Analysis of transient heat conduction with phase change in a spray deposited body

A numerical method is presented to predict and analyze the shape and the temperature history of a growing billet produced from the `spray forming' which is a fairly new near net-shape manufacturing process. It is important to understand the mechanism of billet growing and the cooling history of the spray deposited body, because one can obtain a billet with the desired final shape without secondary operations by accurate control of the billet shape and, moreover, growing velocity together with the cooling rate define the microstructure of the final formed product. The shape of a growing billet is determined by the flow rate of the alloy melt, the mode of nozzle scanning which is due to cam profile, the initial position of the spray nozzle, scanning angle, and the withdrawal speed of the substrate. The temperature history of a growing billet is governed by the heat flux input from the spray, gas convection on the surface of the deposited body, and heat conduction to the substrate. In the present study, a theoretical model is first established to predict the shape of the billet and next the transient axisymmetric heat conduction problem with growing domain is solved using the so called `deforming finite element technique'. The range of mushy zone near the surface of the deposited body is predicted, and the effect of cooling history on the microstructure and possible pore developments are discussed.