Simulation of Thermal Stresses during Hardening of the Product Surface by a Heat Pulse

• Published in: Steel in translation 2021-11, Vol.51 (11), p.764-771
• Main Authors: Temlyantsev, M. V., Bazaikina, O. L., Temlyantseva, E. N., Tsellermaer, V. Ya
• Format: Article
• Language: English
• Subjects: Bessel functions; Boundary conditions; Chemistry and Materials Science; Circular cylinders; Conduction heating; Conductive heat transfer; Differential equations; Equations of motion; Exponential functions; Functionals; Heat; Heat flux; Heat pulses; Independent variables; Materials Science; Mathematical models; Mechanical properties; Surface hardening; Tensors; Thermal simulation; Thermal stress; Thermoelasticity; Time factors
• ISSN: 0967-0912; 1935-0988
• DOI: 10.3103/S0967091221110139

The article contains a particular solution of a linear version of the dynamic thermoelasticity problem as applied to modeling the conditions for surface hardening of metal products by an energy pulse. The equation of motion of the medium is considered together with the model of the temperature pulse, previously tested for compatibility with special cases of the equations of parabolic and hyperbolic heat conduction. The problem of loading a flat plane of a short circular cylinder (disk) with a temperature pulse is presented. The impulse is a consequence of the adopted structure of the volumetric power density of the heat flux, the time factor of which has the form of one wave of the Heaviside function. To construct the thermal stress tensor, the authors used the classical thermoelastic displacement potential and the method of its division into the product of functions of independent variables. Differential equations for the multiplier functions are obtained, and their general solutions are found. Natural boundary conditions are set for the components of the thermal stress tensor. The solutions obtained are in the form of segments of functional series (Bessel functions along the radial coordinate and an exponential function along the axial coordinate). A numerical example of loading a disk made of 40KhN steel, the mechanical properties of which are sensitive to temperature treatment, is considered. In the calculations, the authors used the Maple computer mathematics package. Approximate solutions consider the first 24 terms of the functional series. The calculations of the example make it possible to explain the presence of stress peaks and stress intensity as a result of mutually inverse processes of temperature stress growth and a decrease in elastic coefficients with increasing temperature. The numerical example warns against relying only on estimates of solutions to thermoelasticity problems without considering the plastic and viscous properties of the material.