Analytical and Numerical Modeling of Apparent Yield Strength Reduction Induced by Ultrasonic Nanocrystalline Surface Modification in Inconel 718

In this study, ultrasonic nanocrystalline surface modification (UNSM), one of the surface severe plastic deformation (SSPD) processes, was applied to an aging heat-treated Inconel 718 alloy. Contrary to the strengthening effect generally reported for SSPD processes, the yield strength measured using the 0.2% offset method decreased by 9.6%, from 1070.0 MPa to 966.7 MPa. To explain and predict this behavior, a closed-form 2D plane-stress framework is developed for rounded (axisymmetric) tensile specimens that couples axial loading with near surface circumferential compression and self-equilibrating core tension. The analysis predicts early surface yielding and a net reduction in apparent yield strength (AYS) through area-fraction averaging of the stressed layers. In parallel, a numerical model is formulated by combining a modified Swift–Voce hardening law capturing UNSM-induced strengthening with a depth dependent residual stress field, enabling faithful reproduction of both the initial softening and the transient regime. By moving beyond sheet-based treatments and validating the mechanism on rounded gauges, the study generalizes when SSPD/UNSM can reduce AYS while still enhancing surface durability, and provides a practical route to incorporate residual stress and hardening effects into standard constitutive and FE workflows.