Finite Element Investigation of Cutting Speed Effects on the Machining of Ti6Al4V Alloy

In modern times, titanium alloy has a great application prospect in the medical �eld. Still, the pitiful machinability of titanium alloy material brings incredible di�culty to its ultra-precision cutting. This work presented the effect of parametric sensitivity analysis of the orthogonal cutting process using the �nite element method, which dramatically enhances the cutting performance of Ti-6AL-4V. The simulation results are attained by applying Abaqus® explicit 6.14 software. The mechanical reaction of two-dimensional �nite element models has been examined for cutting forces. Additionally, the impacts of rake angle, clearance angle, and nose radius on the stress distribution in orthogonal cutting of Ti-6AL-4V have been investigated. Also, to make certain numerical accuracy, the Johnson − Cook constitutive models for Ti6Al4V alloy are implemented. In the end, FE simulation outcomes were supported by the reported results in the literature.


Introduction
Titanium alloys are widely utilized in the elds of medicine, sport, and aviation, because of their exceptional characteristics of high speci c strength, biocompatibility, and resistance to corrosion and high-temperatures [1][2].Due to their high-quality properties, the use of titanium alloys (Ti alloys) has been gradually increasing in the eld of health care, such as in hip joints, dentistry, optical instruments and medical endoscopes [3][4][5].Nevertheless, a few characteristics of titanium alloys, such as poor machining performance, high chemical activity, and low heat conduction properties, has restricted their application in the medical eld [6][7][8].The latest studies propose that the number of hip replacements is projected to rise by nearly 170% by 2030 [9].Additionally, researchers are investigating the many attributes of Ti alloys, to reduce the revision of hip replacements and meet the above challenges, such as improvement of wear characteristics [10], and long-term durability [11][12].Many studies examining the failure of Ti alloy implants, suggest gradual loss of bone support across the implant, and poor machining of Ti alloy, as the leading cause of failures [13][14][15][16][17][18].As an e cient examination tool, the nite element method (FEM) is quite popular in the study of the cutting process.Numerous researchers have determined plenty of FE models for studying the cutting process of Ti alloys [19][20][21][22][23]. Numerical simulations are widely used for simulating the different behaviours of various implants under static or dynamic loading, such as hips and dental implants [13][14][15][16].It was noted that the failure of the biomechanical implant is precisely linked to stress concentration across the implant, speci cally at the cross-section of the implant variants where gaps appear in the geometry [24][25].Such failures occurred as fractures of the implant screw under regular cyclic loads [26].Karpat et al. represented a new material constitutive model, and examined cutting simulations for chip formation and shear localization [20].As well as enhancing design parameters, it is also feasible to reduce the mechanical fracture of the implant.Rodriguez et al. revealed that the major design parameters of implants in uencing biomechanical behavior are material properties and wall thickness [27].Thepsonthi et al. [23] studied the FEM of chip formation and examined the impact of micro-end mills on the cutting temperature and cutting force of Ti alloys.Chen et al. [28] investigated the high-speed machining of the Ti6Al4V alloy using the ductile failure model.Likewise, Umbrello [19] used FEM to observe the high-speed and traditional machining of the TiAl6V4 alloy.
The chip segmentation incident has been comprehensively investigated worldwide [29][30].Cook et al. [31] evaluated various titanium chips at the cutting speed limits of 1 in/min to 300 ft/min, and reported the variations in chip morphology and formation at low and high speeds.The literature survey shows that there are only a few accurate studies on FE modelling concerning the prediction of both chip morphology and cutting force (e.g., Hua et al. for high-speed machining [32]).In the current study, the FEM cutting machining model of Ti-6Al-4V was designed using ABAQUS 6.14, and the parameters were optimized to enhance the service life of Ti-6Al-4V under different cutting speeds.Furthermore, various forces were simulated and applied, and a study on the failure modes was presented.This study aims to build an understanding of the cutting forces and the depth of cut of Ti alloy under the in uence of different machining parameters.Due to the high price of titanium alloys and their poor machinability, it is highly recommended to simulate the machining process as accurately as possible using FEM, prior to cutting real specimens.Consequently, the objective of this study is to utilize the existing Jonson Cook damage model (J-C), in order to accurately simulate the various characteristics of the orthogonal machining process of Ti alloy.

Simulation of machining using FEM
The machining process is a complex and highly dynamic process that involves thermo-mechanical features.As a result, conducting experimental studies to investigate the chip removal mechanism, especially in terms of chip segmentation, can be challenging.Therefore, it is crucial to simulate the model to optimize and comprehend the machining process.This approach ensures that the product functions effectively under various conditions and avoids catastrophic failures.In addition, utilizing FEM for simulation can provide accurate results [28, [34][35][36][37], which saves time and money by evaluating the model simulation in computer programs.Dandekar et al. conducted a study on optimizing tool life by modeling and conducting experiments to maximize the material removal rate [38].The FE modeling steps involved two parts, as depicted in the owcharts in Fig. 1.The numerical formulation and Jonson Cook damage model were used to simulate the chip separation [39].This simulation study focuses on examining the elemental elimination of Ti alloy material under different parametric studies applied during machining.The e ciency of the machining process is evaluated by changing the tool material, cutting forces, and tool wear.The study found that hybrid machining signi cantly improved the machinability of Ti-6Al-4V titanium alloy, resulting in improved surface roughness and reduced speci c cutting energy compared to conventional machining.Cheng et al. also investigated the modeling of orthogonal cutting of Ti alloy using a FEM constitutive model [40].
Additionally, A model for orthogonal cutting was utilized to simulate the forces, chip geometry, and residual stress distribution on the machined surface.While Karpat et al. [41] investigated the metal cutting process between a workpiece and tool, they observed two phenomena, namely sliding and sticking, occurring in the secondary shear region.Additionally, high temperature caused metal cutting chips to ow over the rake face of the tool [42,43].The simulation results emphasized various critical points that affect residual stress predictions and thrust force, which should be taken into account in future cutting models.

Material modeling
The simulation material was modeled from ti alloy (Ti-6Al-4V) based on Johnson and Cook [44] model as presented in Eq. ( 1).In detail, the ow stress was stated as a function of the strain hardening index as n, reference strain rate, strain rate, temperature melting (T m ), temperature room (T r ), and strain rate sensitivity index as m.The constants A, B, and C were acquired through an experiment performed by Leseur [45] where A, B, C, m, and n are constant parameters for the Johnson-Cook model, σ is the ow stress, ε and are the strain and strain rate, ε o is the reference strain rate, T is material temperature, T m melting temperature and T r room temperature.Figure 2 represents the workpiece at 2 x 1 mm and tool geometry.
Table 1 provides a list of the usual machining parameters that are utilized for the FEM simulation of Ti-6Al-4V.This study conducts multiple computational simulations while considering the rake angle, clearance angle, depth of cut, and nose radius.The ndings from these simulations aid in comprehending the impact of the selected parameters on cutting force.
The schematic diagram of the orthogonal machining modeling is illustrated in Fig. 3.It displays the process of transforming the turning operation into a 2D orthogonal machining.At the beginning of the simulation, the workpiece is stationary at X and Y = 0, and the stresses are set to zero.The CPE4RT element is used for the workpiece, while the tool is represented by a 2D analytical rigid shell.Initially, the tool is separated from the workpiece.In the FE simulation conducted in this study, Table 1 displays the cutting parameters that were employed.The primary focus was on the cutting speed and depth of cut, while to minimize variables in the cutting simulation, the rake angle, clearance angle, nose radius, and coe cient of friction were held constant.

Dynamic explicit
The Abaqus 6.14 was used to conduct the FEM simulation, and the material dimension is illustrated in Fig. 1.Tables 2 and 3 provide information on the mass percentage of the material used and its physical properties, respectively.Additionally, Tables 4 and 5 present the Johnson-Cook constants and damage, which were utilized in the simulation, as described in [39,46,47].

Meshing
The FEA model consisted of both the tool and workpiece, with the mesh being more re ned in the cutting zone to improve simulation e ciency.The workpiece was meshed with 11,172 plain strain quadrilateral elements, while the tool was modeled as a rigid analytic body.Additionally, this simulation considered a dry-cutting condition.

FEA Simulation
In machining, the cutting forces are the key factors.The forces produced in machining directly impact tool de ection, heat generation, wear, and the surface condition of the machined components [48].Therefore, a su cient understanding of cutting parameters and cutting forces and the effects of cutting forces are highly signi cant in machining.However, the high cost of machining metals like titanium alloys has caused enormous challenges for industries.As a result, this study was performed to simulate the in uence of tool nose radius, clearance angle, and rake angle in the machining of Ti alloy.Few investigations have been conducted to determine the relationships between cutting parameters and cutting forces when cutting titanium alloys using FEM [19,37,49,50,51].The results presented further demonstrate that the JC damage criteria are commonly used in simulating the machining of titanium alloys and in modeling the formation of segmented chips [19,52,53].The JC model and damage criterion take into account plasticity and damage initiation and consider the effects of strain rate and temperature.However, the fracture Energy (G f ) can signi cantly depend on the fracture mode measured (from 11.50 MJ/mm 2 to 33.60 MJ/ mm 2 ) [53,54].The JC fracture model and damage initiation are speci ed in Eq. ( 2), which is mainly used to outline the initial failure strain [55,56].

2
Where is equivalent elastic strain, 'q' the von Mises stress, ' ' is non-dimensional temperature 'p' the pressure stress, d 1 , d 2 , d 3 , d 4 , d 5 are the JC Damage model parameters.Tables 4 and 5 represent the parameters of the JC model applied for this study for Ti6Al4V.However, G f is the criteria for damage evolution shown in Eq. ( 3) 3 Where u p the equivalent plastic displacement, σ˜ is the effective stress.D is the damage, and when it reaches 1, the element is speci ed as fully damaged.In addition, surface-to-surface contact is de ned to ensure the contact between the cutting tool and chips.Element deletion is also utilized, so that elements that reach the distortion level are eliminated from the simulation.However, a friction coe cient of µ = 0.33 is applied, and the contact behavior is assumed to be hard in the normal direction.As illustrated in Fig. 5, the mechanical boundary conditions enforce zero displacements in the y direction, while the cutting speed is applied in the x direction.The tool is xed to a reference point and is assigned zero displacement.To reduce computational time, it is important to avoid excessive element distortion.Therefore, the upper section of the workpiece, which undergoes signi cant deformation during machining, is meshed with smaller elements, while the remaining part is meshed with larger elements.The workpiece has meshed with 11172 elements of type CPE4RT, which provides bilinear displacement, reduced integration, temperature, and 4-node plane strain thermally coupled quadrilateral.
To prevent movement of the workpiece in both the X and Y direction, the bottom surface has been xed constraint under the boundary conditions.

Results and Discussion
The objective of this study is to investigate the impact of various machining parameters, including nose radius, rake angle, clearance angle, depth of cut, and cutting speed, on the interaction between the tool, chip, and workpiece during the machining of Ti6Al4V alloy.The material properties of the workpiece were obtained from relevant literature sources [39,46,47].A frictional model with  = 0.33 was utilized in the nite element simulations of Ti6Al4V alloy.The workpiece had dimensions of 40 mm x 10 mm, and the cutting tool was characterized by rake and clearance angles of o = 7° and o = 3°, respectively, with an initial nose radius (rn) of 25 µm.As stated in the literature, Ti6Al4V alloy usually has a fracture energy of 33.67 mJ/mm2 [53].However, it is di cult to maintain this value for cutting parameters due to variations between experimental and simulation results.Gamboa et al. conducted multiple FE simulations using different Gf values to achieve more accurate cutting force results, as Gf is primarily dependent on changes in the fracture mechanics of the machining cutting process [57].Several machining simulations were performed using different cutting parameters as shown in Table 1. Figure 6 shows the simulation of Ti alloy at a depth of cut of 0.05 with various cutting speeds.Based on the results obtained, there is a correlation between the cutting forces and depth of cut with the reported experimental results.The geometry of Ti has a signi cant impact on fracture energy, as reported by Gamboa et al. who found that Gf tends to approach a speci c value at high feed and speed [57].This indicates that low fracture energy is necessary to fracture the material at high cutting speeds.In addition, machining simulations at different depths of cut are shown in Figs. 6, 7, and 8. To provide a more explicit comparison with experimental results, a geometric analysis of chip formation during Ti alloy processing reported by Hernández et al. has been employed [58].Also, it was reported that the irregular shape of the chips remains constant across different cutting speeds and feeds due to the high plasticity levels and low thermal conductivity of the material, which leads to thermal softening and di culty in breaking the chip.
Despite many studies, it is still not fully understood how to accurately predict the pro le of chip formation in Ti alloys due to their complex material behavior.Several numerical models have been proposed, but they are not adequately modi ed to simulate chip formation in Ti alloys [59,60,61].The simulation results suggest that the cutting velocity is the most in uential parameter, but the geometry of the cutting tool also plays a signi cant role.Xie et al. conducted a study on the effect of micro-grooves on cutting and found that reducing the depth of the grooves leads to a decrease in the cutting temperature of Ti alloy [62].Figure 9 shows the stress distribution and chip morphology at different depths of cut and cutting velocities.Figure 10 presents a comparison between the simulation results and experimental data obtained under different parameters.The maximum error observed in all simulations was 8%, which was considered acceptable given the simulation conditions.The cutting simulations of TI6AL4V revealed that an increase in cutting speed results in a more distinct chip tooth.Figure 10 illustrates the cutting forces calculated for various orthogonal cutting parameters.Initially, the cutting force was examined between 201 to 839 N for cutting speeds of 40 m/min and a doc ranging from 0.05 to 0.2 mm.Minor differences were observed in the increase of cutting force with an increase in cutting speed.For instance, at a doc of 0.05 mm and a cutting speed of 40 m/min to 120 m/min, the cutting force ranged from 201 to 198 N.This can be attributed to the fact that as the cutting speed increases, the material softening also increases, leading to a decrease in cutting force.However, the cutting forces were signi cantly increased by the depth of cut.At the maximum depth of cut of 0.2 mm, the cutting force ranged from 810 to 841 N. The increase in material removal and chip thickness increased the contact area, which further led to a rise in cutting force.Du et al. compared the actual chip's geometric features with the FE-simulated chip and found some differences.The rst reason was that the damage layer was de ned in the FE model, leading to element deletion, which did not happen in the actual machining process.The second reason was the insu ciency of meshing and algorithm of the FE model, which could not entirely compute the complex process and large element deformations.However, in the actual cutting process, the cutting zone may undergo multiple structure destruction and restoration, stretching, and grain sliding [64].
Figures 11 and 12 depict the stress and strain analysis, respectively, under the given cutting parameters of doc and vc.The stresses were measured at de ned elements to analyze the variations under different cutting speeds.As shown in Fig. 11, the stresses were found to be more similar in nature at cutting speeds of 80 m/min and 120 m/min, with the maximum stress of 1250 MPa observed when the cutting tool initially contacted the workpiece.The stress decreased thereafter, and the maximum variation was observed at 40 m/min.However, after the initial ascension, the stress curve became more stable at 80 m/min and 120 m/min.Additionally, the stress curve showed an upward trend around 1250 MPa at the doc of 0.05 mm and a cutting velocity of 40 m/min.Figure 12 shows that the strain reached its highest point at the doc of 0.1 mm and the cutting velocity of 80 m/min.

Conclusion
In this work, the FE-simulated model of TI6AL4V was developed to explore the effect of depth of cut and cutting speed on the orthogonal machining process.The outcomes of this study are expected to aid in comprehending the machining behavior of tool-workpiece interfaces as the cutting speed and depth of cut increase.The validation of the FE model was carried out against previously published articles, and the results were found to be in better agreement with them.The conclusions of this research are outlined as follows: The FE-simulated results revealed that changes in cutting speed under the given parameters did not signi cantly impact the cutting forces' value.However, increasing the depth of cut resulted in higher cutting forces due to the larger material removal and chip thickness increasing the contact area.
The cutting force results obtained from FE simulations under various conditions exhibited an estimated error of up to 8%.These errors were primarily due to large deformations and the FE model's meshing and algorithm limitations.The workpiece of Ti-6Al-4V and Tool Schematic illustration of the modeling of orthogonal machining.
Jaiswal et al. and Du et al. [63, 64] reported experimental results that support the ndings presented in this study.Figures 6, 7, 8 and 9 display the examination of the numbers of chip morphologies of Ti alloy at different depths of cut and cutting speeds.The FE model used a depth of cut of 0.05 mm, 0.1 mm, 0.15 mm, and 0.2 mm, respectively, and a cutting speed of 40 m/min, 80 m/min, and 120 m/min, based on the study by Jaiswal et al. and Du et al. [63, 64].As shown in Fig. 6, pitted chips were observed at a depth of cut of 0.05 mm, but ow chips were observed as the depth of cut and cutting speed increased to 0.1 and 0.15 mm.An increasing trend was observed in the breakdown degree of the chip with the increase in cutting speed.This is consistent with the ndings of Hoffmeister et al. [65], who investigated chip formation in Ti alloys under a cutting speed of up to 100 m/s.

Figure 9
Figure 9 presents a bar graph that compares the reported data [63, 64] with the simulated results of cutting forces at different cutting speeds.The graph indicates different trends during the FE simulation of the machining process, which is consistent with the reported data [63, 64].Therefore, the present study of the FE model is indirectly validated. Figures

Figure 1 Flow
Figure 1

Figure 4 The
Figure 4

Figure 5 FEM model and mesh Figure 6 FE
Figure 5

Figure 10 The
Figure 10

Table 1
Used parameters for the simulation.