Machining induced residual stresses affect the quality and performance of the component, which mainly depends on its direction and magnitude. Higher tensile residual stresses can be very detrimental to machined surface as they can lead to creep, fatigue and stress corrosion cracks [1]. Most of the previous researches focus on single tool path, ignoring the evolution of residual stress in sequential cuts, especially in 3D modeling of turning operations. However, the final surface of parts is always affected by multiple cuts, which emphasizes the significance of investigating the evolution process of residual stresses in sequential cutting.
Numerical models represent a large portion of the researches in analyzing the mechanisms and surface integrity in metal cutting. At present, Lagrangian, Eulerian, Arbitrary Lagrangian-Eulerian (ALE) and CEL are used extensively in numerical simulation of two-dimensional (2D) cutting. The Lagrangian method needs to define damage layers with separation criteria to achieve chip formation and avoid over-deformation of elements. Nevertheless, the magnitude of separation criteria can affect the distribution of residual stress on machined surface [2]. Separation criteria can be avoided by using the updated Lagrangian (remeshing) method [3], but the remeshing of elements is not the behavior of material itself, which reduces the accuracy of the results [4]. The Eulerian method can perfectly solve the element deformation problems but it also has disadvantages. The chip shape needs to be known ahead of time, and the elastic behavior of the material is not considered, making the simulation of machining-induced residual stress not possible [5]. Therefore, Eulerian method is gradually replaced by other methods in cutting simulation. ALE combines the advantages of both Lagrangian and Eulerian methods, where the elements can be moved arbitrarily in cutting simulation to keep them smooth [6]. On the one hand, ALE model with pure Lagrangian boundary, the separation criterion is not required for the cutting process [7]. However, similar to Lagrangian method, excessive deformation and fracture of the mesh will occur during chip formation, which will easily lead to simulation interruption [8]. On the other hand, ALE model with Eulerian and Lagrangian boundaries is not able to simulate the formation of segmented chips and the chip shape also needs to be given in advance when simulating metal cutting processes [9]. CEL method has been proposed by Ducobu et al. [10] for cutting simulation in recent years. In CEL models, the material moves within the mesh with the set boundary conditions, so there are no element deformations or program interruptions. Due to the mentioned reasons, CEL method has become a competitive method to capture the segment chip formation and guarantee the accuracy of simulated results [11].
In 3D modeling of cutting simulation, the element distortion is usually considered and be figured out by continuously remeshing. With the application of this method, Javidikia et al. [12] found that the axial surface residual stresses of AA6061-T6 observed that with the increase of feed rate in any turning environment of dry, minimum quantity lubrication and wet modes. Sahu et al. [13] obtained the surface residual stress by 3D simulation turning Ti-6Al-4V by remeshing, showing excellent agreement with the experimental results. Liu et al. [14] and Tzotzis et al. [15] simulated the cutting force of multiple sequential cuts in turning process, which is achieved by introducing the surface state after the previous cutting into the next cutting model as initial cutting condition [16]. Girinon et al. [5] applied 3D Eulerian model to obtain the temperature distribution during cutting process of H13A material. Arrazola et al. [17] simulated hard turning process through the 3D ALE model, and predicted the residual stress state of AISI 52100 steel on machined surface. CEL model can avoid the shortcomings of other models and can also simulate sequential cutting stably [18]. Weng et al. [19] established a 3D turning model based on CEL and obtained the residual stress and temperature distribution along the depth direction of the machined surface. Xu et al. [20] considered the influence of material side flow on chip formation and cutting force in 3D CEL orthogonal cutting simulations, which is proved to be more accurate when compared against the experimental value.
The researches mentioned above all focused on single cutting path from the perspective of both 2D and 3D simulations. When investigating the multiple sequential cuts, the Eulerian method is not suitable due to its boundary condition properties. Some scholars have investigated the residual stress evolution of sequential cuts in orthogonal cutting using Lagrangian and ALE methods. For instance, Yue et al. [21] summarized in his study of multiple sequential cuts of Ti-6Al-4V that the surface residual stress after the second cutting was lower than that of the first. Liu and Guo [22] proven that by optimizing the parameters of the subsequent cutting, surface residual stress in sequential cutting can be converted into compressive stress. Zhang et al. [23] discovered that the evolution of surface residual stress in the first to third cuts of AISI 52100 steel is gradually reduced using ALE. Liu et al. [24] investigated the residual stress evolution when cutting Inconel 718 using the CEL method and discovered that the residual stress state after the last cutting was affected by the previous cutting. Nevertheless, 2D sequential cutting studies the residual stress in depth direction and simplifies the tool geometry, which may not represent the actual cylindrical turning process. Turning is the result of the continuous tool path in the feed direction on a cylindrical workpiece. Turning is the result of the continuous action of the cutting tool on a cylindrical workpiece. The mechanical and thermal loads provided by the former cut will change the initial stress state of the undeformed material, hence, affect the residual stress induced by current cut. Some researches attempted to investigate this phenomenon by 3D numerical modeling. Mondelin et al. [25] simplified the turning process by adding analytic loads (equivalent thermo-mechanical load model) of the former cut to the workpiece to carry out 3D sequential cuts. Their research obtained the surface residual stress distribution along the feed direction considering the interaction of feed paths, while neglected the dynamic changes of chip generation, cutting force and cutting temperature during machining [26]. Attanasio et al. [16] combined Lagrange with ALE to accomplish the sequential cuts model of 3D turning by using the output of the previous cutting as the input of the next cutting. Both of their studies didn’t establish a continuously turning model to avoid a huge number of elements and possible over deformation, which may interrupt the simulation process. For CEL models, the elements are fixed in Eulerian part at the contact area and the number of elements is independent of the workpiece size, which can perfectly avoid the mentioned problems. Therefore, it is potential to employ CEL method for numerical investigations of the evolution of sequential cuts residual stress during turning operation.
The purpose of this paper is to find out the evolution of residual stress in feed direction of cylindrical turning, and establishes a CEL-based 3D numerical model of multiple sequential cuts for turning, integrated with complete material removal process of each cut. The tool edge microgeometry is measured by the edge measuring device before the experiment and taken into account in the established model. Longitudinal turning experiments of AISI 304 stainless steel are performed and the correctness and accuracy of the established 3D numerical model of multiple sequential cuts are verified from several aspects. The variation trend of mechanical loads and thermal loads from the numerical results of sequential cutting is applied to analyze the formation process of residual stress and the evolution with sequential cutting. In addition, the evolution of surface residual stress is further explored by using different tool nose radius and different feed rates.