Shape of Fusion Zone for the Welding Keyhole Induced by an Electron Beam

Abstract

In this paper analytical predictions of the fusion zone shapes around the welding cavity produced by a moving electron beam are provided. A three-dimensional analytical model in the molten and heat-affected regions surrounding a paraboloid of revolution-shaped cavity is used to predict the shapes of the fusion zones. This work avoids the defect of the infinite temperature at the cavity base for the line-source model. Introducing a new image method, a new analytical solution is provided by satisfying exactly the adiabatic condition at the top surface. The shape of a fusion zone is governed by dimensionless parameters related to beam power per unit penetration, and the depth and shape of the cavity in this work. A three-dimensional shape of fusion zone is computed and presented in this paper. The effect of beam power per unit penetration on the shape of fusion is also discussed.