Depth of melt-pool and heat-affected zone in laser surface treatments

Predictions of penetration depths dα of a melt pool and/or transformation-hardening zone as influenced by laser power and scan speed are developed based on a simple conduction balance in the solid metal substrate. The prediction is dα/d approx. P- 1/2 - (θα - 1) Q-1 where d is the laser beam width, θα is the ratio of 'penetration temperature' to substrate farfield temperature, and P and Q are the dimensionless laser-scan speed and absorbed power, respectively. This scaling law, alternatively derived as an asymptotic limit of a classical closed-form solution, applies for moderate scan speeds and power. Evidence that it captures the dominant experimental behavior in cases of no melting and melting is presented. The predicted depths also compare favorably to numerical simulations by finite elements (a three-dimensional (3D) workpiece of finite extent).