The effect of chip formation on the cutting force and tool wear in high-speed milling Inconel 718

Coated carbide tools are widely used in the processing of nickel-based superalloys due to their excellent wear resistance, high strength, and good hardness at high temperatures. In this paper, the high-speed milling experiments and finite element simulation of Inconel 718 are carried out by using PVD TiAlN-coated carbide tools. Simulations of tool temperature, cutting force, and chip morphology were performed to analyze the effect of cutting speed on the degree of sawtooth chip formation and the effect of sawtooth chip formation on the cutting force and tool wear. The results show that the cutting temperature mainly focuses on the rake face, and with the cutting speed increasing from 60 to 120 m/min, the maximum temperature of the rake face increases from 580 to 660 ℃. The maximum temperature region (MTR) on the rake face gradually approaches the tool nose with a decrease in the cutting speed. The generation of sawtooth chips leads to fluctuations in the cutting force component. As the cutting speed increases, the degree of chip sawing increases. The effect of the sawtooth chip on the fluctuation of the cutting force will also increase, thus increasing the degree of tool wear.


Introduction
Inconel 718 is a nickel-based superalloy with good oxidation resistance, high-temperature resistance, and corrosion resistance. It is widely used in the aerospace, automotive, and energy industries. However, Inconel 718 is one of the most difficult materials due to its high hardness, low thermal conductivity, high work hardening, and poor machinability [1,2]. High-speed machining is one of the most costeffective and efficient modern manufacturing techniques that can improve processing efficiency, high material removal rate, and excellent machinability [3,4]. For difficult cutting materials, high-speed cutting can be achieved through the development and use of new materials for tools and coatings.
Cemented carbide is the most widely used tool material in the industry. This is used due to its low cost, high toughness, and high thermal conductivity. It is also suitable for processing the Inconel 718. However, the high cutting temperatures generated in the high-speed cutting process of Inconel 718 can help nickel and iron to diffuse into the cobalt substrate of the WC-Co tool. This behavior severely limits the high-speed cutting processing of uncoated carbide tools [5]. Grzesik et al. [6] suggested using 2-15 μm coatings as thermal and chemical barriers to improve the cutting performance of coated tools, such as TiAlN and AlTiN. In the cutting process, the coating can play the role of heat insulation to significantly reduce the substrate temperature [7,8]. And the coating can also have better wear resistance [9,10], tool life [11], and higher surface processing quality [10,12] compared to the uncoated tool. Tool wear is one of the main reasons for the poor cutting performance of the Inconel 718. Bhatt et al. [13] discovered that the high temperature and high pressure of the tool-chip interface will induce the adhesive wear of the tool during the cutting of Inconel 718. Halim et al. [14] found that the friction with the hard carbide particles in the workpiece and the tool would cause abrasive wear in the Inconel 718 milling with coated carbide tools. In the case of multi-coated tools, the abrasive wear mechanism leads to the delamination of the coating, thus exposing the tool substrate. In addition to the adhesive wear and abrasive wear, coated tools also suffer from diffusion wear, oxidative wear, and debonding failure due to mechanical shock and thermochemical interactions between tool-workpiece and tool-chip [2,15,16]. Cutting parameters also have an important impact on tool wear during cutting. Xavior et al. [17] analyzed the influence of cutting parameters on tool wear through analysis of variance (ANOVA) when cutting Inconel 718 with PVD TiAlN-coated tools. It found that cutting speed was the main factor affecting tool wear. Kamdani et al. [18] used TiAlN-coated tools to mill Inconel 718 and found that tool wear increased with the increase of radial cutting depth.
Inconel 718 will form sawtooth chips during highspeed cutting. The formation of sawtooth chips has a large impact on cutting force, cutting thickness, etc. As a result, heat generation and conduction are greatly affected during the cutting process. Hao et al. [19] used the finite element method combined with chip metallographic photos to deeply study the plastic evolution behavior of materials in the cutting area. The sawtooth chip formation of the mechanism is revealed in the cut of Inconel 718. Zhang and Wu [20] found that the periodic fluctuation of cutting force corresponds to the sawtooth chip morphology during the hard turning of AISI 1045 steel. The formation of sawtooth chips is the source component fluctuation and severe vibration of the cutting force, which directly limits the material removal rate and thus productivity [21]. Cui and Guo [22] found that the tool temperature periodically changed with cutting time due to the periodic formation of sawtooth chips during the intermittent turning of AISI 1045 steel. The change of chip thickness during the formation of sawtooth chips causes a mechanical and thermal impact on the tool [23], which leads to premature tool failure and reduced machining quality. During the high-speed milling process of the Inconel 718, not only do the sawtooth chips form, but the thickness of the unformed chips also changes, resulting in a large change in thermal-mechanical load. Each time the tool cuts into the workpiece, the cutting force fluctuates, and the effect on tool wear is more complicated. Therefore, it is important to study the damage and failure behavior of TiAlN-coated carbide tools in high-speed intermittent cutting. The effect of sawtooth chips on the cutting force can be studied in high-speed milling of Inconel 718 with TiAlN-coated carbide tools.
Finite element simulation has been widely used to model the metal-cutting process. Through finite element simulation, many researchers have realized the study of chip formation [23][24][25], cutting performance of coated tools [26][27][28], surface integrity [29,30], and so on. The most widely used damage model in metal cutting simulations is the Johnson-Cook shear failure model. In addition, by using appropriate damage initiation and damage evolution techniques, the results of finite element simulations can be improved to make the simulations agree well with experimental results [31].
In this paper, high-speed milling of Inconel 718 was performed using a PVD TiAlN-coated carbide tool. The effect of the cutting speed on the wear of coated tools was investigated. The simulation model was established by the Abaqus finite element simulation software. The temperature distribution of the TiAlN-coated carbide tool was obtained from simulation with different cutting speeds. The effect of sawtooth chip formation on cutting force and tool wear was investigated during the high-speed milling of Inconel 718.

Milling experiment
The workpiece material is Inconel 718 nickel-based superalloy, and its chemical composition is shown in Table 1. The milling experiment was performed on the Korean vertical CNC machining center DNM-415, which was dry cutting. The tools are ISO 345R-13T5M-MM S30T PVD TiAlN-coated carbide tool (tool mounting rake angle γ = 10°, rear angle α = 14°), manufactured by Sandvik Coromant. The milling cutter disc used with the tool is ISO 345-063Q22-13H, with a diameter of 63 mm and can hold 6 inserts at the same time, produced by Sandvik Coromant. The installation of the tool and the milling cutter disc at the center of the machining is shown in Fig. 1. New tools were used for each cut parameter, and only one tool was installed during the experiment. The experimental parameters for milling are given in Table 2.
During the milling process, the cutting forces in three directions (Fx, Fy, Fz) were measured using a Kistler 9159A dynamometer. The installation of the workpiece and dynamometer on the vertical CNC machining center is shown in Fig. 1. After the milling experiment, the chip morphology was observed by a digital microscope (VHX-5000, Keyence, Japan) and used the scanning electron microscope (SEM, Phenom-Prox, Netherlands) to analyze the tool wear morphology. The chemical composition of the worn tool surface was analyzed by energy dispersive spectroscopy (EDS, Phenom-ProX, Netherlands).

Simplified model for 2D milling simulation
In the 3D finite element simulation of high-speed milling, the milling model is complicated and the number of meshes is huge, which seriously affects the accuracy and efficiency of the simulation. Therefore, the milling simulation is generally reasonably simplified. The milling test uses down milling. The tool cuts in the thicker cutting layer and cuts out of the thinner cutting layer. The thickness of the cutting layer varies during the milling process.
And the model is simplified by replacing curves by straight lines. The simplified process is shown in Fig. 2.
In the process of converting milling into 2D cutting, the workpiece shape includes two main parameters: the cutting length (arc length) l oc and the maximum undeformed chip thickness h max , as shown in Fig. 2. The calculation equations of l oc and h max are as follows [32]: where R is the radius of the milling cutter, a e is the radial depth of cut, and f z is the feed per tooth.

Mesh and boundary conditions
The simplified 2D milling model proposed in this research includes four parts (part I-part IV), as shown in Fig. 3. The left, bottom and right sides of the workpiece are fixed in all directions, and the milling tool is defined as a rigid body. The CPE4RT element type with a 4-nodal bilinear structure with reduced integration and hourglass control was chosen to define the elements in the cutting tool and the workpiece. The chip mesh with an element size of 5 μm, and part IV has meshed with a bias ratio to  make the meshes near the chip separation layer denser. Finally, a 3 μm coating is set on the tool. Quad-structured meshing is assigned to the workpiece, and the quad-free mesh function is assigned to the cutting tool. The predefined temperature field is set to 20 °C. Thermal conduction between the cutting area and the air is neglected due to the extremely short time and high cutting speeds involved during one milling cycle.

Material model
In the high-speed milling process, the workpiece undergoes high temperature and large-strain elastic-plastic deformation. The time for the tool to cut into the chip is very short. In this short time, the distribution of strain, strain rate, and temperature in the cutting layer of the cutting material is not uniform, and the gradients vary considerably. Therefore, the Johnson-Cook constitutive model [33], which considers the variation of stress with strain, strain rate, and temperature, is adopted to describe the material characteristics of the workpiece. The model is formulated as follows: Fig. 2 Conversion from 3D milling to 2D orthogonal cutting with variable thickness where σ is the equivalent plastic flow stress, ε is the equivalent plastic strain; ̇ is the plastic strain rate; ̇0 is the reference strain rate; T is the temperature at a given calculation instant; T room is room temperature; T melt is material melting temperature; A is the initial yield stress; B is the hardening modulus; C is strain rate dependency coefficient; n is work-hardening exponent; m is thermal softening coefficient. The parameters of the Johnson-Cook constitutive model for Inconel 718 are shown in Table 3.

Material properties
Material properties have a significant influence on the accuracy of finite element numerical results. In order to bring the simulation results closer to the actual machining process, the temperature-dependent thermo-mechanical properties of the workpiece are taken into account in this paper. Table 4 and Fig. 4 illustrate the performance parameters of Inconel 718, WC-Co substrate, and TiAlN coating in finite element simulations.

Damage model
In the cutting simulation, the appropriate damage properties have an important influence on the chip formation mechanism. In this investigation, chip formation is performed in two steps. The first step is damage initiation, and the second step is damage evolution based on the fracture energy method.
Step 1: Damage initiation. In this investigation, the Johnson-cook damage model is used to explore the plastic strain at damage initiation ( pl f ), which is given by Eq. (4).
The model describes the effects of stress triaxiality (η), strain rate, and temperature on the material damage initiation. The damage parameters d 1 -d 5 are related to the material properties. The J-C damage parameters for Inconel 718 are shown in Table 5.
When the scalar damage parameter D exceeds 1, the damage initiation criterion is reached. This parameter is based on the accumulation law and is defined as: Δ pl is the equivalent plastic strain increment.
Step 2: Damage evolution. When ductile materials are damaged, the stress-strain relationship does not accurately represent the properties. If the stress-strain relationship is resumed, a strong mesh dependence is introduced based on strain localization. As the mesh becomes smaller, the amount of energy dissipated decreases. Using the Hillerborg fracture energy model [39] as the damage evolution model, mesh dependence can be reduced by generating stress-displacement responses after the onset of damage. The model is also able to capture high-strain localization during chip formation. Hillerborg defined the energy G f needed to initiate the crack initiation per unit area as a material parameter, and the expression is as follows:  where L is the characteristic element length, σ y is the yield strength of the material, and u f is the equivalent plastic displacement, which can be expressed by Eq. (7): According to the research of literatures [27,31], two fracture modes can exist simultaneously in the orthogonal cutting process: plane stress and plane strain. Therefore, the plane strain condition exists for part I in the model, while the plane stress condition exists for the relatively thin part II. The damage evolution of the simulation model part I has exponential property, and the parameter D 1 can be defined as: Due to the small thickness, the damage evolution of part II can be considered as linear, and the damage parameter D 2 is defined as: In the simulation, the fracture energy G f(1, 2) of part I and part II can be calculated by Eq. (10).
υ is Poisson's ratio; E is Young's modulus; K c is the fracture toughness of the material.

Contact and friction models of the tool-chip interface
In high-speed milling, there are both adhesive and sliding areas on the tool-chip contact surface. The friction model proposed by Zorev was used to investigate the adhesion areas and sliding areas of friction [27,40].
where τ f is the shear friction stress, μ is the friction coefficient, σ n is the normal stress, and τ max is the ultimate shear stress. According to the literature [41], the friction coefficient μ was set as 0.33.

Cutting force
In the simulations, the largest cutting force components in the x and y directions are selected from the extracted values. For the experiment, 10 groups of the maximum cutting force components were measured in the cutting stability stage. The maximum cutting force component obtained from the finite element simulation is compared to the maximum cutting force component measured in the milling experiment. Compared with the experimental Through the analysis of the cutting force in the milling experiment, it can be found that the cutting force increases when the cutting speed increases from 60 to 100 m/min. When the cutting speed is increased from 100 to 120 m/min, the cutting force decreases. The reason is the thermal softening phenomenon of the material caused by the increase in cutting temperature with the increase in cutting speed [42].
In the milling process, the cutting force fluctuates periodically with the tool cutting in and out periodically, as shown in Fig. 6a. As can be seen from Fig. 6b, the cutting force rapidly increases to the maximum when the tool cuts into the workpiece during the cutting stage. The cutting force gradually decreases as the tool cuts further into the workpiece, which is caused by the gradual reduction of the cutting thickness during the cutting process. The cutting force fluctuates violently during the milling process, which is mainly related to the vibrations caused by the cutting tool entering the workpiece and the formation of sawtooth chips during the cutting process.

Cutting temperature
The temperature distribution in the TiAlN-coated tool at different cutting speeds was analyzed by finite element simulation, as shown in Fig. 7. As the cutting speed increases, the highest cutting temperature increases and is mainly concentrated on the rake face. The cutting tool temperature has an important effect on the wear of the TiAlN-coated tool. The temperature distribution along path AB (Fig. 7) is plotted in Fig. 8. It can be seen that as the cutting speed decreases, the maximum temperature region (MTR) on the rake face gradually approaches the tool nose. This variation is related to the decrease in chip sliding speed as the cutting speed decreases [27]. Figure 9 shows the macroscopic chip morphology of the Inconel 718 for different cutting speeds by TiAlN-coated tools. In the cutting process, the temperature of the chip sliding surface is higher than the temperature of the chipfree surface. Moreover, the thermal gradient between the chip-free surface and the sliding surface causes the chip to curl. The chip curl radius decreases with an increasing temperature gradient between the chip-free surface and the sliding surface. As the cutting speed increases, higher temperatures are generated in the tool-chip contact region, resulting in higher thermal gradients between the chip-free and sliding surfaces. Thus, the chip curl radius decreases as the cutting speed increases.

Chip morphology
The sawtooth chips were generated during the highspeed milling of Inconel 718, as shown in Fig. 10. The formation of the sawtooth leads to periodic changes in Fig. 6 a Experimental cutting force when the cutting speed is 100 m/min, b Detailed characteristics of cutting force during the cutting stage the cutting thickness, which has a significant effect on the periodic fluctuations of the cutting force during the cutting process. In order to intuitively characterize the sawtooth degree of chips, Schulz et al. proposed the sawtooth degree coefficient G s [43]: where h 1 is the average tooth crest height and h 2 is the average tooth valley height, as shown in Fig. 10. According to the calculation equation, the closer the value of G s is to 1, the higher the chip sawtooth degree. The chip measurement is performed from the thicker end of the chip, and 10 groups of values are recorded and averaged. Figure 11 compares the sawtooth degree coefficients calculated at different cutting speeds. It can be seen that with the increase in cutting speed, the sawtooth degree of chips is more obvious.

Effect of chip morphology on cutting force
The chip morphology and the cutting force component Fx obtained from the simulations at 100 m/min are shown in Fig. 12. It can be seen that the cutting force increases rapidly to its maximum when the tool cuts into the workpiece. In the stable cutting stage, the cutting force component Fx has a pronounced fluctuation. Figure 12c shows the corresponding evolution characteristics of sawtooth chip formation in a short period of the cutting process. Compared with the cutting force component Fx corresponding as shown in Fig. 12b, there is an obvious corresponding between sawtooth chip formation and cutting force. In comparison with the sawtooth chip morphology and the cutting force component Fx obtained by simulation in 0-0.001 s, it can be observed that the fluctuation of the cutting force corresponds to the sawtooth chip morphology. Define the amplitude of the cutting force component Fx as A Fx : where F P and F V are the peak and valley values of the cutting force F X in the fluctuation period in Fig. 12b, respectively. The variation law of the Fx amplitude of the cutting force component as a function of cutting speed is shown in Fig. 13. It can be seen that the amplitude of the cutting force shows an increasing trend with the increasing cutting speed. This is mainly related to the increased chip sawtooth as the cutting speed increases (Fig. 11). Therefore, as the cutting speed increases, the degree of the sawtooth chip increases, which has a larger effect on the fluctuation of the cutting force. Figure 14 shows the optical microscopic flank wear of the PVD TiAlN-coated carbide tool at various cutting speeds. It can be seen that the obvious abrasive wear is observed at different cutting speeds, which is caused by the friction between the hard carbide in the Inconel 718 and the tool  Fig. 6a).

Tool wear
And the cutting temperature increases (Fig. 7) with the increase of cutting speed, which can reduce the hardness of cemented carbide materials [44], resulting in more serious tool damage. Figure 15 shows SEM and EDS images of the rake face wear of the PVD TiAlN-coated carbide tool at various cutting speeds. From the EDS analysis of the local area (e) in Fig. 15a, it can be seen that there is a large amount of Ni, Cr, and Fe (elements of the workpiece Inconel 718) in the tool wear area on the rake face, and the tool adhesion wear is serious. When the cutting speed is 80 m/min, crater wear occurs on the rake face, as shown in Fig. (b). When the cutting speed is 100 m/min, the tool material is flaking, and the local magnification (f) of Fig. 15c shows that cracks appear on the rake face. When the cutting speed is 120 m/min, the rake face of the tool material not only flakes, but also has a serious fracture phenomenon.
As can be seen from Fig. 15, the wear on the rake face increases with the increase in cutting speed. This is closely related to cutting temperature and sawtooth chip formation. In the cutting process, the tool temperature is mainly concentrated on the rake face. And the cutting temperature increases with the increase in the cutting speed (Fig. 7), which reduces the hardness of the cemented carbide material [44]. At the same time, the sawtooth chip contacts the rake face in the process of chip formation, resulting in friction and wear on the tool. The thickness of the sawtooth chip in high-speed milling has a large variation, resulting in sharp fluctuations in cutting force. Fluctuating cutting force acts on the rake face, leading to more serious tool wear. And the degree of the sawtooth chip increases with the cutting speed increase, which has a greater effect on the fluctuation of cutting force and makes the wear on the rake face more severe. At the same time, the strength of the cutting edge decreases when the rake face tool material is removed. While the mechanical-thermal load impact cycle caused by the tool periodically cutting in and out of the workpiece acts on the tool, causing serious damage to the cutting edge of the tool, as shown in Fig. 14.

Conclusion
In this paper, a PVD TiAlN-coated carbide tool was milling for Inconel 718 in high speed. The finite element simulation model was also developed for the milling process. Analyzing the experimental and simulation results, the following conclusions are obtained: Simulated cutting force and chip morphology were compared with the experimental results in high-speed milling. They are in good agreement, which proves the accuracy of the model. 2. The tool temperature is mainly distributed on the rake face, and with the cutting speed increases from 60 to 120 m/min, the maximum temperature of the rake face increases from 580 to 660 ℃. An increase in temperature will reduce the hardness of cemented carbide and accelerate tool wear. By analyzing the tool temperature, it was found that the MTR on the rake face gradually approaches the tool nose as the cutting speed decreases. 3. During sawtooth chip formation, the sawtooth degree increases with the cutting speed. By comparing the chip morphology with the cutting force obtained from the simulation, it is found that the fluctuation of the cutting force corresponds to the sawtooth chip morphology. As the degree of sawing increases, its effect on the cutting force is further intensified, resulting in an increase in the amplitude of the vibration of the cutting force, causing a more serious effect on the tool. 4. Fuctuations in the cutting force due to the formation of sawtooth chips have an important effect on the wear