Numerical solution of the problem of stress-strain state of a surface-hardened prismatic V-notched specimen in elastic and elastoplastic formulations

A method has been developed for solving the problem of calculating the stress-strain state in a surface-hardened prismatic V-notched specimen at different values of the opening angle in both elastic and elastoplastic formulations. The method is based on finite element modeling and the known initial stress-strain state for a smooth hardened specimen. A detailed study was conducted on the influence of the notch opening angle and its depth on the level and distribution of residual stresses from the stress concentrator bottom throughout the thickness of the hardened layer for both formulations of the problem. Based on the calculation data, the feasibility of investigating the problem in the elastoplastic formulation was justified when the notch is located completely or partially in the hardened layer, as the magnitudes of residual stresses in the elastic formulation are physically unrealizable, since their values exceed the material's yield strength several times.
In this case, the error between solutions in the elastic and elastoplastic formulations for residual stresses reaches 100–200 % in the root-mean-square norm, and reaches several hundred percent in the uniform estimate (Chebyshev norm). If the depth of the stress concentrator exceeds the thickness of the hardened layer by more than 1.5 times, the elastic and elastoplastic solutions yield similar results.