Formation of the gradient of structural-phase states of high-speed steel during surfacing. Part 1. Solving the Stefan problem with two movable boundaries

Abstract

The article considers theoretical study of solidification of the binary iron–tungsten system at a tungsten content of 18 wt. %. Such tungsten content is typical for heat-resistant alloys used in plasma-arc surfacing on the rolls surface. The axisymmetric Stefan thermal problem is solved for two movable cylindrical boundaries that separate three regions. In region 1, the melt is at the melting point; in region 2, the substance is in a two‒phase state, and in region 3 – a solid. The liquidus temperature was set at the interface of regions 1 and 2, and the solidus temperature – at the interface of regions 2 and 3. At these boundaries, a condition for the heat flows balance was given, from which a system of kinetic equations was obtained. This system was solved by numerical methods, without hypothesizing that the fronts of phase transformations move according to the law R ~ t1/2. Solution of the system of kinetic equations shows that the solidus boundary moves almost linearly. The liquidus boundary moves according to the parabolic law. For regions of the micrometer range in size, the processes of phase transformations take place in a time of about 5 ns, whereas for regions of the order of 10 μm in size – in a time of about 50 ms. Dependences of temperature fields on the radial coordinate at various points in time show that with increasing time, the dimensions of region 2 decrease, and as soon as coordinates of the liquidus and solidus boundaries become close, thecrystallization process stops. Further development of the model consists in taking into account the rotation of one of the media. The results obtained will serve as a material for the study of the Mullins-Sekerka two-front instability.