# Numerical Analysis of Longitudinal Residual Stresses and Deflections in a T-joint Welded Structure Using a Local Preheating Technique

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. T-joint Fillet Weld Geometry and Welding Conditions

_{w}and t

_{p}denote the thicknesses of the horizontal and vertical plates in mm, 2b

_{t}is the tensile zone width of the horizontal plate, b

_{s}is the tensile zone width of the vertical plate, σ

_{y}is the yield stress of the material at room temperature, while A

_{s}is the cross section of the vertical plate in mm

^{2}.

## 3. Numerical Model

_{x}, k

_{y}, and k

_{z}are the thermal conductivity components in the x, y and z directions; T is the body temperature; Q is the generated heat input; ρ is the material density; C is the specific heat capacity of the material; and t is time, respectively. A general solution for Equation (8) can be obtained when the following initial boundary conditions on the outer model surfaces are taken into account:

_{x}, N

_{y}, and N

_{z}are the direction cosine of the normal to the boundary; h

_{c}denotes the convective heat transfer coefficient; h

_{r}is the radiation heat transfer coefficient; q

_{s}represents the heat flux on the outer body boundaries; T

_{r}denotes the radiation temperature; and T

_{∞}is the ambient temperature. Heat loss due to radiation can be expressed by the following expression:

_{Bolt}= 5.67 × 10

^{−8}Wm

^{−2}K

^{−4}denotes the Stefan–Boltzmann constant; ε

_{surf}is the surface emissivity factor; and F is the configuration factor. The generated heat input applied to the weld volume can be expressed as follows:

_{H}is the weld volume. Although it is usual in the literature for the temperature distribution calculation in the MAG welding process to be performed as a combination of Gaussian and a uniformly distributed volumetric heat flux model [5,22], in this study, a pure volumetric heat flux with uniformly distributed heat input was used to speed up the simulation process, Q = 5.22 × 10

^{10}Jm

^{−3}s

^{−1}per weld volume was applied and its value was obtained from Equation (12). The MAG welding process efficiency η = 80% was taken according to the EN 1011-1 [30]. On the model boundaries, the convection heat transfer coefficient h

_{c}= 10 Wm

^{−2}K

^{−1}and the surface emissivity ε

_{surf}= 0.9 were assumed. During the thermal analysis, the element birth and date method [31,32,33] was employed for the simulation of weld filler addition.

_{total}can finally be written as follows:

_{e}}, {dε

_{p}} and {dε

_{th}} are elastic, plastic and thermal strain increments, respectively.

## 4. Application of Preheat Temperature and Interpass Time in the Numerical Models

^{3}dimensions (Figure 1) was preheated before the start of welding. The selected dimensions of the preheated volume satisfied the minimum prescribed requirements according to the ISO 13916 [37] norm. Therefore, it is important to point out that the local preheating technique was applied in this work, where preheating is only applied in areas close to the weld, while the rest of the structure is not preheated. Since the preheated part of the structure attempts to expand, the non-preheated area resists it, which introduces residual stresses into the structure before the start of the welding. This approach differs from Reference [16] where the entire structure was preheated at the same temperature and there was no additional introduction of residual stresses before welding. Also, unlike Reference [20], where the structure was continuously preheated during the welding process, in this study the preheating was applied once at the beginning of the welding process. All the numerical models considered in this study are given in Table 3.

## 5. Results and Discussion

#### 5.1. Residual Stress and Deflection Distributions—Reference Model

_{z}

_{,}stress in z-direction) at the middle plane of the horizontal plate along the A-B line (Figure 1) compared with two analytical solutions from Equations (1) and (2). It can be seen that tensile residual stresses are in the weld area, while in the rest of the model they are compressive. The maximum numerically calculated tensile stresses are approximately 5% higher than the analytically calculated ones. The numerically calculated compressive stresses are very close to the analytical ones calculated according to Equations (1) and (2) of 48.2 MPa and 42.5 MPa, respectively. Comparing the numerically calculated width of the tensile zone with the analytically calculated values it can be seen that they corresponded well. The numerically calculated tensile zone width is approximately 4% lower than the analytically calculated ones. Based on these results, it can be concluded that the numerical model presented is sufficiently accurate and it can be applied to the other four numerical models given in Table 3.

#### 5.2. Influence of Preheat Temperature on the Longitudinal Residual Stress and Horizontal Plate Deflection

#### 5.3. Influence of Interpass Time on the Longitudinal Residual Stress and Horizontal Plate Deflection

## 6. Conclusions

- The increase of the preheat temperature decreases the horizontal plate deflection of a T-joint very quickly.
- The influence of preheat temperature on the longitudinal tensile residual stress and the tensile stress zone width is negligible.
- The application of local preheating increases the compressive longitudinal stresses due to the increased temperature gradients between the preheated and non-preheated parts of the model. This occurrence is much more pronounced than in the models where the entire volume is preheated before the start of welding.
- The increase of interpass time increases the plate deflections. In cases when interpass time is prolonged, the positive effects of preheating vanish.
- The increase of interpass time minimally affects the longitudinal tensile residual stress and its tensile zone width.
- The effect of interpass time increase on compressive longitudinal stresses in preheated models can be neglected.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Thermal properties of SM400A steel [22].

**Figure 3.**Mechanical properties of SM400A steel [22].

**Figure 4.**Idealised longitudinal residual stress distribution [23].

**Figure 6.**Temperature histories at nodes N1 and N2 (Figure 1).

**Figure 7.**Middle-plane deflection profile along A-B line (Figure 1), model M1.

**Figure 8.**Middle-plane longitudinal residual stress profile along A-B line (Figure 1), model M1.

**Figure 9.**Middle-plane deflection profile along A-B line (Figure 1), models M1, M2 and M3.

**Figure 10.**Middle-plane longitudinal residual stress profile along A-B line (Figure 1), models M1, M2 and M3.

**Figure 11.**Middle-plane deflection profile along A-B line (Figure 1), models M3, M4 and M5.

**Figure 12.**Middle-plane residual stress profile along A-B line (Figure 1), models M3, M4 and M5.

**Table 1.**Welding conditions [22].

Welding Current (A) | Welding Voltage (V) | Welding Speed (mm/min) | Angle of Torch (°) |
---|---|---|---|

270 | 29 | 400 | 45 |

**Table 2.**Elemental composition of SM400A steel (mass%) [22].

C | Si | Mn | P | S |
---|---|---|---|---|

0.23 | - | 0.56 | <0.035 | <0.035 |

Model Name | Preheating Application | Interpass Time |
---|---|---|

M1 | No | t = 0 s |

M2 | Yes, T = 100 °C | t = 0 s |

M3 | Yes, T = 150 °C | t = 0 s |

M4 | Yes, T = 150 °C | t = 60 s |

M5 | Yes, T = 150 °C | t = 120 s |

Peak Temperatures (°C) | Node N1 (1st Pass) | Node N2 (1st Pass) | Node N1 (2nd Pass) | Node N1 (2nd Pass) |
---|---|---|---|---|

Current study | 1712 | 496 | 398 | 381 |

Gannon et. al. [5] | 1730 | 500 | 374 | 356 |

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**MDPI and ACS Style**

Perić, M.; Garašić, I.; Nižetić, S.; Dedić-Jandrek, H.
Numerical Analysis of Longitudinal Residual Stresses and Deflections in a T-joint Welded Structure Using a Local Preheating Technique. *Energies* **2018**, *11*, 3487.
https://doi.org/10.3390/en11123487

**AMA Style**

Perić M, Garašić I, Nižetić S, Dedić-Jandrek H.
Numerical Analysis of Longitudinal Residual Stresses and Deflections in a T-joint Welded Structure Using a Local Preheating Technique. *Energies*. 2018; 11(12):3487.
https://doi.org/10.3390/en11123487

**Chicago/Turabian Style**

Perić, Mato, Ivica Garašić, Sandro Nižetić, and Hrvoje Dedić-Jandrek.
2018. "Numerical Analysis of Longitudinal Residual Stresses and Deflections in a T-joint Welded Structure Using a Local Preheating Technique" *Energies* 11, no. 12: 3487.
https://doi.org/10.3390/en11123487