Fatigue performance of corroded fatigue detail of weathering steel

3.1.1. Finite Element Model

Based on the geometric dimensions presented in Table 1, a finite-element model of the butt-weld sample is constructed in ABAQUS. The C3D20 element is selected for this finite-element model. The element size is set to 3.5 mm in the vicinity of the weld, while it is 7 mm in the remaining areas. The element meshing is depicted in Fig. 8(a), the results of the static analysis are presented in Fig. 8(b), and the static analysis of the weld is shown in Fig. 8(c).

Fig. 8ABAQUS model

a) Grid division model

b) Static analysis cloud diagram

c) Butt weld analysis cloud chart

From the static-analysis results, it can be observed that there is a significant stress concentration around the weld, with a maximum value of 437 MPa. To ensure consistency with the test conditions, the lower part of the specimen is fixed and the fatigue load is applied through the upper part. The yield strength of the weathering steel base metal is 413 MPa, and the yield strength of the weld is 426 MPa, both of which are greater than the maximum fatigue load applied. Therefore, it is considered that the sample does not exhibit plastic deformation during the loading process. The material is pure elastic, the elastic modulus $E$ is 206 GPa, and the Poisson’s ratio is 0.3 [27].

3.1.2. Appraisal process

According to the analysis of Fig. 8(c), the stress value at the B2 weld position in Fig. 4 is 436 MPa, and the stress value at the B1 weld position is 338 MPa. It is found that the stress value at the B2 weld position is larger and the stress concentration effect is stronger. Therefore, the initial crack is inserted here during the simulation, and the critical crack size $a_{cr}$ is taken as the plate thickness 16 mm. According to previous studies, the fatigue crack growth rate parameter $\mathrm{l}\mathrm{o}\mathrm{g}C$ is determined to be − 10.37, and $m$ is 2.38[27]. The fatigue crack propagation threshold is assumed to be 0 so the Paris formula is also applicable to the case where the stress intensity factor amplitude is in zone I, and the fatigue life prediction result is safer.

Fig. 9Initial crack insertion and mesh re-meshing

After the finite-element model is exported to FRANC3D, based on the ABAQUS static-analysis cloud diagram, it can be observed that the stress at the welding center is the highest. Therefore, the initial crack is inserted into the weld center, and the mesh is redivided, as depicted in Fig. 9. The region adjacent to the crack tip will be redivided into wedge-shaped and hexahedral elements, while the other regions will be filled with tetrahedral elements. The stress intensity factor amplitude is calculated by the $M$ integral method. The maximum tensile stress criterion is adopted to calculate the crack propagation angle. The effective stress intensity factor amplitude is calculated by employing the composite equivalent stress intensity factor amplitude model [30]:

where $K_I$ is the stress intensity factor amplitude caused by normal stress, $K_{II}$is the stress intensity factor amplitude caused by shear stress, $K_{III}$is the stress intensity factor amplitude caused by torsional stress, and $v$ is Poisson’s ratio. Therefore, Eq. (2) can be written as:

3.1.3. Evaluation results and analysis

The fatigue performance test results of the butt weld, the 95 % confidence S-N curve, the design S-N curve from JTG D64-2015 Code for Design of Highway Steel Structure Bridges, and the numerical calculation results of fatigue crack propagation are presented in Fig. 10. When the initial crack size $a_0$ is 0.5 mm, the fatigue strength of the S-N curve is 97.7 MPa. The results indicate that when the initial crack size is a 0.5 mm circular crack, the data point of the fatigue performance test of the butt weld lies above the numerical-calculation S-N curve. The numerical calculation S-N curve can accurately predict the fatigue life of the butt weld specimen and provide sufficient safety margin.

Fig. 10Numerical calculation results of fatigue crack propagation in butt weld

3.2.1. Stress amplitude

The numerical calculations indicate that an initial crack size $a_0$ of 0.5 mm is inserted at the center of the specimen, and the stress amplitudes are 117 MPa, 126 MPa, 135 MPa, 144 MPa, 153 MPa, 162 MPa, 171 MPa, 180 MPa, 189 MPa, respectively. The variation of crack tip $\mathrm{\Delta }{K}_{eff}$ with crack propagation depth a is shown in Fig. 11. The fatigue life of the butt-weld specimen is shown in Fig. 12. Fig. 11 depicts the magnitude of the stress-intensity factor amplitude $\mathrm{\Delta }K$ at the relative position of the crack front under different stress amplitudes, that is, the ratio of the arc length from the crack point to the starting point on the front edge of the circular crack to the whole arc length. It can be seen from Fig. 11 that the stress intensity factor of the crack is large at both ends and small in the middle. The stress intensity factor near the middle crack front decreases with the increase of the initial crack length. 117 MPa, 126 MPa, 135 MPa, 153 MPa, 162 MPa, 171 MPa, 189 MPa, the corresponding maximum strength factors are 1043 MPa$\sqrt{mm}$, 799 MPa$\sqrt{mm}$, 855 MPa$\sqrt{mm}$, 1262 MPa$\sqrt{mm}$, 1443 MPa$\sqrt{mm}$, 1397 MPa$\sqrt{mm}$, 1604 MPa$\sqrt{mm}$. It can be seen from Fig. 12 that with the increase in stress amplitude, the numerical calculation of fatigue life is significantly reduced. When the stress amplitude is 117 MPa, 126 MPa, 135 MPa, 144 MPa, 153 MPa, 162 MPa, 171 MPa, 180 MPa and 189 MPa respectively, the fatigue life of the butt weld sample is 82.00 %, 70.68 %, 60.21 %, 52.46 %, 46.09 %, 40.23 %, 33.21 % and 31.72 % of the stress amplitude of 117 MPa respectively. Evidently, the stress amplitude also has a substantial impact on the fatigue life of the butt-weld sample.

Fig. 11Stress intensity factors corresponding to different depths of crack propagation

Fig. 12Effect of stress amplitude on fatigue life of butt weld specimen

3.2.2. Initial flaw size

A circular crack with a stress amplitude of 171 MPa was investigated through numerical calculations. When the initial crack sizes $a_0$ were 0.075 mm, 0.1 mm, 0.2 mm, 0.3 mm, 0.4 mm, and 0.5 mm, respectively, the variation of crack-tip $\mathrm{\Delta }{K}_{eff}$with crack propagation depth a of the butt weld specimen was shown in Fig. 13. As can be observed from Fig. 13 that the stress intensity factor of the crack is large at both ends and small in the middle, and the stress intensity factor near the middle crack front decreases with the increase of the initial crack length. The initial crack sizes are 0.075 mm, 0.1 mm, 0.2 mm, 0.3 mm, 0.4 mm, and 0.5 mm, respectively, and the corresponding maximum strength factors are 1313 MPa$\sqrt{mm}\text{,}$ 1477 MPa$\sqrt{mm}\text{,}$ 1497 MPa$\sqrt{mm}\text{,}$ 1772 MPa$\sqrt{mm}$, 1747 MPa$\sqrt{mm}$, 1397 MPa$\sqrt{mm}$. It can be found that with the increase of the initial crack length, the amplitude of the tip stress intensity factor tends to increase. The fatigue life is shown in Fig. 14. From the figure, it can be seen that as the initial crack size increases, the numerically-calculated fatigue life is significantly reduced. When the initial crack size is 0.1 mm, 0.2 mm, 0.3 mm, 0.4 mm, and 0.5 mm, the fatigue life of the butt weld specimen is 90.75 %, 70.00 %, 59.83 %, 53.32 %, and 48.58 % of the initial crack size of 0.075 mm, respectively. Thus, the initial crack size also has a substantial impact on the fatigue life of the butt-weld specimen.

Fig. 13Stress intensity factors corresponding to different depths of crack propagation

Fig. 14Effect of initial crack size on fatigue life of butt weld specimen

3.2.3. Initial crack shape

The crack-tip $\mathrm{\Delta }{K}_{eff}$ of the specimen with an initial crack size of 0.5 mm and the ratio of the short axis to the long axis of the initial crack $a_0$/$c_0$ of 1/1, 1/2, 1/3 and 1/4 is studied by numerical calculation. The variation of the crack – tip $\mathrm{\Delta }{K}_{eff}$ with the crack propagation depth a is presented in Fig. 15. The maximum crack – tip stress – intensity factors corresponding to the crack shapes with the ratio of the short axis to the long axis of 1/1,1/2,1/3 and 1/4 are respectively: 1397 MPa$\sqrt{mm}$, 1426 MPa$\sqrt{mm}$, 1415 MPa$\sqrt{mm}$, 1417 MPa$\sqrt{mm}$, compared with the difference between the stress amplitude and the initial crack size on the maximum crack tip stress intensity factor, the initial crack shape has little effect on the maximum crack tip stress intensity factor. The a-N curve is shown in Fig. 16. When the stress amplitude is 171 MPa, the difference between the fatigue life of the initial crack short axis and the long axis ratio of 1/4 and the fatigue life of the initial crack short axis and the long axis ratio of 1/1, 1/2 and 1/3 is 30.70 %, 24.54 %, and 15.28 %, respectively. Thus, the initial crack shape has a relatively significant influence on the fatigue performance of the uncorroded butt-weld specimen.

3.2.4. Initial crack location

In this section, the fatigue properties of the specimens with initial cracks of center crack, edge crack, and between them are studied, as shown in Fig. 4-10. The initial crack size $a_0$ was set as a circular crack with a diameter of 0.5 mm. The variations of the crack-tip $\mathrm{\Delta }{K}_{eff}$ with the crack propagation depth $a$ for the initial central crack, edge crack, and the crack in-between are presented in Fig. 17, and the $a$-$N$ curve is shown in Fig. 18. The maximum crack tip stress intensity factors corresponding to the initial crack inserted at the center, the boundary, and the crack shape between the two are 1397 MPa$\sqrt{mm}$, 1229 MPa$\sqrt{mm}$, 1305 MPa$\sqrt{mm}$, compared with the difference between the stress amplitude and the initial crack size on the stress intensity factor of the maximum crack tip, the initial crack position has little effect on the stress intensity factor of the maximum crack tip. The difference in fatigue life between the central crack and the boundary crack is 7.3 %, and the difference in fatigue life between the central crack and the crack between the two is 7.4 %. Thus, the initial crack position has a relatively small influence on the fatigue performance of the butt-weld specimen.

Fig. 15Stress intensity factors corresponding to different depths of crack propagation

Fig. 16Effect of initial crack shape on fatigue life of butt weld specimen

3.2.5. Angular misalignment

As presented in Table 1, the average angular dislocation of the butt weld samples in this batch is 0.04°, and the corresponding flatness is 0.7 mm/m, which meets the requirement of JTG/T F50-2011 “Technical Specification for Construction of Highway Bridges and Culverts” [24] that the upper limit of flatness is 1 mm/m. Since angular misalignment can cause stress concentration and influence the fatigue life of the sample, this paper explores the impact of the angular dislocation of the butt-weld on the fatigue life of the sample.

The angular misalignment of circular cracks with a stress amplitude of 171 MPa and an initial crack size of 0.5 mm are calculated to be 0.02°, 0.08°and 0.32°, respectively. The variation of crack tip $\mathrm{\Delta }{K}_{eff}$ with crack propagation depth a is shown in Fig. 19, and the a-N curve is shown in Fig. 20. The angular displacement is 0.02°, 0.08°, and 0.32°, respectively, and the corresponding maximum crack tip $\mathrm{\Delta }{K}_{eff}$is 1513 MPa$\sqrt{mm}$, 1843 MPa$\sqrt{mm}$, 1847 MPa$\sqrt{mm}$. When fatigue failure occurs, the difference of fatigue life between angular dislocation 0 and 0.02°, 0.08°, and 0.32° is 1.18 %, 0.50 % and 30.5 %, respectively. While minor misalignment had only a 1 % effect, exceeding flatness limits led to a fatigue life reduction of over 30 %, making it a critical factor.

Fig. 17Stress intensity factors corresponding to different depths of crack propagation

Fig. 18Effect of initial crack location on fatigue life of butt weld specimen

3.2.6. Summary

The stress amplitude has a great influence on the fatigue life of the specimen. The fatigue life of the specimen decreases with the increase of the stress amplitude, and the fatigue life of the stress amplitude of 117 MPa and 189 MPa is 31.72 %. The initial crack size has a great influence on the fatigue life of the specimen. The fatigue life of the specimen decreases with the increase of the initial crack size. The initial crack sizes are 0.075 and 0.5 mm, and the difference between the fatigue life of the two is 48.58 %. Therefore, it is very important to accurately evaluate the initial crack size for predicting the fatigue life of the structure. The initial crack shape has a great influence on the fatigue performance of the sample. The fatigue life of the initial crack with the ratio of the short axis to the long axis of 1/4 and 1/1 is 30.70 % different. The initial crack position has little effect on the fatigue performance of the specimen, and the difference in fatigue life at different positions is less than 10 %. The angular dislocation of the butt weld specimen has little effect on the fatigue performance of the specimen under the premise of meeting the flatness requirements of the specification, but the effect on the specimen when exceeding the flatness requirements of the specification can not be ignored.

Fig. 19Stress intensity factors corresponding to different depths of crack propagation

Fig. 20Effect of angular dislocation on fatigue life of butt weld specimen