Analytical modeling of through depth strain induced by deep rolling

The material properties of the surface layer caused by deep rolling are closely related to the degree of strain hardening. It is of great significance to establish the prediction model of strain distribution to realize the surface strain control and improve the service performance of deep rolling parts. In this study, the analytical models of elastic-plastic strain based on the Hertz contact theory were established by two different methods. The accuracy of the analytical prediction model of elastic-plastic strain was examined by deep rolling simulation. Then, the influence of deep rolling parameters, such as rolling force, the ball diameter, and material on the elastic-plastic strain along the depth was studied and validated by the microhardness profiles along the depth. The results indicate that the analytical model established by the first method is more accurate, and the error between maximum elastic-plastic strain obtained by the first method and finite element (FE) simulation is 12.6%. The elastic-plastic strain along the depth increases with the increasing rolling force and decreases with the increasing ball diameter, and its effective depth increases with the increasing rolling force. The tungsten carbide ball generates more elastic-plastic strain than balls of the other two materials (silicon nitride and steel). In addition, the elastic-plastic strain profiles are in accordance with the change of microhardness along the depth. In a word, the model can be used to predict the strain distribution along the depth induced by deep rolling.