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Investigation of temperature distribution of submerged arc welded plates is essential while designing submerged arc welding joint because the key parameter for the change of weld bead geometry dimension, thermal stress, residual stress, tensile stress, hardness, and so forth is heat input, and heat input is the function of temperature distribution of GMAW process. An attempt is made in this paper to find out the exact solution of the thermal field induced in a semi-infinite body by a moving heat source with Gaussian distribution by selecting appropriate inside volume for submerged arc welding process. It has been revealed that for GMAW, best suitable heat source shape is a combination of semispherical and semioval.

An attempt of development of mathematical model of travelling heat source was made more than fifty years ago. After that, lots of research work has been continuing on this area. Initially two-dimension surface Gaussian heat source with effective arc radius was adopted to find out temperature distribution on welded plates and weld pool geometry (Eager and Tsai, [

Nguyen et al. [

Sabapathy et al. [

Ghosh et al. [

In this analysis, an attempt is made in this paper to find out the approximate analytical solution of the thermal field induced in a semi infinite body by a moving heat source with Gaussian heat distribution by selecting inside volume of combined spherical and oval shape for GMAW process.

Heat energy is lost mainly through conduction along the base metal. During this process, the areas adjoining the weld metal are heated to fairly high temperature. The temperature at different points in the base is taken by infrared thermometers.

GMAW unit, mild steel plates size 22 × 95 × 300 mm, Omega scope OS524E, temperature range 2482 °C, accuracy is ±1% rdg or 2 °C whichever is greater, resolution 1°C, response time is 10 ms.

Thermal history of GM welded plates is described in Table

Temperature readings (taken at the intervals of 10 sec up to 160 sec).

Time (sec) | Temperature (at 1,1,0) on welded plates | Temperature (at 1,1.5,0) on welded plates | Temperature (at 1,2.5,0) on welded plates | Temperature (at 1,5,0) on welded plates |
---|---|---|---|---|

10 | 30 | 30 | 30 | 30 |

20 | 230 | 183 | 97 | 30 |

30 | 260 | 190 | 100 | 30 |

40 | 275 | 303 | 115 | 30 |

50 | 291 | 235 | 121 | 43 |

60 | 310 | 240 | 129 | 54 |

70 | 330 | 250 | 140 | 53 |

80 | 320 | 254 | 145 | 55 |

90 | 313 | 247 | 151 | 58 |

100 | 289 | 242 | 155 | 58 |

110 | 270 | 235 | 147 | 60 |

120 | 250 | 230 | 140 | 63 |

130 | 235 | 215 | 135 | 63 |

140 | 225 | 202 | 128 | 65 |

150 | 217 | 197 | 123 | 65 |

160 | 205 | 187 | 116 | 68 |

In developing the thermal model, an attempt has been made to accommodate the actual welding conditions as far as possible. However, the following have been assumed in the thermal model of the welding process.

Density remained constant and did not change with temperature change.

All other thermal properties were considered as a function of temperature.

Convective heat lost through all surfaces of the welded plates.

Heat loss due to radiation.

Let us consider a combination of semispherical and semi oval heat source in which heat is distributed in a Gaussian manner throughout the heat source’s volume. The heat density

respectively, where

Comparison between ellipsoid (indicated by dotted line) and combination of semi oval and semi spherical heat source shape (indicated by conditions line).

3D combination of semi oval and semi spherical heat source shape.

As it has been assumed that 50% of total heat input distributed through semi oval shape and remaining 50% through semi spherical shape.

Here,

where

Arc efficiency is taken 0.9 for GMAW:

Transient temperature field of heat source in a semi-infinite body is based on solution for the instant point source (

If heat is distributed throughout the semi infinite body, then the instant increase of temperature is

So,

Here, term

If heat is distributed throughout the semi infinite body for duration

When heat source is moving with constant speed v from time

where,

Here

Where,

Measured temperature data (Table

Values of heat source parameters.

Heat source parameters | Values of heat source parameters |
---|---|

431250 | |

312506 | |

312502 | |

312508 | |

0.2 |

With the help of (4.6) and measured temperature reading, graph has been plotted and excellent agreement between measured and calculated temperature reading has been found (as shown in Figure

Comparison of measured and calculated thermal history for GMAW.

This type of numerical investigation is made to estimate two- and three-dimensional transient heat conduction field in semi infinite metallic solid because surface heat transfer strongly affected the temperature distribution in the welded pates. In this study, analytical solutions for the transient temperature field of a semi infinite body subjected to 3D power density moving heat source (such as combined spherical and oval heat source) were found and experimentally validated. Also, it was shown that the analytical solution obtained for combined spherical and oval heat source was a general one that can be applied for any welding process by choosing appropriate values of heat source parameters, and also it can be reduced to 2D Gaussian distributed heat source and classical instant point heat source. Very good agreement between the calculated and measured temperature data indeed shows the creditability of the newly found solution and potential application for various simulation purposes, such as thermal stress, residual stress calculations and microstructure modeling. Previously, in many research works, or heat source shape was assumed double ellipsoidal heat source, but most suitable heat source shape is a combination of semi spherical and semi oval for this particular GMAW machine.