Determination and Verification of the Johnson–Cook Constitutive Model Parameters in the Precision Machining of Ti6Al4V Alloy

Abstract

Numerical simulations of the cutting process play a key role in manufacturing and cost optimization. Inherent in finite element analysis (FEA) simulations is the correct description of material behavior during machining. For this purpose, various material models are used to describe the behavior of the material in the range of high deformation, high temperature values, and high strain rates. Very often the Johnson–Cook (JC) material model is used for this purpose; however, the correct determination of the material constants of this model is a key aspect. Therefore, this paper presents a procedure for determining the material constants of the JC model using an analytical method based on normalized tensile and compression testing of the material for different strain rates over a wide temperature range. After determining the material constants, the authors conducted numerical simulations of the orthogonal turning of Ti6Al4V titanium alloy using the obtained constants. Validation of the obtained results with those obtained in experimental studies was also carried out. The outcomes demonstrated that the difference between FEM simulation and experimental tests did not exceed 0.02 mm (14%) in the case of chip thickness,. Much smaller differences were obtained for the temperature in the cutting zone, where the maximum difference was about 45 °C (4%). Comparing the components of the cutting force, we found that, in the case of the main cutting force, in most cases, the differences did not exceed 70 N (8%). After the verification of the obtained results, it was also found that the determined material constants of the Johnson–Cook model can be successfully used in FEM modeling of the cutting process of Ti6Al4V titanium alloy for the adopted range of values of technological parameters.

1. Introduction

In today’s dynamic and developing industrial world, the continuous improvement of production processes is an integral part of achieving higher efficiency, quality improvement, and cost optimization. In this context, numerical modeling and FEM (Finite Element Method) simulations play a key role in the design and analysis of engineering processes [1,2]. One of the key aspects of production processes is machining [3]. Machining is widely used in various industries such as the automotive, aerospace, and defense industries [4]. To ensure effective and precise machining, it is necessary to understand the behavior of the material under cutting conditions and to properly model and prepare simulations of these processes [5,6]. One of the popular material models used in cutting analysis is the Johnson–Cook model [7,8]. This model describes the behavior of the material under conditions of large deformations and high strain rates. In the basic model, there are only five material constants to determine. For comparison, other constitutive models have much more material constants to determine [9,10]. The stresses in the deformation area in the JC model are expressed by Equation (1) [11]:

$${\sigma }_p=\stackrel{\left(1\right)}{\overbrace{\left(A+B{{\epsilon }_p}^n\right)}}\stackrel{\left(2\right)}{\overbrace{\left[1+C ln\left({\displaystyle \frac{{\dot{\epsilon }}_p}{{\dot{\epsilon }}_0}}\right)\right]}}\stackrel{\left(3\right)}{\overbrace{\left[1-{\left({\displaystyle \frac{T-T_0}{T_t-T_0}}\right)}^m\right]}}$$

(1)

where A is the initial yield stress of the materials at the reference strain rate and reference temperature; B is the strain hardening modulus; C is the strain rate hardening parameter; m is the temperature softening coefficient; n is the hardening index; T_o is the room temperature; T_t is the melting temperature; T is the working temperature; ε_p is the plastic strain; ${\dot{\epsilon }}_0$ is the reference strain rate.

The proposed model covers the range of large deformations, high temperature values, and high strain rates. The Johnson–Cook model is the basic and most frequently used equation in FEM simulations of the cutting process. Moreover, it is also implemented in the most important commercial FEM programs for calculating fast-changing phenomena [12,13]. The correct determination of the parameters of the Johnson–Cook model is necessary for effective numerical simulation of the cutting process, and they can be determined using various methods, such as laboratory tests, analysis of experimental data, or numerical optimization. The most common way to determine the material constants of the constitutive Johnson–Cook material model is to conduct experimental tests to determine the material strengthening curve for various temperature values and a wide range of strain rates. Parameters A, B, and n are determined from a uniaxial tensile test in quasi-static conditions at room temperature [14]. The value of parameter A is taken as the value of the yield strength, and parameters B and n are determined using the logarithmic graph method. The value of the m parameter is determined for higher temperature values because it is a parameter responsible for thermal softening. The C parameter is determined for dynamic loads, where there is a significant increase in the strain rate. In the field of dynamic loads, the most commonly used tests are the Hopkinson split bar test and the Taylor test [15,16,17]. In their study, the authors of [18] presented an analytical method for determining material constants using the MATLAB R2019b program. The proposed method consisted in fitting the strengthening curves to experimental tests using the least squares method. After determining several sets of material constants of the JC model, a comparison of the obtained data was presented on a 3D graph in the stress–strain–temperature function. In [19], Farahani and his co-authors determined the material constants of the Johnson–Cook model, the hybrid method, in two stages consisting in supplementing experimental research with FEM analysis. Karkalos et al. [20] used a relatively new stochastic method to determine and optimize the material parameters of the JC model, i.e., the fireworks algorithm. In [21], the authors used a genetic algorithm to determine the parameters of the JC model, which is able to determine the Johnson–Cook material constants in a very short time based on previously prepared data from strength tests. Bergs and his co-authors [8] presented a method for determining the material constants of a constitutive material model using the Downhill Simplex algorithm (also known as the Nelder–Mead algorithm). In [22], the authors proposed to determine the material constants of the Johnson–Cook model based on the results of FEM simulations, assessing the cutting force components and the chip shape. During repeated calculations, the parameters of the material model are determined iteratively in such a way that the obtained FEM simulation results are consistent with the experimental results for identical turning tests.

This article presents the procedure for determining the material constants of the Johnson–Cook model using an analytical method based on standardized tensile and compressive tests of the material for various strain rates in a wide temperature range. This is a simplified concept for determining the material constants of the Johnson–Cook model presented in [18]. The idea stemmed from the fact that this approach can be more easily and cheaply translated for industry to test new materials. The following section presents the results of the FEM simulation using the obtained material constants of the orthogonal turning process of the Ti6Al4V titanium alloy. The obtained results were compared with experimental tests for identical parameters as in the FEM simulation.

2. Methodology for Identifying the Parameters of Constitutive Equations

In order to obtain the material data necessary for simulation studies of the turning process of titanium alloy Ti6Al4V, it is necessary to carry out strength tests on this material to determine the effect of the temperature and the strain rate on the values of the plasticizing stress and, consequently, on the determination of material constants, for the Johnson–Cook material model, for example. The first stage of strength testing consisted of conducting a standard static tensile test for a low strain rate (0.002604 s^-1) and a wide temperature range (20 °C to 700 °C). The tests were carried out on the INSTRON 5982 testing machine made in the USA. Figure 1 shows the complete methodology of the process. The results of the experimental tests are presented in Figure 2.

The next part of the experimental research consisted in determining stress–strain curves for a higher strain rate, which in the conducted research was 12.5 s⁻¹. The tests were carried out on a BÄHR 850 D/L dilatometer equipped with a special strain attachment, which made it possible to carry out measurements in a vacuum or inert gas atmosphere. A cylindrical test specimen with dimensions d = 5 mm and L = 10 mm was placed between ceramic anvils and heated inductively at a rate of 1 °C/s to the appropriate temperature value. It was then annealed isothermally for about 180 s, in order to achieve a homogeneous temperature distribution across the sample. The specimen was then subjected to deformation and cooled to room temperature at a cooling rate of 30 °C/s after the test. The tests were carried out over a wide temperature range. The experimental results are presented in Figure 3.

After the appropriate preparation of the input data, the process of determining curves began in order to obtain the values of the material constants of the Johnson–Cook constitutive model. Figure 4 graphically presents the method of determining individual parameters. For this purpose, a tool in the MATLAB R2019b program, the CURVE FITTING TOOL (CFT), was used.

It is emphasized that, when mathematically matching the charts, the main criterion was the best fit of the experimentally determined measurement points to the stress–strain curve described by the JC model equation. The first step in determining the parameters is to calculate the material constants of the JC model for the element responsible for strain hardening. Parameters A, B, and n were determined on the basis of the experimental stress–strain curve for a temperature of 20 °C. For the mathematical adjustment to proceed correctly, the appropriate equation of the Johnson–Cook model, describing the element responsible for strain hardening, had to be introduced into the program, which was Equation (2), where y is the stress and x is the strain:

$$f\left(y\right)=A+B\times x^n$$

(2)

After the input parameters were prepared in this way, the process of matching the set of input data to the expected curve was carried out. Figure 5 presents a set of experimental points relating to the course of the stress–strain curve in the range of plastic deformations, along with an approximate curve.

For the described case, we strived to obtain the best possible fit, and the following values of parameters A, B, and n were obtained (

Table 1. Values of material constants of the Johnson–Cook constitutive model.

A	B	C	n	m
775.2	440.3	0.01483	0.1668	0.6269

) with the R2 coefficient of 0.9988. Using the obtained constants, an approximation of a set of points in 3D space was made, adding temperature as a variable in order to determine the next parameter of the constitutive model, which is the parameter m. This parameter is responsible for thermal softening. For this purpose, it was necessary to introduce the plane equation (part (1) and (3) of the JC material model equations, responsible for the deformation and temperature), described by Equation (3):

$$f\left(y\right)=\left(775.2+440.3\ast x^{0.1668}\right)\ast (1-(\mathrm{T}-20)/(1660-20\left)\right)^m)$$

(3)

Figure 6 graphically presents the obtained approximation results and the basic sets of experimental points corresponding to the stress–strain data of the titanium alloy for various temperature values with a determination R2 coefficient of 0.9866.

In this way, the constant m of the JC material model was obtained (Table 1). The full Johnson–Cook material model also includes the effect of strain rate. The parameter values for this model element ((1) element (3)) were determined on the basis of experimental data for a higher strain rate, which was 12.5 s⁻¹. To be able to use the CFT toolbox, it was necessary to enter the equation of the full JC material model with all previously determined constants and the searched parameter C corresponding to the influence of the strain rate. This equation took the following form (Equation (4)):

$$\begin{gathered} f\left(y\right)=\left(775.2+440.3\ast x^{0.1668}\right)\ast \\ (1-(\mathrm{T}-20)/(1660-20\left)\right)^0.6269) \\ \ast (1+\mathrm{C}\ast \mathrm{l}\mathrm{n}(12.5/2.604\left)\right) \end{gathered}$$

(4)

In the presented manner, the last parameter of the JC constitutive model was calculated with an R2 coefficient of determination of 0.998. Table 1 presents the set of obtained values of material constants.

Figure 7 graphically shows the approximation result and the basic stress–strain curves (black dots) for higher strain rates.

Globally, for the entire range of adopted input data, the model was consistent with the experiment at the level of R2 = 0.9782. For a strain rate of 0.002604 s⁻¹, the largest difference in stress was observed for a temperature of 700 °C and amounts to a maximum of 35%. For the remaining temperature values, the difference in stress between the mathematical model and the experimental data was a maximum of 8%, and as the temperature decreases, the difference decreases. In turn, for the strain rate of 12.5 s⁻¹, a smaller difference was observed between the stress–strain curves obtained for the analytical model and experimental tests. In this case, the greatest difference was observed for the temperature value of 700 °C, which amounts to a maximum of 10%. However, for the remaining temperature values, a maximum difference not exceeding 6% was observed. After determining all the material constants of the constitutive Johnson–Cook model, the assessment of the impact of the determined material constants on the results of the FEM simulation of the orthogonal turning process of the Ti6Al4 titanium alloy began. Experimental tests of the turning process with identical technological parameters as in the numerical simulation were also carried out.

3. Experimental and Simulation Approach

The main goal of the conducted experimental tests on orthogonal turning is their verification with FEM simulation tests. It was assumed that the validation of these two processes would be based on the analysis of the cutting force components, the temperature at the chip–tooth interface, and the dimensional and shape characteristics of the chip. The evaluation of experimental studies was carried out in two stages: the in-process and post-process stages. The first stage was carried out on a CNC lathe. During these tests, the cutting force components were recorded in the Cartesian system using a force gauge. A system was also used to measure the temperature at the chip–tool interface. During turning tests, a chip was collected and assessed in the second stage. The station for measuring the components of cutting force and temperature at the chip–tooth interface was installed on a multi-tasking 3-axis CNC lathe (Okuma Genos L200E-M). One of the most important elements of this station was a piezoelectric force meter from Kistler, model 9129AA. Figure 8a shows how the dynamometer is mounted in the toolhead of a CNC lathe. It is noted that, by using a suitable adapter, it was possible to directly mount the force gauge, with the appropriate lathe tooling, in a standard VDI chuck, which affects the quality of machining. The force meter was used to measure the main component of the cutting force F_c and the back force F_p. The signal from the force meter is transmitted in real time, through the Kistler 5070 signal amplifier, to the National Instruments NI9215 measurement card placed in the NI cDAQ-9188 terminal. The terminal is connected to the computer via a LAN link, where a dedicated proprietary program written in the LabView environment allows for the appropriate conditioning of the received signals, their archiving, and preliminary analysis. The natural thermocouple method was used to measure the temperature at the chip–tooth. It can be classified as a technique based on heat conduction. In the described method, the thermocouple is the cutting tool together with the workpiece material (chip). The contact of the natural thermocouple in this case is the contact surface of the cutting insert with the workpiece material. When measuring the temperature at the contact between the tool and the workpiece, it is required to isolate the cutting tool from the rest of the lathe. The same is completed with the workpiece. The most important issue is the calibration of the mated materials to determine the relationship between the generated thermoelectric force and the temperature value in the contact zone. For this purpose, the results of a calibration study on this type of thermocouple, which was conducted jointly with the Rzeszow University of Technology [23], were used. A National Instrument NI9214 measurement card and an appropriate track in dedicated, proprietary software, also used to measure the cutting force, were used to record the thermoelectric force signals. Figure 8c schematically shows the measurement path for measuring the components of the cutting force and temperature using the natural thermocouple method.

In experimental tests, for orthogonal turning of the Ti6Al4V titanium alloy (Figure 8b), a cutting insert from TUNGALOY, marked DGG500-0400, was used. It is a carbide insert used for cutting (uncoated, KS05F grade), which was ground to obtain the smallest possible radius for rounding the cutting edge. After mounting the cutting insert in the CTER2020-5T12 holder, the following angles were obtained in the working system:

• Orthogonal rake angle γ_o = 20°;
• Normal clearance angle α_o = 7°.

The tests were carried out at an ambient temperature of approximately 20 °C, in a treatment process without cooling. The tests were carried out for 6 cutting speeds (v_c = 40, 50, 60, 70, 80, and 90 m/min), 3 feed rates (0.05, 0.1, 0.15 mm/rev), and a constant cutting depth of a_p = 3 mm. Technological parameters were selected based on the manufacturer’s recommendations, which were v_c = 40–80 m/min and f = 0.05–0.15 mm/rev.

In order to compare the experimental results with the results of numerical simulations for the designated JC material models, an FEM simulation of the orthogonal turning process was prepared for identical parameters to the experimental studies. An engineering computing system from Scientific Forming Technologies Corporation called Design Environment for Forming (DEFORM) was used for the simulation study. The program’s material library was used to input the other material constants needed for the simulations, such as the friction model, the thermal conductivity, Young’s modulus, and others. Figure 9 shows a view of the DEFORM v12.0.2 program.

4. Results and Discussion

After conducting FEM simulation tests of turning in orthogonal cutting, they were verified on the basis of experimental tests. The cutting force components, temperature in the cutting zone, and chip morphology were verified. It is noted that, for vc = 90 m/min and the feed rate f = 0.15 mm/rev, every time during the tests, the cutting tool was destroyed, so the values of the components of the cutting force, temperature in the cutting zone, and chip morphology were not marked for these parameters.

4.1. Chip Characteristics

Industries such as the aerospace, automotive, and biomedical industries are huge supporters of titanium due to its remarkable strength-to-weight ratio. To avoid tool wear and deformation, precise control during machining is essential for materials with this strength. Therefore, an understanding of chip characteristics is critical for effective manufacturing since titanium’s unique material properties offer particular difficulties while machining. During FEM simulation tests, observations were made of the chip created during machining. This allowed for a comparison of the characteristic features of the chip with the experimental tests performed. During the course of the experimental research, the resulting chips were stored and then properly prepared for in-depth analysis. In the first stage, representative chips for all values of cutting speeds and feed rates were selected for further processing. The selected chip batches were encapsulated with a special resin. These samples were then properly ground and polished. The samples prepared in this way were subjected to observation under a metallographic microscope, with the help of which it was possible to analyze the chip. Measurements were carried out on a modern Olympus IX70 series inverted metallographic microscope. This workstation is equipped with dedicated Olympus OptaView-IS v4.1.3 digital image analysis software. The microscope is also equipped with a set of lenses with different magnifications in the range of 5×–150×. Measurements of chip thickness were carried out at five different locations with a minimum of 10 measurements. The evaluation of the dimensions, shape, and type of the chip allowed the correlation of these data with FEA simulations. Figure 10a–c shows the selected representative shapes of the chips obtained along with the stress distribution in the cutting zone for the same machining time. Figure 10d shows a view of the analysis and chip measurement program.

The analysis of the chip shape (Figure 10a–c) clearly shows that, in the tested range of technological parameters, a sawtooth chip with a clearly visible tendency to twist was obtained during FEM simulation in each case. A similar nature of the chip can be seen in experimental studies. The best fit of the chip shape was found for the feed f = 0.15 mm/rev (Figure 10c) for the entire range of cutting speeds. The greatest discrepancies in the results between experimental tests and FEM simulations (Figure 10a) were observed for the feed rate of f = 0.05 mm/rev. Analyzing Figure 10b, it was found that, as the cutting speed increases, the differences in the chip shape decrease. However, in order to better validate the chip shaping effects, it was decided to compare the chip thickness measurement results.

Based on Figure 11, it can be concluded that, for both sources of obtaining chip thickness information, as expected, the chip thickness increases with the increase in feed. This is because a higher feed causes the cutting tool to advance further for each revolution or tooth engagement, hence cutting a thicker part of the workpiece in each pass. A thicker chip is produced because more material is sheared off (i.e., chips) in a single pass when the feed is increased [24]. Comparing the obtained FEM simulation results with experimental tests, one can notice a very good match. For the entire range of tested technological parameters, the dispersion of the simulation results compared to the experimental data, for the average chip thickness, ranged from 1 to 14%. The best chip thickness adjustment was found for the highest feed, where the differences did not exceed 6%.

4.2. Cutting Forces

When machining, the term “cutting forces” describes the forces exerted by the cutting tool on the workpiece as they remove material [25]. Because these forces affect tool wear, surface smoothness, and operation efficiency, they are vital for machining process optimization and comprehension. In addition, one of the main causes of tool wear is cutting forces, and premature tool failure can occur because of the acceleration of wear caused by high forces [26]. Maximizing tool life and decreasing operational expenses are both achieved through an understanding of cutting forces and their optimization. In this work, a comparison of the main component of the cutting force F_c and the resistance (back) component F_p was made with experimental data. Figure 12 presents representative selected results obtained from the DEFORM 2D/3D program for various selected cutting times.

Figure 12 shows the FEM simulations of the orthogonal turning process of Ti6Al4V titanium alloy for selected technological parameters (v_c = 40m/min, f = 0.15 mm/rev, a_p = 3 mm). Figure 12 also shows an example map of the stress distribution in the workpiece for selected cutting times (0 s, 0.000416 s, 0.00105 s, and 0.00191 s). The graph shows the change in the main cutting force as a function of the cutting time. The X-axis shows the cutting time, and the Y-axis shows the value of the main cutting force. The vertical red dashed line shown on the graph represents the current value of the main cutting force for the selected machining time. Due to the dynamic nature of the changes in the cutting force waveform, a data filtering algorithm was built within ± 5% of the most common cutting force. Based on this, it was possible to calculate the average maximum value of the cutting force component in both experimental tests and FEM simulations. Figure 13 shows the results of experimental testing (line) and simulation (bars).

Analyzing the test results for the main cutting force presented in Figure 13, no clear change in the cutting force value as a function of cutting speed was observed. The main technological parameter determining the cutting force is the feed. Comparing the results of experimental tests with FEM simulation tests (Figure 13), it can be noticed that the largest difference in the values of the main cutting force occurs for the highest feed value and amounts to a maximum of 21% (66 N) for v_c = 70 m/min and v_c = 80 m/min. This is because the phenomenon of cutting forces increasing with the increase in the feed rate is a fundamental aspect of machining operations. In addition, the tool’s ability to remove chip thickness is directly proportional to the feed rate. More material is being sheared off with each cutting action when the chip is thicker. As the thickness of the chip grows, the cutting tool encounters more resistance from the workpiece material. This is because a higher amount of force is required to displace and distort a greater amount of material. The cutting tool has to use more force, leading to larger cutting forces, in order to overcome this increased resistance. If more material needs to be removed, the tool will essentially have to work harder [24]. For the remaining feed values, the differences are much smaller. For f = 0.1 mm/rev, the largest difference in cutting force values between experimental tests was found for a cutting speed of 60 m/min and amounts to 6% (32 N). The best agreement between the simulation results and the experimental ones was observed for a feed of 0.05 mm/rev, where the difference in force values for four speeds was below 2% and for the remaining two speeds a maximum of 8% (18 N). Taking into account the measurement errors calculated for the main cutting force for both experimental and simulation tests, it can be concluded that the obtained results are comparable to each other at a good, acceptable level, which generally correlates around the value of ±3%.

When analyzing the influence of the cutting speed and the feed on the values of the cutting back force F_p (Figure 14), it was noticed that both variables have a clear impact on the obtained force values. Comparing the average values obtained in experimental tests with FEM simulation tests, the agreement between the simulation and experiment for the F_p component deteriorated with the increase in feed has been observed. For the analyzed FEM model, the maximum discrepancies for the lowest feed were 6% has been noiced. For the subsequent feed values, the maximum difference was 34% (22 N) for f = 0.1 mm/rev and 42% (29 N) for f = 0.15 mm/rev, respectively.

4.3. Temperature in the Cutting Zone

Because titanium alloys have their own unique characteristics, cutting temperature is an important consideration when machining the material. Tool life, surface finish, and overall machining performance can be greatly affected by the high temperatures generated during cutting [27]. By optimizing cutting parameters, using appropriate coolants, and selecting the right tooling, manufacturers can effectively control cutting temperatures, leading to more efficient and cost-effective titanium machining processes. Figure 15 presents example results obtained directly from the FEM numerical simulation program.

Figure 15 shows the orthogonal turning process of Ti6Al4V titanium alloy for selected technological parameters (vc = 40m/min, f = 0.15 mm/rev, and ap = 3 mm). Figure 15 also shows an example map of the temperature distribution on the workpiece for selected cutting times (0 s, 0.000416 s, 0.00105 s, and 0.00191 s). The chart shows the change in the maximum workpiece temperature as a function of the cutting time. This is the maximum temperature recorded in the workpiece at a given cutting time. The X-axis shows the cutting time, and the Y-axis shows the maximum recorded temperature in the workpiece. The vertical red dashed line shown on the graph represents the current maximum temperature for a given selected cutting time. The impact of changing the cutting speed and feed on the temperature value is presented in Figure 16.

Based on the analysis of the influence of the cutting speed and the feed on the change in temperature values, it was noticed that both variable parameters have a clear impact on the temperature values in the cutting zone. For instance, as the cutting speed increases, the relative velocity between the tool and the workpiece also increases, leading to more frictional heat. In addition, the higher cutting speeds result in more intense shearing of the material, generating additional heat. Finally, at higher speeds, there is less time for the heat to dissipate into the workpiece or tool, causing the temperature to rise more rapidly. On the other hand, the higher feed rate results in thicker chips, meaning more material is being cut in each pass. This increases the volume of material being sheared and thus generates more heat [24]. When comparing the temperature values obtained in experimental tests, a similar trend and values can be noticed as in FEM simulation tests. The smallest differences were observed for the feed f = 0.05 mm/rev, where the average difference was approximately 3.3% (maximum 38 °C) for the entire cutting speed range. However, for the feed rate f = 0.1 mm/rev and f = 0.15 mm/rev, the average difference is 4% (with a maximum of 45 °C). Taking into account the measurement errors calculated for the temperature for both experimental and simulation tests, it can be stated that the results obtained are comparable with each other at a good, acceptable level not exceeding 2%.

5. Conclusions

Based on the FEM simulation tests and their verification using experimental tests, the following conclusions were made:

• It is possible to determine the material constants of the Johnson–Cook model based on strength tests in a simple way using the analytical method. The fit of the obtained curves of the mathematical model to the experimental tests is at a good level, and the differences in the curves for different temperatures do not exceed 8% (R² = 0.9782).
• The material constants determined by the Johnson–Cook model can be successfully used in FEM modeling of the cutting process of the Ti6Al4V titanium alloy for the adopted range of technological parameter values.
• The material constants of the JC model allowed for very good agreement between the FEM simulation results and the experimental results.
• The best match between FEM simulation results and experimental tests was found for the temperature in the cutting zone, where the differences did not exceed 40 °C (4%).
• It was also noticed that, with the increase in the feed rate and cutting speed, the match between the simulation and experimental results deteriorated. The reason for this could be a significant increase in the strain rate and temperature for which no strength tests were conducted and were not included in the determination of the material constants of the Johnson–Cook model.
• Conducting the whole range of both simulation and experimental studies raises the question, “To what extent do individual values of material constants affect the change in stress–strain curves as well as the results of FEM simulations?” Therefore, in the future, the authors will attempt to evaluate the effect of changing individual parameters of the Johnson–Cook material model on the results of numerical simulations.