Thermal analysis of the arc welding process: Part I. General solutions

An analytical solution for the temperature-rise distribution in are welding of short workpieces is developed based on the classical Jaeger's moving he at-source theory to predict the transient thermal response. It, thus, compl ements the pioneering work of Rosenthal and his colleagues land others who extended that work), which addresses quasi-stationary moving heat-source pr oblems. The are beam is considered as a moving plane (disc) heat source wit h a pseudo-Gaussian distribution of heat intensity, based on the work of Go ldak et al. It is a general solution (both transient and quasi-steady state ) in that it can determine the temperature-rise distribution in and around the are beam heat source, as well as the width and depth of the melt pool ( MP) and the heat-affected zone (HAZ) in welding short lengths, where quasi- stationary conditions may not have been established. A comparative study is made of the analytical approach of the transient analysis presented here w ith the finite-element modeling of are welding by Tekriwal and Mazumder. Th e analytical model developed can determine the time required for reaching q uasi-steady state and solve the equation for the temperature distribution, be it transient or quasi-steady state. It can also calculate the temperatur e on the surface as well as with respect to the depth at all points, includ ing those very close to the heat source. While some agreement was found bet ween the results of the analytical work and those of the finite-element met hod (FEM) model, there were differences identified due to differences in th e methods of approach, the selection of the boundary conditions, the need t o consider image heat sources, and the effect of variable thermal propertie s with temperature. The analysis presented here is exact, and the solution can be obtained quickly and in an inexpensive way compared to the FEM. The analysis also facilitates optimization of process parameters for good weldi ng practice.