Crater wear prediction in turning Ti6Al4V considering cutting temperature effect

Tool wear has great impacts on tool life and cutting parameter selection in the machining process. As ceramic inserts are widely employed in efficient machining, it is of great significance to predict accurately the wear of ceramic tools. Crater wear is one of the most significant tool wear modes when turning difficult-to-cut materials at high speeds. The purpose of this research is to demonstrate the forming and influence mechanisms of crater wear in Ti6Al4V turning with ceramic inserts while considering cutting temperature at the tool-chip interface. An effort is made to describe quantitatively the appearance of crater wear from the perspective of temperature distribution based on crater wear experiments under various cutting conditions. In order to obtain the cutting temperature distribution efficiently, an analytical temperature prediction model is used in this paper. Then, a prediction model for crater wear depth and width considering the influence of the maximum temperature is developed. The maximum crater wear depth and width models are validated by a series of cutting experiments, and the outcomes prove that the proposed models are practical. Additionally, the influence of various cutting parameters on crater wear is discussed. The cutting speed has the greatest impact on crater wear, followed by the feed rate. Furthermore, this research can be used to improve cutting parameters for controlling crater wear.

The maximum depth of crater wear K B The maximum width of crater wear T max The maximum temperature value at the tool-chip interface V c Cutting speed F t Feed rate a p Cutting depth DMZ Dead metal zone PDZ The primary deformation zone SDZ The secondary deformation zone q pr , q se , q d Intensity of the heat source in the primary deformation zone, secondary deformation zone and dead metal zone, respectively A 0 , B 0 , C 0 , n 0 , m 0 Material constants T m , T r Melting temperature and room temperature σ Shear strain dσ Shear strain rate dσ 0 Reference shear strain rate V s Shear velocity V ch Chip flow velocity V m DMZ velocity τ s , τ m , τ c Local shear flow stresses θ Slip-line angle γ Rake angle ϕ Shear angle ϕ s Immersion angle η r Chip flow angle on the rake plane ξ 1 , ξ 2 Friction factor angle θ c Addition of chamfer angle α 0 Initial rake angle α n Local rake angle l m Side length of the dead metal zone l c Side length of the secondary heat source l s Side length of the primary heat source w Cutting width B tool Dynamic heat distribution coefficient of the heat sources on the tool side B chip Dynamic heat distribution coefficient of the heat sources on the chip side B c , B t , ΔB, C 1 , m, k Adjusting factors S 0 , K 0 Constant coefficients α w , λ w Thermal diffusivity and conductivity of workpiece α t , λ t Thermal diffusivity and conductivity of tool α Angle of crater wear R Radius of crater wear S Volume of crater wear

Introduction
Titanium alloy is widely applied to many fields, such as biomedical, aerospace, automotive and chemical industries, owing to its excellent biocompatibility, good toughness and high fatigue endurance at high temperatures [1]. Meanwhile, it is considered to be a material that is particularly difficult to process due to the following characteristics: high strength, low thermal conductivity and easily adhering to the tool surface during cutting [2]. During turning Ti6Al4V with coated cemented carbide tools, it is found that high cutting temperature concentrates at the tool-chip interface adjacent to the cutting edge, where the highest temperature can exceed 1000 °C, accelerating the formation of wear [3,4]. This restricts cutting speed and feed speed and thus reduces the machining efficiency of titanium alloy. As a result, high-speed turning tactics with ceramic inserts are progressively used by manufacturers due to their high temperature resistance and wear resistance. Nevertheless, severe tool wear still happens because of the poor processability of titanium alloy. Crater wear on the rake face is the most important failure mechanism in the machining process of Ti6Al4V [5].
A slew of studies have been conducted on the formation mechanisms of the crater wear during machining Ti6Al4V using carbide tools. Experimental research has been the most common principal method for crater wear analysis. Venugopal et al. [3] noted that adhesion-dissolution-diffusion wear resulted in the crater wear during machining Ti6Al4V with uncoated carbide cutting inserts under cryogenic cooling. Similar findings were observed by Liang et al. [6] while turning Ti6Al4V with WC-10Ni3Al and WC-8Co carbide tools. In high-speed end-milling Ti6Al4V with uncoated cemented tungsten carbide inserts, Zhang et al. [7] stated that adhesion and diffusion were the predominant tool wear mechanisms in milling Ti6Al4V. Many studies indicated that the high temperature generated on the rake face caused co element diffusion from tool to workpiece, weakening the tool and accelerating crater wear [8][9][10][11][12]. To further study tool wear, some efforts have been devoted based on analytical models and the finite element method (FEM). Usui et al. [13] investigated the process of wear development based on the wear characteristic equation. It was found that the projected wear progress and tool life and the experimental findings were in good accordance. Malakizadi et al. [14] put forward a FEM-based method for predicting the evolution rate of the flank wear during turning operations. Thepsonthi and Özel [15] predicted the tool wear and life employing FEM with DEFORM software, and concluded that the CBN-coated carbide tool was superior to the uncoated carbide tool during micro-milling of Ti6Al4V. A crater wear prediction method based on dimensional analysis and FEM simulation with DEFORM-2d software was proposed by Ramírez et al. [16], which described the tool wear rate considering the combined effect of different thermo-mechanical wear mechanisms acting on the tool-chip interface.
On the basis of crater wear studies, cutting temperature on the rake face has a vital impact on crater wear during turning Ti6Al4V [11]. Norihiko [17] investigated the cutting temperature during titanium alloy machining and experimentally concluded that the serious tool wear was mainly caused by high cutting temperature. Usui et al. [13] regarded the temperature at the contact surface as one of the decisive variables to establish a wear model based on the equation of adhesive wear. Molinari and Nouari [18] found that the temperature-sensitive diffusion process had the strongest effect on the wear rate, particularly at higher cutting speeds. Sun et al. [19] studied the crater wear patterns of carbide tools and discovered that pressure and temperature had a significant impact on the wear rate when turning Ti6Al4V. To give a clear description, available wear models developed in the previous studies considering temperature variable are summarized in Table 1.
From the research mentioned above, numerous investigations have been conducted about the crater wear in machining Ti6Al4V from experimental and simulation methods; however, few studies have been reported on the prediction of crater wear profile considering the influence of tool-chip interface temperature distribution applying analytical models when machining Ti6Al4V with ceramic round inserts.
The primary purpose of this work is to demonstrate the forming and influence mechanisms of crater wear considering cutting temperature at the tool-chip interface in the turning of Ti6Al4V with ceramic inserts. A quantitative prediction model for the crater wear is proposed, including the maximum depth of crater wear (K T ) and width of crater wear (K B ), based on an analytical cutting temperature model. By inputting different sets of cutting parameters into the analytical cutting temperature model, the corresponding maximum temperature value and the temperature distribution along the longest contact length can be obtained. Thereby, a crater wear prediction model is established based on the maximum temperature at the tool-chip interface. Finally, the model is validated by experiments under a broad range of T max . The effects of cutting speed (V c ), feed rate (F t ) and cutting depth (a p ) on crater wear are analyzed based on this prediction model. Then, a suitable combination of cutting parameters is proposed to decrease crater wear and thus promote machining efficiency in turning Ti6Al4V.
This paper consists of six sections. Section 1 summarizes the research on the wear behavior during machining Ti6Al4V. The detailed experimental settings are described in Sect. 2. An analytical cutting temperature model is elaborated, and experimental results are analyzed in Sect. 3. A prediction model for crater wear considering the temperature distribution at the tool-chip interface is presented in Sect. 4, followed by model verification and discussion in Sect. 5. Conclusions are drawn in Sect. 6.

Experiments
A set of turning experiments were carried out in this section under dry cutting conditions. Figure 1 shows the machining center and devices used in the experiment. The cutting experiments were performed on a three-axis CK6180 lathe, as given in Fig. 1a. Figure 1b, c depicts the tool holder (CRSNR 2525 M 12-ID) and the round ceramic insert (RNG 45T6015 650) used in this work, respectively. The digital microscopy system (KEYENCE VHX-970F) served to extract data from the crater surface to form three-dimensional graphics and measure the profiles of crater wear, as shown in Fig. 1d. Table 2 shows the chemical composition of the Ti6Al4V cylindrical workpiece. The hardness and density of the workpiece are approximately 36 HRC and 4430 kg/m 3 , respectively. The solid cylindrical workpiece with 120-mm diameter and about 200 mm long was turned with round ceramic tools. The material of the tool is the most advanced Si 3 N 4 , which belongs to the professional category of hightemperature refractories and shows splendid impact strength, wear performance and heat resistance. It is suitable for processing difficult-to-cut alloys. In the tool manufacturer's recommendation manual, this sort of cutting insert is frequently utilized for high-speed cutting of titanium alloys. The geometry information of the insert is shown in Table 3.
The cutting settings were configured as roughing operation in dry cutting mode during the cutting process. Each experiment was repeated three times under the identical conditions, and the measurement results were the average of the three experiments. A L9 (3 4 ) orthogonal array was established to investigate the impact of cutting depth (a p ), cutting speed (V c ) and feed rate (F t ) on crater wear, as shown in Table 4. Experiments Nos. 1-9 were carried out. In view of rapid tool wear in the case of high-speed turning of Ti6Al4V, the cutting stroke remained a small constant for all the experiments.

Analytical cutting temperature model
In cutting experiments, it is difficult to measure precisely the temperature distribution at the tool-chip interface by experimental methods [21]. Many studies have shown that FEM simulation is able to effectively deal with nonlinear problems such as material and thermal-mechanical coupling [22], while its efficiency is insufficient. In this section, an analytical cutting temperature model based on Johnson-Cook's material constitutive law was proposed to Crater wear depth was predicted considering σ n , v sl , T int , t and (σ n , v sl , T int ) were calculated from the 2D finite element model Molinari and Nouari [18] Crater wear depth was predicted considering σ n , v sl , T int , t based on diffusion wear mechanism, and diffusion was dominated by contact temperature Sun et al. [19] ln k 1ẇ Wear rate was predicted considering σ n , v sl , T int , and the change of temperature had a great effect on the wear volume calculate the temperature distribution at the cross section perpendicular to the primary cutting edge and throughout the location of the K T during turning Ti6Al4V. The model can provide a fairly accurate cutting temperature prediction with a substantially reduced computing cost compared with FEM simulation. Then, the maximum temperature values for experiments Nos. 1-9 were obtained by the temperature model for analysis of variance (ANOVA). Furthermore, a series of cutting experiments are designed to obtain different cutting temperatures according to the results of analysis of variance.

Cutting temperature model
Zhuang et al. [23] studied the three-dimensional temperature field during turning and proposed an analytical model for predicting the temperature distribution at the toolchip interface. Then, the presented model was validated by a succession of finite element simulations and cylindrical turning experiments. The approach for determining the related heat sources, as well as the geometry and   [24,25]. Due to plastic deformation and friction, it is generally assumed that four principle heat sources coexist in the process of metal cutting: the primary heat source, the secondary heat source, the shear heat source and the induced heat source. It should be noted that the shear and induced heat sources are two parts of the dead metal zone (DMZ) heat source. According to previous studies, the intensity of the heat source in the primary deformation zone (PDZ), secondary deformation zone (SDZ) and DMZ can be respectively written as the following function: where V s is the shear velocity, V ch is the chip flow velocity, V m is the DMZ velocity. τ s , τ m and τ c are the local shear flow stresses of the cutting element, the DMZ-workpiece interface (EF) and SDZ, respectively. τ s can be calculated with Johnson-Cook's constitutive law as suggested in Eq.
(2) [26]. The parameters of the Johnson-Cook's model for Ti6Al4V are shown in Table 5. τ m and τ c can be determined by Eq. (3). As the hodograph given in Fig. 2, V s , V ch and V m can be determined by Eq. (4). (1) where A 0 , B 0 , C 0 , n 0 and m 0 stand for yield strength, strength coefficient, strain rate sensitivity coefficient, strain hardening exponent and thermal softening coefficient of the workpiece, respectively. Shear strain, shear strain rate and the reference shear strain rate are represented by σ, dσ and dσ 0 , respectively. T r and T m are the room temperature and melting temperature, respectively. ξ 1 and ξ 2 are the determined friction factor angles, ε is the angle between V c and V m , ϕ stands for the shear angle, as shown in Fig. 2. Figure 3 shows the distribution of each heat source and the corresponding image heat source, based on the heat source image theory [1]. By determining the heat sources in the primary deformation zone, secondary deformation zone and dead metal zone, the temperature rise generated at the tool-chip interface can be determined by integrating Table 5 The Johnson-Cook parameters for Ti6Al4V [26] A 0 /MPa The slip-line field geometry and the corresponding hodograph the effect of each basic heat source. According to the twodimensional analytical model proposed by Komanduri and Hou [27], the tool, workpiece and chip can be considered as semi-infinite medium under steady-state machining conditions. Therefore, the image heat sources are used in the semi-infinite medium with assuming chip upper surface as adiabatic boundary and chip upper surface and machined surface as adiabatic boundaries. Figure 3a shows the distribution of the primary and shear heat sources (a, c) with related images (b, d) considering chip upper surface as adiabatic boundary. Figure 3b presents the distribution of the secondary and induced heat sources (e, g) with related images (f, h, i, j) considering the chip upper surface and machined surface as adiabatic boundaries. The temperature rise of the chip (T Pchip ) was determined by a combination of eight heat sources labeled by a~d in Fig. 3a and e~h in Fig. 3b, which can be formulated as follow [27]: where R 1~R4 and R 1 ′~R 4 ′ are the distance variables for the eight heat sources (a~h). α n is the local rake angle, and θ c is the addition of chamfer angle. These angles are shown in Fig. 3. Y stands for the Y-axis coordinate value of point P. S 0 and K 0 are constant coefficients. The constants α w and λ w are the thermal diffusivity and conductivity of the workpiece. B chip is the dynamic heat partition coefficient of heat sources on the chip side of the tool-chip contact face, which can be determined by Eq. (6).
where B c , ΔB, C 1 , m and k are adjustment factors that accurately match the temperature rise on both sides. The exponential Y in Eq. (5) is the corrected coordinate value of point P (x, y, z) on the Y′ axis, where the original Cartesian system X-Y-Z has been converted to X′-Y′-Z′, and point E is the center of the transformed coordinate system. The threedimensional coordinate transformation matrix was used to get the coordinate values of point P in the new system as follows: where ϕ s is the immersion angle, and η r is the chip flow angle on the rake plane.
The temperature of the tool was generated by a combination of four heat sources labeled by e, g, i and j in Fig. 3, which can be calculated by: where R 5 , R 6 , R 5 ′ and R 6 ′ are the distances from point P to the four heat sources (e, g, i, j) respectively. w is the contact width between the tool cutting edge and the workpiece. Fig. 3 Distribution of heat sources with relevant images λ t is the thermal conductivity of the tool. Table 6 lists the mechanical properties of Si 3 N 4 and Ti6Al4V applied in the proposed model. B tool is the dynamic heat partition coefficient of heat sources on the tool side of the chip-tool contact face, which can be expressed by: where B t is an adjustment factor that accurately matches the temperature rise on both sides of the tool-chip contact face.
According to the investigation of Huang and Liang [29], the temperature of point P can be ultimately calculated by considering the thermal effects of every related heat source as below: where n is the number of the total heat sources.

Temperature model validation
The temperature distribution results obtained from the analytical cutting temperature model and FEM simulation are compared in Fig. 4. Figure 4a depicts the temperature field at the tool-chip interface by AdvantEdge (Version 7.1). Figure 4b was obtained through the analytical cutting temperature model by MATLAB 2018a. Comparing the two results, it can be observed that the temperature distribution (10) obtained using the analytical cutting temperature model matches well with the FEM simulation. Temperature profile from the FEM simulation (blue line) is compared with the result from the proposed model (red line) in Fig. 4c to illustrate a clear comparison of the temperature distribution. The temperature profile was extracted along the longest contact length. It can be observed that the two temperature curves are in good agreement.
In terms of calculation time, it took much more time for FEM simulation compared with the proposed analytical model. It took about 4 h to obtain a stable cutting state using 4 cores in parallel for the professional cutting simulation software AdvantEdge, while it only costs 567 s for the analytical model calculated by MATLAB 2018a using i5-7300HQ processor. Therefore, compared with FEM simulation, the analytical model can significantly improve calculation efficiency and reduce the computational cost with the same accuracy. It is interesting to find that the trend of the wear depth and temperature from the major cutting edge are in good agreement. The maximum crater wear depth (represented by K T ) and width (represented by K B ) were defined along the longest tool chip contact length. The fitting data for experiment Nos. 1-9 were listed in Table 7. According to Ref. [30], the cutting inserts were declared worn out when the average flank wear width was 400 μm, or the maximum flank wear width was 700 μm, or the K T was restricted to 140 μm.  The orthogonal test was designed according to three factors and three levels, as shown in Table 4. The data of crater wear depth (K T ) from Table 7 was selected as the dependent variable for analysis of variance to determine the effects of various cutting parameters on crater wear. By using SPSS data analysis software, the results of the analysis of variance were obtained in Table 8. It is worth noting that the crater depth is used as the standard to judge whether the tool is invalid [16], so it is acceptable to analyze only the wear depth. As shown in Table 8, V c is significant at 3.0% and hence has a major impact on crater wear depth. F t is crucial at a 4.5% level and has a secondary influence. However, the influence of a p on crater wear depth is not obvious. Consequently, a number of cutting parameters were selected with constant cutting depth to obtain different maximum temperatures (T max ) at the tool-chip interface. The selected cutting parameters were listed in Table 9.

Crater wear model considering temperature distribution
In this section, according to the previous fitting results, an experiment-based hypothesis was put forward considering the temperature distribution at the tool-chip interface. Further, a crater wear prediction model considering the effect of temperature was established through experimental results and analytical approaches. Figure 6 demonstrates the 3D schematic diagram of the wear mechanism in turning operations. The maximum wear depth occurs very close to the position where the highest temperature appears at the tool-chip interface. It is in qualitative agreement with the observations of Ramírez et al. [16], Dearnley and Grearson [31], and Komanduri [32]. Figure 7 shows the crater wear with ceramic cutting inserts under various cutting conditions. From the figure, it can be observed that the crater areas marked with yellow circles are located at the tool-chip interface. The formation pattern of crater wear during machining processes is typically approximated as an arc [33][34][35], as shown in Fig. 8. It is interesting to find that the most serious crater wear occurs at the place with the greatest temperature in Fig. 8. This leads to a hypothesis that crater wear may be caused by temperature at the tool-chip interface. A quantitative relation between crater wear depth and temperature at the tool-chip interface, as well as crater wear width, will be presented in this section.

Crater wear formation and temperature profiles
The measurement of crater wear and the temperature distribution along the longest tool chip contact are shown in Figs

Crater wear model
Based on the geometry of tool crater wear in Fig. 18, the relationship between K B , K T and radius R is as follow: Given K B and K T at a certain time, the radius R is calculated as Then, the area of the shaded region (S) in Fig. 18 can be calculated by the following formula: 2 > K T is assumed in this study, which is suitable in turning Ti6Al4V.
Supposing the contact width is w, then the total volume loss can be determined by Assuming K B remains unchanged with the development of tool wear under the same cutting conditions, the following relationship can be obtained by differentiation of V wear to the variable K T : where Similarly, K T is assumed to remain constant as temperature at the tool-chip interface increases under the same turning conditions, and by differentiation of V wear to the variable K B , the following relation is derived:  17 The linear fit between the maximum temperature and crater wear width According to the chain rule, the K T progress rate to the variable K B can be written as follow: Equation (22) depicts the relation between K T and K B of the rake face.
As illustrated in Fig. 17, the relation of K B with the maximum temperature value T max on the rake face can be expressed as With the maximum temperature value and crater wear data from Table 10, the results can be estimated. According to the assumed linear relationship, the relation between K T and T max can be written as where The average ratio can be calculated using the data from Table 10: Then, the relation between crater wear depth K T (unit: μm) and the maximum temperature value T max (unit: °C) can be further rewritten as: This relationship is depicted in detail in Fig. 19. The figure shows that no crater wear appears when the maximum temperature value is restricted, and a crucial maximum temperature value (about 816 °C) exists for the appearance of crater wear depth, as sector S in Fig. 19. The depth of crater wear increases with the increasing temperature when the temperature exceeds the critical value. It should be noted that the model is invalid when the temperature rises to the melting point of Ti6Al4V.

Model verification and discussion
In this section, a set of cutting experiments were performed via dry turning of Ti6Al4V with ceramic tools to verify the effectiveness of the proposed crater wear prediction model. Then, the full study is discussed technically.

Model verification
Cutting experiments were carried out to validate the proposed crater wear prediction model. To verify that there is no obvious wear when the cutting temperature is small enough, an experiment was done with a set of small cutting parameters (a p = 0.5 mm, F t = 0.1 mm/rev, V c = 60 m/min). The experiment results are shown in Fig. 20. From the temperature distribution given in Fig. 20b, it can be obtained that the maximum temperature at the tool-chip interface is about 810 °C (less than the limitation value of 816 °C). No obvious crater wear was observed (see Fig. 20c). It indicates that no crater wear appears when the temperature is restricted, as region S illustrated in Fig. 19.
As shown in Table 11, to validate the crater wear prediction model established in this paper, a series of cutting experiments under various conditions were conducted. The maximum temperatures of these experiments obtained from the proposed cutting temperature model are also listed in Table 11. The wear profiles and temperature distributions are shown in Figs. 21, 22, and 23. The crater wear width and depth from fitting results and predictions with the proposed models are given in Fig. 24. From the figure, it can be seen that the predicted maximum wear depths and widths match quite well with the measured results. The maximum error is roughly 12.6%, showing that the proposed model is workable. Fig. 19 The relation between crater wear depth and the maximum temperature

Discussion
As shown in Figs. 9,10,11,12,13,14,15, and 16, both the temperature and crater wear profile first increase and then decrease along the longest contact from the main cutting edge of the tool. The positions where the maximum wear depth and the highest temperature appear are very close, and the crater wear depth increases with increasing temperature and decreases with decreasing temperature. It indicates that the change trends of the temperature and crater wear profile are in good agreement, which meets the assumptions proposed in Sect. 4.1.
It is worth further discussing why observations from Figs. 9,10,11,12,13,14,15, and 16 appear. It is obviously noticed that the position of the highest temperature always appears near the tool major cutting edge, not anywhere else at the tool-chip interface. Figure 25 clearly shows the variation trends of shear stress and chip flow velocity at the tool-chip interface. According to the theory of dual contact zone proposed by Zorev [36], there is a mixed friction characteristic on the contact surface between the tool and the chip. Figure 25a shows that in the machining of metal processing, sticking friction first occurs and then changes to sliding friction along the contact length between the tool and the chip. These two kinds of friction dominate the tool-chip interface. The chip flow velocity near the tool major cutting edge is close to zero. With the increase of the distance from the tool major cutting edge, the chip flow velocity gradually increases and finally reaches the maximum at the starting   Fig. 25b. The tendency of shear stress is opposite to that of chip flow velocity. Firstly, the shear stress starts at the maximum value and gradually decreases from the starting point of the sliding zone until it becomes zero as given in Fig. 25b. At the junction of sticking zone and sliding zone, the chip flow velocity and shear stress of the cutting element reach the maximums simultaneously. According to Eq. (1) in Sect. 3.1, the heat source intensity reaches the maximum, which eventually leads to the maximum temperature at this position. High temperature promotes diffusion and softening of the material on the tool surface, which accelerates crater wear [8][9][10][11][12]. It can be found the higher the temperature is, the more serious the carter wear is. The above discussion further confirms the hypothesis proposed in this paper.
According to the analysis in Sect. 3.3, the crater wear depth is affected differently by cutting parameters. Based on the crater wear prediction model proposed in this paper, the effect of the combination of different cutting parameters on    Figure 26 shows the maximum temperature T max at the tool-chip interface and the maximum depth of crater wear K T with respect to V c and F t . Figure 26a depicts the increasing trend of T max and K T with increasing V c . The tendencies of T max and K T with increasing F t are given in Fig. 26b. It can be seen that these two machining parameters have positive effects on T max and K T . It is also observed that the growing tendency slows down when the cutting speed reaches 105 m/min and the feed rate approaches 0.15 mm/ rev. This might be attributed to the thermal-softening effect when the cutting temperature reaches extremely high levels.
The most important influencing factor is cutting speed, according to the ANOVA result. Cutting temperature increases as cutting speed increases from 75 to 120 m/min when other machining parameters remain constant. When cutting speed is sufficiently small, no evident crater wear occurs due to low cutting temperature (such as Nos. 1 and 10). For some large cutting speeds (such as Nos. 19 and 20), crater wear can easily form, and even collapsed edges can occur as the high cutting temperature softens the tool. Observing from Fig. 26b, it is found that feed rate has a vital influence on crater wear. Cutting temperatures increase with the increasing of feed rate when the cutting depth and speed stay constant. According to the ANOVA result, cutting depth has a slight effect on crater wear compared with cutting speed and feed rate. For the reason that too low cutting speed will cause very large vibration during turning, cutting speed should not be too low. Consequently, a combination of large feed rate, large cutting depth and medium cutting speed is recommended for increasing tool life and improving machining efficiency.

Conclusions
In this work, a study is conducted to quantitatively elaborate the crater wear in turning of Ti6Al4V alloy. A crater wear depth and width prediction model considering the cutting temperature distribution at the tool-chip interface is proposed. In addition, a quantitative analysis of the relationship between the maximum cutting temperature at the toolchip interface and the maximum crater wear depth as well as width is carried out. The investigation is an attempt to quantitatively describe the crater wear during difficult-to-cut metal machining. The major contributions can be concluded as follows: 1. A novel crater wear prediction model has been developed to demonstrate the relationship between K T and T max . According to the proposed model, no crater wear occurs when the maximum temperature is restricted, and the depth and width of crater wear increase as the maximum temperature increases. 2. The good agreement between experimental and predicted results over a broad range of cutting parameters indicates that the crater wear depth and width prediction model is feasible. 3. Cutting speed has a strong effect on K T and K B , followed by feed rate. In general, K T and K B increase with increasing V c and F t . Besides, a p has a negligible effect on K T and K B . A combination of large feed rate, large cutting depth and medium cutting speed can be used to decrease crater wear and improve machining efficiency in turning.

Author contribution
The ranking of the authors in the manuscript has been sorted according to their contributions. All the authors have approved the ranking of authors and the affiliation of the corresponding author.

Availability of data and material
The data in this study is obtained or measured through the corresponding experiments, and the materials have been given in this paper. They can be used as a reference for the related researchers.

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Competing interests
The authors declare no competing interests.