Asymptotic Analysis for Penetration Depth During Laser Welding

Abstract

Determination of the penetration depth is of fundamental and practical importance to understand properties and microstructures of joints. In this work, the keyhole is idealized by a paraboloid of revolution in a semi-infinite workpiece subject to an incident flux of a Gaussian distribution. Introducing analytical solutions of three-dimensional analytical temperature field, the dimensionless penetration depth are analytically found to be functions of the dimensionless parameters governing beam power per unit penetration, depth and shape of the keyhole. The penetration depth can be simply predicted by asymptotically expressing the temperature field involving the sum of product of complicated Laguerre functions and confluent hypergeometric functions of the second kind. A significant difference in the penetration depth was predicted by a line-source solution and this study.