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Residual stresses developed during heat treatment have a significant effect on the mechanical performance, dimensional accuracy, and service life of metallic components. Therefore, the estimation of these stresses is an important issue in the design and optimization of heat treatment processes. In this paper, a mathematical model for estimating residual stresses in metals after heat treatment is proposed. The transient temperature distribution within the material is determined by solving the second Fourier heat conduction equation. Based on the obtained temperature field, an analytical approach is developed to evaluate the evolution of residual stresses during the heat treatment process. The proposed methodology provides a simple and efficient framework for estimating residual stresses and investigating the influence of thermal conditions on their development. The presented approach can be used as a basis for further studies on the optimization and control of heat treatment processes in metallic materials.
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