Mathematical Modeling and Finite Element Analysis of Residual Stress (RS) Field after Multipass Ultrasonic Surface Rolling

In order to achieve the change rule of the induced residual stress (RS) field after multipass ultrasonic surface rolling (USR), a mathematical model of the induced residual stress (RS) field after multipass ultrasonic surface rolling is first established. Then, the coupling mechanisms of the RS field after dual-pass USR and multipass USR are analyzed, respectively. Subsequently, a finite element (FE) model is established, and the influence of the interval between two adjacent rolling paths $L_S$ is investigated. Finally, both the mathematical model and the FE model are experimentally verified. The results show that both the mathematical model and the FE model can predict the RS field after multipass USR. Two adjacent RS fields will couple with each other in their overlapping regions. For a relatively small interval $L_S$ , the RS field after multipass USR can be fully coupled, so as to form a uniform compressive RS layer. In this study, when $L_S$ = 0.05 mm, the values of the surface compressive RS, the maximum compressive RS, the depth of the maximum compressive RS, and the depth of the compressive RS layer reach 426.71 MPa, 676.54 MPa, 0.05 mm, and 0.54 mm, respectively.