Mathematical estimation of melt depth in conduction mode of laser spot remelting process

Abstract

A one-dimensional mathematical model based on the front tracking method was developed to predict the melt depth as a function of internal and external parameters of laser spot remelting process in conduction mode. Power density, pulse duration, and thermophysical properties of material including thermal diffusivity, melting point, latent heat, and absorption coefficient have been taken into account in the model of this article. By comparing the theoretical results and experimental welding data of commercial pure nickel and titanium plates, the validity of the developed model was examined. Comparison shows a reasonably good agreement between the theory and experiment. For the sake of simplicity, a graphical technique was presented to obtain the melt depth of various materials at any arbitrary amount of power density and pulse duration. In the graphical technique, two dimensionless constants including the Stefan number (Ste) and an introduced constant named laser power factor (LPF) are used. Indeed, all of the internal and external parameters have been gathered in LPF. The effect of power density and pulse duration on the variation of melt depth for different materials such as aluminum, copper, and stainless steel were investigated. Additionally, appropriate expressions were extracted to describe the minimum power density and time to reach melting point in terms of process parameters. A simple expression is also extracted to estimate the thickness of mushy zone for alloys.