Mathematical modeling of melting during laser materials processing

Melting is encountered in almost all laser materials processing. This article deals with a one-dimensional heat conduction problem to investigate the melting rate during laser materials processing. The problem is solved approximately to obtain a correlation among melt depth, power density, and laser irradiation time. Based on this correlation, the dynamics of melting, a relationship between the melt depth and power density and an average melting velocity are expressed by simple analytic formulas. These expressions are further simplified for high power densities (${\text{I⩾10}}^9$ ${\mathrm{W/m}}^2$ ). The times to reach the melting and boiling temperatures at the surface of the workpiece are also calculated.