The method of reconstruction of residual stresses in a prismatic specimen with a notch of a semicircular profile after advanced surface plastic deformation

The stress-strain state in a surface-hardened bar (beam) with a stress concentrator of the semicircular notch type is investigated. A numerical method for calculating the residual stresses in the notch region after an advanced surface plastic deformation is proposed. The problem is reduced to the boundary-value problem of fictitious thermoelasticity, where the initial (plastic) deformations of the model are simulated by temperature deformations in an inhomogeneous temperature field. The solution is constructed using the finite element method. For model calculations, experimental data on the distribution of residual stresses in a smooth beam made of EP742 alloy after ultrasonic mechanical hardening were used. The effect of the notch radius and beam thickness on the nature and magnitude of the distribution of the residual stress tensor components in the region of the stress concentrator is studied. For the normal longitudinal component of the residual stress tensor, which plays an important role in the theory of high-cycle fatigue, it was found that if the radius of a semicircular notch is less than the thickness of the hardened layer (area of material compression), an increase (in modulus) of this component of residual stresses occurs in the smallest section of the part (in the volume immediately adjacent to the bottom of the concentrator). If the depth of the notch is greater than the thickness of the hardened layer, then a decrease (in magnitude) of this value is observed in comparison with a smooth hardened sample. It is shown that in a reinforced notched beam, the deflection value due to induced self-balanced residual stresses is less than in a smooth beam. Experimental verification of the developed numerical method is done for a surface-hardened smooth beam made of EP742 alloy.