Numerical method for calculating the stress-strain state in~a~prismatic surface-hardened spacemen with a~notch in elastic and~elastoplastic formulations

V. P. Radchenko ; D. M. Shishkin

Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 21 (2021) no. 4, pp. 503-519

Résumé

The problem of calculating the stress-strain state in the region of through stress concentrators in the form of a transverse notch of semicircular, through and V-shaped shape in a prismatic sample after advanced surface plastic deformation in elastic and elastoplastic formulations based on the finite element method is solved. The initial formulations are reduced to fictitious problems of thermoelasticity and thermoelastoplasticity using the method of initial deformations. At the first stage, the field of residual stresses and plastic deformations in a smooth sample after hardening is determined. At the second stage, residual plastic deformations are modeled by temperature deformations in an inhomogeneous temperature field along the depth of the hardened layer. At the third stage, a through notch of a given geometric shape is applied, and the problem of fictitious thermoelasticity or thermoelastoplasticity on the redistribution of stresses in the concentrator area is solved. Model calculations were performed on the basis of experimental data for a smooth sample made of EP742 alloy after vibro-shock ultrasonic hardening of one of its faces. There is a significant discrepancy between the solutions for the elastic and elastoplastic formulations in the notches, the depth of which does not exceed the thickness of the hardened layer. The results obtained for problems with notches in linear elastic and elastoplastic formulations, along with the results for a smooth sample, were subjected to a comparative analysis of the distribution of residual stresses to establish the influence area of the stress concentrator. It was found that, regardless of the shape of the notch, the values of residual stresses outside the stress concentrator zone when solving elastic or elastoplastic problems practically coincide with the corresponding values for a smooth sample.