Analytical expressions for the threshold of deep-penetration laser welding

Explicit analytical expressions are derived based on a simplified model as a convenient estimation of the requirements to reach the threshold of deep-penetration laser welding. For materials with high heat conductivity and low surface tension the simple formulas allow determining the material-dependent minimum power required for deep-penetration laser welding as a function of the diameter and the travel speed of the beam on the work piece surface. Within this area of application of the model the derived formulas agree well with experimental results.