Abstract
Due to the complexity of analyzing residual stress, which involves numerous cutting parameters encompassing both mechanical and thermal stresses, various modeling and simulation methods, including analytical, numerical, and machine learning approaches have been summarized. An analytical model for predicting 2D orthogonal cutting and 3D milling residual stress is presented based on the cutting mechanism as well as the loading and unloading history of the stress field. The advancement in computational methods has prompted a review of finite element methods and mesh-free methods along with their principles, advantages, disadvantages, and application fields. Furthermore, machine learning models are employed to predict and control cutting residual stress based on data-driven approaches. These include support vector regression machines, artificial neural networks, and gradient boosted trees. A significant challenge for future work lies in addressing multi-scale size cutting residual stresses through hybrid methodologies.
Introduction
In the metal cutting of difficult-to-cut materials, such as bearing steel, titanium alloys, and nickel-based alloys, significant forces and high temperatures are generated, leading to induced residual stresses. Residual stress is an important index of surface integrity that affects fatigue life and deformation in the machining of thin-walled parts. 1 The prediction methods for residual stress are crucial and represent a hot topic in the manufacturing field. The parameters influencing residual stress include the material properties of the workpiece, tool geometry parameters, cutting conditions, among others. Due to the complex physical mechanisms underlying residual stress generation, understanding its prediction and control methods poses challenges within the manufacturing industry. Therefore, developing effective prediction methods for residual stress remains a challenging task in metal cutting processes.
The primary methods for predicting residual stress can be categorized into four approaches: experimental methods, analytical models, numerical methods, and machine learning techniques. 2 The experimental methods are further divided into two measurement categories: contact measurements and non-contact measurements. Among these, the hole-drilling method and X-ray diffraction technique are widely employed for measuring residual stress. 3 A significant challenge associated with these measurements is the uncertainty of results in certain materials. Thus, establishing standardized measurement protocols is essential to facilitate comparisons among different prediction models. Residual stresses typically exist in both surface and subsurface regions; therefore, plane strain measurements are utilized when assessing cutting-induced residual stress. Experimental procedures often require extensive data collection and can be costly; consequently, this study summarizes and reviews various modeling and simulation approaches. The analytical model relies on metal cutting theory as well as plastic-elastic theory to predict parameters such as cutting force, cutting temperature, stress fields, and residual stresses.4,5 However, existing analytical models predominantly focus on conventional turning and milling processes while offering limited predictions regarding residual stresses in advanced manufacturing contexts. With advancements in computational capabilities, numerical methods have become increasingly prevalent for simulating the cutting process using commercial software packages such as ABAQUS, AdvantEdge, ANSYS, and Deform. 5 It should be noted that current applications primarily address macro-scale cutting processes; hence there is a need to develop new numerical methodologies tailored for micro-scale machining operations. 7 Furthermore, with the rise of artificial intelligence technologies, machine learning techniques have been applied to predict cutting forces based on extensive experimental datasets without necessitating a physical model. 6
In recent years, numerous researchers have summarized and reviewed the topic of residual stress in machining, focusing on its generation mechanisms, prediction techniques, and control methods. Akhtar et al. 1 provided a comprehensive overview of the predictive and control strategies for cutting residual stress and distortion in aerospace components. Notably, they highlighted the coupling effects between residual stress and distortion, particularly when milling thin-walled parts. Similarly, Jiang et al. 4 examined the formation mechanisms and predictive methodologies associated with milling residual stress, with an emphasis on complex thin-walled structures. To achieve controlled compressive residual stresses, various assistive machining techniques can be employed. These include laser-assisted technology, pre-stress applications, ultrasonic vibration-assisted machining, cryogenic processing, and minimal quantity lubrication. Ammar et al. 5 presented a summary of numerical methods, analytical approaches, and experimental techniques for predicting turning-induced residual stresses. They also outlined how cutting conditions – such as cutting speed, feed rate, depth of cut, lubrication state, nose radius designations; rake angles; tool coatings; tool wear characteristics; material hardness; stretching effects; and pre-stressing during turning – affect these stresses. Malakizadi et al. 6 discussed advanced computational methods alongside machine learning approaches to predict surface integrity during machining processes. In a similar vein, Korkmaz and Gupta 7 compiled insights into finite element modeling techniques as well as predictive modeling and molecular dynamics simulation methods applicable to machining operations.
The field still faces several challenges, and new predictive methods need to be discussed in the context of residual stress (RS) during metal cutting. This includes understanding the mechanisms of residual stress from micro to macro scales, as well as developing predictive and control methods based on machine learning techniques. A primary issue is that existing research predominantly focuses on the cutting mechanisms at a macro scale. Although advancements in computational capabilities have made microscopic analysis feasible, there has been little discussion on how to integrate macroscopic and microscopic aspects into a unified framework. Many studies concentrating on microscopic analyses tend to focus specifically on diamond cutting and glass material processing. Furthermore, with the rise of artificial intelligence, some machine learning approaches have emerged for predicting cutting forces and surface topography; however, predictions related to residual stress remain scarce.
In this review, motivated by these considerations, the author analyzes and summarizes various simulation models pertaining to residual stress. The models addressing orthogonal cutting and milling residual stresses based on analytical methods are outlined. Additionally, numerical methods utilizing finite element analysis (FEA) and mesh-free techniques are examined, encompassing both macro-scale and micro-scale cutting processes. The review also consolidates machine learning methodologies aimed at prediction, optimization, and control. Finally, key issues regarding current predictive models are discussed along with future trends in this area of research.
Analytical method
In this section, the orthogonal cutting residual stress model based on predictive analytical model is summarized. Based on the 2D cutting model, the 3D cutting residual stress model are discussed. Many simplifications and assumption are needed, such as the continuity of chips, quasi steady state, isotropy, etc.
Turning
The principle of orthogonal cutting serves as the foundational study for understanding cutting mechanisms, leading to numerous research efforts focused on developing analytical models for residual stress in orthogonal cutting. The primary stages involved in calculating residual stress include: cutting force, cutting temperature, mechanical stress, thermal stress, cycles of elastic and plastic stress loading and unloading, and the process of stress relaxation, 8 as illustrated in Figure 1. Input parameters influencing residual stress encompass cutting parameters, tool characteristics, cooling and lubrication methods, workpiece materials, and geometry. Cutting force and temperature act as intermediate variables within the stress field.
Flow chart approach for deriving a residual stress model. 8
Three main algorithms are employed to determine residual stress during the relaxation procedure: McDowell-Moyar (M-M) algorithm, Sehitoglu-Jiang (S-J) algorithm, and Hybrid algorithm. In their relaxation procedure stage, Huang et al. 9 utilized inclusion theory to calculate residual stresses while considering only mechanical stresses. This approach is straightforward and does not require complex cycling through loading and unloading histories; moreover, plastic strain directly influences residual stresses. Zhang et al. 10 introduced an analytical model based on equivalent stress methodology that accounts for both tool nose radius and flank wear length. Shan et al. 11 developed comprehensive models encompassing all stages of cutting force modeling, temperature modeling during cuts, as well as a model for predicting residual stresses. Liang et al. 12 proposed a multi-physical model addressing residual stresses while factoring in tool wear; they outlined steps for predicting these stresses with results depicted in Figure 2.
The residual stress mode and steps. 12
The distribution of residual stress in orthogonal cutting exhibits a “spoon type” profile with respect to depth. The surface stress is characterized as tensile and decreases with increasing depth. Beneath the surface layer, compressive stresses are induced, which diminish to zero as one moves deeper into the material. Wang et al. 13 employed the radial return (R-R) method for calculating plastic stress and predicting residual stress. Since the proposal of an analytical model for residual stress, improvements can be made in the inverse analysis of this cutting residual model, enabling control over residual stress through optimization of cutting parameters. 14 A primary challenge lies in the fact that the residual stress model is represented by nonlinear equations, complicating the development of an inverse model; thus, fitting methods are commonly utilized. A summary of analytical modeling approaches for residual stress in orthogonal cutting is presented in Figure 3. This methodology is grounded in metal cutting principles and assumes an idealized scenario where orthogonal cutting occurs under two-dimensional conditions. In these analytical models, hybrid methods within relaxation procedures are predominantly used due to their consideration of material hardness without imposing strict constraints on limitations.
The summarized of analytical mode to predict residual stress.
Conventional cutting methods are widely employed in various industries and manufacturing processes. However, when it comes to cutting specialty materials and utilizing advanced processing techniques, sophisticated machining technologies are essential to ensure surface integrity. Liquid nitrogen (LN2) cryogenic machining is considered a green machining approach. 15 The predictive method used in this context is analogous to the orthogonal cutting model, which incorporates heat transfer considerations into temperature calculations, as illustrated in Figure 4.
Residual stress modeling in cryogenic machining. 15
Milling
Based on the orthogonal cutting model, a three-dimensional milling model has been established that takes into account the tool path, workpiece geometry, and periodic variations in cutting force and temperature. The relationship between milling residual stress and orthogonal cutting residual stress is illustrated in Figure 5. 16 The surface of the workpiece adjacent to the cutter tooth envelope experiences plastic deformation; notably, this deformation increases as one approaches the tip of the cutter tooth. Figure 5(b) depicts a point on the cutting edge where the cutting element can be approximated as an oblique cut. In this oblique cutting scenario, instantaneous micro-element cutting forces are generated. As shown in Figure 5(c), these forces induce stresses on the workpiece surface, with their distribution being analyzed using contact mechanics theory.
Formation process of milling stress field: (a) schematic diagram of milling, (b) oblique cutting of micro element cutting edge, and (c) stress distribution in main shear zone. 16
Wan et al. 17 introduced an analytical modeling process for milling residual stress by discretizing the cutting edge as an oblique cutting micro-element. They analyzed the stress distribution at a specific point on the workpiece and performed coordinate transformations to convert the stresses induced by loads in the shear zone into the workpiece’s reference system for further analysis. Yue et al. 18 employed a hybrid algorithm to predict residual stresses while considering thermal-mechanical coupling effects. Lu et al. 19 developed an analytical model of milling residual stress that accounts for tool wear, three-dimensional contact states, and relaxation mechanisms for stress release. In thin-walled workpiece milling, such as in blade component manufacturing, there exists a coupling between workpiece deformation and residual stress. 20 Guo et al. 21 created simulation models of residual stress based on multi-process analyses, taking into account both toolpath variations and initial stresses. Wang et al. 22 proposed a three-dimensional model of milling residual stress that incorporates milling properties; they calculated plastic stresses using a radial return method with iterative updates. A significant challenge associated with 3D cutting-induced residual stresses is that both cutting forces and temperatures vary incrementally along different segments of the toolpath; furthermore, previously established residual stresses influence current stress distributions. The existing analytical models typically consider only one specific toolpath while simplifying thermal stresses to two-dimensional distributions.
Zeng et al. 23 predicted the residual stress induced during laser-assisted milling, taking into account thermal stress and material softening behavior. Feng et al. 24 employed an inverse analysis model to optimize cutting parameters based on an analytical framework in laser-assisted milling. Niu et al. 25 utilized an analytical model to forecast the residual stress in ultrasonic-assisted milling processes. In contrast to conventional milling, the chip thickness in vibration-assisted machining (VAM) varies sinusoidally. Liu et al. 26 developed an analytical model that incorporates the effects of ultrasonic vibrations on residual stress in ultrasonic vibration machining (UVM). To achieve a compressive residual stress state, pre-stressing techniques have been implemented. 27 This approach is widely adopted for hard cutting of difficult-to-machine materials under dry conditions.
Despite advancements in research regarding analytical models for predicting cutting-induced residual stresses, several issues remain that require improvement: current models predominantly focus on orthogonal cutting scenarios based on S-J and hybrid methods, which often involve complex calculation processes. Additionally, certain assumptions within these models can lead to inaccuracies in predictions. Factors such as the milling process itself, tool path configurations, and workpiece surface curvature significantly influence the formation of residual stresses.
Numerical method
The numerical methods primarily encompass the finite element method (FEM) and mesh-free methods. The numerical solutions are derived from material constitutive equations, flow stress models, chip separation criteria, and failure criterion equations to address the nonlinear equations of the residual stress model.
Turning
The flow stress of the workpiece and the constitutive model serve as fundamental input parameters. Numerous studies have employed experimental methods and finite element method (FEM) analysis in orthogonal cutting to predict flow stress. Given that cutting involves large deformations and is challenging to measure, the material constitutive model and cutting stress field are derived through FEM techniques alongside orthogonal cutting experiments,28,29 as illustrated in Figure 6.
FEM combine with experiment to analysis the cutting mechanism: (a) deformation, (b) temperature field, (c) SHPB test, (d) orthogonal cutting test, (e) strain field, and (f) stress field.
The finite element method primarily involves the following steps: input of material properties, creation of a mesh grid, application of implicit and explicit solving methods, specification of boundary conditions, and establishment of chip separation criteria, as illustrated in Figure 7.
The residual stress prediction step of FEM methods.
The mesh grid significantly influences both numerical accuracy and computation time. There are primarily four mesh methods: pure Lagrangian (LAG), 30 Updated Lagrangian (Remeshing), 31 Arbitrary Lagrangian-Eulerian (ALE), 32 and Coupled Eulerian-Lagrangian (CEL). 33 The principles and advantages of these methods are summarized in Table 1. To control mesh distortion, the remeshing method is employed. Given that metal cutting involves large deformation and strain processes, the Arbitrary Lagrangian-Eulerian (ALE) method effectively mitigates grid distortion and numerical instability compared to pure Lagrangian or pure Euler methods when addressing large deformation problems. In recent years, adaptive and automated meshing grids have been implemented in finite element method (FEM) software. Rajaguru et al. 33 utilized the CLE approach to predict residual stress during an orthogonal cutting process; the steps for numerical simulation are illustrated in Figure 8.
The summarized of mesh methods in FEM.
Numerical modeling steps used CEL method. 33
The commercial FE codes are used to simulated the cutting residual stress, such as Deform, Abaqus, AdvantEdge FEM, ANSYS, MSC Marc, SYSWELD. The commercial FEM soft principle and characteristic are summarized in Table 2. 34
The summarized of FEM softwares to predicted residual stress in cutting. 34
Since the Finite Element Method (FEM) has certain limitations, such as challenges in balancing accuracy and simulation time across multiple scales, as well as issues related to excessive meshing grids, meshless methods have been employed. Markopoulos et al. 35 reviewed various simulation models for machining, including Smoothed Particle Hydrodynamics (SPH), Particle Finite Element Method (PFEM), Discrete Element Method (DEM), and Molecular Dynamics (MD). Additionally, in orthogonal cutting at the grain size scale, dynamic recrystallization can be analyzed using both FEM and Cellular Automata (CA) methods. The numerical modeling approaches utilized for cutting simulations are summarized in Table 3. Zhao et al. 36 employed MD models to analyze atomic stress distribution, surface quality, and plastic deformation mechanisms that can be used to calculate residual stress. Since MD models operate at an atomistic level, they effectively simulate nano-cutting sizes. D’Oliveira et al. 37 applied a hybrid FEM approach incorporating equivalent stress and equivalent strain rates to predict residual stresses during machining. González et al. 38 predicted dynamic recrystallization during orthogonal cutting using 2D FEM models while considering the microgeometry of the cutting edge and its relative roundness. Soufian et al. 39 utilized ABAQUS Explicit along with a CEL mesh method to simulate residual stresses effectively. Dumas et al. 40 introduced an updated method based on a two-scale approach for predicting turning-related residual stresses.
The summarized of numerical modeling to predicted residual stress in cutting.
Milling
Compared to orthogonal cutting, 3D cutting presents greater complexity due to variations in chip thickness, cutting force, and temperature. This complexity poses significant challenges for predicting residual stress during milling operations. Additionally, the simulation duration is lengthy; current research predominantly focuses on 2D turning while 3D milling simulations can take several hours to complete. To simplify the process in milling simulations, an equivalent chip thickness is employed to convert 3D milling into a 2D cutting scenario, as illustrated in Figure 9. 41
3D milling to 2D orthogonal cutting in FEM. 41
Rahul et al. 42 discussed a 3D finite element method (FEM) model for milling residual stress, taking into account the uncut chip thickness. Yao et al. 43 employed the FEM approach to predict residual stress while considering both initial residual stress and the toolpath effect during the milling process. Wang et al. 44 proposed an FEM model for multi-axis milling of Ti-6Al-4V, as illustrated in Figure 10. Given that milling involves varying chip thicknesses, Jiang et al. 45 analyzed the impact of undeformed chip volume on residual stress in milling operations. Khandai et al. 46 introduced a micro-turning residual stress model based on a 3D finite element method, which incorporates size effects.
FE model for multi-axis milling. 44
Machine learning method
Although this review focuses on the numerical simulation of the metal cutting process, it is essential to note that numerical simulations require experimental validation. Therefore, the content of experimental research is crucial for comparing the advantages and disadvantages of various numerical simulation methods.
Experiment method
The cutting process is a typical nonlinear phenomenon influenced by multiple factors that affect residual stress, including cutting parameters, cutting fluids, tool geometry, and tool materials. The experimental method is widely employed to analyze the impact of cutting parameters on residual stress during hard machining processes. Measurement techniques include the drilling hole method, ring-core method, X-ray diffraction method, neutron diffraction method, nanoindentation method, stripping method, and contour method. Measuring residual stress has consistently posed challenges in both academic and engineering fields; a primary issue being the significant errors associated with measurement results. Therefore, it is essential to consider test errors and calculate reliability. Among these methods, X-ray diffraction and drilling hole methods are predominant as they rely on plane strain assumptions. In the context of the cutting process where the residual stress layer is relatively shallow, surface residual stresses can meet application requirements; additionally, measuring residual stress along depth layers can be achieved through electrolytic polishing techniques.
Currently available methods for measuring residual stress primarily focus on two-dimensional planes in both feed direction and cutting depth direction. However, in milling operations where the residual stress field exhibits three-dimensional characteristics across feed direction, cutting depth direction, and width directly – there remains limited research addressing three-dimensional residual stress measurement. Empirical models based on experimental data are commonly utilized; such approaches include fitting curve methods, response surface methodologies (RSM), and regression analysis which predict residual stresses using inputted cutting parameters without necessitating an understanding of underlying physical mechanisms. These methodologies function as black-box systems whose accuracy relies heavily on potential errors present within experimental data.
Artificial intelligence method
With the development of artificial intelligence methods, predictive models and optimization techniques for machining processes based on data-driven approaches have gained widespread application. Given that residual stress during cutting operations influences numerous parameters and that the underlying physical processes are complex, machine learning offers a viable solution to these challenges by optimizing parameters and controlling residual stress.
The statistical based on experiment data is widely used, such as machine learning method, response surface method, Taguchi method and regression analysis, etc., can predict residual stress with input cutting parameters without understanding the physical mechanism.47–49 Das et al. 50 used machine learning method to predict the surface integrity in hard turning AISI D6 steel. Pimenov et al. 51 discussed the artificial intelligence methods and tool condition monitoring application in control machining quality. Xu et al.52,53 used improved case based reasoning (ICBR) to predict the residual stress in high speed milling, the flow chart is shown in Figure 11. Schott et al. 54 used multiple linear regression model to predict the hard turning residual stress. Cheng et al. 55 used gaussian process regression to predict the surface residual stress in end milling. Sreejith et al. 56 used grey relational analysis to multi optimization of residual stress in machining. BP neural network has nonlinear mapping ability, which consistent with non-linear characteristics of the relationship between residual stress and parameters. 57 Since the experiment is expensive, the numerical simulation results as data-drive for machine learning method.
The control and monitoring of cutting force, tool wear, cutting temperature, and residual stress is application in intelligence machining. Based on the data drive, the effect of parameters on residual stress easy to understand and control. Also, with the monitoring on line, such as cutting force, lathe power, cutting temperature, the input of mechanical stress and thermal stress can be controlled, the residual stress can be controlled to compressive residual stress in cutting.58,59 Chen et al. 60 proposed an integrated method to analyze and optimization of residual stress in milling process, which is shown in Figure 12.
The methodology flow chart of BP and NSGA-III algorithm. 60
Discussion
Comparison of three methods
Table 4 summarizes the differences among four methods used to simulate and predict residual stress in hard cutting. Additionally, numerous studies have employed optimization techniques in conjunction with finite element method (FEM) and experimental approaches to control residual stress. A primary challenge is that the white layer and phase transformation must be considered when predicting residual stress during hard turning, as significant pressure and high temperatures occur without the use of cutting fluids.
The summarized of three methods to predicted residual stress in metal cutting.
Challenge and trends
With the development of predictive models, future research directions are as follows:
(1) A significant shortcoming of typical analytical approaches is their oversimplification. Current analytical models require improvement to enhance their comprehensibility and usability in industrial applications. This is particularly relevant in milling processes, where a transition from two-dimensional to three-dimensional analysis necessitates a deeper understanding of stress fields and tensor analysis. Furthermore, it is essential to establish a multi-physical model that incorporates both micro and macro scale dimensions.
(2) The primary limitation of conventional numerical approaches lies in the assumption of material continuity for chip formation and separation criteria. The Finite Element Method (FEM) for analyzing cutting residual stresses should focus on physically-based cutting mechanisms across micro to macro scales, incorporating critical parameters such as friction models, Johnson-Cook constitutive parameters, and fracture criteria. Additionally, improvements in 3D simulations and computational speed are necessary for broader application in processes like 3D turning and milling. It is crucial to manage simulation time and accuracy effectively by employing new methods such as meshless techniques. Moreover, innovative grid partitioning methods must be developed to accommodate cutting simulations at various scales while balancing simulation time with accuracy.
(3) The measurement of residual stress still presents several challenges, such as the wide dispersion of results within the confidence interval. The measuring methods and devices need to be user-friendly and widely adopted in industry. Through the accumulation of experimental data, a standardized measurement protocol can be established. Machine learning methods require large datasets; therefore, it is essential to create a process library that encompasses various cutting parameters, including tool materials, workpiece materials, minimal quantity lubrication, and cutting conditions. A significant issue is the inconsistency of data. It is crucial to collaborate with manufacturing enterprises and laboratories to establish standards that ensure the authenticity and validity of the data collected.
Conclusions
The review provides a comprehensive summary of machine learning and micro-scale simulation, contrasting it with existing literature. It discusses the modeling and simulation methods for residual stress in the cutting process. The conclusions are as follows:
(1) The analytical model is grounded in the cutting mechanism, employing certain assumptions and simplifications. Its physical significance is clear, making it widely applicable in academic research. Advanced assistive machining techniques are utilized to control residual stress during difficult-to-cut operations; however, further development of cutting theory is necessary.
(2) The numerical method predominantly employs Finite Element Method (FEM) models to simulate residual stress in both 2D and 3D cutting scenarios. In micro-scale applications involving multi-size simulations, new mesh techniques and mesh-free methods have been introduced. Currently, a significant limitation for 3D finite element simulations lies in the computational power available from computers.
(3) With advancements in artificial intelligence, numerous data-driven methods have emerged within manufacturing processes. Machine learning approaches require less prior knowledge and physical theory, indicating their potential for widespread application in manufacturing.
Footnotes
Handling Editor: Divyam Semwal
Declaration of conflicting interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Funding
The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This study is supported by science and technology research project of Hubei provincial department of education (No. Q20222603).
