Influence of residual stresses on geometric parameters of surface-strengthened beam

V. P. Radchenko ; O. S. Afanaseva ; V. E. Glebov

Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 19 (2019) no. 4, pp. 464-478

Résumé

The сomprehensive study of the formation of residual stresses and plastic deformations in prismatic samples of the EP742 alloy after ultrasonic hardening and their influence on the geometric parameters of the beam was conducted. Phenomenological model for the reconstruction of residual stress fields is proposed, and the verification of its adequacy to experimental data with four hardening modes is performed. The correspondence of the calculated and experimental data is observed. To assess the effect of the formed residual stresses on the geometric parameters of the beam the calculation method for initial strains based on using the analogy between the initial (permanent) plastic deformations and temperature deformations in an inhomogeneous temperature field is applied. This enabled us to reduce the consideration of the problem to the boundary value problem of thermoelasticity, which was further solved by numerical methods. The detailed study showed that residual stresses lead to bending effects. For a beam $100\times 10 \times 10$ mm, the calculated value of the arrow of maximum deflection was $210\,\mu$m. The kinetics of changes in this quantity is determined depending on the beam thickness which in the calculations ranged from $2$ to $10$ mm with the same distribution of residual stresses in the hardened layer. It is shown that the magnitude of the deflection nonlinearly increases with a decreasing thickness while with a thickness of $2$ mm it is $6.6$ mm with a beam length of $100$ mm. Illustrated material in the form of graphic and tabular information on the calculation results is given.