In this study, thermal analysis and optimization of the material composition in functionally graded (FG) cutting tools were carried out to achieve the minimum thermal stress. Since cutting tool particularly rotating ones in milling process are exposed to thermal shock during machining, a complicated analysis is required to analyze the thermal shock response. Therefore, a generalized coupled thermoelasticity theory of Lord–Shulman based on second sound effect is adopted. Lord–Shulman theory, as a generalized coupled thermoelasticity, is chosen as governing equation in terms of temperature and displacement. The coupled equations are transferred to Laplace domain and then Galerkin finite element method is employed to solve the equation in the Laplace domain. Then, a numerical Laplace inversion has been applied to transform back the equation from Laplace domain to real time. Results are obtained for several material compositions so that the proper composition will be found for design. It is shown that FG materials (FGMs) exhibit lower stresses, lower displacement, and lower temperature levels compared to multilayer materials. Furthermore, the effect of FGM is increased by increasing the power law index, representing the change in concentration.

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