Theoretical models are presented for the temperature field and transformation temperatures for the heat treatment of steel samples by a scanning electron beam. Analytical formulae for the quasi-stationary temperature field caused by moving heat sources can easily be found. Considering the High Speed Scanning technique, the time dependent energy distribution caused by a two dimensional scanning electron beam can be substituted with a stationary effective energy distribution. Assuming that electron beam hardening is based on the same metallurgical mechanisms as other martensitic hardening techniques, the transformation temperature for austenite formation can be calculated using the rule of additivity of phase transformations. Then the dependence of the transformation temperature can be developed from the most relevant material properties. The calculated results are in good agreement with measured surface temperatures, hardening depths, and microstructure of carbon steel samples.
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