Prediction of USP-induced gradient nanostructuring: A novel DEM-FEM coupling approach using probability distribution function

Ultrasonic shot peening (USP) is an effective surface severe plastic deformation (SPD) technique for fabricating gradient nanostructured (GNS) materials. However, predicting the resultant gradient nanostructure remains challenging owing to the inherent randomness of multi-shot impacts. This study proposes a novel probability distribution function (PDF)-based coupling approach that integrates the discrete element method (DEM) and finite element method (FEM) to simulate the USP process and predict the gradient nanostructure in pure copper. The DEM simulation was initially validated against single-shot impact experiments, confirming its accuracy in capturing shot dynamics under ultrasonic excitation. Subsequently, the positions and velocities of multiple shots impacting the specimen, derived from DEM simulations, were statistically characterized using PDFs. These PDFs were incorporated into the FEM to construct a realistic finite element model. A physics-based constitutive model, which accounts for thermal activation, dislocation density evolution, the Hall–Petch effect, and dislocation drag, was implemented within this framework. The coupled model successfully predicted depth-dependent distributions of equivalent plastic strain, dislocation density, and dislocation cell size. The predicted gradient in dislocation density exhibited a direct correlation with microhardness profiles, showing good agreement with experimental measurements. Finally, the validated model was employed to systematically investigate the influences of key USP parameters, including ultrasonic vibration amplitude, shot diameter, USP time, and USP height, on the resultant gradient nanostructure. The proposed PDF-based DEM-FEM method provides an efficient and accurate numerical tool for optimizing USP processes aimed at fabricating gradient-nanostructured metallic materials. © 2026 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.