Abstract
This article presents a method for determining dilatational curves in phase transformation kinetics for the hardening processes of cylindrical steel elements of an arbitrarily shaped cross section. The analysis is based on Lomakin's theory modified by Inoue and Raniecki and on the model of Hildenwall The laws of phase transformation kinetics of J. W. Cahn are used in the analysis. In the calculation a spline shaft with an optional cross section is considered with the assumption that heat exchange takes place at the lateral surface of the spline shaft. The elaborated program of numerical calculations refers to steel grades that are characterized by C-shaped T-T-T curves and have a carbon content close to that ofeutectoid steel. The solution of the problem is based on the variational finite difference method, which is a combination of the finite element method and the finite difference method. The algorithm of numerical calculations makes it possible to determine the temperature field and the weight fractions of particular structures and phases (Le., austenite, pearlite, and martensite) and the relative volumetric dilatation,
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