An analytical solution for temperature distribution in fillet arc welding based on an adaptive function

This paper presents an analytical solution that can be applied to predict temperature distribution in fillet welds using adaptive function approach developed by authors. The adaptive function method is a general approach to solve the partial differential equation of engineering problem based on developing a flexible function of dimensionless parameters, which circumvent the simplification assumptions required in numerical and analytical solutions proposed so far. This paper intends to develop the adaptive function by manipulating Rosenthal’s equation so that it can be adjusted according to the experimental data, which are the weld pool dimensions and temperature measured at some arbitrary points. To apply the adaptive function in a fillet weld, a new coordinate system is defined in which the x-axis is parallel to the legs of the fillet weld (width direction of the weld plate), the y-axis is parallel to the welding trajectory, and the z-axis is parallel to the penetration of the weld (depth direction of the weld plate). A polar coordinate system is defined for the corner part of the fillet weld. The adaptive function in this part is defined to preserve the consistency of the isotherms. The experimental data were provided by performing GTAW on a stainless steel 316L with various welding current. The results indicate that the novel approach is fast and simple and agrees well with results from experiments.