A mathematical model for penetration laser welding as a free-boundary problem

Abstract

A detailed model is constructed in order to determine the full 3D weld pool and keyhole geometry by setting the appropriate energy and pressure balances. The energy balance takes into account heat conduction, ablation losses and evaporation effects at the keyhole open surfaces, as well as the most relevant energy-absorption mechanisms, namely Fresnel and inverse Bremsstrahlung. The pressure balance ensures mechanical stability of the keyhole by including ablation pressure against surface tension pressure. The model provides a full description of the temperature field, electronic density, degree of ionization and absorption coefficient within the plasma, as well as setting the maximum penetration depth for a given set of laser parameters such as power, focusing radius and oscillation transversal mode. The keyhole boundary is initially taken to be an unknown free boundary and is obtained as a part of the solution of the problem. For low and medium welding speeds this boundary is successfully described with a family of ovoids. Good agreement with experimental results is achieved for a wide range of laser powers and plate thicknesses.

Experimental determination of temperature threshold for melt surface deformation during laser interaction on iron at atmospheric pressure

“…(  ) is the emissivity of the surface at the central wavelength   of the spectrum band selected. B(T) represents the temperature dependence of the black body radiation (11) where is the width (FWHM) of the selected band, and h and c are the Planck constant and the speed of light, respectively. B(T) can easily be calculated from eq.…”

“…Consequently our understanding of the threshold temperature is not at all conclusive. Concerning a deep keyhole welding, for example, not a few studies have assumed that the keyhole surface temperature is equal to T v [8][9][10][11][12][13], implying that this is the minimal temperature in order to carry out the keyhole welding process. In the well-known paper by Semak and Matsunawa [2], however, this assumption was denied.…”

Modeling of laser keyhole welding: Part I. mathematical modeling, numerical methodology, role of recoil pressure, multiple reflections, and free surface evolution

“…They showed that the front part of the keyhole has a steplike shape, which occurs when the component of the keyhole velocity along the sample surface exceeds the welding speed. Solana and Ocana [52] developed a model to determine the three-dimensional weld pool and keyhole geometry by considering heat conduction, evaporation losses, and evaporation effects at the keyhole surfaces, neglecting the fluid flow. Sudnik et al [54,55] found a linear correlation between the depth and the length of the (a) weld pool with the laser power intensity.…”

Estimation of Composition Change in Pulsed Nd:YAG Laser Welding

“…Knudsen layer provokes a rapid change in the density and temperature of the vapor state by its treatment as a gas dynamic discontinuity. In fact, temperature, density, pressure and mean velocity of vapor at the edge of the Knudsen layer can be related to such quantities of vapor on the liquid surface [2][3][4][5]28]. The variations in quantities throughout the Knudsen layer are given by: The main forces acting on the keyhole wall are assumed to be the ablation pressure opposed by the surface tension forces.…”

“…Vaporization of the alloying elements is due to the difference in partial vapor pressure and concentration gradient of each component. Pressure and concentration of alloying elements are higher near the weld pool surface in the Knudsen layer than in the bulk shielding gas and in the keyhole bulk [2][3][4][5]28] (In fact, the pressure of the vapor inside the keyhole is close to the ambient pressure [23]). Partial pressure of each alloying element in the Knudsen layer is related to equilibrium temperature of this layer and can be calculated using the equation (14).Where A, B, C, D, and E are constant coefficients, which usually differs for the various elements, and T refers to the temperature.…”