An analytical model of residual stress in orthogonal cutting based on the radial return method

Residual stress in metal cutting is critical due to its direct influence on the performance of components. An analytical model of residual stress in orthogonal cutting is established in this paper. A constitutive stress updating algorithm based on the radial return (R-R) method is firstly employed in the plastic stress calculation of the residual stress analytical model. A thermal-mechanical model for the elastic stress in orthogonal cutting is established. Subsequently, the plastic stress is calculated based on the R-R method. The R-R method and corresponding stress release method are employed to model the residual stress on the machined surface. Orthogonal cutting experiments and residual stress measurements are conducted to verify the theoretical model proposed in this work. The consistency between the prediction values and the experiment results demonstrates the accuracy of the prediction model developed in this work. According to the theoretical model, the variations in the stress components, equivalent stress and yield stress during the stress updating process are analyzed. Comparisons for the discrepancy of the accuracy between the R-R method and the present plastic stress updating methods are carried out. The characteristics and advantages of the R-R method are discussed in detail to explain the reasons for the discrepancy in the accuracy compared with current methods. The results show that the analytical model proposed in this work can achieve a better prediction accuracy than the existing models, since the R-R method can avoid the problems of stress mutation and yield drift, and exhibits excellent flexibility and extensibility by reasonable assumptions and implicit calculation method.