Residual stresses effects on fatigue crack growth behavior of rib-to-deck double-sided welded joints in orthotropic steel decks

Abstract

Rib-to-deck (RTD) innovative double-sided welded joints have the potential to enhance the fatigue resistance of orthotropic steel decks (OSDs). However, welding residual stress (WRS) has been reported to be a contributing factor to fatigue cracking of steel bridges. This paper performed fatigue crack growth of the RTD innovative double-sided welded joints of OSD considering WRS. Firstly, a thermal-mechanical sequential coupling finite element model (FEM) of the RTD double-sided welded joints was established. The WRS distribution along the direction of deck thickness was analyzed. Secondly, the FEM of the OSD segment with crack was established. The fatigue crack behavior of RTD double-sided welded joints under the combined action of vehicle load and WRS was studied. Finally, the influences of initial crack on fatigue life was analyzed. Results indicate the distribution of the transverse WRS along the direction of deck thickness is tension-compression-tension stress, which has the characteristics of the sinusoidal function. The ∆K_eff value increases significantly considering WRS than without considering WRS during crack growth. WRS has a significant effect on fatigue life, and the fatigue life of the weld toe without considering WRS is about twice that of considering WRS. The crack depth and aspect ratio (a₀/c₀) of the initial crack affect the fatigue life of RTD double-sided welded joints.

Keywords

orthotropic steel deck rib-to-deck double-sided welded joints fatigue crack weld residual stress

Highlights

(1) A method for fatigue crack growth of rib-to-deck double-sided welded joints in OSD for the effects of residual stresses was presented.

(2) The WRS distribution of the rib-to-deck double-sided welded joints was fitted by sinusoidal function.

(3) Fatigue crack growth behavior of rib-to-deck double-sided welded joints of OSD was simulated with or without the effect of WRS.

(4) Fatigue life evaluation integrated with the effect on WRS was performed for the rib-to-deck double-sided welded joints.

Introduction

Orthotropic steel decks (OSDs) are widely used in long-span steel box girder cable-stayed bridges and suspension bridges due to their advantages of lightweight, high strength, ease of prefabrication and speedy construction, among other benefits (Zhuang et al., 2022; Wang et al., 2020). However, due to significant welding residual stress (WRS), welding defects, and increases in traffic load over time, fatigue cracking of existing OSD has continuously occurred during its service life (Cui et al., 2018; Zhu et al., 2020; Song et al., 2016). Fatigue crack defects have been observed in rib-to-deck (RTD) conventional single-sided welded joints in serviceable OSD. Based on a review of fatigue cracks occurring in these joints (Wang et al., 2019; Fisher et al., 2015), four failure modes of fatigue cracking have been identified: root-deck, toe-deck, toe-trough, and root-throat. The fatigue issues associated with RTD welded joints of OSD directly threaten the safety and durability of the structure.

With the development of advanced internal welding technology, the RTD innovative double-sided welded joints have been proposed (Yang et al., 2022), as shown in Figure 1. The RTD innovative double-sided welded joints has brought a new opportunity to solve the fatigue cracking of RTD welded joints of OSD. RTD innovative double-sided welded joints are formed by adding a fillet weld inside the U-rib through intelligent robot automatic welding technology, on the basis of RTD conventional single-sided welded joints. Compared with the RTD conventional single-sided welded joints, the RTD innovative double-sided welded joints are welded at the interior and exterior of the joint to improve the fatigue resistance of welded joints. Firstly, the bilateral fillet welds increase the cross-sectional area of the RTD connection weld and improve local weld stiffness. Secondly, the bilateral fillet welds are aligned with the center of the U rib, which changes the eccentricity of the weld to the U-rib and avoids the cracking of the weld root. Finally, the bilateral fillet welds transform the incomplete penetration area of the weld root into a closed rigid area to avoid propagation of crack-like defects generated by the RTD conventional single-sided welded joints under cyclic loading. Practical application of RTD innovative double-sided welded joints has been successful in bridge construction projects in China, making this a current research hot spot (Zhang et al., 2019a; Chen et al., 2023).

Figure 1.

RTD innovative double-sided welded joints.

Recently, researchers have conducted experimental and theoretical studies on fatigue performance and fatigue crack growth of the RTD innovative double-sided welded joints of OSD. You et al. (2018) and Zhang et al. (2021a) conducted tests on full-scale OSD models fabricated with RTD single-sided and double-sided weld joints. It was found that the double-sided welded joints provided significantly higher fatigue life than the single-sided welded joints. Yang et al. (2022) conducted experimental and numerical investigations of the fatigue resistance properties of RTD single-sided and double-sided welded joints using the traction structural stress method. Zhang et al. (2019a) and Liu et al. (2021) explored the fatigue crack growth behavior of the RTD double-sided welded joints of OSD using the finite element method (FEM) and linear elastic fracture mechanics, and found that the fatigue crack growth was a mixed mode dominated by opening-mode (type I). Furthermore, Fang et al. (2020) evaluated the notch stress at the weld details of RTD double-sided welded joints by FEM, and discussed the factors that influence the fatigue failure mode of these joints. Additionally, Zhang et al. (2019b) investigated the fatigue performance of the RTD double-sided welded joints of OSD by employing the equivalent structural stress method. It was found that the predominant fatigue failure of RTD double-sided welded joints is the crack that initiates at the weld toe and grows through the deck plane.

In addition, the double-sided welding process with multiple passes can result in complex WRS distribution at the weld heat-affected zone of RTD double-sided welded joints (Zhang et al., 2021). This type of WRS is considered one of the main factors contributing to fatigue cracking of steel bridges (Gadallah et al., 2020; Gu et al., 2020; Cheng et al., 2017). Therefore, researchers have conducted experimental and theoretical studies on the WRS and its distribution at RTD double-sided welded joints of OSD. Zhang et al. (2021b) and Cui et al. (2019) utilized ultrasonic methods and FEM simulation techniques to measure the WRS at RTD double-sided welded joints. Qiang et al. (2020) investigated the distribution of WRS along the thickness direction of RTD double-sided welded joints by performing experimental measurements and numerical simulations, and used the weight function method to explore the effects of WRS on the stress intensity factors (SIFs) of surface crack. The results revealed that transverse WRS had significant effects on SIFs. Liu et al. (2019) investigated the SIF of the RTD double-sided welded joints considering WRS by a FEM, and found that the WRS can significantly influence the SIF values. However, the WRS would affect the fatigue crack growth behavior of RTD double-sided welded joints of OSD is still ambiguous.

This study investigated the fatigue crack growth behavior of the RTD double-sided welded joints of OSD considering the effect of WRS using linear elastic fracture mechanics (LEFM). Firstly, A three-dimensional FEM of RTD double-sided welded joints of OSD is established to obtain the WRS distribution through a thermal-mechanical sequential coupling analysis. Secondly, the FEM of the OSD segment with crack was established by ABAQUS, 2020, FRANC3D, 2020 software. The fatigue crack behavior of RTD double-sided welded joints of OSD was simulated with or without the effect of WRS. Finally, the influences of initial crack depth and aspect ratio (a₀/c₀) on fatigue life were analyzed.

Details of rib-to-deck double-sided welded joints

In this study, the WRS effects on fatigue crack behavior of RTD double-sided welded joints of OSD were analyzed taking the OSD in Jiayu Yangtze River Bridge in China as an example. Figure 2 shows the details of RTD double-sided welded joints. The thickness of deck, and U-rib is 16 mm, 8 mm, respectively. The size of the U-ribs is 300 mm × 300 mm × 8 mm. The dimensions of the inner and outer welds of the RTD double-sided welded joints are 6 mm and 10 mm, respectively. The deck and U-ribs are connected by double-sided welds with an 80% partial penetration rate, and the clearance between the U-rib and the deck plate assembly is less than or equal to 0.5 mm.

Figure 2.

Details of RTD double-sided welded joints (unit: mm).

Figure 3 illustrates the typical fatigue crack patterns at the RTD double-sided welded joints of OSD. Among them, the dominating cracks are Crack I, Crack II, Crack III, and Crack IV, which initiate from the weld toe or weld root and propagate through the deck (Zhang et al., 2019b, 2021b).

Crack I: outside toe-deck, initiates at the outside weld toe and propagates into the deck.

Crack II: outside root-deck, initiates at the outside weld root and propagates into the deck.

Crack III: inside root-deck, initiates at the inside weld root and propagates into the deck.

Crack IV: inside toe-deck, initiates at the inside weld toe and propagates into the deck.

Figure 3.

Typical crack patterns at the welded joints.

Flow of fracture analysis considering WRS

Figure 4 illustrates the proposed procedure for predicting fatigue crack growth in RTD double-sided welded joints of OSD considering the effect of WRS. The procedure is comprised of three parts. In the first part, the WRS is simulated through the establishment of a FEM in ABAQUS. The thermal-mechanical sequential coupling method (Cui et al., 2019), i.e., the temperature field is initially simulated and then set as the predefined condition for mechanical analysis, was adopted in this research. The WRS values at initiation points along the direction of deck thickness are obtained by mechanical analysis. The second part involves the establishment of a FEM for fracture analysis. Initially, an uncracked FEM is established in ABAQUS and subsequently imported into FRANC3D to establish a local sub-model. Subsequently, an initial semi-elliptical surface crack is inserted at the weld root or weld toe of the local sub-model using FRANC3D and re-meshed to establish a cracked local sub-model. In the third part, the WRS is introduced as the initial stress in the cracked sub-model. Subsequently, the SIF and fatigue crack propagation caused by the applied fatigue loading and WRS are calculated.

Figure 4.

Procedure for fatigue crack propagation prediction.

Welding numerical simulation

Description of the FEM of WRS

The thermal-mechanical sequential coupled FEM was developed by ABAQUS to calculate the temperature field, WRS of RTD double-sided welded joints of OSD. Figure 5 shows the dimensions of the FEM. The global and local mesh sizes are determined by mesh size convergence analysis. The global mesh size is 10 mm, and the refined mesh size in the vicinity of the welded joints is 1 mm. In thermal analysis, the DC3D8 element type are employed in heat transfer analysis. In the welding process of RTD double-sided welded joints, the element birth-death method is developed using Python script files to simulate the filling of cladding metal materials of multi-pass welds. The ambient temperature is assumed to be constant at 20°C. In terms of thermal boundary conditions, the effects of both convection and radiation are modeled with consideration of the heat loss on the surface of the RTD welded joints. In mechanical analysis, the same FEM as that used in thermal analyses is used, except for the element type and boundary conditions. The DC3D8R element type are employed in WRS analysis. The boundary conditions in the mechanical analysis: symmetric constraints (Ux = Ry = Rz = 0) are applied at the y-z plane of the deck and U-rib, and vertical constraints (Uy = 0) are applied on the left deck while constraints (Uz = 0) are applied on the deck (z = 0) to simulate the actual boundary conditions.

Figure 5.

FEM for WRS simulation.

Heat source and thermal analysis

Temperature-dependent properties of the material is a key factor affecting the simulation results. In the numerical simulation of the welding process, it is difficult to obtain the temperature-dependent thermal and mechanical properties of the material used for welding numerical simulation. In this case, some scholars often use assumptions and simplified methods to deal with the temperature-dependent thermal and mechanical properties of materials in welding (Cui et al., 2019; Qiang et al., 2020; Jiang et al., 2021). In this study, the temperature-dependent properties of steel Q345qD are adopted according to the literature (Deng et al., 2008; Jiang et al., 2021), as plotted in Figure 6.

Figure 6.

Temperature-dependent properties of Q345qD: (a) thermal properties and (b) mechanical properties.

During the welding, the governing equation for thermal analysis is given by:

ρ c \frac{\partial T}{\partial t} = λ (\frac{\partial^{2} T}{\partial x^{2}} + \frac{\partial^{2} T}{\partial y^{2}} + \frac{\partial^{2} T}{\partial z^{2}}) + \bar{Q}

(1)

where, T is the temperature at the point (x, y, z);

\bar{Q}

is the internal heat generation rate; ρ is density of material; λ is thermal conductivity; c is specific heat; t is the heat transfer time.

In this study, the moving heat source is simulated using the double ellipsoidal heat distribution model proposed by Goldak et al. (1984), which is expressed by the follows equations:

For the front heat source

q_{1} (x, y, z, t) = \frac{6 \sqrt{3} (f_{1} Q)}{a_{1} b c π \sqrt{π}} e^{- \frac{3 x^{2}}{b^{2}} - \frac{3 y^{2}}{c^{2}} - \frac{3 {(z - v t - z_{0})}^{2}}{a_{1}^{2}}}, z \geq 0

(2)

For the rear heat source

q_{2} (x, y, z, t) = \frac{6 \sqrt{3} (f_{2} Q)}{a_{2} b c π \sqrt{π}} e^{- \frac{3 x^{2}}{b^{2}} - \frac{3 y^{2}}{c^{2}} - \frac{3 {(z - v t - z_{0})}^{2}}{a_{2}^{2}}}, z < 0

(3)

where Q is the effective heat power, Q = ηUI, η is the welding thermal efficiency (η = 0.80), U and I are welding voltage and current, respectively; f₁ and f₂ are the proportion of heat distribution in the front and rear hemisphere, which satisfies, f₁ + f₂ = 2; t is the heat transfer time; z₀ is the heat source in the z-direction of the initial position; v is the welding speed; a₁, a₂, b and c are geometric parameters of double ellipsoid heat sources, as shown in Figure 7.

Figure 7.

Double-ellipsoidal heat source model.

The DFLUX subroutine is compiled by FORTRAN during the welding process to implement the moving heat source loading for multi-pass welding with variations in position and time. The parameters of the welding heat source are adjusted according to the molten pool profile. The boundary of the molten pool is obtained by using the isothermal curve at the melting point of steel Q345qD (1440°C). Figure 8 compares the simulated molten pool profile with the experimental molten pool profile by Zhang et al. (2021b). The simulated molten pool profile is similar to the experimental molten pool profile. The dimensions of the simulated molten pool are about 0.75 times of the dimensions of the experimental welds. Noteworthy, the dimensions of the inner and outer welds in the simulation are 6 mm and 10 mm, respectively. While the dimensions of the inner and outer welds in the experiment are 8 mm and 13 mm, respectively. Therefore, it is feasible to simulate the heat input of the welding process. The welding parameters used in the present simulation are listed in Table 1.

Figure 8.

FEM compared to the molten pool profiles of the literature (Zhang et al., 2021b) (Units: °C).

Table 1.

Main welding parameters.

Welding pass	Welding voltage(V)	Welding current (A)	Welding speed (Mm/min)	Welding heat source (mm)
Welding pass	Welding voltage(V)	Welding current (A)	Welding speed (Mm/min)	b	c	a ₁	a ₂
Interior welding	30	280	480	3.0	3.5	3.5	14.0
Backing welding	32	300	400	2.5	5.5	3.0	12.0
Cosmetic welding	33	320	300	3.5	2.5	4.3	17.2

Mechanical analysis

During the welding, the material undergoes the local plastic deformation, resulting in WRS and strain. For the mild steel, the total strain can be composed of three component neglecting of the phase transition effect (Deng et al., 2008; Zhang et al., 2021b), as follows:

ε^{t} = ε^{e} + ε^{p} + ε^{th}

(4)

where ε^t is total strain; ε^e, ε^p and ε^th are elastic, plastic strain and thermal strain, respectively.

The elastic strain ε^e is obtained using the isotropic Hooke’s law with temperature-dependent Poisson’s ratio and Young’s modulus. The thermal strain ε^th is obtained by the thermal expansion coefficient. The plastic strain ε^p is obtained from the elastic-plastic constitutive equation with the following features: von-Mises yield criterion, isotropic hardening rule and temperature-dependent mechanical properties.

Experimental verification of WRS

The stress field of the RTD double-sided welded joints was simulated by mechanical analysis. The initial WRS at the RTD double-sided welded joints of OSD was measured using an ultrasonic method. Details of the experimental procedure and data can be found in literature (Cui et al., 2019). Figure 9 compares the simulation results from thermal-mechanical sequential coupling analysis and the experimental data of WRS. This indicated that the numerical simulation results were in good agreement with the experimental data. Thus, it is feasible to simulate WRS by using thermal-mechanical sequential coupling method, and the results are reasonably accurate.

Figure 9.

Comparison of measurement (Cui et al., 2019) and simulation results of the WRS.

WRS analysis

The WRS is determined by the last cooling stage of welding calculations. Figure 10 illustrates the stress distribution of RTD double-sided welded joints during the cooling stage with a stress cloud diagram. After cooling after welding, the Mises stresses of the whole weld area reaches the yield stress of the steel Q345qD (the yield stress is 345 MPa), and there is a large residual stress in the weld area. According to the crack orientation, the transverse WRS contributes a lot to crack growth. Hence, the focus of this study is placed on the transverse WRS effect on the fatigue crack growth at the crack initiation point (toe or root) and along the direction of deck thickness. The distribution of the transverse WRS along the direction of deck thickness is plotted in Figure 11. The distribution of the transverse WRS along the thickness of the deck is not uniform, presenting the state of tension-compression-tension stress distribution. Additionally, there are peaks of WRS values that differ based on various paths. The curves demonstrate a sinusoidal function pattern, indicating that the distribution of WRS for the RTD double-sided welded joints is also sinusoidal along the deck thickness direction.

Figure 10.

Mises stress distribution (Units: Pa).

Figure 11.

Distributions of WRS along deck thickness.

A sinusoidal function (Figure 12) can be used to fit the distribution of the WRS, which is expressed by the equation (5).

σ_{x} = σ_{0} + ∆ σ \sin (π • \frac{y - y_{d}}{ω_{d}})

(5)

where σ_x is the transverse WRS along the deck thickness; σ₀ is the mean value of the WRS; ∆σ is the range of the WRS; y_d is the initial phase (mm); ω_d is the coefficient associated with the period (mm); y is the thickness of the deck (mm).

Figure 12.

Sinusoidal function.

A fitting model for the distribution of WRS (σ_x) of welding details of RTD double-sided welded joints along the deck thickness was established, as shown in Figure 13. The scatters are fitted by a sinusoidal function according to their distribution, and the coefficient of determination, R², suggests the sinusoidal functions form a good fit to the scattered data.

Figure 13.

Fitting curves of WRS: (a) outside weld toe, (b) outside weld root, (c) inside weld root, and (d) inside weld toe.

Fracture simulation

Cracked FEM

The FEM of the OSD segment with a crack was established by ABAQUS and FRANC3D software. Figure 14 shows the modeling process of the FEM, which consists of two levels: the complete model (shell-solid element) - the cracked sub-model (solid element). Firstly, a complete segment FEM without crack including shell-solid element is established by ABAQUS. The complete segmental model of OSD consists of four diaphragms and seven U-ribs. The transverse spacing of the U-rib is 600 mm, and the longitudinal spacing of the diaphragm with a thickness of 8 mm is 3000 mm. Secondly, the complete model is imported into FRANC3D and divided into local sub-model (solid element). An initial semi-elliptical surface crack with a size of a₀/c₀ = 0.2 mm/0.5 mm is then inserted at the weld root or weld toe of the local sub-model by FRANC3D, and re-meshed to establish a cracked sub-model. The size of the local cracked sub-model is 300 mm × 300 mm × 316 mm.

The steel Q345qD with a Young's modulus of 206 GPa and a Poisson's ratio of 0.3 were assigned to the FEM. In the complete model, the shell element is simulated by a 4-node shell element (S4R) with mesh size of 100 mm. The solid element is simulated by a 20-node solid element (C3D20R) with global mesh size of 10 mm, refined to 1 mm in the vicinity of welded joints. In the cracked sub-model, the element near the innermost circle of the crack tip is a 15-node wedge element, and the element in the outer circle is a C3D20 hexahedron element. The mesh size of the local cracked sub-model is 0.02 mm. The following boundary conditions of the complete model were preassigned in ABAQUS: (a) The vertical translation (U_y = 0) and rotations (R_x = R_z = 0) are constrained for all nodes of the lower edge of the diaphragm to simulate the support of the diaphragm; (b) The longitudinal translation (U_z = 0) and rotations (R_x = R_y = 0) are constrained for all nodes of two ends of model to simulate the boundary conditions at the interior U-rib and deck plate; and (c) The transverse translation (U_x = 0) and rotations (R_y = R_z = 0) are constrained for all nodes of two sides of the model to simulate the boundary condition at the interior diaphragm and deck plate. In the complete model, the boundary between the solid element and the shell element is constrained by the shell-solid coupling in ABAQUS. The contact surfaces of the sub-model and the local cracked sub-model are connected by tie constraints.

The fatigue load model III (JTG D64-2015, 2015) was used for simulation. The geometry of mode III is shown in Figure 15. The stress at the RTD double-sided welded joints of OSD was dominated by significant local effects under wheel loads. The stress generated by one side of the wheel was not superimposed on that from the other side of the wheel. In the longitudinal direction of the bridge, each axle could produce an individual stress cycle at the detail of the RTD double-sided welded joints only when the detail was underneath the deck plate covered by the wheel load distribution width (Zhu et al., 2021). Hence, the one-sided twin axle loading model with a contact surface of 600 mm × 200 mm is used in the FEM analysis of the RTD double-sided welded joints of OSD. Moreover, the heavy vehicle load is one of the leading causes of fatigue cracking of OSD (Lu et al., 2019). Thus, this study considered the influence of overloading of the vehicle, the weight of each axle of 250 kN was used to perform fatigue analysis. The load position of the vehicle load (X = 100 mm, Z = 0 mm) is shown in Figure 16. The geometry of mode III and computational fatigue load are shown in Figure 15.

Figure 14.

FEM of RTD double-sided welded joints of OSD (Unit: mm).

Figure 15.

Fatigue load mode III and computational wheel load.

Figure 16.

Loading cases (Unit: mm): (a) transversal loading condition and (b) longitudinal loading condition.

SIF analysis of crack

A numerical method using the volumetric integral known as “M-Integral” is presented for calculating the SIF of cracks in three modes. The M-Integral method was first developed by Yau et al. (1980) and has been implemented into the three-dimensional fracture mechanics software FRANC3D. Numerical examples and verification as explained in a previous paper (Liu et al., 2019).

The SIF values of cracks in RTD welded joints of OSD may be significantly influenced by the WRS, which can influence the fatigue crack growth behavior (Liu et al., 2019; Cui et al., 2019). To evaluate fatigue crack growth considering WRS, the superposition principle of LEFM is employed by Glinka (1979). The equation used to calculate the SIF of the crack under the combined action of external load and WRS is as follows:

K_{tot} = K_{res} + K_{app}

(6)

where, K_tot is the total SIF value due to vehicle load and WRS; K_res is the SIF value due to WRS; K_app is the SIF value due to vehicle load.

In the present study, the distribution of WRS in the RTD double-sided welded joints is depicted in Figure 13. The equivalent SIF values, K, of the mixed mode of opening-mode (type I), sliding-mode (type II), and tearing-mode (type III) were calculated for the considered OSD by using the FEM depicted in Figure 14. The SIFs along the crack fronts of the initial fatigue crack of the four weld details of the RTD double-sided welded joints considering WRS and without considering WRS are presented in Figure 17. The SIFs along the crack fronts of the crack identified by means of a normalized coordinate. It is observed that WRS has a greater influence on the SIF at the midpoint of the crack front than at the ends of the crack front at the surface. Moreover, the SIF value considering WRS is much higher than that without considering WRS. Therefore, WRS can significantly influence the SIF values of the crack front of the RTD double-sided welded joints. Regardless of whether or not WRS is considered, the SIF value at the weld toe of the RTD double-sided welded joints is higher than at the weld root. Thus, the worst fatigue vulnerability of the RTD double-sided welded joints exists at the weld toe. In this study, only the crack growth behavior at the weld toe of RTD double-sided welded joints was studied.

Figure 17.

SIF of initial crack: (a) outside weld toe, (b) outside weld root, (c) inside weld root, and (d) inside weld toe.

Fatigue crack growth analysis

The Paris-Erdogan law (Paris et al., 1963) is a well-known power model to predict the fatigue crack growth based on LEFM. On this basis, Elber (1971) has introduced the concept of crack closure and applied the effective SIF range (∆K_eff) instead of the SIF range (∆ K) as the driving force for fatigue crack growth, known as Paris-Elber law:

d a / d N = C {(∆ K_{eff})}^{m}

(7)

where the material constants of C, and m are determined experimentally. In the current study, these parameters were based on the recommendations given by BS 7910 (1999) for steels, m = 3 and C = 5.21×10 ⁻¹³ (MPa and mm); Elber has developed the concept of ∆K_eff as follows:

∆ K_{eff} = U ∆ K

(8)

where ∆ K = K_max– K_min and U represents the stress range ratio. In this paper, U is only dependent on R as reported by Elber. U was applied using the following equation for structural steel (Kumar, 1992):

U = 0.722 + 0.278 R_{eff}

(9)

where R_eff is the SIF ratio, which is determined based on the calculated values of K_tot,max, and K_tot,min. When the influence of WRS is not considered (R_eff = 0), U = 0.722.

In the residual stress field, under the cyclic loads, the total SIF range ∆K_tot and effective SIF ratio R_eff is determined based on the calculated values of K_tot,max and K_tot,min, which are given as:

∆ K_{tot} = ∆ K = (K_{app, \max} + K_{res}) - (K_{app, \min} + K_{res}) = ∆ K_{app}

(10)

R_{eff} = K_{tot, \min} / K_{tot, \max} = (K_{app, \min} + K_{res}) / (K_{app, \max} + K_{res})

(11)

The SIF values at the midpoint of the crack front along the growth path of the welded toe of RTD double-sided joints at each stage of crack growth are determined. Figure 18 presents the variation curve of SIF values versus the crack depth a. It is observed that the variation of the SIF values at the outer and the inner weld toes of RTD double-sided welded joints with the crack depth are similar. The K_app,max curve represents the maximum SIF values of the crack of the midpoint due to the vehicle load without considering WRS. The K_app,max initially increases with the increasing crack depth, and then begins to decrease. The K_tot,max curve represents the maximum SIF values for the case when the WRS are taken into account along with the vehicle load. It can be seen that WRS significantly increases K_tot,max values in the area where tensile WRS. The existence of WRS makes the fatigue crack at a high tensile stress level during the fatigue growth stage, which significantly increases the SIF values of the crack.

Figure 18.

SIF values versus the crack depth: (a) outside weld toe and (b) inside weld toe.

According to equation (11), the R_eff values considering WRS are calculated. Figure 19 presents the R_eff values versus the crack depth a. The variation of the R_eff value at the outer and the inner weld toes of RTD double-sided welded joints with the crack depth is similar. The R_eff values of the crack at the midpoint increase rapidly and then decrease slowly with increasing crack depth. In the region of the RTD double-sided welded joints, where positive WRS prevail, R_eff values are positive, which could increase fatigue crack growth rate.

Figure 19.

Variation curves of R_eff.

According to equation (9), the U values considering WRS are calculated. Figure 20 presents the U versus the crack depth a. The U of the fatigue crack at the outer and the inner weld toes is consistent with the change rule of the crack depth. The U value of the midpoint crack increases first and then decreases with the increase of the crack depth.

Figure 20.

Variation curves of U.

According to equation (8), the effective SIF range ∆K_eff is calculated. Figure 21 presents the variation curves of the ∆K_eff at the midpoint of the crack front along the growth path (0.5) of the welded toe of RTD double-sided joints at each stage of crack growth. It is observed that the variation trends of ∆K_eff of the weld toe considering WRS and without considering WRS are consistent during crack growth. The ∆K_eff increases gradually and then decreases gradually. The ∆K_eff considering WRS are very high compared to the ∆K_eff without considering WRS.

Figure 21.

Variation curves of ∆K_eff: (a) outside weld toe and (b) inside weld toe.

Fatigue life predictions

The residual fatigue life can be directly estimated by integrating Paris’law (Elber, 1971):

N = \int_{a_{0}}^{a_{f}} \frac{d a}{C {(∆ K_{eff})}^{m}}

(12)

where, a₀ is the initial crack depth, a_f is the final crack depth, and the number of cycles N for a crack growth from a₀ to a_f.

Based on the ∆K_eff values and material’s constants C and m, the number of load cycles of the outside weld toe and inside weld toe of the RTD double-sided welded joints of OSD were calculated by the equation (12), as given in Figure 22. According to the IIW (Hobbacher, 2016), it is assumed that the structure fatigue failure occurs when the crack front is close to 50% of the thickness of the deck plate. From Figure 22(a), the fatigue life of the outside weld toe without considering WRS and considering WRS is 7045594 cycles and 3408849 cycles, respectively. Similarly, from Figure 22(b), the fatigue life of the inside weld toe without considering WRS and considering WRS is 10606958 cycles and 5128441 cycles, respectively. The fatigue life of the weld toe of without considering the influence of WRS is approximately twice that when considered, indicating that the existence of WRS reduces the crack closure effect and accelerates the fatigue crack growth rate of the structure. Therefore, the influence of WRS should be fully considered when designing or evaluating the fatigue life of OSD.

Figure 22.

Fatigue crack depth versus the number of cycles: (a) outside weld toe and (b) inside weld toe.

Discussion

Effect of initial crack depth on fatigue life

As discussed previously, the surface semi-elliptical crack is assumed to be the initial defect in the RTD double-sided welded joints of OSD to simulate the fatigue crack growth due to the combined action of vehicle load and WRS. To investigate the impact of initial fatigue crack with a fixed aspect ratio (a₀/c₀ = 0.4) on fatigue life, the geometry of the initial fatigue crack is varied in three cases as follows: Case 1 in which a₀ = 0.2 mm, c₀ = 0.5 mm, Case 2 in which a₀ = 0.4 mm, c₀ = 0.1 mm, and Case 3 in which a₀ = 1.0 mm, c₀ = 2.5 mm. Figure 23 shows the curves of crack depth versus the number of cycles for the three cases of the RTD double-sided welded joints of OSD. The curves demonstrate that when the initial crack aspect ratio (a₀/c₀) is the same, the initial crack depth has a significant effect on the fatigue life of the RTD double-sided welded joints of OSD. As depicted, the fatigue life decreases with an increase in the initial crack depth, meaning that the larger the initial crack depth, the lower the number of cycles before structural fatigue failure occurs.

Figure 23.

Fatigue Crack depth versus the number of cycles: (a) outside weld toe and (b) inside weld toe.

Effect of initial crack aspect ratio on fatigue life

In addition, to investigate the impact of the initial crack aspect ratio (a₀/c₀) on fatigue life, the initial crack depth is assumed to be a constant a₀ = 0.2 mm, while crack aspect ratio is varied between 0.4 mm, 0.6 mm, and 0.8 mm. Figure 24 shows the curves of crack depth versus the number of cycles for the three cases of the RTD double-sided welded joints of OSD. The curves demonstrate that when the initial crack depth is the same, the initial crack aspect ratio has an effect on the fatigue life of the RTD double-sided welded joints of OSD. As the initial crack aspect ratio decreases, the fatigue life of OSD decreases.

Figure 24.

Fatigue Crack depth versus the number of cycles: (a) outside weld toe and (b) inside weld toe.

Conclusions

In this paper, the influence of the WRS on the fatigue crack behavior of RTD double-sided welded joints in OSD was investigated. Firstly, The WRS was simulated by the thermal-mechanical sequential coupling FEM to investigate the WRS distribution of the RTD double-sided welded joints. Secondly, the cracked FEM of OSD was established to investigate the influence of WRS on the fatigue crack behavior of surface cracks at the weld toe. The influence of initial crack size on fatigue life is also discussed. Based on the above investigations, the following conclusions can be drawn:

(1) The WRS simulation results indicate that the distribution of transverse WRS along the deck thickness direction is tension-compression-tension stress, which has the property of a sinusoidal function. Therefore, the sinusoidal function can be used as an empirical distribution model of WRS for fatigue analysis.

(2) The fatigue crack growth simulation results indicate that the variation of ∆K_eff at the weld toe considering WRS and without considering WRS are consistent during crack growth. The ∆K_eff value increases significantly considering WRS. It shows that the WRS will significantly increase the average stress level at the weld toe under vehicle load, thereby promoting fatigue cracking.

(3) Under vehicle load, the fatigue life of the weld toe without considering WRS is approximately twice times that of considering WRS. Therefore, it is crucial to fully consider the influence of WRS when designing or evaluating the fatigue life of OSD.

(4) The size of the initial crack plays a crucial role in determining the fatigue life of the outside weld toe of RTD double-sided welded joints of OSD. Specifically, when the initial crack shape ratio remains constant, the fatigue life of OSD decreases as the initial crack depth increases. Similarly, when the initial crack depth is consistent, the fatigue life of OSD decreases as the initial crack aspect ratio decreases.

(5) Material parameters are important factors affecting the WRS of structures. WRS distribution of the RTD double-sided welded joints considering actual material properties is a follow-up research work.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the Natural Science Foundation of Hunan Province (2023JJ50180, 2023JJ50188), the Scientific Research Foundation of Hunan Provincial Education Department (22C0300, 22B0567), and the Open Fund of Industry Key Laboratory of Traffic Infrastructure Security Risk Management (Changsha University of Science & Technology) (18KF04).

ORCID iDs

Fanghuai Chen

Zhaochao Li

Yuan Luo

Xinhui Xiao

References

ABAQUS (2020) Abaqus/CAE User’s Manual. V2021: Dassault Systems, Inc. Available at: http://www.simulia.com.

BS 7910:1999 (2000), Guide on Methods for Assessing the Acceptability of Flaws in Fusion Welded Structures. London: BSI.

Chen

Wei

Zhao

(2023) Fatigue resistance of orthotropic steel deck system with double-side welded rib-to-deck joint. Advances in Structural Engineering 26(5): 952–965.

Cheng

Cao

, et al. (2017) Experimental study on fatigue failure of rib-to-deck welded connections in orthotropic steel bridge decks. International Journal of Fatigue 103: 157–167.

Cui

Bao

, et al. (2018) Strain energy-based fatigue life evaluation of deck-to-rib welded joints in OSD considering combined effects of stochastic traffic load and welded residual stress. Journal of Bridge Engineering 23: 04017127.

Cui

Zhang

Bao

, et al. (2019) Residual stress relaxation at innovative both-side welded rib-to-deck joints under cyclic loading. Journal of Constructional Steel Research 156(3): 9–17.

Deng

Murakawa

(2008) Prediction of welding distortion and residual stress in a thin plate butt-welded joint. Computational Materials Science 43: 353–365.

Elber

(1971) The significance of fatigue crack closure. Damage Tolerance in Aircraft Structures. American Society for Testing and Materials 23: 230–242.

Fang

Ding

Wei

, et al. (2020) Fatigue failure and optimization of double-sided weld in orthotropic steel bridge decks. Engineering Failure Analysis 116: 104750.

10.

Fisher

Barsom

(2015) Evaluation of cracking in the rib-to-deck welds of the bronx-whitestone bridge. Journal of Bridge Engineering 21: 04015065.

11.

FRANC3D (2020) Franc3D Reference Manual. V7.5.5: Fracture Analysis Consultants, Inc. Available at: http://www.fracanalysis.com.

12.

Gadallah

Tsutsumi

Yonezawa

, et al. (2020) Residual stress measurement at the weld root of rib-to-deck welded joints in orthotropic steel bridge decks using the contour method. Engineering Structures 219: 110946.

13.

Glinka

(1979) Effect of residual stresses on fatigue crack growth in steel weldments under constant and variable amplitude loads. Fracture Mechanics 2: 198–214.

14.

Goldak

Chakravarti

Bibby

(1984) A new finite element model for welding heat sources. Metallurgical Transactions A B 15: 299–305.

15.

Zhou

, et al. (2020) Numerical simulation and measurement of welding residual stresses in orthotropic steel decks stiffened with u-shaped ribs. International Journal of Steel Structures 20: 856–869.

16.

Hobbacher

(2016) Recommendations for Fatigue Design of Welded Joints and Components. Paris: IIW.

17.

Jiang

, et al. (2021) Fatigue life evaluation of deck to U-rib welds in orthotropic steel deck integrating weldment size effects on welding residual stress. Engineering Failure Analysis 124: 105359.

18.

JTG D64-2015 (2015) Specifications for Design of Highway Steel Bridge. Peking: PCP.

19.

Kumar

(1992) Review on crack closure for constant amplitude loading in fatigue. Engineering Fracture Mechanics 42(2): 389–400.

20.

Liu

Chen

, et al. (2019) Fatigue performance of rib-to-deck double-side welded joints in orthotropic steel decks. Engineering Failure Analysis 105: 127–142.

21.

Liu

Chen

Wang

, et al. (2021) Fatigue crack growth behavior of rib-to-deck double-sided welded joints of orthotropic steel decks. Advances in Structural Engineering 24(3): 556–569.

22.

Liu

(2019) Evaluating probabilistic traffic load effects on large bridges using long-term traffic monitoring data. Sensors 19: 5056.

23.

Paris

Erdogan

(1963) A critical analysis of crack propagation laws. Journal of Basic Engineering 85: 528–533.

24.

Qiang

Wang

(2020) Evaluating stress intensity factors for surface cracks in an orthotropic steel deck accounting for the welding residual stresses. Theoretical and Applied Fracture Mechanics 110: 102827.

25.

Song

Ding

Wang

, et al. (2016) Fatigue-life evaluation of a high-speed railway bridge with an orthotropic steel deck integrating multiple factors. Journal of Performance of Constructed Facilities 30: 04016036.

26.

Wang

Pei

Dong

, et al. (2019) Traction structural stress analysis of fatigue behaviors of rib-to-deck joints in orthotropic bridge deck. International Journal of Fatigue 125: 11–22.

27.

Wang

Cui

, et al. (2020) Numerical simulation of distortion-induced fatigue crack growth using extended finite element method. Structure and Infrastructure Engineering 16(1): 106–122.

28.

Yang

Wang

Qian

, et al. (2022) An experimental investigation into fatigue behaviors of single- and double-sided U rib welds in orthotropic bridge decks. International Journal of Fatigue 159: 106827.

29.

Yau

Wang

Corten

(1980) A mixed-mode crack analysis of isotropic solids using conservation laws of elasticity. Journal of Applied Mechanics 47: 335–341.

30.

You

Liu

Zhang

, et al. (2018) Study on fatigue performance of U rib-to-deck connection with double sides welding in orthotropic steel bridge deck. Journal of China & Foreign Highways 38(3): 174–179. (in Chinese).

31.

Zhang

Guo

, et al. (2019a) Fatigue crack propagation characteristics of double-sided welded joints between steel bridge decks and longitudinal ribs. China Journal of Highway and Transportation 32(7): 49–56. (in Chinese).

32.

Zhang

Yuan

Wang

, et al. (2019b) Fatigue performance of innovative both-side welded rib-to-deck joint. China Journal of Highway and Transportation 32(7): 49–56. (in Chinese).

33.

Zhang

Yuan

, et al. (2021a) Fatigue performance of high fatigue resistance orthotropic steel bridge deck I: model test. China Journal of Highway and Transportation 34(3): 124–135. (in Chinese).

34.

Zhang

Cui

, et al. (2021b) Experimental investigation and numerical simulation on welding residual stress of innovative double-side welded rib-to-deck joints of orthotropic steel decks. Journal of Constructional Steel Research 179: 106544.

35.

Zhu

Xiang

, et al. (2020) Fatigue behavior of orthotropic bridge decks with two types of cutout geometry based on field monitoring and FEM analysis. Engineering Structures 209: 109926.

36.

Zhu

Chen

, et al. (2021) Stress behaviors of rib-to-deck double-sided weld detail on orthotropic steel deck. Journal of Constructional Steel Research 187: 106947.

37.

Zhuang

Wang

Sun

(2022) Experiment and numerical simulation investigation for crack growth of deck-to-rib welded details in orthotropic steel bridge decks. Structures 41: 1109–1121.