Analytical solutions for heat flow in multiple pass welding

Abstract

The purpose of this paper is to present analytical solutions for the heat distribution in the base metal during and after serial heating in multiple pass arc welding. Recent literature on welding heat transfer has covered extensively numerical models for different aspects of the process. Most of these aspects are non-linear problems in heat flow, e.g. varying thermal properties, inclusion of radiative transfer in the arc, and/or convective flow in the welding pool. The basic analytical models in use were established long ago in classical papers, but these refer to single heat cycles. The present paper addresses the circumstances of multiple cycles. In these cases, depending on the bead length and the interpass time, as shown by the proposed solution, the thermal effects of each successive pass will accumulate. When modelling the heat transfer in each pass, the effects of previous passes enter into the differential equations as non-homogeneous initial conditions. The complexity introduced by these conditions requires special treatment: an analytical solution employing the Green's function method was used. The main focus in this work is on welding of thin plates. Simple changes to the models take account of the convective heat loss to the surroundings and enable temperature dependent properties to be calculated. The solutions were checked against experimental results obtained from a specially designed laboratory setup. Thermal cycles provided by the analytical solutions compare well with temperature histories measured at different locations during three pass gas metal arc welding of a 0.5 in (∼1 cm) AISI 304 stainless steel plate. Measured data and model results show very good agreement. The analytical solutions are also extended to the geometries of moderately thick plates.