Effects of Edge Radius and Coating Thickness on the Cutting Performance of AlCrN-Coated Tool

Abstract

High-speed machining is a practical way to attain high productivity with lower costs. Under this condition, the tool geometry needs to be optimized to sustain high cutting forces and temperatures. The sharpness of the cutting edge and the coating thickness (CT) are two key parameters that affect the tool’s performance. While a sharp edge eases the cutting process, it causes a high stress concentration, which increases the wear rate and eventual edge fracture. In this study, we use a combination of finite element simulations and experimental testing to evaluate the effects of CT ( 1–3 μm), edge radius ($r_{\beta }$ , 6–15 μm), and coefficient of friction ($\upmu = 0 - 0.2$) on the stress distribution at the cutting edge. Our simulations showed that the larger the CT, the higher the stress magnitude inside the coating, but the lower the maximum stress depth percentile. Considering an industrial case of cutting steel workpieces using AlCrN-coated tungsten carbide tools under given cutting parameters, our simulations suggested an optimum CT of 3 μm. By manufacturing a series of milling tools with different CTs and edge radii, we validated the simulation results using a set of well-controlled milling experiments. Finally, the edge radius should be selected considering the size of rake/flank angle mainly to control stress distribution over the cutting edge.

1 Introduction

The performance of a coated tool in cutting operations can be significantly influenced by different parameters, including the edge radius, coating type, and coating thickness. Coating technology and its relevant parameters, such as material type and thickness, is one of the important aspects of modern cutting tool development [1,2,3,4,5,6,7,8]. Coating the tool helps to maintain its best performance by reducing adhesion [9] while increasing the wear resistance and tool life [10]. Furthermore, cutting forces and cutting-edge temperatures can be reduced by coating the tool [5, 11]. The effects of the coating thickness (CT) on the tool behavior have been reported in several works. Kanda et al. [12] reported that a thicker thickness generally contributes to the tool life extension but it reduces the transverse fracture strength. Wang and Kato [13] explored the CT effects of diamond-like carbon type, observing no influence on the wear resistance for the thickness of $0.7-3.5$ μm. Tuffy et al.[14] studied the influence of TiN CTs of $1.75-7.5$ μm on the machining performance of cemented carbide inserts. Based on the dry external cylindrical turning of AISI 1040 carbon steel tests, they reported that CT of $3.5 \, \mu$m was found to exhibit the best turning performance on the WC inserts. Torres et al. [15] investigated two levels of CT on diamond-coated micro-millers, reporting thinner coating leads to cutting force reduction. Abdoos et al. [16] analyzed experimentally three different TiAlN coatings with thicknesses of $5, \, 11, \, \text { and }17$ μm and corresponding cutting edge radii of 10, 40, and $70$ μm, reporting a thickness range within $10$ μm to be the optimum. Zhao et al. [17] investigated the tool-chip friction coefficient and coating thermal barrier effects by the CT (ranging $1.6 - 3$ μm) for $\text {Ti}_{0.55}\text {Al}_{0.45}$N coated tools. They concluded that CT of $2$ μm resulted in superior physical properties and reduced the cutting temperature of Inconel 718.

The edge radius of a cutting tool has a substantial impact on the cutting force, temperature, tool wear, and the quality of the machined surface [18, 19]. For a perfectly sharp edge tool, the material is predominantly removed by the mechanical shear force due to the interaction between the sharp tool and workpiece, thereby forming a chip, as shown in Fig. 1a [20]. This is for the case where there is no contact between the cutting tool and workpiece material along the flank face. However, the sharp cutting edge leads to stress concentration over the edge, and hence results in edge fracture at the early stage of the cutting process [21,22,23]. To prevent this, tools are generally designed with round cutting edges, with different values for the radius of the cutting edge ($r_{\beta }$) [7]. Increasing the edge radius can reduce the cutting force and temperature, which is related to the strength and impact resistance of the edge [19]. Cutting edge radius, amount of elastic recovery, and required cutting force are important parameters affecting minimum uncut chip thickness (h), while different analytical, numerical, and experimental investigations proposed a range between $0.1-0.5 \, r_{\beta }$ for minimum h ($h_{\text {min}}$) [24]. Therefore, the value of the $r_{\beta }$ dictates how small $h_{\text {min}}$ can be [20]. When $h < h_{\text {min}}$, the cutting tool compresses workpiece material as shown in Fig. 1b, and then recovers back due to elastic deformation after the tool passes, and hence, no chip formation [21]. In the case of $h \approx h_{\text {min}}$ as shown in Fig. 1b, a coupled plastic-shearing chip formation and elastic deformation and recovery occur for the workpiece material, leading to a cut chip thickness smaller than the selected h value. For $h_3 > h_{\text {min}}$, the chip is formed over the whole depth of cut equal to the chosen h value.

Fig. 1

Representation of the chip formation progressed by a cutting tool having (a) a sharp cutting edge, and (b) a round edge with $h_1 < h_{\text {min}}$, $h_2 \approx h_{\text {min}}$, and $h_3 > h_{\text {min}}$, adopted and redraw from Aramcharoen and Mativenga [20]

Finite element method (FEM) is a powerful tool used to simulate and analyze the metal cutting process [25]. It has been used to understand different aspects of the metal cutting process such as cutting forces [26, 27], chip formation process [28,29,30], and measuring residual stresses over the workpiece [31, 32], among others. There have been several investigations in the literature analyzing the effects of different geometrical parameters of the tool on the overall stress and temperature distributions via FE-based simulations [33,34,35,36,37,38,39]. Ozel [40] utilized FE modeling to predict forces, temperatures/stresses, and tool wear on tools while changing the edge geometry. Agmell et al. [41] concluded that changing tool micro-geometry decreases the maximum principal stress over the tool, showing that chamfering the tool leads to a decrease in the maximum principal stress by around 20%. Du et al. [42] performed a coupled FE simulation and Genetic algorithm optimization of high-speed cutting of Ti6Al4V with rake angle ($\alpha$), flank angle, and $r_{\beta }$ ranging $0-20 ^o$, $2-10 ^o$, and $0.01-0.13$ mm, respectively. The optimum values for force and temperature were obtained with $\alpha$ of $18.5 ^o$, flank angle of $5.6 ^o$, and $r_{\beta }$ of 0.02 mm. However, these values do not produce a strong cutting edge, as both rake and flank angles are relatively high, and also the $r_{\beta }$ is very small. Of course, the force and temperature can be low for this scenario, but the weak cutting edge might break at the early cutting stage. Bounif et al. [43, 44] analyzed the effects of CT (6, 10 and $15 \,\mu$m), edge radius (10, 15 and $20 \,\mu$m), rake angle ($-7$, 0, and $7^o$), and rigidity on the crack initiation and propagation over the thickness and also at the coating-base material interface using extended FEM and cohesive zone modeling. They have concluded that a coating with low rigidity and large thickness, large edge radius, and high rake angle of the tool leads to protection of the cutting tool from possible cracking and fracture. Qin et al. [45] experimentally studied the effects of the CT of diamond-coated tools on machining performance and also used FE simulation to quantify stresses over the tool. Their results showed that: (i) increasing CT significantly elevates the interface residual stresses; (ii) increasing CT for thicker coatings decreases the critical load for coating failure; the trend is opposite for thin coatings; and (iii) increasing the diamond coating thickness (for CTs of $4-29$ μm) increases tool life by delaying the coating delaminations.

A clear understanding of the effect of different tool parameters helps tool manufacturers to optimize the tool performance before conducting any expensive field testing. It allows users of the cutting tools to assess tool life under different cutting/working conditions. It’s important to note that while FEM is a powerful tool to perform cutting process analyses, it also has its limitations and challenges. For example, it requires significant computational resources, especially for complex three-dimensional cutting operations. An alternative way is to use a robust two-dimensional numerical model of the milling process which simulates cutting with a short calculation time and the simplest model setup [46,47,48,49]. Considering the literature review presented here, the main contribution and novelty of this paper can be described as conducting a series of two-dimensional numerical modeling combined with experimental studies to understand the effects of coating thickness (CT - range from 1 to $3$ μm), edge radius ($r_{\beta } \text { of } 6 - 15 \, \mu$m), and coefficient of friction (CoF, $\mu = 0 - 0.2$) on stress distribution of a tool made of tungsten carbide coated with AlCrN while cutting a workpiece made of steel. This work aims to fill a gap that covers these combinations. It’s important to note that the optimal edge radius and coating thickness can vary depending on the specific cutting operation and the material being machined. To cover this, a comparison was done first with the cutting forces reported in the literature to validate the FE model. Then, the evolution and distribution of stresses along the tool cutting edge were studied while changing the coating thickness, edge radius, and friction parameters. Finally, a comparison was made with experimental testing to assess the applicability of the FE simulations.

2 Methodology

As it was mentioned in Sect. 1, this work combines numerical simulation with experimental testing to obtain optimum values for a few selected parameters, as shown in Fig. 2. An FE simulation model of the cutting process is a key tool to study tool geometrical variables such as edge radius and coating thickness. This was used to analyze the influence of these parameters on tool performance and evaluate any possible damage to the tool. The whole FE analysis starts with a simplification of a 3D milling model to a 2D model, following Yao et al. [46], Yadav et al. [47], Li et al. [48], Kyratsis et al. [49]. This is mainly to analyze the problem with less computational time. For example, a single 3D milling simulation takes 25–35 h [50] while our 2D simulation took less than 5 h. Besides, the effects of coating thickness, edge radius, and friction coefficient can be analyzed in 2D with a very good approximation. Then, there were iterations over different sets of parameters in building the FE model. This could be done either in the FE model or imported from another program. This step mainly included geometric creation and modeling, defining the material model, specifying loading, boundary conditions, possible contact, and meshing. Then the model should be checked, and once ready, it can be solved. The effectiveness of the simulation method and the material model is the key to ensuring the simulation accuracy [19]. A detailed explanation of the FE model is given in Sect. 3. Once solutions were ready, results analyses were done by plotting necessary field variables (such as Mises stress and principal stress). The next step was to choose a few selected sets of tool parameters and start experimental testing with those cases. The experimental setup was used to mainly test the selected parameters and assess the outputs of the numerical simulation; see Sect. 5 for a detailed explanation.

Fig. 2

Cutting process finite element simulation flow chart

3 Simulation Setup

The classical Johnson-Cook (JC) constitutive law was chosen to model behaviour of the 42CrMo4 Steel as follows [51]:

$$\begin{aligned} \overline{\sigma } = \underbrace{\left[ A + B \varepsilon ^n \right] }_{\text {Elasto-Plastic term}} \underbrace{\left[ 1 + C \ln \left( \frac{\dot{\varepsilon }}{\dot{\varepsilon }_0} \right) \right] }_{\text {Viscosity term}} \underbrace{\left[ 1 - \left( \frac{T - T_{\text {room}}}{T_{\text {melt}} - T_{\text {room}}} \right) ^m \right] }_{\text {Thermal softening term}} \end{aligned}$$

(1)

The first term corresponds to work hardening, where A is the initial yield strength, B and n represent the linear and non-linear work hardening parameters, and $\varepsilon$ is the accumulated plastic strain. The second and third terms represent the rate and temperature dependency of the material, in which m and C are the material-dependent constants, $\dot{\varepsilon }_0$ is the reference strain rate, T, $T_{\text {room}}$ and $T_{\text {melt}}$ being the working temperature, room temperature, and melting temperature, respectively. We assumed that only the workpiece experiences plastic deformation and the cutting tool was modeled as an elastic body [52,53,54,55]. Mechanical parameters used in Eq. (1) are presented in Tables 1 and 2. Assuming the strain rate and temperature to be constant $T = T_{\text {room}}$, the last two terms of Eq. (1) are neglected, and therefore:

$$\begin{aligned} \overline{\sigma } = \left[ A + B \varepsilon ^n \right] \end{aligned}$$

(2)

Table 1 Thermo-physical properties of the workpiece material, Steel [56]

Johnson and Cook [57] proposed a fracture criterion that was sensitive to stress triaxiality, strain rate and path, and temperature. Damage accumulates in this model in the material element during plastic straining. This accelerates immediately when the damage reaches a critical value. One can define a damage variable D varying between 0 and 1 (0 for undamaged material and 1 for fully damaged material), and define it as:

$$\begin{aligned} D = \Sigma \frac{\Delta \varepsilon _{\text {pl}}}{\varepsilon _{\text {fail}}} \end{aligned}$$

(3)

where $\Delta \varepsilon _{\text {pl}}$ is an increment of the equivalent plastic strain and $\varepsilon _{\text {fail}}$ is defined as the plastic strain at damage initiation. Therefore, failure is assumed to occur when this D parameter reaches/exceeds 1.

The $\varepsilon _{\text {fail}}$ can be calculated as [57]:

$$\begin{aligned}{} & {} \varepsilon _{\text {fail}} = \left[ D_1 + D_2 \exp {D_3 \frac{P}{\sigma }} \right] \left[ 1 + D_4 \ln \left( \frac{\dot{\varepsilon }}{\dot{\varepsilon }_0} \right) \right] \nonumber \\{} & {} \quad \left[ 1 + D_5 \left( \frac{T - T_{\text {room}}}{T_{\text {melt}} - T_{\text {room}}} \right) ^m \right] \end{aligned}$$

(4)

where $D_1$ to $D_5$ are material failure constants and are determined experimentally, P is the mean or hydrostatic stress. Different JC material parameters for 42CrMo4 Steel are presented in Table 2. Similar to the case of the hardening equation ($\overline{\sigma }$), the second and third terms of Eq. (4) are neglected because they correspond to strain rate increment and temperature change, respectively. Now, the resultant stress with damage evolution is calculated using:

$$\begin{aligned} \sigma _D = (1 - D) \overline{\sigma } \end{aligned}$$

(5)

in which $\sigma _D$ is the stress at damaged state and $\overline{\sigma }$ is calculated using the JC constitutive relation, Eq. (2).

Table 2 Johnson-Cook failure model constants for Steel [56]

The milling process, in general, includes different operations such as face-, side-, angular-, and end-milling operations [58]. Orthogonal cutting can be considered as a part of the end-milling process (as a simplified problem), as shown in Fig. 3 [46, 48]. Therefore, this orthogonal cutting configuration was used for the FE simulation mainly to study the effects of edge radius, friction coefficient, and more importantly, coating thickness on the stress distribution over the tool. The full end-milling process was used as a short-time experimental test to compare with the numerical results (corresponding results are presented at the end of Sect. 5).

Fig. 3

End-milling schematic and a single flute representation of the orthogonal cutting during the end-milling process

The cutting process involves a number of very complicated physical processes, including heating, adiabatic shear bands, friction, enormous stresses, and strain rates. Two-dimensional FE simulation was carried out using the Abaqus/Explicit commercial package. FE model consists of a workpiece and a cutting tool as shown in Fig. 4. It should be noted that cutting force decreases at the elevated rake angles, as reported by Gunay et al. [59]. One should use effective rake angle ($\alpha _e$) when the cutting tool is manufactured to have edge radius ($r_{\beta } > 0$), calculating as [60]:

$$\begin{aligned}&\text {for } h < r_{\beta } \left[ 1 - \cos (\alpha + \pi /2) \right] : \qquad \alpha _e = -\frac{\pi }{2} + \cos ^{-1} \left( 1 - \frac{h}{r_{\beta }} \right) \end{aligned}$$

(6a)

$$\begin{aligned}&\text {for } h > r_{\beta } \left[ 1 - \cos (\alpha + \pi /2) \right] : \qquad \alpha _e = \alpha \end{aligned}$$

(6b)

Fig. 4

Schematic of the problem along with the dimension (in mm) and mesh discretization. Adaptive and fixed mesh regions are highlighted, with fine mesh for regions to be cut and also close to the tool tip and over the CT

We have $h > r_{\beta } \left[ 1 - \cos (\alpha + \pi /2) \right]$ for all the cases presented in this work, and hence, $\alpha _e = \alpha$. Three different thicknesses were analyzed for the coating: 1, 3, and 5 $\mu$m. The left and bottom sides of the workpiece were clamped meaning that neither displacement nor rotation was allowed ($U_x = U_y = UR_z = 0$). Boundary conditions over the tool were: displacement at the right side of the tool is fixed in the y direction ($U_y = 0$), but it was allowed to move in the x direction. Tool geometrical and cutting parameters for the simulation setup are presented in Table 3. Tool moved with a velocity of $V_c = 180$ m/min in the x direction. Uncut chip thickness was assumed to be constant and equal to 0.12 mm. Maximum value for the minimum uncut chip thickness can be estimated as $\max (h_{\text {min}}) = 0.5 \, r_{\beta }|_{\text {max}} = 7.5$ μm. Therefore, the assumed uncut chip thickness is large enough to remove material and form chip accordingly.

Table 3 Tool and cutting parameters for the simulation setup

FE model was discretized using CPE4 elements (4-node bilinear plane strain quadrilateral element), with a size range from $0.001 - 0.075$ and $0.001-0.016$ mm for workpiece and tool parts, respectively. The coarse mesh was used for areas far from the cutting, while finer mesh was used mainly at the areas around the edge of the tool and the cutting area of the workpiece. Total number of elements of the workpiece and tool models were approximately 37,500 and 8,250 elements, respectively. These element sizes were chosen after conducting a mesh sensitivity analysis of an orthogonal cutting simulation with material properties presented in Tables 1, 2, and 4, and with cutting parameters presented in Table 5. Considering orthogonal cutting, an FE model should result in acceptable tool-chip contact definition and chip formation while changing different cutting parameters (see 15 in the Appendix Appendix A in the case of changing friction coefficient), and trustworthy cutting force validated by reference work. The FE model was validated by comparing cutting force with reported values in Pantale et al. [56] using the same cutting and geometrical parameters. Table 6 summarizes the mesh sensitivity analysis results together with a validity study. Although, the cutting parameters used in Pantale et al. [56] were different than those presented in Table 7 for detailed analyses, once validated, the same model could be used with different cutting parameters, similar to an investigation reported in Vasu et al. [61], using the same model for different cutting velocities ($270 - 650$ rpm) and feed rates ($0.08 - 0.32$ mm/rev). There are two types of contact algorithms available in Abaqus/Explicit: Kinematic and Penalty contacts [62]. We adopt Penalty contact in the current simulation, which uses one extra element in the model where no stiffness is considered when a gap occurs between two master and slave surfaces. Once contact occurs between two surfaces, stiffness will get a high value.

Table 4 Mechanical properties of the tool base material and coating

Table 5 Cutting parameters mesh sensitivity and validation analyses Pantale et al.[56]

Table 6 Mesh sensitivity analysis (both tool and workpiece) of the orthogonal cutting simulation considering an experimental cutting force of 1860 N from Pantale et al.[56]. The number of elements is the sum of both tool and workpiece elements

Figure 4 shows the dimensions of the workpiece and the cutting tool used in the finite element model. It also shows how we discretized the coating and tip of the tool to capture stress variation properly. A classical Coulomb friction law was used to model the contact behavior between the tool and chip at the rake face, defined by:

$$\begin{aligned} \tau = \mu \sigma _n \end{aligned}$$

(7)

where $\tau$ is the stress due to the frictional stress mainly on the tool rake face, and $\sigma _n$ is the normal stress. The frictional stress is assumed to be proportional to the normal stress by a $\mu$. The friction coefficients can vary significantly from 0.1 to about 0.7 depending on cooling conditions (dry or with lubrication), operating pressure, temperature, and sliding velocity in the tool-chip interface [63,64,65,66]. In particular, the difference resulting from the grade of work materials and their physical and mechanical properties is very significant for low sliding velocities in dry friction conditions [67]. An experimental was done on the dry cutting of AISI 1045 which reported three friction regimes: (i) regime 1 when $V_c < 60$ m/min with an apparent friction coefficient of almost constant of $\mu = 0.54$, (ii) regime 2 when $60< V_c < 180$ m/min with $\mu = 0.54-0.23$, and (iii) when $V_c > 180$ m/min with a constant $\mu$ of 0.23 [68]. In this work, the friction coefficient was considered to be varied between 0 (an ideal condition that can happen theoretically) and 0.2 to mainly evaluate its effect on stress distribution over the tool.

4 Simulation Results

Mises stress and principal stress were chosen to be plotted in the simulation. The Mises stress is a scalar number, always positive, and has no direction that specifies if the material is close to or above its yielding point. This is true for ductile materials such as Tungsten Carbide [69], but one has to use maximum principal stresses to predict failure in case of brittle materials, such as AlCrN coating [22, 70]. The maximum Mises stress on the cutting edge as a function of edge radius and CT for different CoFs are illustrated in Fig. 5. It compares the effects of $r_{\beta }$ and CT on the stresses and clearly shows a bigger effect of the $r_{\beta }$ than the CT on the maximum Mises stress. As an example and for CoF of 0.1, maximum Mises stress varies between 2800 to 3850 MPa against $r_{\beta }$ for CT of $1$ μm, while it varies between 2650 to 3700 MPa against CT for $r_{\beta } = 8$ μm.

Fig. 5

Maximum Mises stress for CoFs of $0.0-0.2$ over tip of the tool. CTs are 1, 3, and 5  μm for $r_{\beta }$ of $6-15$ μm

The presence of edge radius leads to improvement in tool life while reducing tool wear rate, hence achieving a better-produced part [4, 71]. Cutting and thrust forces rise with increasing edge radius, and therefore they elevate the level of the stresses and temperature over the tip and edge of the tool [71]. Figure 6 also shows maximum principal stress variations while changing different geometrical parameters, and also CoF values. For both Mises and principal stresses, larger CT leads to higher stress over the tool.

Fig. 6

Maximum principal stress for CoFs of $0.0-0.2$ over tip of the tool. CTs are 1, 3, and 5  μm for $r_{\beta }$ of $6-15$ μm

Figures 7a and b present Mises and maximum principal stress variations, respectively, along a path over the edge of the tool for all three coating thicknesses for a tool $r_{\beta } = 8$ μm and with $\mu = 0.2$. The path is shown at the bottom left corner of the Fig. 7. It can be seen that the Mises stress values were increased for higher CT values, with the maximum Mises values of 3500 MPa, 3300 MPa, and 3000 MPa for CTs of $5$ μm, $3$ μm, and $1$ μm, respectively. A similar trend is seen for maximum principal stress variation for different CTs: 725 MPa for CT of $1$ μm, 1015 MPa for CT of $3$ μm, and 1325 MPa for CT of $5$ μm.

As shown in Figs. 5 and 6, reducing the cutting edge radius and increasing coating thickness reduce the magnitude of both the Mises and principal stresses on the tool surface for all studied coefficients of friction. The effect is more pronounced with radius reduction and comparatively lesser with increased coating thickness.

Fig. 7

Variation of (a) Mises and (b) maximum principal stresses along edge of the tools with different coating thickness. The results are presented for $\mu = 0.2$, $r_{\beta } = 8$ μm, and CTs of $1-3$ μm

To optimize coating performance, one should consider not only the magnitude of stress on the coating surface but also the variation of stress over cutting edge surface. Fig. 8 illustrates the variation of the maximum Mises and principal stresses through the coating thickness at a location over the tool highlighted in Fig. 7 for edge radii of $8 \text { and } 15$ μm. Values were extracted from the outer surface, tool-coating interface, and four points inside the coating. The larger the CT higher the stresses over the outer surface, similar to reported analysis in Wang et al. [

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Acknowledgements

The authors acknowledged financial support from the Innovation Fund Denmark (Innovationsfonden) for the project “Cutting Edge, 8090-00010B”. Part of the simulations have been performed on the Prime cluster, Department of Mechanical and Production Engineering, Aarhus University, and all the experiments were done at the DAMRC technology center, Denmark.

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1. Centre for Industrial Mechanics, Institute of Mechanical and Electrical Engineering, University of Southern Denmark, 6400, Sønderborg, Denmark

   Mohammad Malekan

2. Danish Advanced Manufacturing Research Center (DAMRC), 7400, Herning, Denmark

   Charlotte F. Ilvig

3. Department of Mechanical and Production Engineering, Aarhus University, 8000, Aarhus C, Denmark

   Ramin Aghababaei

Corresponding author

Correspondence to Mohammad Malekan.

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Appendix A. Shear Angle Extraction from FE Simulation

Figure 14 presents contour area of 75% of the maximum Mises stress per coating thickness for all the CoFs, CTs, and $r_{\beta }$ used in the numerical model and for $\alpha = 4^o$. An illustration of what area we are referring to was shown in Fig. 10c. The pattern here is contrary to what we presented for maximum Mises and principal stresses in Figs. 5 and 6, where maximum stresses were increased by having higher CTs. It should be worth mentioning that the gross area was smaller for CT of $1 \, \mu$m than two other CTs and for all radii, but its deep (along the thickness) and width (perpendicular to the thickness deep) with respect to the CT are also very important, as it defines how much deep and how widely that area is distributed over the coating thickness. This is why we plotted area/CT and not the gross area of 75% of the maximum Mises stress itself.

Fig. 14

Contour area of 75% maximum Mises stress per CT, for $\mu$ of $0.0-0.2$, CTs of 1, 3, and 5 $\mu$m, $r_{\beta }$ of $6-15 \, \mu$m, and for rake angle of $4^o$

The CoF at the tool-chip interface changes the chip shape by imposing additional tangential stress over the rake face. So, chip curls when there is no friction and the level of curling gets lower for higher $\mu$, see Fig. 15. This results in higher chip thickness compression ($\lambda = h_c / h$, see Fig. 1a for h and $h_c$ definitions), and therefore, the shear angle ($\phi$) decreases considering the relationship between $\phi$ and $\lambda$ as $\phi = \arctan \left( \lambda ^{-1} \right)$. Ernst and Merchant [76] also realized a relationship between $\alpha$ and friction angle ($\beta$, with $\beta = \arctan {\mu }$) aiming to quantify the shear angle of the cutting process ($\phi$) as, assuming the work to form the chip is a minimum [77]:

$$\begin{aligned} \phi = \pi /4 + \alpha /2 - \beta /2 \end{aligned}$$

(A.1)

There is a good relation in the tendency between the Merchant solution, Eq. (A.1), and the numerical results as shown in Fig. 16 in A. The only difference is an offset of approximately $6-8$ degrees on average. The reason for this offset comes from the presence of radius of the cutting edge (compared to zero $r_{\beta }$ assumption in Eq. (A.1)).

Fig. 15

A schematic of effect of the CoF on the chip geometry and shape ($\mu = 0.0-0.2$). Larger the CoF smaller level of curling of the chips

An important effect of increasing the $r_{\beta }$ is decreasing behavior of the shear angle, $\phi$. This decrease results in a larger area of the shear plane and thereby larger cutting forces, larger strain, and the power consumption [77]. Larger the shear angle smaller the chip thickness (i.e. to have fine cutting), smaller the shear plane area, and hence, smaller required cutting force. Figure 16a presents variation of the shear angle against $r_{\beta }$, $\mu$, and $\alpha$ angle, showing a decrease pattern of $\phi$ angle for higher $\mu$. Figure 17 presents how we measured the shear angle from the FE simulations.

Fig. 16

Variation of the shear angle versus: (a) $r_{\beta }$ ($6-15$)  μm, $\mu$ ($0-0.2$), and $\alpha$ angle ($0-9.9$), and (b) $\alpha$ as a comparison between analytical, Eq. (A.1), and numerical results for $r_{\beta } = 10$ μm

We plotted plastic strain distribution over our model aiming to capture the shear transition location happening at the primary shear zone. Then, we can measure the shear angle. Figure 17 shows shear angle measurements for tools with $r_{\beta }$ of 8 and $15 \, \mu {\text {m}}$, and $\mu = 0.2$. Only workpiece experienced plastic strain as the tool was modeled as an elastic body.

Fig. 17

Shear angles from FE simulations for rake angle of $\alpha = 4^o$ with $r_{\beta }$ of $8 \, \mu {\text {m}}$ (a) and $15 \, \mu {\text {m}}$ (b), with CoF of 0.2

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Malekan, M., Ilvig, C.F. & Aghababaei, R. Effects of Edge Radius and Coating Thickness on the Cutting Performance of AlCrN-Coated Tool. Int. J. Precis. Eng. Manuf. (2024). https://doi.org/10.1007/s12541-024-01074-9

• Received: 10 February 2024

• Revised: 14 June 2024

• Accepted: 18 June 2024

• Published: 08 July 2024

• DOI: https://doi.org/10.1007/s12541-024-01074-9

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