieved,so using the Paris fatigue crack growth formula and linear elastic fracture mechanics theory to study the fatigue crack growth increment and cycles of the quantitative relationship at this connection part under load of constant amplitude vehicles,and to obtain fatigue crack propagation path and rule of initial cracks that initiat from U-rib welding toe and diaphragm welding toe under the most unfavorable loading positions.It was found that the fatigue crack at the u-rib welding toe maintained an elliptical shape and extended along the direction of the initial crack surface,and the fatigue crack at the diaphragm welding toe would stop under the action of vehicle load.(3)Establish finite element model of U-rib-deck and U-rid-diaphragm that contain weld joint,based on elastic-plastic finite element method,then establishing the constitutive of double linear isotropic strengthen and using life to simulate the temperature field of the welding details of U-rib-deck and U-rib-diaphragm under the heat source of double ellipsoid by the birth-death element technology.Then the temperature field is introduced into the structural analysis model to solve the welding residual stress of the joint by using the thermal-structure sequence coupling analysis method.(4)Analyzed the influence of welding residual stress field on typical fatigue crack propagation of orthotropic bridge deck based on the theory of linear elastic fracture mechanics.Based on multi-scale finite element model,by applying the load of the vehicle and introducing the residual stress field at the connecting part,the typical fatigue crack growth law under the welding residual stress is analyzed.Then the energy release rate of the crack tip and the fatigue crack growth rate when considering the residual stress field were calculated,and the fatigue crack growth and the redistribution curve of the welding residual stress with the crack growth of the typical fatigue cracks of the orthotropic bridge deck were obtained.Comparing the results of fatigue crack growth without considering the residual stress field,the influence of welding residual stress on fatigue crack growth was analyzed.The simulation results show that the fatigue crack propagation types of initial crack at deck welding toe,deck welding root,U-rib welding toe and diaphragm welding toe are composite cracks except the crack at the opening of diaphragm.The propagation of fatigue crack caused the welding residual stress to change with the propagation of fatigue crack,but the maximum residual stress in the crack surface area would not reach the yield strength of the material.In addition,the welding residual stress field increased the tensile stress of the crack surface,then promoted the fatigue cracks at typical fatigue details that can't expand under the action of the single vehicle load to extend,and the crack propagation rate of fatigue details of fatigue crack propagation under single vehicle load was accelerated.(5)In order to considering the plastic zone at the tip of fatigue crack caused by residual stress,the elastic-plastic constitutive relationship of material was introduced to consider the effect of elastic-plastic zone at crack tip on the law of fatigue crack propagation.By judging the state of residual stress field at the crack tip,different fatigue crack propagation rates formula were selected to analyze the propagation law of fatigue crack after considering the plastic deformation,and the propagation path and rate of fatigue crack in orthotropic bridge were obtained.Adopting the research methods of this paper can be used to obtain extension and extension rate of fatigue crack that initiate from typical welding details at orthotropic bridge deck under conditions of the vehicle load,the combined of residual stress field and vehicle load,and considering the effects of the crack tip plastic zone,the results of this paper can provide the basis for the anti-fatigue performance of steel bridge deck study,anti-fatigue design and maintenance methods and the durability of long span bridges in service guarantee.