Formation of the gradient of structural-phase states of high-speed steel during surfacing. Part 2. The role of the Mullins–Sekerka instability in formation of crystallization structures

Abstract

The authors studied the crystallization process of the Fe – W system, which is the basis of heat-resistant high-speed steel used in plasma arc surfacing on the surface of rolls and various cutting tools. The structure of this material consists of two components: cellular and dendritic. Histogram of the structural elements distribution shows the presence of a single maximum. The most probable size takes a value in the range of 10 – 15 μm. The paper considers the morphological instability of crystallization front (the Mullins-Sekerka instability). The model includes the equations of convective thermal conductivity and diffusion. The Stefan conditions for temperature were set at interface of the phases. Linear analysis of this instability is carried out for two cases: when the convective term in the equations of thermal conductivity and diffusion can be neglected; when convection prevails over diffusion processes. In all cases, it was assumed that the value (1 – ks ) was close to zero, which corresponds to a concentration of the alloying element approximately equal to or exceeding the eutectic one, and a short-wave approximation was also used. In the first case, the analytical view of dependence of the wavelength, which accounts for the maximum rate of interface disturbances growth, coincides with generally accepted concepts. In the second case, the value of this wavelength is directly proportional to square root of the interphase boundary velocity. The limits of applicability of these approximations for various mechanisms of crystal growth were determined. In the case of normal growth, both approximations provide an adequate explanation for the formation of structural elements up to 5 μm in size at a crystallization front velocity of about 2 m/s. For the case of growth due to screw dislocations, the wavelength value corresponding to the fastest-growing perturbation mode in the first case coincides with experimental data at a crystallization front velocity of the order of 10–7 m/s, whereas in the convective approximation such a coincidence is observed at 10–4 m/s. Further development of the model consists in simultaneous consideration of the convective and diffusion components. The results obtained will serve as a material for the research of the Mullins–Sekerka instability for two interface boundaries.