# The Evolution of Residual Stress in Rib-Diaphragm Joints of Orthotropic Steel Decks Subjected to Thermal Cutting and Welding

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## Abstract

**:**

## 1. Introduction

## 2. Numerical Simulation Model

#### 2.1. Geometry and Method

#### 2.2. Material Properties

#### 2.3. Boundary Conditions

## 3. Heat Source Model and Thermal Analysis

- a.
- the heat flux was considered as a load, and all thermal properties were expressed as a function of temperature.
- b.
- the cutting flame acting on the plate surface was expressed by heat flux in terms of Gaussian functions.
- c.
- the heat generation of the droplets can be simplified, and the heat from the chemical reaction at the cutting line was assumed to be uniformly distributed.

_{1}is the effective radius of the superficial gaussian heat flux, the heat efficiency $\eta $ is set to be 0.3, and Q

_{1}is the combustion heat at surface in Equation (1); R

_{2}is the effective radius of chemical reaction zone of steel with oxygen, Q

_{2}is the oxidation energy of steel, and H is the effective height of cylindrical distribution in Equation (2). In the present study, H was taken as the thickness of the steel plate, and R

_{2}was identical to the half width of the cutting seam. In addition, the comparison of simulated and experimental cross-section profiles is considered as a standard for judging the accuracy of numerical simulation [34]. So, the isotherms (Figure 5) were adjusted in accordance with the experimental cross-section [33,36,37,38,39,40], which was considered to satisfy the accuracy of the study. The total parameters for the cutting heat source model are summarized in Table 1.

## 4. Experimental Work

## 5. Results and Discussions

#### 5.1. Stress and Temperature Time History

#### 5.2. Residual Stress Distribution

#### 5.3. Effects of Cutting and Welding Speed

## 6. Conclusions

- (1)
- The residual stress around the diaphragm cutouts is mainly caused by the flame cutting process and distributes along longitudinal direction of the cutting line. The established heat source model caused by cutting can accurately describe the temperature distribution along the cutting line. The high residual stress region with a width of about 10 mm is responsible for the fatigue cracking of the diaphragm cutouts.
- (2)
- Near the welding area, the residual stress is mainly introduced by the welding. The longitudinal residual tensile stress (along the weld direction) exists in the weld joints between U-rib and diaphragm, and the peak residual stress even exceeds the yield strength. Moreover, the residual stress concentrates at the boundary of the weld fillets, which should be paid more attention.
- (3)
- The numerical simulation of residual stress distribution during cutting and welding process was validated by experimental measurements using both x-ray diffraction and HD methods. The longitudinal residual stress was found to be higher than the transversal one. In the high residual stress zone, the HD method underestimates the residual stress, while the x-ray diffraction method can accurately predict the actual residual stress.
- (4)
- The width of the high stress zone near the cutting line decreases with cutting speed. The residual stresses in diaphragm cutouts increases with welding speed, but the width of the high stress zone does not change significantly. Hence, choosing a fast cutting speed and a slow welding speed during fabrication processes can reduce the residual stresses and its concentration area at diaphragm cutout, which is beneficial for the fatigue performance of U rib-diaphragm joints in OSDs.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**A typical U rib-diaphragm joint in OSD (unit: mm): (

**a**) orthotropic steel bridge deck; (

**b**) half symmetrical model of a U rib-diaphragm joint.

**Figure 2.**Temperature-dependent properties of Q345 Steel: (

**a**) physical properties; (

**b**) mechanical properties.

**Figure 3.**Finite element meshes and boundary conditions: (

**a**) schematic diagram of cutting; (

**b**) schematic diagram of welding.

**Figure 5.**Temperature (unit: °C) contours in the fusion zone and heat-affected zone (HAZ) of the cutting domain: (

**a**) top of the cutting line and (

**b**) cross-section of the cutting line.

**Figure 7.**Temperature (unit: °C) contours at the fusion zone and HAZ during welding process: (

**a**) top of the fillet (

**b**) first side of the fillet, and (

**c**) second side of the fillet.

**Figure 8.**Residual stress measurement: (

**a**) measuring points arrangement; (

**b**) XRD method, and (

**c**) hole-drilling (HD) method.

**Figure 9.**Real-time von Mises stress and temperature: (

**a**) measuring point A; and (

**b**) measuring point B.

**Figure 10.**Residual stress distributions around U rib (units: Pa): (

**a**) von Mises stress; (

**b**) transverse residual stress, and (

**c**) longitudinal residual stress.

**Figure 11.**Residual stress distributions in diaphragm cutout (units: Pa): (

**a**) von Mises stresses; (

**b**) transverse residual stress, and (

**c**) longitudinal residual stress.

**Figure 12.**Residual stress distributions in diaphragm cutout (units: Pa): (

**a**) von Mises stresses; (

**b**) normal residual stress, and (

**c**) tangential residual stress.

**Figure 13.**Residual stress distributions along Path A: (

**a**) longitudianal direction, (

**b**) transverse direction.

**Figure 14.**Residual stress distributions along Path B: (

**a**) longitudinal direction, (

**b**) transverse direction.

**Figure 15.**Residual stress distributions along Path B under different cutting speeds: (

**a**) longitudinal direction, (

**b**) transverse direction.

**Figure 16.**Residual stress distributions along Path B under different welding speeds: (

**a**) longitudianal direction, (

**b**) transverse direction.

Parameters | ${\mathit{Q}}_{1}/\mathbf{J}\xb7{\mathbf{m}}^{-3}$ | ${\mathit{Q}}_{2}/\mathbf{J}\xb7{\mathbf{m}}^{-3}$ | ${\mathit{R}}_{1}/\mathbf{m}\mathbf{m}$ | ${\mathit{R}}_{2}/\mathbf{m}\mathbf{m}$ | $\mathit{H}/\mathbf{m}\mathbf{m}$ | $\mathit{V}/\mathbf{m}\mathbf{m}\xb7{\mathbf{s}}^{-1}$ |
---|---|---|---|---|---|---|

Value | $3.005\times {10}^{4}$ | $3.525\times {10}^{10}$ | 4.1 | 1 | 10 | 7 |

Parameters | $\mathit{b}/\mathbf{m}\mathbf{m}$ | c/mm | ${\mathit{a}}_{\mathit{f}}/\mathbf{m}\mathbf{m}$ | ${\mathit{a}}_{\mathit{r}}/\mathbf{m}\mathbf{m}$ | $\mathit{V}/\mathbf{m}\mathbf{m}\xb7{\mathbf{s}}^{-1}$ | $\mathit{I}/\mathit{A}$ | $\mathit{U}/\mathit{V}$ |
---|---|---|---|---|---|---|---|

Value | 9 | 8 | 6 | 14 | 4 | 250 | 25 |

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**MDPI and ACS Style**

Xiong, Y.; Li, C.; Chen, Z.; He, J.; Xin, H.
The Evolution of Residual Stress in Rib-Diaphragm Joints of Orthotropic Steel Decks Subjected to Thermal Cutting and Welding. *Materials* **2020**, *13*, 3804.
https://doi.org/10.3390/ma13173804

**AMA Style**

Xiong Y, Li C, Chen Z, He J, Xin H.
The Evolution of Residual Stress in Rib-Diaphragm Joints of Orthotropic Steel Decks Subjected to Thermal Cutting and Welding. *Materials*. 2020; 13(17):3804.
https://doi.org/10.3390/ma13173804

**Chicago/Turabian Style**

Xiong, Yongming, Chuanxi Li, Zhuoyi Chen, Jun He, and Haohui Xin.
2020. "The Evolution of Residual Stress in Rib-Diaphragm Joints of Orthotropic Steel Decks Subjected to Thermal Cutting and Welding" *Materials* 13, no. 17: 3804.
https://doi.org/10.3390/ma13173804