A finite-element (FE) program is developed and used to analyse the distributions of residual stresses generated in the surface induction hardening of steel bars. It is found that there is no significant effect of the transformation latent heat and that the transformation induced plasticity (TRIP) reduces the compressive stress near the outer surface. The results with TRIP are in good agreement with experiment. Although many physical and mechanical parameters control the final microstructure and the residual stresses in the bar during surface induction hardening, the final residual stresses are mainly determined by the ratio of the hardening thickness to the radius of the bar and by the initial yield stress of the material. Based on a large number of FE numerical results, a set of simple formulae are given by use of the least-squares method. Instead of complicated FE analysis, the residual stresses in a bar induced by surface induction hardening can be easily predicted by use of these formulas from the final hardening thickness and the initial yield stress of the material.
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