Explicit analytical expressions for the influence of welding parameters on the grain structure of laser beam welds in aluminium alloys

Highlights: • Explicit analytical equations for the prediction of the grain structure • Mathematical identification of the key parameters, which influence the size and the type of the grain structure • Derivation of a threshold and a hyperbolic relation for the formation of an equiaxed dendritic grain structure • Calculation of the required depth specific power for the formation of an equiaxed dendritic grain structure • Experimental validation of the model by metallographic analysis -- Abstract: An explicit analytical model to express the influence of the welding parameters on the grain structure that is formed in laser beam welds in aluminium alloys is proposed and verified for the AlMgSi alloy AA6016. It results by linking the solution of the two dimensional heat conduction equation for a moving line source with the solidification structure map. Metallographic analyses prove that the model predicts the grain structure of laser beam welds with suitable accuracy. The model describes the morphology of the resulting grain structure as a function of the laser power absorbed per unit length in the depth of the material. The formation of an equiaxed dendritic grain structure was found to show a characteristic threshold behaviour. The derived model provides explicit analytical equations to calculate the minimum laser power per depth, which is required for an equiaxed dendritic grain structure. It further reveals that the absorbed line energy per depth is the key parameter to influence the average grain size. These findings explain how to optimize laser welding processes by means of spatial beam oscillation in order to obtain an equiaxed dendritic grain structure and how to reduce the grain size by means of high-speed laser welding.