# A New Approach to Simulate HSLA Steel Multipass Welding through Distributed Point Heat Sources Model

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{c}

_{1}and A

_{c}

_{3}, is favorable to MA microconstituent formation in multipass weldments [2,5,8], as it can deteriorate the steel toughness, depending on its size and distribution in the ferritic matrix [9,10]. The following sub-region is reheated in the subcritical temperature range: it arises the SC-CGHAZ. For the last, remains the unaffected root CGHAZ. Similarly, the third welding pass, shown in Figure 2c, affects the previous HAZ and the root pass HAZ, but is less intense than the second one.

_{0}is a component of energy generation.

- Physical properties constant at room temperature (λ and α), independent of temperature;
- Point heat source moves in a straight line with constant speed ν;
- No energy generated or consumed within the plate, i.e., Q
_{0}= 0; - All the heat flow is transmitted by conduction. Radiation and convection through surfaces are neglected;
- The plate is semi-infinite, with a thickness d;
- The initial condition is defined by Equation (2).$$T\left(0\right)={T}_{0}$$
- The boundary conditions are defined by Equation (3);$$\{\begin{array}{c}\frac{\partial T}{\partial z}=0,z=0\\ \frac{\partial T}{\partial z}=0,z=d\end{array}$$

_{−2}, 2q

_{−1}, 2q

_{1}, 2q

_{2}, …), in relation to the planes z = 0 and z = d, as shown in Figure 3.

_{i}is the radius vector which measures the distance between the imaginary source q

_{i}and the point P where it is intended to calculate its peak temperature. The real heat source is presented by q

_{0}at the origin of the coordinate system, α is the thermal diffusivity, (x, y, z) are the coordinates of the point P and ν is the weld speed.

_{a}) along the y-axis and those immersed in the molten pool (q

_{b}) along the z-axis, as shown in Figure 7.

_{0}) is the sum of the contributions of all point heat sources, considering the welding arc efficiency (η), arc voltage (V) and welding current (I), as presented by Equation (6).

_{z}into the weld pool, in the z direction. Thus, the point sources could be located on the y-axis, or below it, located anywhere in the y-z plane, since confined inside the weld pool [28]. This model was developed due to the need to simulate multipass welding [28]. The authors considered physical properties independent of temperature and they still used Gleeble

^{®}system equipment (Dynamic Systems Inc., Poestenkill, NY, USA) to simulate physically the HAZ. According to the authors, the results were quite satisfactory when compared with experimental and physically simulated data.

## 2. Materials and Methods

^{®}, The Lincoln Electric Company, Cleveland, OH, USA) throughout the mentioned pipe extension. Subsequent passes were welded by the Flux Cored Arc Welding (FCAW) process. The beginning of each weld pass has been displaced to maintain an extension of the previous one free of microstructural changes due to the subsequent beads, as shown in Figure 8.

#### Extended Myhr and Grong′s Model

_{i}, and their displacements will assume values of their own coordinates related to system origin, (y

_{qi}, z

_{qi}). The quasi-stationary heat flow regime, in this case, is represented by Equation (7).

_{i−}

_{1}) until it reaches a maximum value. The instant t

_{i}at which the temperature at the P-point is increased by 1 °C is calculated by Equation (8).

_{i−}

_{1}and T

_{i}. For the calculation of $\Delta {t}_{1}$, the physical properties were considered constant and calculated at the temperature T

_{i−}

_{1}. An analytical thermal cycle was then calculated from these physical property values and other variables defined in Equation (7). The calculation of $\Delta {t}_{1}$ was determined from reading in the thermal cycle, when the temperatures ranged from T

_{i−}

_{1}–T

_{i}in the P-point.

_{2}was calculated using the same methodology, but with the physical properties calculated at temperature T

_{i}. This calculation scheme is shown in Figure 9, which depicts part of the analytical thermal cycles during heating at temperatures (T) and (T + 1), using the physical properties depending on the respective temperatures. The Δt

_{mean}was calculated by the arithmetic mean of $\Delta {t}_{1}$ and $\Delta {t}_{2}$.

_{i}, the values of the thermal properties, the respective analytical thermal cycle and its maximum temperature—${T}_{\mathrm{max}\left(\lambda \left({T}_{i}\right)\right)}$—are calculated. The maximum temperature of the discretized heat cycle—${T}_{\mathrm{max}\left({T}_{i}\right)}$—is calculated according to Equation (9).

_{i}and ${T}_{\mathrm{max}\left(\lambda \left({T}_{i}\right)\right)}$ was chosen to calculate ${T}_{\mathrm{max}\left({T}_{i}\right)}$ because the temperature T

_{i}is increased by 1 °C in the discretized thermal cycle. This value was enough to ensure the convergence criterion.

_{1}and Δt

_{2}, following the same criterion. However, the next temperature value will decrease by 1 °C with respect to the latest one. Finally, the cooling time interval from 800 °C–500 °C (Δt

_{8−5}) was obtained from the final numerically simulated thermal cycle at the interest point.

## 3. Results

#### 3.1. Comparison between Different Analytical Models

^{2}/s.

^{®}software (Version 10.2.0.0 Student Edition, Wolfram Research, Champaign, IL, USA) to determine the isotherms profiles and thermal cycles, using the resource of finding roots, like Newton-Raphson and bisection methods, because the temperature field equations presented before are transcendental functions.

_{c}

_{3}and A

_{c}

_{1}temperatures. The first one was obtained through Thermo-Calc

^{®}software (Version 2.2.1.1, Foundation for Computational Thermodynamics, Stockholm, Sweden), the second value was based on Pickering [31] and the last two of them were determined using dilatomety analysis.

_{max}) reached by a thermocouple and its $\Delta {t}_{8-5}$. The thermal cycles whose physical properties are temperature independent are presented by λ(25 °C) and those whose physical properties are temperature dependent are presented by λ(T). The position used to simulate them was the same where the thermocouple was installed, i.e., 7.15 mm right of the weld center line or 2.35 mm from the molten zone, in which T

_{max}= 1004.34 °C and $\Delta {t}_{8-5}=47.98\mathrm{s}.$

_{max}, but not in relation to $\Delta {t}_{8-5}$, whose calculated value was higher than the experimental one. It means that the effect of neglecting heat losses has a small but consistent effect on simulation of the maximum temperature, and probably also has a consistent effect on the time lag difference shown in Figure 15 for thermal cycling.

#### 3.2. Multipass Welding Simulation through DHS Model

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Easterling, K.E. Introduction to the Physical Metallurgy of Welding, 2nd ed.; Butterworth-Heinemann: London, UK, 1992. [Google Scholar]
- Grong, O. Metallurgical Modelling of Welding, 2nd ed.; The Institute of Materials: London, UK, 1997. [Google Scholar]
- ASM HANDBOOK. Properties and Selection: Irons Steels and High Perfomance Alloys, 3rd ed.; ASM International: Cleveland, OH, USA, 1993. [Google Scholar]
- Adams, C.M., Jr. Cooling rates and peak temperatures in fusion welding. Weld. J.
**1958**, 37, 210s–215s. [Google Scholar] - Lomozik, M. Effect of the welding thermal cycles on the structural changes in the heat affected zone and on its properfies in joints welded in low-alloy steels. Weld. Int.
**2000**, 14, 845–850. [Google Scholar] [CrossRef] - Bang, K.S.; Kim, W.Y. Estimation and Prediction of HAZ Softening in Thermomechanically Controlled-Rolled and Accelerated-Cooled Steel. Weld. J.
**2002**, 8, 174–179. [Google Scholar] - Yurioka, N.; Suzuki, H.; Okumura, M.; Ohshita, S.; Saito, S. Carbon Equivalents to Assess Cold Cracking Sensitivity and hardness of steel welds. Nippon Steel Tech. Rep.
**1982**, 20, 61–73. [Google Scholar] - Fairchild, D.P.; Bangaru, N.V.; Koo, J.Y.; Harrison, P.L. A Study Concerning Intercritical HAZ Microstructure and Toughness in HSLA Steels. Weld. J.
**1991**, 70, 321s–330s. [Google Scholar] - Di, X.J.; Cai, L.; Xing, X.-X.; Chen, C.-X.; Xue, Z.-K. Microstructure and mechanical properties of intercritical heat-affected zone of X80 pipeline steel in simulated in-service welding. Acta Met. Sin.
**2015**, 28, 883–891. [Google Scholar] [CrossRef] - Bhadeshia, H.K.D.H. About calculating the characteristics of the martensite-austenite constituent. In Proceedings of the International Seminar on Welding of High Strength Pipeline Steels, Araxa, Brazil, 28–30 November 2013; pp. 99–106. [Google Scholar]
- Chunyan, Y.; Cuiying, L.; Bo, Y. 3D modeling of the hydrogen distribution in X80 pipeline steel welded joints. Comput. Mater. Sci.
**2014**, 83, 158–163. [Google Scholar] - Nóbrega, J.A.; Diniz, D.D.S.; Silva, A.A.; Maciel, T.M.; Albuquerque, V.H.C.; Tavares, J.M.R.S. Numerical evaluation of temperature field and residual stresses in an API 5L X80 steel welded joint using the finite element method. Metals
**2016**, 6, 28. [Google Scholar] [CrossRef] - Cho, S.H.; Kim, J.W. Analysis of residual stress in carbon steel weldment incorporating phase transformations. Sci. Technol. Weld. Join.
**2002**, 7, 212–216. [Google Scholar] [CrossRef] - Pasternak, H.; Launert, B.; Krausche, T. Welding of girders with thick plates—Fabrication, measurement and simulation. J. Constr. Steel Res.
**2015**, 115, 407–416. [Google Scholar] [CrossRef] - Bate, S.K.; Charles, R.; Warren, A. Finite element analysis of a single bead-on-plate specimen using SYSWELD. Int. J. Press. Vessel. Pip.
**2009**, 86, 73–78. [Google Scholar] [CrossRef] - Azar, A.S.; Ås, S.K.; Akselsen, O.M. Analytical modeling of weld bead shape in dry hyperbaric GMAW using Ar-He chamber gas mixtures. J. Mater. Eng. Perform.
**2013**, 22, 673–680. [Google Scholar] [CrossRef] - Azar, A.S.; Ås, S.K.; Akselsen, O.M. Determination of welding heat source parameters from actual bead shape. Comput. Mater. Sci.
**2012**, 54, 176–182. [Google Scholar] [CrossRef] - Lindgren, L.; Runnemalm, H.; Näsström, M.O. Simulation of multipass welding of a thick plate. Int. J. Numer. Methods Eng.
**1999**, 44, 1301–1316. [Google Scholar] [CrossRef] - Börjesson, L.; Lindgren, L.E. Simulation of Multipass Welding with Simultaneous Computation of Material Properties. J. Eng. Mater. Technol.
**2001**, 123, 106. [Google Scholar] [CrossRef] - Deng, D.; Kiyoshima, S. Numerical Investigation on Welding Residual Stress in 2.25Cr-1Mo Steel Pipes. Trans. JWRI
**2007**, 36, 73–90. [Google Scholar] - Deng, D.; Murakawa, H. Numerical simulation of temperature field and residual stress in multi-pass welds in stainless steel pipe and comparison with experimental measurements. Comput. Mater. Sci.
**2006**, 37, 269–277. [Google Scholar] [CrossRef] - Maekawa, A.; Kawahara, A.; Serizawa, H.; Murakawa, H. Fast three-dimensional multipass welding simulation using an iterative substructure method. J. Mater. Process. Technol.
**2015**, 215, 30–41. [Google Scholar] [CrossRef] - Duranton, P.; Devaux, J.; Robin, V.; Gilles, P.; Bergheau, J.M. 3D modelling of multipass welding of a 316L stainless steel pipe. In Proceedings of the International Conference on Advances in Materials and Processing Technologies—AMPT2003, Dublin, Ireland, 8–11 July 2003; pp. 974–977. [Google Scholar]
- Rosenthal, D. Mathematical Theory of Heat Distribution during Welding and Cutting. Weld. J.
**1941**, 20, 220s–234s. [Google Scholar] - Rosenthal, D.; Schmerber, R. Thermal study of arc welding: experimental verification of theoretical formulas. Weld. J. Res. Suppl.
**1938**, 17, 2s–8s. [Google Scholar] - Rosenthal, D. The theory of moving sources of heat and its application to metal treatments. Trans. ASME
**1946**, 43, 849–866. [Google Scholar] - Jhaveri, P.; Moffatt, W.G.; Adams, C.M., Jr. The effect of plate thickness and radiation on the heat flow in welding and cutting. Weld. J.
**1962**, 41, 12s–16s. [Google Scholar] - Ramirez, A.J.L.; Brandi, S.D. Application of discrete distribution point heat source model to simulate multipass weld thermal cycles in medium thick plates. Sci. Technol. Weld. Join.
**2004**, 9, 72–82. [Google Scholar] [CrossRef] - Astm Committee E20 On Temperature Measur. Manual on the Use of Thermocouples in Temperature Measurement, 4th ed.; ASTM International: Philadelphia, PA, USA, 1993. [Google Scholar]
- Eagar, T.W.; Tsai, N.S. Temperature fields produced by traveling distributed heat sources. Weld. J. Res. Suppl.
**1983**, 62, 346s–355s. [Google Scholar] - Pickering, F.B. High-Strength, Low-Alloy Steels—A Decade of Progress. In Microalloying 75, Proceedings of an International Symposium on High-Strength, Low-Alloy Steels; Union Carbide Corp.: New York, NY, USA, 1977. [Google Scholar]
- Goldak, J.; Chakravarti, A.; Bibby, M. A new Finite Element Model for welding heat sources. Metall. Trans. B
**1984**, 15B, 299–305. [Google Scholar] [CrossRef] - Pavelic, V.; Tanbakuchi, R.; Uyehara, O.A.; Myers, P.S. Experimental and Computed Temperature Histories in Gas Tungsten-Arc Welding of Thin Plate. Weld. J. Res. Suppl.
**1969**, 48, 295s–305s. [Google Scholar] - Myhr, O.R.; Grong, Ø. Dimensionless maps for heat flow analyses in fusion welding. Acta Metall. Mater.
**1990**, 38, 449–460. [Google Scholar] [CrossRef] - Poorhaydari, K.; Patchett, B.M.; Ivey, D.G. Estimation of cooling rate in the welding of plates with intermediate thickness. Weld. J.
**2005**, 84, 149s–155s. [Google Scholar]

**Figure 1.**Experimental representation of heat affected zone (HAZ) regions, root pass welding of an API 5L X80 steel.

**Figure 2.**Schematic representation of multipass welding HAZ regions of the high-strength low-alloy steel (HSLA) HT50. In (

**a**) root pass; in (

**b**) root pass reheated one time and (

**c**) root pass reheated twice and filling pass reheated one time, reproduced from [5], with permission from Taylor & Francis, 2000.

**Figure 3.**Disposition of actual and imaginary heat sources on MTP model [2].

**Figure 5.**Convection effects in weld bead shape [2].

**Figure 7.**Point heat sources distribution in y-z plane to simulate finger effect in weld bead shape [2].

**Figure 9.**Thermal cycle calculation scheme using physical properties temperature dependent at temperatures T and T + 1.

**Figure 11.**Macrograph and front view of the root pass welding simulation through the MTP model with properties independent of temperature.

**Figure 12.**Macrograph and front view of the root pass welding simulation through the DHS model with properties independent of temperature.

**Figure 13.**Macrograph and front view of the root pass welding simulation through MTP model with temperature-dependent properties.

**Figure 14.**Macrograph and front view of the root pass welding simulation through DHS model with temperature-dependent properties.

**Figure 16.**$\Delta {t}_{8-5}$ variation depending on the maximum temperature reached on the HAZ width.

Alloy | C | Mn | Si | Cr | Ni | Mo | Al | Cu | Ti | V | Nb | B |
---|---|---|---|---|---|---|---|---|---|---|---|---|

wt% | 0.06 | 1.597 | 0.216 | 0.192 | 0.198 | 0.002 | 0.049 | 0.012 | 0.015 | 0.027 | 0.0649 | 0.0003 |

**Table 2.**Relative error between MTP and DHS isotherms in relation to reference positions within the HAZ with temperature-independent physical properties.

Position | MTP | DHS | ||
---|---|---|---|---|

1520 °C | 903 °C | 1520 °C | 903 °C | |

1 | 12.4% | 19.1% | 9.2% | 20.7% |

2 | −18.3% | 18.7% | 2.1% | 22.3% |

3 | −48.8% | 19.8% | 1.5% | 27.0% |

**Table 3.**Relative error between MTP and DHS isotherms in relation to reference positions within the HAZ with temperature-dependent physical properties.

Position | MTP | DHS | ||
---|---|---|---|---|

1520 °C | 903 °C | 1520 °C | 903 °C | |

1 | 6.9% | 3.4% | −1.1% | −1.9% |

2 | −24.9% | 1.4% | −2.3% | −0.9% |

3 | −60.0% | −0.8% | −2.3% | 1.6% |

Physical Property | MTP Simulation | DHS Simulation | ||||||
---|---|---|---|---|---|---|---|---|

T_{max} (°C) | T_{max} Error (%) | $\mathbf{\Delta}{\mathit{t}}_{8-5}\text{}\left(\mathbf{s}\right)$ | $\mathbf{\Delta}{\mathit{t}}_{8-5}\text{}\mathbf{Error}\text{}(\%)$ | T_{max} (°C) | T_{max} Error (%) | $\mathbf{\Delta}{\mathit{t}}_{8-5}\text{}\left(\mathbf{s}\right)$ | $\mathbf{\Delta}{\mathit{t}}_{8-5}\text{}\mathbf{Error}\text{}(\%)$ | |

λ(T) | 1108.58 | 10.38 | 50.82 | 5.92 | 994.62 | −0.97 | 52.04 | 8.47 |

λ(25 °C) | 1168.18 | 16.31 | 62.43 | 30.12 | 1103.53 | 9.88 | 63.18 | 31.68 |

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**MDPI and ACS Style**

Ferreira, D.M.B.; Alves, A.d.N.S.; Cruz Neto, R.M.d.A.; Martins, T.F.; Brandi, S.D.
A New Approach to Simulate HSLA Steel Multipass Welding through Distributed Point Heat Sources Model. *Metals* **2018**, *8*, 951.
https://doi.org/10.3390/met8110951

**AMA Style**

Ferreira DMB, Alves AdNS, Cruz Neto RMdA, Martins TF, Brandi SD.
A New Approach to Simulate HSLA Steel Multipass Welding through Distributed Point Heat Sources Model. *Metals*. 2018; 8(11):951.
https://doi.org/10.3390/met8110951

**Chicago/Turabian Style**

Ferreira, Dario Magno Batista, Antonio do Nascimento Silva Alves, Rubelmar Maia de Azevedo Cruz Neto, Thiago Ferreira Martins, and Sérgio Duarte Brandi.
2018. "A New Approach to Simulate HSLA Steel Multipass Welding through Distributed Point Heat Sources Model" *Metals* 8, no. 11: 951.
https://doi.org/10.3390/met8110951