Surface Roughness Investigation and Stress Modeling by Finite Element on Orthogonal Cutting of Copper

: In this paper, a modern non-contacting optical technique was used to study the surface roughness of commercially pure copper. Finite element (FE) method was applied to predict the stress during orthogonal cutting by simulating the machining process. The experimental work empathized mainly on the effect of cutting speed (N) and feed rate (f) on the surface roughness of copper. Scanning electron microscope (SEM) was utilized to evaluate the surface variations at different machining conditions. Johnson-Cook mathematical model was adopted and employed to determine the parameters of the material. Furthermore, the maximum Von-Mises stress was predicted as a function of machining conditions. A software package of code (ABAQUS/CAE) was used for the analysis and response surface methodology (RSM) was applied to visualize the results. The results showed a signiﬁcant effect of the feed rate/cutting speed interaction on surface roughness and Von-Mises stress of copper. An enhancement of 14% in surface roughness was perceived with increasing the cutting speed. A good agreement was observed between experimental and analytical results.


Introduction
The mechanical and surface properties are essential for the characterization of materials. The requirement of products with good quality in terms of high strength, good surface finish, lower cost and less environmental effects is the challenge of the manufacturing industries [1]. The roughness of surfaces is considered as an essential parameter in many industries because it is an indication of the surface quality of the machined parts [2]. The efficiency of the machining processes can be improved by controlling the machining conditions such as cutting speed, depth of cut, and feed rate. Moreover, surface roughness plays an important role in the appraisal of machining accuracy [3][4][5]. Many researchers studied the effects of the machining parameters on the surface quality of metals, alloys, and composites. Shoba et al. [6] studied the effect of cutting speed, feed, and depth of cut on surface roughness during the turning process of hybrid composites. The results showed the optimum parameters that give minimum surface roughness. Suresh et al. [7] proposed a prediction model for surface roughness after turning operation of mild steel. The response surface methodology was used to determine the factors affecting the process. Davim [8] reported that, the cutting speed has the most significant effect on roughness followed by the feed rate, while the depth of cut has a slight influence on surface roughness. Gouveiaet et al. [9] examined the machining process of duplex stainless steel. The results determined the advantages of various tools based on coating Cylindrical samples of commercially pure copper (99.5% purity) with an initial diameter of 30 mm and length of 200 mm were used. Each bar was cut into five samples for orthogonal machining by turning operation. The samples were classified according to the studying conditions into three groups A, B, and C. The turning operation was carried out at different conditions by using a center lathe machine. The tool geometry has the following specifications: nose radius 1.15 mm, approach angle 40°, clearance angle 7°, and back rake angle −5°. The longitudinal and face turning with similar conditions for each sample were conducted. Table 1 shows the cutting parameters and work piece samples used in the study. Cylindrical samples of commercially pure copper (99.5% purity) with an initial diameter of 30 mm and length of 200 mm were used. Each bar was cut into five samples for orthogonal machining by turning operation. The samples were classified according to the studying conditions into three groups A, B, and C. The turning operation was carried out at different conditions by using a center lathe machine. The tool geometry has the following specifications: nose radius 1.15 mm, approach angle 40°, clearance angle 7°, and back rake angle −5°. The longitudinal and face turning with similar conditions for each sample were conducted. Table 1 shows the cutting parameters and work piece samples used in the study. Cylindrical samples of commercially pure copper (99.5% purity) with an initial diameter of 30 mm and length of 200 mm were used. Each bar was cut into five samples for orthogonal machining by turning operation. The samples were classified according to the studying conditions into three groups A, B, and C. The turning operation was carried out at different conditions by using a center lathe machine. The tool geometry has the following specifications: nose radius 1.15 mm, approach angle 40°, clearance angle 7°, and back rake angle −5°. The longitudinal and face turning with similar conditions for each sample were conducted. Table 1 shows the cutting parameters and work piece samples used in the study. Cylindrical samples of commercially pure copper (99.5% purity) with an initial diameter of 30 mm and length of 200 mm were used. Each bar was cut into five samples for orthogonal machining by turning operation. The samples were classified according to the studying conditions into three groups A, B, and C. The turning operation was carried out at different conditions by using a center lathe machine. The tool geometry has the following specifications: nose radius 1.15 mm, approach angle 40°, clearance angle 7°, and back rake angle −5°. The longitudinal and face turning with similar conditions for each sample were conducted. Table 1 shows the cutting parameters and work piece samples used in the study. Cylindrical samples of commercially pure copper (99.5% purity) with an initial diameter of 30 mm and length of 200 mm were used. Each bar was cut into five samples for orthogonal machining by turning operation. The samples were classified according to the studying conditions into three groups A, B, and C. The turning operation was carried out at different conditions by using a center lathe machine. The tool geometry has the following specifications: nose radius 1.15 mm, approach angle 40°, clearance angle 7°, and back rake angle −5°. The longitudinal and face turning with similar conditions for each sample were conducted. Table 1 shows the cutting parameters and work piece samples used in the study.

Surface Roughness Measurement
An optical profiling system made by (Contour GT-K1, Bruker, Billerica, MA, USA) working by interferometry technique was used to measure the surface roughness after turning operation. The setup of roughness measurement is shown in Figure 1. lathe machine. The tool geometry has the following specifications: nose radius 1.15 mm, approach angle 40°, clearance angle 7°, and back rake angle −5°. The longitudinal and face turning with similar conditions for each sample were conducted. Table 1 shows the cutting parameters and work piece samples used in the study.

Surface Roughness Measurement
An optical profiling system made by (Contour GT-K1, Bruker, Billerica, MA, USA) working by interferometry technique was used to measure the surface roughness after turning operation. The setup of roughness measurement is shown in Figure 1.

Finite Element Model
The correlation between the cutting parameters and stress was implemented through a simulation approach. The Von-Mises theory (maximum distortion energy theory) was applied to determine the maximum stress during turning operation at different cutting conditions. Von-Mises theory proposes for the ductile materials that the yield stress begins when the stress reaches a certain limit [27]. It is considered that the removal (separation) of the material during the machining operations behaves similarly. The finite element method (FE) was applied to simulate the process by using the software package (ABAQUS/Explicit). A discrete rigid form was proposed to model the

Finite Element Model
The correlation between the cutting parameters and stress was implemented through a simulation approach. The Von-Mises theory (maximum distortion energy theory) was applied to determine the maximum stress during turning operation at different cutting conditions. Von-Mises theory proposes for the ductile materials that the yield stress begins when the stress reaches a certain limit [27]. It is considered that the removal (separation) of the material during the machining operations behaves similarly. The finite element method (FE) was applied to simulate the process by using the software package (ABAQUS/Explicit). A discrete rigid form was proposed to model the cutting tool which movement was represented by the movement of a single node, identified as a rigid body reference node. The cutting tool was meshed with (R3D4) elements. The number of elements and nodes of the cutting tool were 589 and 591 respectively. Consequently, the work piece of pure copper (12 mm in length and 4 mm in height) was modeled as a deformable solid extrude and meshed with 3D stress element type of reduced integration (C3D8R) elements [27,28]. The number of elements and nodes used for the workpiece were 4400 and 9246 respectively. The model for single point orthogonal cutting is shown in Figure 2. Coulomb friction was assumed between the cutting tool and workpiece, with a coefficient µ = 0.2. cutting tool which movement was represented by the movement of a single node, identified as a rigid body reference node. The cutting tool was meshed with (R3D4) elements. The number of elements and nodes of the cutting tool were 589 and 591 respectively. Consequently, the work piece of pure copper (12 mm in length and 4 mm in height) was modeled as a deformable solid extrude and meshed with 3D stress element type of reduced integration (C3D8R) elements [27,28]. The number of elements and nodes used for the workpiece were 4400 and 9246 respectively. The model for single point orthogonal cutting is shown in Figure 2. Coulomb friction was assumed between the cutting tool and workpiece, with a coefficient µ = 0.2.

Material Properties for Modeling
Throughout the study, the pure copper was considered as an elastoplastic object. The mechanical properties of the material are shown in Table 2.

Material Modeling
In metal cutting processes, the material undergoes rapid elastoplastic deformation under severe and harsh conditions. In order to give acceptable results the material model must be able to explain the deformation behavior such as hardening and softening over great ranges of strain, strain rate and temperature [30]. Johnson-Cook constitutive material model is the common model for describing the thermo-visco-plastic behavior of the material during the cutting process [31]. Johnson-Cook model [32] gives the flow stress as a function of strain, strain-rate, and temperature as shown in Equation (1):

Material Properties for Modeling
Throughout the study, the pure copper was considered as an elastoplastic object. The mechanical properties of the material are shown in Table 2.

Material Modeling
In metal cutting processes, the material undergoes rapid elastoplastic deformation under severe and harsh conditions. In order to give acceptable results the material model must be able to explain the deformation behavior such as hardening and softening over great ranges of strain, strain rate and temperature [30]. Johnson-Cook constitutive material model is the common model for describing the thermo-visco-plastic behavior of the material during the cutting process [31]. Johnson-Cook model [32] gives the flow stress as a function of strain, strain-rate, and temperature as shown in Equation (1): where: Table 3 shows the values of the five constants of pure copper. In ABAQUS/Explicit, the cumulative Johnson-Cook damage is considered the dynamic shear failure model. This was previously used by Agmell [33] and Zouhar [34] for the chip/workpiece separation in the orthogonal cutting simulation. For Johnson-Cook damage formula, the strain at failure is given as follows: Depending on the variables (σ* = σ m / σ, (  Table 3 shows the values of the five constants of pure copper. In ABAQUS/Explicit, the cumulative Johnson-Cook damage is considered the dynamic shear failure model. This was previously used by Agmell [33] and Zouhar [34] for the chip/workpiece separation in the orthogonal cutting simulation. For Johnson-Cook damage formula, the strain at failure is given as follows: Depending on the variables (σ* = σm/ , (έ*), T*), the dimensionless pressure-stress ratio is defined as σ* = σm/ . where: σm-average of the three normal stresses, -Von-Mises equivalent stress. The dimensionless strain rate, έ* and homologous temperature, T*, are identical to those used in Equation (1). Table 4 displays the values of the five material constants (D1, D2, D3, D4, and D5). The failure model is based on the calculation of damage parameter D, which is defined by the following equation: The damage parameter (D) is continuously updated in every FEA solving step. When (D) exceeds unity, the elements are supposed to fail and then discarded [35]. The tensile test data in a typical stress-strain curve with progressive damage degradation are shown in Figure 3. This curve consists of three zones. The first zone (oa) represents the linear elastic deformation stage. When the stress increased and exceeds the yield stress σ o the material passes in the second zone (ab), at which material experiences stable plastic deformation. In this stage, the effect of strain hardening is dominated. When the damage parameter (D) equals to zero (at point b), the plastic instability starts and the material transfers to the third stage (bd). Afterward, the stage of failure (damage evolution region) initiates and the thermal effect softens the material. Therefore, the equivalent stress decreases. When the stress-strain curve approaches to point (d) the damage parameter (D) equals to unity. At  Table 3 shows the values of the five constants of pure copper. In ABAQUS/Explicit, the cumulative Johnson-Cook damage is considered the dynamic she failure model. This was previously used by Agmell [33] and Zouhar [34] for the chip/workpie separation in the orthogonal cutting simulation. For Johnson-Cook damage formula, the strain failure is given as follows: Depending on the variables (σ* = σm/ , (έ*), T*), the dimensionless pressure-stress ratio is defin as σ* = σm/ . where: σm-average of the three normal stresses, -Von-Mises equivalent stress. The dimensionless strain rate, έ* and homologous temperature, T are identical to those used in Equation (1). Table 4 displays the values of the five material constan (D1, D2, D3, D4, and D5). The failure model is based on the calculation of damage parameter D, which is defined by t following equation: The damage parameter (D) is continuously updated in every FEA solving step. When ( exceeds unity, the elements are supposed to fail and then discarded [35]. The tensile test data in typical stress-strain curve with progressive damage degradation are shown in Figure 3. This cur consists of three zones. The first zone (oa) represents the linear elastic deformation stage. When t stress increased and exceeds the yield stress σ o the material passes in the second zone (ab), at whi material experiences stable plastic deformation. In this stage, the effect of strain hardening and homologous temperature, T*, are identical to those used in Equation (1). Table 4 displays the values of the five material constants (D 1 , D 2 , D 3 , D 4 , and D 5 ). Table 4. Johnson-Cook damage model parameters for copper [32].
The failure model is based on the calculation of damage parameter D, which is defined by the following equation: The damage parameter (D) is continuously updated in every FEA solving step. When (D) exceeds unity, the elements are supposed to fail and then discarded [35]. The tensile test data in a typical stress-strain curve with progressive damage degradation are shown in Figure 3. This curve consists of three zones. The first zone (oa) represents the linear elastic deformation stage. When the stress increased and exceeds the yield stress σ o the material passes in the second zone (ab), at which material experiences stable plastic deformation. In this stage, the effect of strain hardening is dominated. When the damage parameter (D) equals to zero (at point b), the plastic instability starts and the material transfers to the third stage (bd). Afterward, the stage of failure (damage evolution region) initiates and the thermal effect softens the material. Therefore, the equivalent stress decreases. When the stress-strain curve approaches to point (d) the damage parameter (D) equals to unity. At that point, the stiffness of the material is completely degraded and the crack initiates as an indication of failure [35][36][37][38][39].

Von-Mises Stress Criterion
Generally, Von Mises stress (σV.M.) is used for ductile materials to estimate the yield criteria. Von-Mises stress formula in three dimensions is as follows [40]: where: σ1, σ2, and σ3-principal stresses.
In the case of plane stress, σ3 is zero and the equation can be defined in terms of two principle stresses as follows [35]: A schematic illustration of the distortion energy in-plane stress is shown in Figure 4.
In the case of plane stress, σ 3 is zero and the equation can be defined in terms of two principle stresses as follows [35]: A schematic illustration of the distortion energy in-plane stress is shown in Figure 4. In the case of plane stress, σ3 is zero and the equation can be defined in terms of two principle stresses as follows [35]: A schematic illustration of the distortion energy in-plane stress is shown in Figure 4.

Microscopic Observations and Surface Roughness Results
Scanning Electron Microscope (SEM) was used to investigate the micrograph of the machined surface of copper samples. The surface variations at different cutting speeds are shown in Figure 5.

Microscopic Observations and Surface Roughness Results
Scanning Electron Microscope (SEM) was used to investigate the micrograph of the machined surface of copper samples. The surface variations at different cutting speeds are shown in Figure 5. In Figure 5a, at a cutting speed of 500 rpm, the surface has grooves and ridges parallel to the machining direction. This indicates a high roughness of the surface. At the higher cutting speed of 1000 rpm, the ridges become narrower indicating an improvement of surface roughness as shown in Figure 5b. A smoother surface is observed in Figure 5c at a high cutting speed of 1500 rpm. The results are consistent with the previous researchers that showed better surface finish at higher cutting speeds. For more investigation, the surface roughness of copper samples was determined based on single acquisition and stitching measurement. Figures 6-8 show the 2D and 3D surface textures of copper samples. The surface roughness parameters of at low, medium and high cutting speeds were also determined.
The roughness was also assessed in terms of Ra, Rp, Rq, Rt, and Rv parameters to evaluate the surface quality after orthogonal cutting by turning operation [41]. The variations of roughness parameters as a function of the cutting speed at constant feed rate and depth of cut are displayed in Figure 9. In Figure 5a, at a cutting speed of 500 rpm, the surface has grooves and ridges parallel to the machining direction. This indicates a high roughness of the surface. At the higher cutting speed of 1000 rpm, the ridges become narrower indicating an improvement of surface roughness as shown in Figure 5b. A smoother surface is observed in Figure 5c at a high cutting speed of 1500 rpm. The results are consistent with the previous researchers that showed better surface finish at higher cutting speeds. For more investigation, the surface roughness of copper samples was determined based on single acquisition and stitching measurement. Figures 6-8 show the 2D and 3D surface textures of copper samples. The surface roughness parameters of at low, medium and high cutting speeds were also determined.
The roughness was also assessed in terms of R a , R p , R q , R t , and R v parameters to evaluate the surface quality after orthogonal cutting by turning operation [41]. The variations of roughness parameters as a function of the cutting speed at constant feed rate and depth of cut are displayed in Figure 9.
single acquisition and stitching measurement. Figures 6-8 show the 2D and 3D surface textures of copper samples. The surface roughness parameters of at low, medium and high cutting speeds were also determined.
The roughness was also assessed in terms of Ra, Rp, Rq, Rt, and Rv parameters to evaluate the surface quality after orthogonal cutting by turning operation [41]. The variations of roughness parameters as a function of the cutting speed at constant feed rate and depth of cut are displayed in Figure 9. It can be noticed that at a low cutting speed (500 rpm) the highest Ra and Rt values were 2.056 µm and 63.739 µm respectively. At the medium cutting speed of 1000 rpm, the highest Ra and Rt were 2.170 µm and 66.822 µm respectively. At the high cutting speed of 1500 rpm, the highest Ra value was 2.174 µm and the Rt was 54.893 µm. Hence, for the machined samples, both 2D and 3D surface textures gave a reasonable comparison and correlation between surface roughness and cutting speed. The values of Ra and Rq are almost constant for all cutting speeds. It can be interpreted that as the cutting speed increases, the temperature in the cutting zone increases and the diffusion rate of the material increases accordingly. The generated hardened chip due to the machining process slides on It can be noticed that at a low cutting speed (500 rpm) the highest R a and R t values were 2.056 µm and 63.739 µm respectively. At the medium cutting speed of 1000 rpm, the highest R a and R t were 2.170 µm and 66.822 µm respectively. At the high cutting speed of 1500 rpm, the highest Ra value was 2.174 µm and the R t was 54.893 µm. Hence, for the machined samples, both 2D and 3D surface textures gave a reasonable comparison and correlation between surface roughness and cutting speed. The values of R a and R q are almost constant for all cutting speeds. It can be interpreted that as the cutting speed increases, the temperature in the cutting zone increases and the diffusion rate of the material increases accordingly. The generated hardened chip due to the machining process slides on the tool surface. Then slight particles are detached from the tool and adhere to the machined surface making it rougher. This is consistent with the results of Biermann and Hollmann [42] who discussed the thermal influences in machining and cutting processes.

Results of Simulation Model
One of the most important objectives of the current work is to minimize the Von Mises stresses in terms of the cutting parameters. The simulation model that generated by finite element analysis was employed to evaluate the influence of machining conditions on Von-Mises plane stress (σV.M.). Here, the response surface method (RSM) was applied to visualize the simultaneous and interaction effects of both cutting speed and feed rate on Von-Mises stress as shown in Figure 10. Originally, RSM was established to model the experimental response. The application of RSM is aimed at reducing the cost of expensive analysis methods and giving accurate results. Furthermore, RSM

Results of Simulation Model
One of the most important objectives of the current work is to minimize the Von Mises stresses in terms of the cutting parameters. The simulation model that generated by finite element analysis was employed to evaluate the influence of machining conditions on Von-Mises plane stress (σ V.M. ). Here, the response surface method (RSM) was applied to visualize the simultaneous and interaction effects of both cutting speed and feed rate on Von-Mises stress as shown in Figure 10. Originally, RSM was established to model the experimental response. The application of RSM is aimed at reducing the cost of expensive analysis methods and giving accurate results. Furthermore, RSM reduces the effects of noise and allows using derivative-based algorithms. It can be noticed that Von-Mises stress (σ V.M. ) decreases with increasing the cutting speed for all feed rate values. This can be explained as follows: at higher cutting speed the temperature of work piece raises in the cutting region. Therefore, the material softening increases and lower stress value is observed [42,43]. It is also clear that Von-Mises stress (σ V.M. ) increases with increasing the feed rate. However, the combined effect of cutting speed and feed rate is more significant on the stress variation [44]. On the other hand, the tool-chip /tool workpiece interactions also affect the stress during the cutting process [45]. Increasing the feed rate means shorter contact period between the tool and workpiece. Consequently, the contact area decreases and this leads to an increase in the normal stress. Furthermore, a plastic deformation occurs in the deformation zone (shown in Figure 2a). This zone has an essential effect on the penetration depth of the plastic deformation of the workpiece due to the lack of strain hardening. reduces the effects of noise and allows using derivative-based algorithms. It can be noticed that Von-Mises stress (σV.M.) decreases with increasing the cutting speed for all feed rate values. This can be explained as follows: at higher cutting speed the temperature of work piece raises in the cutting region. Therefore, the material softening increases and lower stress value is observed [42,43]. It is also clear that Von-Mises stress (σV.M.) increases with increasing the feed rate. However, the combined effect of cutting speed and feed rate is more significant on the stress variation [44]. On the other hand, the tool-chip /tool workpiece interactions also affect the stress during the cutting process [45]. Increasing the feed rate means shorter contact period between the tool and workpiece. Consequently, the contact area decreases and this leads to an increase in the normal stress. Furthermore, a plastic deformation occurs in the deformation zone (shown in Figure 2a). This zone has an essential effect on the penetration depth of the plastic deformation of the workpiece due to the lack of strain hardening. It became clear that Von-Mises stresses are affected by the interaction of both cutting speed and feed rate rather than the effect of the individual parameter. Table 5 summarizes the obtained optimum results for Von-Mises stress in terms of the cutting speed and feed rate.  It became clear that Von-Mises stresses are affected by the interaction of both cutting speed and feed rate rather than the effect of the individual parameter. Table 5 summarizes the obtained optimum results for Von-Mises stress in terms of the cutting speed and feed rate.  Figure 11 displays an example of Von-Mises stress distribution along the work piece during orthogonal cutting for two selected conditions. Figure 11a shows the stress distribution at the low cutting speed of 500 rpm and high feed rate of 0.5 mm/rev, while Figure 11b shows the stress distribution at high cutting speed of 1500 rpm and low feed rate of 0.15 mm/rev. It is observed that the stress is higher at low cutting speed and high feed rate than that at high cutting speed and low feed rate. This result matches with the experimental results obtained by profiling system and shown in Figure 9.

Conclusions
In this work, the influence of machining parameters on the surface roughness of pure copper was investigated. Finite element analysis (FEA) was applied to simulate and determine a correlation between the roughness parameters and stress of the material by using Von-Mises theory. A modern non-contacting (optical) technique using light interferometry system was used successfully to measure and display the surface roughness and surface texture of pure copper after turning operation at various cutting conditions. The results provided the surface parameters in terms of Ra, Rq, Rt, and Rp. At higher cutting speed, the surface roughness enhanced in terms of some parameters. For Rt parameter, an enhancement of ~14% in surface roughness was observed. However, the Ra and Rq parameters remained constant with increasing the cutting speed. For good surface roughness, it can Tool Workpiece Tool Workpiece Figure 11. Von-Mises stress distribution in orthogonal cutting at two cutting conditions.

Conclusions
In this work, the influence of machining parameters on the surface roughness of pure copper was investigated. Finite element analysis (FEA) was applied to simulate and determine a correlation between the roughness parameters and stress of the material by using Von-Mises theory. A modern non-contacting (optical) technique using light interferometry system was used successfully to measure and display the surface roughness and surface texture of pure copper after turning operation at various cutting conditions. The results provided the surface parameters in terms of R a , R q , R t , and R p . At higher cutting speed, the surface roughness enhanced in terms of some parameters. For R t parameter, an enhancement of~14% in surface roughness was observed. However, the R a and R q parameters remained constant with increasing the cutting speed. For good surface roughness, it can be recommended that turning operation on pure copper is to be conducted at cutting speed higher than 1000 rpm but at a feed rate up to 0.2 mm/rev and depth of cut less than 0.5 mm. The SEM images showed the better surface quality of copper at high cutting speed rather than lower speeds and this validates the obtained experimental and numerical results. The finite element (FE) model and surface roughness methodology are suitable and accurate for correlating and visualizing the machining conditions and the maximum value of Von-Mises stress and can be applied to similar materials. Furthermore, a good agreement was observed between experimental and analytical results.