Mathematical modelling of laser alloying for graded surface layer fabrication

On the base of the partial solution of the heat transfer differential equation (the Stefan problem) time-dependencies for temperature distribution and molten bath depth were obtained and an analytical model for laser cladding and alloying with direct powder injection into the molten bath was developed. Dimensionless process parameters (dimensionless layer depth and laser impact function), taking into account variation of properties in layers of a graded coating and determined by energy and powder consumption, were suggested. The experimental observations of laser treated high-speed steel substrates with direct injection of WC powder under various conditions were analyzed in terms of the developed model. The power absorption coefficient and the maximal molten bath surface temperature under the laser treatment were estimated. The mathematical model developed is relevant for the analysis of homogeneous as well as graded surface layer fabrication.