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A strategy for rib-to-deck crack propagation analysis and strengthening of orthotropic deck bridges
Abstract
Rib-to-deck connections are one of the most critical fatigue-prone locations in orthotropic steel decks. Initiated cracks in the root of a fillet weld in this location can propagate towards the deck plate due to the existence of transversal tension within the deck plate near the cracking area. Such cracks can put the structure in a very critical situation since they can reach their critical length without being inspected. The main goal of this paper, therefore, is to investigate the influence of the transversal tension on the crack propagation direction in this region. For that, one translates the loading and boundary conditions from a 3D model to a 2D model to avoid computational issues with 3D modelling. Then, a 2D crack propagation analysis is performed using XFEM method, enabling the comparison of several repair solutions. To illustrate the proposed concepts, this paper investigates the fatigue problem on a real bridge case study and characterizes the effectiveness of two possible repair solutions to cope with such fatigue issues.
... Due to residual stress and prolonged exposure to vehicular loads, fatigue cracks inevitably develop in the orthotropic steel bridge decks over time [1][2][3]. The welded joint of the deck and U-rib is a susceptible area to fatigue [4][5][6]. This vulnerability is primarily due to the prevalence of partial penetration welds in the early construction of steel bridges, which leads to crack initiation at the weld root, as depicted in figure 1. ...
... The curve after projection (marked as 'pr' in the figure, indicated by dashed lines) shares better trend with the curve angle (solid red line). This indicates the validity of by equation (5). The crack depth and angle can be calculated by depth-strength curves of two different K values. ...
... The received echo height of the root-deck crack is positively correlated with the crack depth, while the root-weld crack is negatively correlated. Applying equation (5), the crack depths for the 75 • and 195 • curves were converted, resulting in the projected curves. The projected curves exhibit good consistency with the corresponding position curves. ...
Weld root crack represents a significant concern in terms of fatigue on orthotropic steel decks (OSDs). This study presents a crack detection method based on ultrasonic penetration signals, to effectively distinguish and quantify cracks in decks. Firstly, based on the principles of sound diffusion and the structural characteristics of orthotropic steel decks, the parameters were established. Then, the propagation mechanism of ultrasonic waves in decks containing cracks was investigated by finite element analysis. The variations in received signal intensity caused by root-deck and root-weld crack parameters were analyzed and the methods for distinguishing between crack types and determining characteristics were proposed. Finally, experimental tests were conducted on weld root cracks to validate the feasibility of the detection method. The research findings demonstrate that the selected detection parameters adequately meet the requirements for crack detection. By utilizing fitting functions between the transmission signals from two sets of detection parameters and the projected crack length, the method achieves accurate identification of crack length and angle, with an error rate of less than 10%.
... Studies show that increasing the thickness of deck plate can significantly improve the fatigue life welded joints (Kainuma et al., 2017;Xiao et al., 2008). Ahmadivala et al. (2022) investigated the effect of applying a cementbased horizontal overlay by thickening the deck plate in the FE model. Some researchers proposed that a thickened U-rib edge can increase the fatigue strength of U-rib to deck joints (Heng et al., , 2020Luo et al., 2019;Zheng et al., 2019). ...
... To obtain function parameters, the SIF values at different crack lengths were measured. Since the cracks initiated in these details are mainly type-I cracks [26,27], the two-strain-gauge (TSG) technique applied to typed I crack was adopted [28]. TSG technique calculates SIF by solving a set of equations, which involves the values of two strain gauges arranged normal to the crack tip, as shown in Fig. 9. Due to the impracticality of measuring a crack located on the weld joint, the SIF of DV3 before penetration was not measured. ...
... For crack propagation life prediction of welded joints, it is a common way to utilize the Paris law with correction of crack configurations and local notch for the stress intensity factors (SIF) [27]. With the aid of finite element analysis (FEA), the virtual crack closure-integral method (VCCM) [28] and extended finite element method (XFEM) [29] are also widely used to simulate the crack propagation of welded joints with structural discontinuities. Zong [30] assessed the crack propagation life of weld root by both numerical and analytical approaches, and an appropriate prediction was achieved considering the multi-crack condition. ...
Conventional S-N curve methods for fatigue life assessment fail to consider the different cracking mechanisms of crack initiation and propagation, resulting in less accurate predictions of fatigue life. The present study aims to assess the fatigue crack initiation and subsequent propagation life of rib-to-deck welded joints separately by accurate prediction of local cyclic elastoplasticity. The welding residual stress was simulated with high precision by thermal-mechanical analysis based on the real bead geometry and welding parameters, and defined as initial stress condition. The performance of an unconventional Fatigue Subloading Surface constitutive model (FSS model, hereafter) to predict the cyclic elastoplasticity in the sub-yield stress state was proved by comparing to the experiment results and conventional plasticity theory. The FSS model was then embedded to distinct zones of welded joints for cyclic structural analyses. Considering the relaxation of residual stress, the fatigue crack initiation by the local strain approach based on the local cumulative plasticity damage, and propagation life was assessed by the analytical approach based on the LEFM parameters of materials. As a connection between the crack initiation and propagation, the initial crack featured by 0.5 mm depth and semi-circular shape was proposed. The current work is verified to assess the fatigue life of rib-to-deck welded joints with high accuracy under the pure bending load against experiment results.
... An analysis of crack propagation in orthotropic bridge slabs by Ahmadivala, et al. (2022) showed that the most dangerous is the weld in the area of fixing the flooring and the stiffener. The numerical analysis made it possible to reveal the destruction mechanism and give suggestions for strengthening the structure. ...
Heavily loaded frame structures of transport vehicles, such as railway locomotives or road trains, are exposed to high stresses in the areas of welded joints. Fatigue accumulation of damage leads to cracking along the welds, which necessitates machining of the welds and strengthening of individual sections. The seam processing technology and hardening treatments depend on a large number of factors, the accounting of which is an urgent scientific problem. This article discusses a frame structure of channels connected by manual arc welding. The fusion and heat-affected zones are hardened by the impact action of a rod with a spherical head. The contact interaction between the impactor and the frame is analyzed numerically using the FEM method. The numerical analysis results in the form of fields of stresses, deformations, and displacements made it possible to choose rational modes of indentation and processing.
... This sub-section reviews some basic knowledge about the cracking behavior of a simply-supported RC beam with flexural and webreinforcement, under uniform loading [37,[49][50][51][52][53]. ...
This paper is devoted to Reinforced Concrete (RC) beams that can be subjected to accidental falls of substantial masses (hard impacts at low velocities), such as the beams of bridges, industrial buildings, or factories. Here the reference is to existing RC beams, which have no purposely designed reinforcement to resist impacts.
The paper focuses on a mass that falls around the midspan, where the capacity of a RC beam to resist an impact is minimum, due to a potential primary cracking pattern that consists of vertical cracks.
The impact here is defined by the combination of the mass that falls down and its velocity at the impact. The paper provides an analytical formulation to predict the combinations that trigger the collapse of a RC beam (i.e., ultimate combinations). After having framed the research question, the paper presents the two possible failure modes, the derivation of the equations, the sensitivity of the bearing capacity to the main parameters, comparisons with existing results from literature, and two applications, whose results are discussed.
In order to study the mechanical behavior of U-rib internal welding of orthotropic plate, the three-dimensional thermal coupling model of U-rib of orthotropic plate was established by using ABAQUS finite element software, and the structural stress distribution law of welded joints in three groups of welded joints was analyzed in four kinds of loading conditions by taking into consideration of the presence of weld toe on the inner side, different sizes of weld toe on the inner side, and different welding melt depths. The results show that the structural stress distribution law of single-sided welding and double-sided welding is the same, the structural stress of the outer weld toe of the bridge deck plate and the outer weld toe of the U-rib is more than 80 MPa under unfavorable working conditions, and the cracking chance is the greatest, the change of melting depth has the greatest influence on the structural stress of the outer weld, and the setting of inner welding can effectively improve the structural stress and improve the welding quality.
The rib-to-deck joints are one of the most critical vulnerable details of orthotropic steel deck subjected to vehicle loads. Specially, fatigue cracks initiating from the weld root and propagating along the thickness of the deck at the rib-to-deck joints is most difficult to repair. In this study, the interior repair weld is adopted to enhance the fatigue resistance of rib-to-deck joint. Three specimens of rib-to-deck joint were designed and tested to investigate the effectiveness and applicability of the interior repair weld. The fracture mechanics method associated with numerical simulation is adopted to analyze the failure mechanism and remaining life of rib-to-deck joints after reinforcement. The results indicate that the region of fatigue crack initiation will be transferred from the interior weld root before repairing to the exterior weld toe after repairing. The interior repair weld can effectively prevent fatigue crack propagation and significantly improve the remaining fatigue life of the rib-to-deck joints. The simulated fatigue life agrees well with the measurement in fatigue tests, revealing the accuracy of fracture mechanics method to estimate the remaining life.
Fatigue of materials, like alloys, is basically fatigue-crack growth in small cracks nucleating and growing from micro-structural features, such as inclusions and voids, or at micro-machining marks, and large cracks growing to failure. Thus, the traditional fatigue-crack nucleation stage (Ni) is basically the growth in microcracks (initial flaw sizes of 1 to 30 μm growing to about 250 μm) in metal alloys. Fatigue and crack-growth tests were conducted on a 9310 steel under laboratory air and room temperature conditions. Large-crack-growth-rate data were obtained from compact, C(T), specimens over a wide range in rates from threshold to fracture for load ratios (R) of 0.1 to 0.95. New test procedures based on compression pre-cracking were used in the near-threshold regime because the current ASTM test method (load shedding) has been shown to cause load-history effects with elevated thresholds and slower rates than steady-state behavior under constant-amplitude loading. High load-ratio (R) data were used to approximate small-crack-growth-rate behavior. A crack-closure model, FASTRAN, was used to develop the baseline crack-growth-rate curve. Fatigue tests were conducted on single-edge-notch-bend, SEN(B), specimens under both constant-amplitude and a Cold-Turbistan+ spectrum loading. Under spectrum loading, the model used a “Rainflow-on-the-Fly” subroutine to account for crack-growth damage. Test results were compared to fatigue-life calculations made under constant-amplitude loading to establish the initial microstructural flaw size and predictions made under spectrum loading from the FASTRAN code using the same micro-structural, semi-circular, surface-flaw size (6-μm). Thus, the model is a unified fatigue approach, from crack nucleation (small-crack growth) and large-crack growth to failure using fracture mechanics principles. The model was validated for both fatigue and crack-growth predictions. In general, predictions agreed well with the test data.
Orthotropic Steel Decks (OSDs) are widely used in various types of steel bridges due to its benefits of light weight, high load bearing capacity and speedy construction. However, fatigue remains as the predominant problem for OSDs. Many researchers have investigated fatigue issues of welded joints through experiments but is not a cost-effective solution. Therefore, it is necessary to combine experimental data with numerical approaches. Fracture mechanics approach has already shown its reliability and can be used to model and analyze fatigue crack propagation. In this paper, a numerical simulation is performed to predict the fatigue crack propagation using extended finite element method (XFEM). Two numerical models were considered namely CT-specimen and OSD, to evaluate the modelling efficiency. To verify the simulation, the results were compared with the experimental data. In predicting the fatigue crack propagation rate using two-dimensional CT-specimen, numerical results provided a good agreement with a maximum difference of 0.03% in the slope (m) and 1.48% in the intercept (C) of the power law equation. Furthermore, a simulation was performed on three-dimensional OSD structure to predict the fatigue crack growth.
Since the developments of the so-called D.S.P materials in 1978 and C.R.C in 1986 by
civil engineer Hans Henrik Bache and co-workers at Aalborg Portland Denmark
different changes to the original concept have been made. For the use in civil
engineering, accentuate emphasize to industrial floors, pavements and concrete
renovation, there are 3 main disadvantages from the original concept i.e. the
workability, the finishability and the chemical shrinkage, all related, direct or indirect,
to the extreme low water/ binder ratio and the high amount of micro-silica containing
binder. Especially in cases where it is important to get full benefit of the properties of
an ultra high strength concrete like in ultra thin overlays in combination with high
volumes of traditional steel bars and steel fibres the workability and finishability is of
main importance for the final result and the qualities from the hardened matrix.
Since the developments of the so-called D.S.P materials in 1978 and C.R.C in 1986 by civil engineer Hans Henrik Bache and co-workers at Aalborg Portland Denmark different changes to the original concept have been made. For the use in civil engineering, accentuate emphasize to industrial floors, pavements and concrete renovation, there are 3 main disadvantages from the original concept i.e. the workability, the finishability and the chemical shrinkage, all related, direct or indirect, to the extreme low water/ binder ratio and the high amount of micro-silica containing binder. Especially in cases where it is important to get full benefit of the properties of an ultra high strength concrete like in ultra thin overlays in combination with high volumes of traditional steel bars and steel fibres the workability and finishability is of main importance for the final result and the qualities from the hardened matrix.
Since the initial development by German engineers after the Second World War, steel orthotropic bridge decks are widely used for large and medium span bridges. Unfortunately, this type of bridge deck has several disadvantages which are mostly related to the flexural deformations of the deck plate under traffic load and their effect on the ribs or stiffeners, crossbeams, girders and the wearing course (Boersma and De Jong 2003, Wolchuk, 2002). In the Netherlands a large research project is executed during the last five years to develop a new revolutionary concrete-based wearing course on orthotropic steel bridges which extends the service life of the total structure by solving fatigue problems in specific deck details. Project initiator is the Civil Engineering Division of the Dutch Ministry of Transport, Public Works and Water Management in close co-operation with Contec ApS, the Delft University of Technology and TNO. KEY WORDS: High performance concrete, ultra thin overlay, orthotropic bridge decks.
The influence of welding residual stresses in stiffened panels on effective stress intensity factor (SIF) values and fatigue crack growth rate is studied in this paper. Interpretation of relevant effects on different length scales such as dislocation appearance and microstructural crack nucleation and propagation is taken into account using molecular dynamics simulations as well as a Tanaka–Mura approach for the analysis of the problem. Mode I SIFs, KI, were calculated by the finite element method using shell elements and the crack tip displacement extrapolation technique. The total SIF value, Ktot, is derived by a part due to the applied load, Kappl, and by a part due to welding residual stresses, Kres. Fatigue crack propagation simulations based on power law models showed that high tensile residual stresses in the vicinity of a stiffener significantly increase the crack growth rate, which is in good agreement with experimental results.
Over the past years, with increasing traffic volumes and higher wheel loads, fatigue damage in steel parts of typical orthotropic steel bridge decks has been experienced on heavily trafficked routes. A demand exists to find a durable system to increase the fatigue safety of orthotropic steel bridge decks. A solution might be to enhance the stiffness of the traditional orthotropic bridge deck by using a cement-based overlay. In this paper, an orthotropic steel bridge deck stiffened with a cement-based overlay is analyzed. The analysis is based on nonlinear fracture mechanics, and utilizes the finite-element method. The stiffness of the steel deck reinforced with an overlay depends highly on the composite action. The composite action is closely related to cracking of the overlay and interfacial cracking between the overlay and underlying steel plate (debonding). As an example, a real size structure, the Farø bridges located in Denmark, are analyzed. The steel box girders of the Farø bridges spans 80 m, and have a depth of 3.5 m, and a width of 19.5 m. The focus of the present study is the top part of the steel box girders, which is constructed as an orthotropic deck plate. Numerous factors can influence the cracking behavior of the cement-based overlay system. Both mechanical and environmental loading have to be considered, and effects such as shrinkage, temperature gradients, and traffic loading are taken into account. The performance of four overlay materials are investigated in terms of crack widths. Furthermore, the analysis shows that debonding is initiated for a certain crack width in the overlay. The load level where cracking and debonding is initiated depends on the stress-crack opening relationship of the material.
This study examines a two-state interaction integral for the direct computation of mixed-mode stress intensity factors along curved cracks under remote mechanical loads and applied crack-face tractions. We investigate the accuracy of stress intensity factors computed along planar, curved cracks in homogeneous materials using a simplified interaction integral that omits terms to reflect specifically the effects of local crack-front curvature. We examine the significance of the crack-face traction term in the interaction integral, and demonstrate the benefit of a simple, exact numerical integration procedure to evaluate the integral for one class of three-dimensional elements. The work also discusses two approaches to compute auxiliary, interaction integral quantities along cracks discretized by linear and curved elements. Comparisons of numerical results with analytical solutions for stress intensity factors verify the accuracy of the proposed interaction integral procedures.
Gmsh is an open-source 3-D finite element grid generator with a build-in CAD engine and post-processor. Its design goal is to provide a fast, light and user-friendly meshing tool with parametric input and advanced visualization capabilities. This paper presents the overall philosophy, the main design choices and some of the original algorithms implemented in Gmsh. Copyright © 2009 John Wiley & Sons, Ltd.
An improvement of a new technique for modelling cracks in the finite element framework is presented. A standard displacement-based approximation is enriched near a crack by incorporating both discontinuous fields and the near tip asymptotic fields through a partition of unity method. A methodology that constructs the enriched approximation from the interaction of the crack geometry with the mesh is developed. This technique allows the entire crack to be represented independently of the mesh, and so remeshing is not necessary to model crack growth. Numerical experiments are provided to demonstrate the utility and robustness of the proposed technique.
This study is dealing with the effect of the grain size on the fatigue lifetime of metallic components, which is represented in the form of (S-N) Wöhler curves of two different grain sizes. The micro-models containing the microstructures of the two different grain sizes are handled by employing the Finite Element Method (FEM) and the required number of cycles for crack initiation was calculated by using the physically-based Tanaka-Mura model. By implementing the different grain sizes in the micro-model, the effect of the grain size on the fatigue life and especially on the endurance limit, in the form of the S-Nini diagram, can be obtained.
The aim of the paper is to investigate the influence of compressive residual stresses on the fatigue initiation life (S-Nini) curve of AISI 1141 steel. The analysis has been performed by means of a micro-structurally-based fatigue crack initiation modelling approach. The focus is set on the local (surface) residual stresses typically imposed by a surface treatment technique known as shot -peening. By superimposing such stresses on stresses resulting from outer cyclic loading, it could be shown that an impact on the fatigue curve in the S-Nini diagram can be achieved.
Fatigue of orthotropic steel decks (OSDs) has significantly limited the service life of such structures, and the welding residual stress (WRS) has been reported as a prominent factor that should be considered in their fatigue life evaluations. However, the weldment size effect on WRSs is often neglected in the conventional evaluation. This paper performed fatigue life evaluations of deck to U-rib welds in an OSD integrating the weldment size effects. First, the concept and hypotheses of the weldment size effect on WRSs were outlined in detail. Second, the sequential coupling method was selected for the WRS simulation, which was then experimentally verified using the blind hole method. Third, the influences of longitudinal and transverse weldment sizes on WRSs were analyzed by comparing the simulated WRS results corresponding to welding structures with different longitudinal sizes and U-rib numbers, respectively. Finally, fatigue life evaluation of the welds was conducted based on a modified S-N curve. The results show that (1) the WRSs at the welds can be accurately simulated through the adopted thermal-structural sequential coupling method; (2) the weldment size has a definite influence on the local distribution of WRSs: the WRS decreases exponentially with the increase of the longitudinal welding length; (3) the proposed method, which integrates the size effect on WRSs with the life evaluation, provides a relatively reasonable fatigue life for the deck to U-rib welds. In summary, the findings of this study enhance our understanding of the distribution laws of WRSs in OSDs, and suggest that it is vital to integrate the weldment size effects on WRSs in the process of accurately predicting fatigue life.
This paper describes an investigation of fatigue strength enhancement for transverse to longitudinal rib connections in orthotropic steel decks with open ribs by structural modification. A structural hot-spot stress approach was used to evaluate the fatigue strength. The results of a finite-element analysis revealed that the fatigue strength decreased with increasing span length of the longitudinal ribs. The structural modifications to the connection, which reduced the stiffness of transverse ribs due to section loss, absorbed the local deformation of the deck plate and consequently reduced the structural hot-spot stress.
Double-sided weld is an effective way to improve the fatigue performance of orthotropic steel bridge decks (OSBD). However, the fatigue performance and optimization design methods of double-sided welds connecting the U-rib and the deck in OSBD require further study. In this paper, the finite element modeling method suitable for the notch stress approach in double-sided welds is discussed, and its variance from that of the single-sided weld is revealed. All possible fatigue failure modes of double-sided welds, the transfer phenomenon of fatigue crack initiation location and the change of fatigue failure modes under different vehicle loading conditions are revealed. It is further discussed that how the change of the deck plate thickness and the weld foot length alters the fatigue failure mode under the same loading condition. According to the above analysis, in order to obtain the optimal fatigue performance of double-sided welds, an optimal design method based on the fatigue damage factor per unit time under real vehicle loading conditions is proposed. The analysis results show that the fatigue failure modes of the double-sided welds of the U-rib-to-deck welded joint in the OSBD is determined by three factors: loading condition, deck plate thickness and weld foot length. According to the optimization factor proposed in this paper, the thickness of the deck plate and the length of the weld foot can be reasonably determined under different traffic loading conditions, so that the fatigue performance of the rib-to-deck joint in the OSBD is optimized.
The research presented in this paper is based on the use of extended finite element method (XFEM) for stress intensity factors (SIFs) determination in the case of fatigue crack presented in the wing-fuselage attachment lug used in light aerobatic aircraft. The presence of the through crack at the attachment lug hole is not allowed since its growth due to high dynamic loads is usually fast and can lead to catastrophic consequences. To demonstrate how dangerous the appearance of the crack could be, as well as to estimate the residual strength and fatigue life of cracked component, finite element model of attachment lug was made, and analyses were carried out using the maximum load that can occur during the flight (load factor n=6). The predicted number of cycles to complete failure was – as expected – low, confirming the fact that attachment lugs must be designed using safe-life approach.
This study focuses on the orthotropic steel deck (OSD) of a cable-stayed bridge with a plate-truss composite structure. Fatigue tests and numerical simulations were conducted to investigate fatigue features in an OSD with a broad U-rib and embedded sections, considering the assembly tolerance. For the purpose of this study, the pre-stressing force method was adopted to simulate the initial axial pressure in the deck. Fatigue tests were done on three full-scale segment specimens (a total of 6.5 million variable amplitude fatigue cycles). Initial long macro cracks are observed in the arc segment of butt welds. The length of these initial cracks is proportional to the stress amplitude. Fatigue crack propagation stages in the broad U-rib can be divided into four parts with clear demarcation points. The crack growth rate is proportional to the crack length; this increases as a result of the axial force. The initial axial pressure accelerated the crack propagation rate of fatigue details of butt welds. It is recommended that the butt welds of the broad U-rib embedded section can be designed using the fatigue strength of category FAT112 in Eurocode 3. In addition, empirical correction formulas for fatigue strength correction for assembly tolerance of the embedded section are proposed.
This paper provides comparative results on stress behavior and fatigue performance of two types of cutout geometry on orthotropic bridge decks based on simultaneous field monitoring and finite-element method (FEM) analysis. The two types of cutout are incorporated in two closely spaced diaphragms with distance of 6 m and at the same transverse location on a real bridge, allowing simultaneous stress measurement under random traffic flows. The research was conducted on the Pingsheng Bridge in Southern China, a self-anchored suspension bridge with a main span of 350 m and a steel box girder with orthotropic steel bridge decks (OSBD). Results of the study reveal that the two types of cutout geometry present high stress response and severe stress concentration at the floorbeam (FB) cutout, and that the excessively large stress at the original FB cutout contributes greatly to the early cracks of this detail. Compared to the original cutout geometry, the new cutout geometry with large radius increases the stress level at the FB cutout, resulting in a further low fatigue life at this detail. Meanwhile, the new cutout geometry also deteriorates the fatigue resistance at the rib-to-floorbeam (RF) weld connection, particularly at the detail of rib wall at cutout, where the stress level is significantly increased and its fatigue life becomes substantially lower than the design life of 100 years. In addition, the new cutout geometry only slightly improves the out-of-plane distortion under direct wheel loading, and the in-plane stress still dominates the total stress at the FB cutout. Since the new cutout geometry weakens the FB web, the total stress at FB cutout will increase due to the increased in-plane stress. The research also finds that if the free edge of cutout did not satisfy the fabrication requirement per the AASHTO LRFD, category B is suggested for fatigue evaluation at the FB cutout, which is confirmed by the observed fatigue life of the original FB cutout on the real bridge. It is concluded that the new cutout geometry lowers the fatigue resistance both at the FB cutout and at the RF weld connection, hence it will no longer be recommended to retrofit the present bridge in the future.
The orthotropic steel decks (OSDs) are widely used in bridge engineering to support traffic loads. A possible crack, initiating from the weld toe of rib-to-deck welded joint and growing into the deck plate, is studied using linear elastic fracture mechanics. A detailed FE model is created and the results are compared with the fatigue tests published. Good agreement is found between beach marks from experiments and calculated crack fronts in FE. An engineering approach with the crack shape simplified as a semi-ellipse is applied. Geometric correction factors for a hand calculation method is proposed based on the parametric analysis. Using the proposed correction factors, Monte Carlo simulation is carried out with failure criteria defined with respect of the crack depth reaching “50%” of the deck thickness, “75%” of the deck thickness, and the failure criterion “2A FAD” according to BS7910. Predicted results using the failure criterion “75%” show good agreement with experimental data, for 5%, 50%, and 95% survival probabilities. Effects of initial crack shapes and sizes are discussed using the improved hand calculationmodel. Lower fatigue resistance is foundwhen the initial crack is shallowor large. In addition to the standard weld geometry in which the weld profile is represented by a straight line, concave and convex arc shapeweld profiles are studied. Fatigue resistance is improved in the case with assumption of concave arc weld profile. The difference of fatigue resistance between the cases with a straight line and convex arc weld profiles is small.
Keywords: Orthotropic steel bridge deck Rib-to-deck welded joints Fatigue failure mode Equivalent structural stress Mater S-N curve Weld penetration ratio A B S T R A C T Rib-to-deck welded joints in orthotropic steel decks have demonstrated different fatigue failure modes that have different fatigue resistance. Among the different failure modes, the mode corresponding to the lowest fatigue resistance governs the fatigue resistance of the welded joint. The ability of determining the governing failure mode is essential for predicting the fatigue resistance of the welded joints. This research establishes a fatigue evaluation framework for determining the dominant failure mode of rib-to-deck welded joints. The framework is established based on the equivalent structural stress method and validated using model test data. The results indicate that the proposed framework provides accurate prediction of the dominant fatigue failure mode of rib-to-deck welded joints. Based on the presented framework, the fatigue resistance of the welded joints is reasonably predicted, and the effect of weld penetration ratio on the fatigue failure mode is investigated.
Fatigue cracks at rib-to-crossbeam welded joints in orthotropic steel decks (OSDs) accelerate degradation of steel bridges. This research aims to investigate fatigue cracking characteristics of rib-to-crossbeam welded joints, and assess the fatigue strength of the welded joints through fatigue testing and finite element analysis. Nine large- scale specimens were tested under static and fatigue loading to explore the failure mode, fatigue life, and failure process. The fatigue test results were compared with the fatigue strength values recommended in different de- sign specifications. Based on the hot spot stress and notch stress approaches, S\N curves for rib-to-crossbeam welded joints were derived and compared with the existing fatigue test data. The results indicate that fatigue cracks that initiate from the weld end at the weld toe controls the fatigue resistance of the rib-to- crossbeam welded joints. A statistical analysis was performed to study the probability distribution of the fatigue strength.
The numerous welded joints in orthotropic steel decks (OSDs) lead to a high probability of fatigue damage. One of the most detrimental problems is the severe reduction of the serviceability due to cracks in rib-to-deck welded joints, which require in-depth studies on the entire fatigue process. The linear elastic fracture mechanics has been proven to be effective in this aspect. When put into practice on actual projects, however, its accuracy and feasibility are largely dependent on features in various scales. This paper presents an investigation on the fatigue behavior of orthotropic steel decks with respect to multiscale concerns. By performing fatigue tests on OSD specimens welded by 15-mm-thick deck plates and 6-mm-thick stiffeners of S355 steel, the rib-to-deck weld toe crack that penetrates the deck plate is produced and the crack growth path is addressed using beach mark method. Afterwards, a two-dimensional local model of the rib-to-deck weld toe crack is built using the extended finite element method by which the stress intensity factors for early-stage cracks can be obtained. Based on the similar concept of nominal stresses, it can easily be linked to the macroscopic model and forms a non-concurrent method that enables to simulate the crack growth at rib-to-deck weld toe. As a result, a crack growth rate curve for the test specimen is given and different stages are analyzed with respect to the Paris law, indicating a clear influence of the early-stage fatigue cracks. The material constants of crack growth are obtained and validated, which may further be introduced to the fatigue assessment and life estimation for the maintenance work of OSDs.
During the latest 20 years, the extended finite element method (XFEM) has been gradually used to investigate the crack growth behaviors of different materials in combination with various mechanics models and became the most popular computational tool in analyzing crack problems. This paper classifies three typical theoretical frameworks of the XFEM, namely the linear elastic fracture mechanics, the cohesive zone model and the elastic-plastic fracture mechanics based XFEM. A review of brittle and ductile crack growth under both monotonic and cyclic loadings using the XFEM was given from both macro-scale and micro-scale after a systematic literature survey. In contrast, the framework of the XFEM for modeling brittle fracture is the most comprehensive and widely used theory, but the theory for the ductile crack growth has still to be developed. Additionally, the XFEM becomes more complicated in microcrack growth simulations than macrocrack by considering the effects of microstructures of materials. The XFEM can introduce an arbitrary discontinuity into the finite element and can be employed to analyze different crack growth problems in engineering materials and structures, this paper is served as a valuable reference for the future study in this field.
Tests on a full-scale orthotropic steel deck (OSD) specimen were conducted to investigate the effects of inner bulkheads set inside the U-ribs on the static and fatigue behaviours of the OSD. The total length and width of the OSD specimen are 5 m and 2.24 m, respectively. It contains three longitudinal floorbeams and four transversal U-ribs. U-ribs with and without inner bulkheads are symmetrically arranged in the cross section of the specimen. Finite element (FE) analyses on the OSD specimen model and sub-models were conducted to further study the effects of the inner bulkhead design and different bulkhead shapes. Results of the test and corresponding FE analysis of the specimen showed that inner bulkheads can be used to improve the fatigue life of the OSD. Meanwhile, fatigue cracking in the rib-to-bulkhead details was introduced by installing the inner bulkhead. Results of the FE analysis of the sub-models showed that the distance from the bottom edge of the inner bulkhead to the tip of the floorbeam cutout affects the stress state of the rib-to-floorbeam connection weld significantly. Additionally, the bulkhead shape affects the hot spot stress of the weld toe of the rib-to-floorbeam connection weld significantly. Thus, proper bulkhead shape should be determined by considering the specific stress distribution of the rib-to-floorbeam connection area.
Steel orthotropic decks in bridges and ferries have shown to be prone to fatigue cracking. A typical fatigue crack observed in these structures initiates at the root of the weld between the deck plate and stringer and grows into the deck plate. Due to limited fatigue test data available and the deviating characteristics of this type of crack as compared to other types of fatigue cracks, the fatigue strength is uncertain. In this study, a linear elastic fracture mechanics model has been developed for this type of crack, providing insight into its fatigue performance. The model predicts a relatively high fatigue resistance which is close to the results of fatigue tests. The model further predicts a relatively long residual fatigue life after crack detection, providing large inspection intervals.
This research presented the fatigue tests of longitudinal stringer-to-deck (SD) welded connections, which have been identified as the locations most sensitive to fatigue damage in the orthotropic steel decks (OSDs) of railway bridges. Four full-scale SD connections were fabricated, and two loading patches were considered. Static loading was first carried out to obtain the structural hot spot stresses at weld toes as well as stress concentration factors (SCFs), by which the hot spots providing the highest stresses were identified. Cyclic loading was then implemented next to the static loading, and the behaviors including fatigue crack initiation and propagation process, fatigue failure mode, characteristic fatigue life, as well as degradation of vertical rigidity, were all obtained from the test. The crack growing process can be totally divided into four stages, and the fatigue lives after the crack arrived at the deck edge were very short. Variations of crack dimensions were also obtained, and the simplified formulae of crack growth rate were numerically fitted so that the crack propagation lives can be predicted by using the crack dimensions. Comparisons also show that the FAT 100 curve in IIW fatigue design recommendation could overestimate the fatigue resistance of such connections where double-sided fillet welds were used to connect the stringer web and the deck plate, and therefore double-sided groove welds with partial or full penetrations are recommended for the stringer-to-deck connections in railway bridge decks.
This paper presents a method for predicting fatigue crack propagation in welded stiffened panels accounting for the effects of residual stresses. Well known power law models were employed to simulate fatigue life for a welded stiffened panel specimen damaged with a central crack. Stress intensity factor values (SIF) were obtained in finite element (FE) analyses by a linear superposition of the SIF values due to the applied load and due to weld residual stresses. The FE models included idealized, rectangular or triangular, residual stress distribution profiles. The effect of welding residual stresses on the crack propagation rate is taken into account by replacing the nominal stress ratio R in the power laws by the effective stress intensity factor ratio Reff. The considered stiffened panel specimen, made of mild steel commonly used in ship structures and manufactured by electric arc welding process, was subjected to the fatigue test with constant amplitude loading until failure occurred. By using the presented method remaining fatigue life of welded stiffened panel specimen was analysed. The simulated crack growth rate was relatively higher in the region of tensile residual stresses and lower between the stiffeners where compressive residual stresses prevail, which is in good agreement with physical principles and experimentally obtained results.
The main bridge of the Zhuankou Changjiang River Highway Bridge is a semi-floating system PK (Pasco-Kennewick Bridge) section steel box girder cable-stayed bridge with double pylons, double cable planes and with a main span of 760 m. The bridge is the first expressway bridge that is to carry dual four lanes and that has the total deck width of 46 m over the Changjiang River. In the light of the characteristics of the wide deck, long span and heavy traffic load of the bridge, the key techniques of the general constraint system of the structure, shear lag effect of the main girder, fatigue performance of the orthotropic steel deck and the transverse forces of the pylons have been researched in the design. The optimizing of the constraint system of the structure, using the new type of the heavy load “spring+damping” composite dampers, is proposed. To weaken the shear lag effect of the wide deck, the PK section box girder with the central longitudinal webs is chosen and the depth of the girder is appropriately increased. The two-side fillet weld joints connecting the steel deck plates and the longitudinal U ribs are to be realized, using the small smart welding robots. The fatigue details of the cutouts of the U ribs at the diaphragms are optimized, the transverse local stiffness of the steel decks of the two lanes at the outer sides are reinforced and by setting the transverse precambering on the middle columns of the pylons, the transverse forces of the pylons are to be improved. © 2017, Journal Press, China Railway Bridge Science. All right reserved.
A triaxiality-dependent Cohesive Zone Model for the numerical prediction of failure loads of notched specimens under different loading modes is presented. Since the cohesive crack is modelled by means of the embedded crack approach, one can express the cohesive parameters with variables from the continuum, such as pressure or triaxiality. The model is validated by its application to two experimental campaigns previously developed by the authors on notched specimens subjected to mode I and III loadings respectively, made of gray cast iron, a strongly pressure dependent material.
The rib-to-deck (RD) welded connections are the most sensitive locations to encounter the fatigue failure in orthotropic steel decks (OSDs), and numbers of fatigue cracks arising from these areas have been found in existing OSD bridges. This research focus on the fatigue cracking process, fatigue characteristics as well as failure mechanics of RD connections under cyclic loading. Six full-scale RD welded joints were fabricated, and two load cases of centric and eccentric loading were considered. Static loading was first conducted with aims of measuring elastic strain distributions at potential hot spots. Structural hot spot stresses at weld toes as well as stress concentration factors (SCFs) were linearly extrapolated by using the recorded strains, based on which critical locations were identified. High-cycle repeated loading was subsequently implemented, from which the fatigue crack initiation and propagation process, fatigue failure mode, characteristic fatigue life, as well as degradation of vertical rigidity, were obtained. Four stages of crack propagation were mainly observed, and the remaining fatigue lives after the crack reached the deck edge were short to be neglected. Variations of crack dimensions including the longitudinal length and the depth in the plate thickness were also revealed. The simplified formulae of crack growth rate were proposed to estimate the crack propagation lives based on crack dimensions. Comparison between experimental numbers of cycles and standard S-N formulae indicates that the FAT 100 curve provided in the IIW fatigue recommendation could be conservatively used to estimate the fatigue resistance of such rib-to-deck welded connections composed of 16 mm thick deck plates and 80% PJP welds.
Forty specimens were tested under different stress amplitudes to study the roof and U-rib weld fatigue performances of orthotropic steel bridge decks, considering different penetration rates and thicknesses. Nominal and hot-spot stresses were measured. The crack propagation and microstructure were analyzed, and the cracked sections were cut out to observe the metallographic means. On the basis of test results, the fatigue life and strength were investigated. In addition, crack-propagation processes and stress-intensity factors were analyzed by the finite-element method (FEM). The results reveal that an increased penetration rate can decrease the crack-propagation rate and enhance fatigue life. An increase in deck thickness can cause a more obvious improvement in slowing the rate of crack propagation and the fatigue life under high-stress amplitudes. A lower penetration rate resulted in a larger decrease in bearing capacity after cracking, especially in a thicker deck. The increased penetration rate contributed to a decrease in the local stress-intensity factor but had little effect on crack angle and path. The fatigue strengths of nominal and hot-spot stress methods were suggested to be 70 and 75 MPa, respectively.
Modern fatigue design in civil constructions is mainly limited to the use of S-N curves and the hypothesis of Palmgren-Miner, as described in design standards and Eurocode. While using the latter, the fatigue evaluation may be conservative, since the outdated S-N curves are compared to current construction technology and weld properties. This shortcoming has a direct influence on the current design of orthotropic steel decks. To increase the understanding of the fatigue behaviour, an improved analysing tool using linear elastic fracture mechanics and extended finite element model is proposed. As a result, thickness effects are evaluated for both the longitudinal stiffener and the deck plate. These calculations indicated that increasing the thickness of the deck plate and the longitudinal stiffener increases the fatigue life of the structure. However, the thickness should be limited to maintain the advantage of a light-weighted construction.
Engineering Damage Mechanics is deliberately oriented toward applications of Continuum Damage Mechanics to failures of mechanical and civil engineering components in ductile, creep, fatigue and brittle conditions depending upon the thermomechanical loading and the materials: metals and alloys, polymers, elastomers, composites, concretes. Nevertheless, to help engineers, researchers, beginners or not, the first two chapters are devoted to the main concepts of damage mechanics and to the associated computational tools.
This study experimentally investigated the fatigue behavior of the weld root in orthotropic steel decks stiffened with U-ribs in relation to the loading conditions and welding details. To examine the structural response and local stress near the welded joint, field loading tests, measurement of residual stress, and fatigue tests were carried out. A total of 12 specimens were manufactured, and the fatigue tests were performed by simulating the double tire loading of an actual vehicle. The welding residual stress distribution at the root was examined to understand the mechanism of root crack initiation and propagation behavior. Thus, fatigue behavior of the root crack was investigated and evaluated by considering different stress ratios and weld penetration rates. Based on the fatigue test results and crack patterns, it was revealed that both tensile stress and stress range could affect the root crack initiation. However, the tensile stress rather than the magnitude of stress range would be the effective stress after a crack initiated, and it was seen to be an important factor for root crack propagation. In addition, a penetration rate in the range of 0% to 75% was beneficial for fatigue durability of this structural detail.
This study reported fatigue test results of 300-mm-wide specimens with three details: 80% partial joint penetration (80%PJP), weld melt-through (WMT), and both. The specimens were cut out from full-scale orthotropic deck specimens of 16-mm-thick deck plate. In the fatigue test, the deck plate was subjected to cyclic bending loading and the rib was free from loading. The fatigue fracture surfaces showed that the presence of WMT may affect the initiation of fatigue cracks. A propensity to root cracking rather than toe cracking was observed. Plotting fatigue test results in an S-N diagram showed that the specimens with WMT seemed to have slightly lower fatigue strengths than the 80%PJP specimens, but the difference is more likely to be within a usual scatter of test data, which means that both details have comparable fatigue strength. The present test results satisfied the S-N curves of JSSC-E (80 MPa at 2x10(6) cycles) or AASHTO-C (89 MPa at 2x10(6) cycles). DOI: 10.1061/(ASCE)BE.1943-5592.0000181. (C) 2011 American Society of Civil Engineers.
Abstract Fatigue tests of full-scale orthotropic steel decks were recently conducted to evaluate the fatigue performance of rib-to-deck partial-joint-penetration (PJP) groove welded joints. The test results indicated that rib-to-deck joints are more prone to fatigue cracks in the deck plate than in the rib wall. A shallower weld penetration (for example, an 80% PJP) also appeared to have a slightly higher fatigue resistance than a deeper one (for example, a 100% weld penetration). These PJP welds were also more vulnerable to cracking initiated from the weld toe than from the weld root. Finite-element analyses of the test specimens, using the effective notch stress method, were performed to supplement the laboratory testing and provide additional information on the behavior of these welded joints. The analysis results showed a good correlation with the observed crack patterns. A parametric study also showed that the fatigue resistance of the PJP joint can be significantly influenced by the transverse loading location, deck plate thickness, and the weld penetration ratio. Increasing the deck plate thickness was effective in reducing the stresses, while the rib wall thickness had a little effect. A shallower weld penetration at the PJP joint appeared to have a positive effect in enhancing the fatigue resistance.
Ductile crack growth in a grain boundary layer is modeled under mode I plane-strain, small-scale yielding conditions. The calculations are carried out for planar polycrystals using an elastic–viscoplastic constitutive relation for a progressively cavitating solid with two populations of void nucleating second-phase particles. The material properties in the grain boundary layers are taken to be representative of those for the α phase boundaries in metastable Ti β alloys, while the grain properties are homogenized representations of the grain properties in such alloys. Void nucleation is taken to occur rather early in the deformation history in the grain boundary α phase layers by a stress-controlled nucleation criterion. Subsequent strain-controlled void nucleation occurs within the grains as well as in the grain boundary α layers. The effects of grain flow strength, average grain size, grain morphology and grain boundary α layer continuity on the crack growth resistance and on the plastic dissipation during fracture are considered. The main effects on the crack growth resistance are found to be the grain morphology and the α layer continuity. The fracture surface roughness is characterized in terms of the fracture surface height fluctuations and the computed small-scale regime Hurst exponents in the crack growth direction are consistent with the “universal” values found for other materials and loading conditions. A model for the estimation of the crack growth resistance is also presented. The model gives a very good representation of the crack growth resistance when crack branching does not occur. The model also shows that the crack path taken in the calculations is not necessarily the path of least resistance.
This paper studies propagation criteria in three-dimensional fracture mechanics within the extended finite element framework (XFEM). The crack in this paper is described by a hybrid explicit–implicit approach as proposed in Fries and Baydoun (Int J Numer Methods Eng, 2011). In this approach, the crack update is realized based on an explicit crack surface mesh which allows an investigation of different propagation criteria. In contrast, for the computation of the displacements, stresses and strains by means of the XFEM, an implicit description by level set functions is employed. The maximum circumferential stress criterion, the maximum strain energy release rate criterion, the minimal strain energy density criterion and the material forces criterion are realized. The propagation paths from different criteria are studied and compared for asymmetric bending, torsion, and combined bending and torsion test cases. It is found that the maximum strain energy release rate and maximum circumferential stress criterion show the most favorable results.
The effective notch stress approach for the fatigue strength assessment of welded structures as included in the Fatigue Design Recommendations of the IIW requires the numerical analysis of the elastic notch stress in the weld toe and/or weld root which is fictitiously rounded with a radius of 1 mm. In order to establish guidelines for modelling the structure and evaluating the results, several numerical analyses have been performed in a round robin. This covers three welded details of different complexity where either the weld toe or the weld root is the potential crack location. The first example is a cruciform joint with non-load carrying fillet welds in one load case and load carrying in the other. The second is a complex T-joint of rectangular hollow section (RHS) members which was also subject of the so-called SAE-FDE weld challenge to predict fatigue life. The third is the fillet-welded end connection of a RHS joint being prone to fatigue failure at the weld root with non-fused root faces. The results are compared with each other and conclusions are drawn with regard to appropriate modelling and to the scatter of results to be expected.
The present study is intended as analysis investigations of fatigue durability of the trough to deck plate welded joint failed at weld root in deck plate. The investigations are carried out on the basis of three key factors: fatigue strengths of the welded details obtained by analysis method in conjunction with fatigue tests, stress ranges by FEM analyses with a unit wheel load, and the loads and their frequencies for the fatigue evaluations are the wheel loads in service, represented by an equivalent wheel load, assumed from the axle load measurements. Consistency between fatigue strength and stress range is simply demonstrated. Using this method for fatigue evaluation, it is found that large-rib-deck model has longer fatigue life than standard-deck models. An increase in deck plate thickness may prolong fatigue life of the orthotropic steel deck. Load distribution due to the rigidity of pavement may also help enhancement the fatigue life.
Final design of the replacement orthotropic deck panels for the rehabilitation of the Williamsburg Bridge in New York City was based on laboratory fatigue tests of a full-scale prototype and an as-built orthotropic deck panel carried out at Lehigh University in the latter 1990s. The tests focused on determining and comparing the fatigue resistance of two different welded rib-to-diaphragm connection details that were recommended in the 1994 AASHTO LRFD Bridge Design Specifications and an alternative proposed by Steinman. The test on the prototype panel demonstrated that the fatigue resistance of the alternative detail was superior and influenced additional design changes that were incorporated into the replacement panels installed on the southern inner and outer roadways. Subsequent tests on the as-built panel further confirmed that the fatigue resistance of the alternative detail was superior and demonstrated that the additional design changes were also beneficial. Static and dynamic tests revealed the complex behavior of the orthotropic deck panels and demonstrated the effectiveness of retrofit and repair options at cracked connections. An assessment of fatigue resistance based on fracture mechanics models provided theoretical correlation. This research has led to the revision of design specifications for steel orthotropic decks first provided in the 2000 Interim AASHTO LRFD Specifications.
The relationship between m and log C of Paris law for fatigue crack growth in a commercial low-alloy steel was examined over a range of material variables (microstructure, yield stress, toughness) and of experimental variables (thickness, load ratio, frequency).
The transverse distribution of wheel loads in orthotropic decks generates significant out-of-plane bending moments in the deck plate and rib wall at the rib-to-deck joint. Due to the relatively small thickness of both the deck plate and rib wall, the out-of-plane bending moments result in high local flexural stresses causing fatigue cracks to develop at the joint. In this study, the transverse stresses within the joint region that arise under the action of wheel loads are investigated with finite element analyses. Based on the stress results and the basic theories of linear elastic fracture mechanics, the design fatigue strength is determined for the joint. Factors affecting the stress range are also studied. The analyses show that the surface stresses in the deck plate are much larger than those in the rib wall in the case of 75% weld penetration into the rib wall, indicating that the fatigue strength of the joint is governed by the fatigue cracks propagating into the thickness of deck plate. It is also shown with finite element analyses that increasing the distribution area of wheel load or the thickness of deck plate can reduce the stress range of the deck plate and increase significantly the fatigue life of the joint.
The practice of attempting validation of crack-propagation laws (i.e., the laws of Head, Frost and Dugdale, McEvily and Illg, Liu, and Paris) with a small amount of data, such as a few single specimen test results, is questioned. It is shown that all the laws, though they are mutually contradictory, can be in agreement with the same small sample of data. It is suggested that agreement with a wide selection of data from many specimens and over many orders of magnitudes of crack-extension rates may be necessary to validate crack-propagation laws. For such a wide comparison of data a new simple empirical law is given which fits the broad trend of the data.
This dissertation presents the research into renovation techniques for orthotropic steel bridge decks. These techniques are needed to solve fatigue problems in the decks of these bridges, as several fatigue cracks have been detected in the deck structure of these bridges the last decade. A well-known example of fatigue cracks are those observed in the deck plate of the Van Brienenoord bascule bridge in 1997, at that time a 7 year old bridge. The renovation techniques are part of a proposed maintenance philosophy for steel bridge decks. Lifetime calculations, inspections and renovation techniques are the three essential parts of this philosophy. A reliable lifetime calculation model for fatigue damage in the deck plate is described, including the influence of the asphalt surfacing. Accurate calculation results are obtained, both for movable and fixed bridges. Inspection programs can be based on the lifetime calculation results. Several innovative inspection techniques are presented briefly. For fixed bridges the replacement of the asphalt surfacing with a reinforced high performance concrete surfacing is an effective renovation method. For movable bridge decks three solutions that extend the lifetime of the orthotropic deck structure were researched in this thesis.