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PROOF COPY [JMNM-14-1032]

Jing Shi1AQ1Mem. ASME

Department of Industrial and

Manufacturing Engineering,

North Dakota State University,

Dept. 2485, PO Box 6050,

Fargo, ND 58108

e-mail: Jing.shi@ndsu.edu

Chunhui JiAQ2School of Mechanical Engineering,

Tianjin University,

Nankai District,

Tianjin �, China

e-mail: ji_chunhui_love@126.com

Yachao WangDepartment of Industrial and

Manufacturing Engineering,

North Dakota State University,

Dept. 2485, PO Box 6050,

Fargo, ND 58108

e-mail: yachao.wang@my.ndsu.edu

Steve Hsueh-Ming WangDepartment of Engineering Science

Project Management,

University of Alaska Anchorage,

Anchorage, AK 99508

e-mail: hswang@uaa.alaska.edu

Tool/Chip Interfacial Friction1 Analysis in Atomistic Machining2 of Polycrystalline Coppers3

4 Three-dimensional (3D) molecular dynamics (MD) simulation is performed to study thetool/chip interface friction phenomenon in machining of polycrystalline copper at atomis-tic scale. Three polycrystalline copper structures with the equivalent grain sizes of 12.25,7.72, and 6.26 nm are constructed for simulation. Also, a monocrystalline copper struc-ture is simulated as the benchmark case. Besides the grain size, the effects of depth ofcut, cutting speed, and tool rake angle are also considered. It is found that the frictionforce and normal force distributions along the tool/chip interface in both polycrystallineand monocrystalline machining exhibit similar patterns. The reduction in grain size over-all increases the magnitude of normal force along the tool/chip interface, but the normalforces in all polycrystalline cases are smaller than that in the monocrystalline case. Inatomistic machining of polycrystalline coppers, the increase of depth of cut consistentlyincreases the normal force along the entire contact area, but this trend cannot beobserved for the friction force. In addition, both higher cutting speed and more negativetool rake angle do not bring significant changes to the distributions of normal and fric-tion forces on the interface, but both factors tend to increase the magnitudes of the twoforce components. [DOI: 10.1115/1.4028025]

5 Introduction

6 With the miniaturization of precision components, the develop-7 ment of MEMS/NEMS devices and the availability of new instru-8 ments such as atomic force microscope (AFM), tool based9 machining at nanoscale need to be investigated. The interfacial

10 interaction between the tool and chip is a critical issue for any11 machining processes. The characteristics of nanoscale friction12 were first reported by Mate et al. [1] in AFM surface measure-13 ment, and the experiment clearly demonstrated the nanoscale14 stick-slip phenomenon. To date, researchers have made significant15 efforts to clarify the atomic-scale friction mechanism using the16 AFM, and some valuable results have been reported [2–6].17 MD simulation is a simulation methodology built on the classi-18 cal Newton’s second law, and it is well suited to complement the19 modern nanoscale experimental techniques such as AFM meas-20 urements [7]. MD simulation has been adopted for investigating21 the indentation, adhesion, fracture, and machining at nano and at-22 omistic scales [8–11]. It provides the in situ analysis capability23 that many experimental approaches are lacking of. Ikawa et al.24 [12] and Shimada [13] simulated the 2D nanometric cutting of25 copper with a diamond tool to investigate the effect of tool edge26 radius and depth of cut on the chip formation process and surface27 deformation. Belak et al. [14] used this simulation approach to28 study the orthogonal cutting of copper with a rigid tool using the29 embedded-atom method (EAM) as the potential energy formula-30 tion. Belak [15] also investigated the machining of silicon using a31 deformable diamond tool at 540 m/s and reported that the silicon

32in the chip and the first few layers of the newly cut surface33appeared amorphous. Furthermore, the nanowear characteristics34and silicon surface such as material transfer, structure transfer,35and stick-slip behaviors were revealed by the MD simulations.36Isono and Tanaka [16,17] carried out a 3D analysis of the effects37of temperature, machinability, and interatomic force on nickel38metal. Shi et al. [18] simulated the surface creation in nanoma-39chining by multiple-groove cutting under the common 3D40machining configuration. The effects of various cutting parame-41ters were investigated. It was also found that the stress distribu-42tions of nanomachining actually resemble those of conventional43machining. Wang et al. [19] recently analyzed the formed residual44stress in monocrystal silicon in atomistic machining. It was found45that large negative rake angles and depths of cut induce more46significant phase transformation and more compressive in-depth47residual stress distribution.48For the friction analysis in nanoscale machining, the common49approach adopted by most existing literature regards the tangential50cutting force as the friction force and the thrust cutting force as51the normal force, and the overall coefficient of resistance (or52friction) is computed as the ratio of cutting force to thrust force.53Maekawa and Itoh [20] carried out an MD simulation study to54investigate the friction phenomenon between the single crystal55copper and a diamond cutting tool. The results showed that the56chip thickness and tool/chip contact length became larger with57the increase of bond energy at the interface, and this in turn led to58the increase of system temperature and cutting forces. Shimizu59et al. [10] analyzed the friction behavior in nanomachining of60monocrystalline copper by MD simulation, and the results con-61firmed the existence of the stick-slip phenomenon in nanomachin-62ing. The average friction coefficient was reported to vary from 0.563to 5, while the maximum friction coefficient varied from 4 to 1964depending on the spring force of the system and spring constant.

1Corresponding author.Contributed by the Manufacturing Engineering Division of ASME for publication

in the JOURNAL OF MICRO- AND NANO-MANUFACTURING. Manuscript received April 16,2014; final manuscript received July 14, 2014; published online xx xx, xxxx. Assoc.Editor: Hongqiang Chen.

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65 Shen and Sun [21] examined the atomic-scale friction behavior of66 an infinite flat–flat contact between copper and the diamond sur-67 face, and suggested that the friction behaviors were independent68 of the sliding velocity in the wearless sliding regime. Yang and69 Komvopoulos [22] investigated the effects of velocity and tool tip70 geometry on sliding friction. It was found that the frictional force71 increased from 20 to 30 nN as the sliding velocity increased from72 1 to 100 m/s. Ye et al. [23] analyzed the mechanism of material73 removal, chip formation, and friction in the nanometric machining74 of monocrystalline copper. The overall coefficient of friction,75 being equal to the ratio of the cutting force to the thrust force, was76 reported to be 0.64. Fang and Weng [24] proposed 3D MD simu-77 lations to study the effects of tool geometry and processing resist-78 ance on the atomic-scale cutting mechanism. The coefficient of79 resistance, namely, the ratio of the cutting force to the thrust force,80 was found to vary from 0.4 to 1.2 as the half-conic angle of pin81 tool changed from 15 deg to 75 deg. Until recently, the research82 effort was progressed to investigate the detailed tool/chip interac-83 tion along the interface. Ji et al. [25] modeled the atomistic84 machining process of monocrystalline copper with MD simula-85 tion. The analysis of tool/chip interface revealed that the distribu-86 tion patterns of friction force and normal force are actually more87 complicated than those classical friction models developed for88 macromachining.89 Most existing literature on MD simulation of machining usually90 adopts monocrystalline materials as the work material [26]91 because they are much easier to be modeled in simulation. This92 practice is not consistent with the fact that the majority of crystal-93 line materials are in the form of polycrystalline structures. To94 address this, Shi et al. [27] investigated how the grain size impacts95 the machining performance at atomistic level and found that sig-96 nificant smaller forces were required to cut the copper workpiece97 with the increase of grain size. Meantime, Shi and Verma [28]98 compared the machining performance in machining of a polycrys-99 talline and a monocrystalline copper structure using MD method.

100 It was found that smaller cutting forces are required to machine101 the polycrystalline than the monocrystalline structure for all con-102 ditions investigated.103 In this research, the tool/chip interface friction in atomistic104 machining of polycrystalline copper structures is investigated, and105 the effect of grain size on friction is revealed. Meanwhile, the106 effects of machining parameters, such as depth of cut and cutting107 speed in polycrystalline machining, are also studied.

108 MD Simulation Methodology

109 Model Construction. Figure 1 shows a schematic of the MD110 model for atomistic orthogonal machining of polycrystalline111 copper. The work material is of copper structure and divided112 into three different zones, namely, boundary layer, thermostat113 layer, and Newtonian layer [27,28]. The boundary atoms are114 fixed in position to hold the structure of the bulk system. The115 thermostat atoms are arranged to surround the Newtonian atoms116 to make the boundary temperature close to environment temper-117 ature. The periodic boundary conditions [29] are applied in the118 transverse (Z) direction to reduce the boundary effect. The dia-119 mond cutting tool is assumed to be infinitely rigid such that the120 relative positions between tool atoms are unchanged during the121 machining process. The workpieces for all cases have the identi-122 cal dimension of 39.6� 21.6� 18.0 nm3, which consists of123 1,247,591–1,290,253 atoms depending on the grain size of the124 polycrystalline structures and 1,320,000 atoms for the monocrys-125 talline structure. Three polycrystalline structures with different126 average equivalent diameters (12.25 nm, 7.72 nm, and 6.26 nm)127 are generated, and the corresponding structures consist of 8, 64,128 and 120 grains, respectively.129 For the interaction between copper atoms, the EAM potential130 [30] can describe well the energies and geometries, which is a131 multibody potential energy function in the following form:

Etot ¼1

2

Xi;j

Uij rij

� �þX

i

Fi �qið Þ (1)

132where Uij is the short-range pair-interaction energy between atoms133i and j, describing the electrostatic contributions, Fi is the embed-134ding energy of atom I, and �qi is the host electron density at site i135induced by all other atoms in the system. The related EAM poten-136tial parameter values are shown in Table 1.137Morse potential [31,32] is used to describe the interactions138between copper atoms and carbons of the diamond cutting tool,

u rij

� �¼ D e�2aðrij�r0Þ � 2e�aðrij�r0Þ

n o(2)

139where D is the cohesion energy, a is the elastic modulus, rij is the140distance between the jth copper atom and the ith carbon atom in141the cutting tool, and r0 is the atom distance at equilibrium. The142parameters for the Morse potential between copper–carbon143atoms are: D¼ 0.1 eV, a¼ 1.70� 10�10 m�1, r0¼ 2.22� 10�10 m144[31,32].145In this work, Gear’s predictor–corrector method is adopted to146simulate the positions, velocities and accelerations of atoms under147displacement conditions [29]. Both truncated radius method and148Verlet’s neighbor lists are applied to reduce the computation bur-149den. The first relaxation phase is completed with 4000 times steps150by controlling the bulk temperature at 300 K with an NVT ensem-151ble [31], where N represents the number of particles, V represents152volume, and T represents temperature. Thereafter, the atomistic153machining is simulated by moving the diamond tool by a small154distance toward the negative X-direction at each time step.155Finally, the tool is retracted and another 4000 time steps are simu-156lated for the final relaxation. The time step of 1 fs is used in all157cases. The cutting tool adopts negative rake angles. The cutting158tool is initially placed outside the workpiece. The initial offset dis-159tance, namely the distance between the cutting edge and the work-160piece in X-direction (see Fig. 1), needs to be carefully selected.161The distance depends on the rake angle a and depth of cut d. To

Fig. 1 Schematic of MD simulation model of polycrystallinemachining

Table 1 EAM potential parameters for copper–copper pairinteraction [27,28]

Lattice constant (10�10 m) 3.62Cohesive energy (eV) �3.49Bulk modulus (GPa) 137C0 (GPa) 23.7C44 (GPa) 73.1D(Ebcc�Efcc) (meV) 42.7D(Ehcc�Efcc) (meV) 444.8Stacking fault energy (mJ/m2) 39.5Vacancy: Ef (eV) 1.21

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162 prevent the tool edge from touching the workpiece in the initiali-163 zation process, the offset distance is set slightly larger than164 d� tana.

165 Normal and Friction Forces Along Tool/Chip Interface. The166 interaction between the formed chip and tool rake face is critical167 to the formation of chip morphology, cutting forces, and other168 phenomena observed in machining. As mentioned above, it has169 not been well addressed by the existing literature on nanometric170 or atomistic machining. Most only consider the total friction effect171 in nanomachining or nanoscratching by regarding the total force172 in the tool movement direction as the friction force. However, that173 is too simplified to reveal the interaction along the tool/chip inter-174 face. In our study, the friction behaviors on tool rake face are175 determined by only considering the cutting forces exerted on the176 tool/chip interface using a two-step approach. First, the atoms in a177 thin surface layer of tool rake face are divided into multiple178 groups. To accurately calculate the force along the tool/chip inter-179 face during the atomistic machining process, the length of groups180 should be as small as possible, for example, L1 is kept at 0.4 nm181 (slightly larger than one C-lattice constant of 0.3567 nm), and L2

182 is kept at 0.8 nm, as shown in Fig. 2.183 The force (denoted as Fm) of the mth group can be calculated184 by adding up the forces of individual atoms in the group, which185 are the direct outputs of MD simulation. Second, the friction and186 normal force on the rake face of each group can be evaluated187 according to the tangential and normal cutting force of the same188 group. Meanwhile, the total cutting force along the interface can189 be obtained by adding up the force components of all groups in190 different axial directions. To calculate the action force Fm of the191 mth atom group, the individual interaction force acting on the car-192 bon atom i in the tool due to the surrounding copper atom j in the193 material should be computed first by differentiating the potential194 energy, and then the action force Fm can be obtained by summing195 all the interaction forces on the tool atoms of the mth group

Fm ¼Xn

i¼1

Xj

@uðrijÞ@rij

(3)

196 where Fm is the cutting force of the mth group, n is the quantity of197 atoms in the diamond tool of mth group. The action force Fm in198 vector form can be obtained by summing all the interaction forces199 on the tool atoms of the mth group.AQ3 For each carbon atom, the200 reaction forces should also be summed up among its neighbor201 atoms, the truncated radius method [29] is employed to reduce the202 calculation time.203 Then, the total cutting forces of all groups along the interface204 can be obtained by following equations:

FTx ¼XM

m¼1

Fmx (4)

FTy ¼XM

m¼1

Fmy (5)

205where M is the quantity of groups at the tool/chip interface, Fmx

206and Fmy are the tangential and thrust cutting force of the mth207group, respectively.208In this work, we investigate the stress distributions including209the friction and normal forces along the tool/chip interface by210computing the cutting forces of each atom group defined along the211tool/chip interface. It should be noted that the force profiles are212equivalent to the stress profiles since the contact area of each213atom group is identical. The positive directions of the friction and214normal force are shown in Fig. 2. The friction force s and the nor-215mal force rn generated by the mth group can be obtained by the216following equations:

s ¼ Fmy cosð�aÞ � Fmx cosð90 degþ aÞ (6)

rn ¼ Fmy sinð�aÞ þ Fmx sinð90 degþ aÞ (7)

217where Fmx and Fmy are the tangential and normal forces of the mth218group, respectively.

219Cutting Conditions for Atomistic Machining Simulation. To220study the effect of machining parameters on the tool/chip interfa-221cial friction, 14 cutting conditions are selected for MD simulation.222The machining parameters of these cutting conditions are sum-223marized in Table 2. By comparing cases C1–C4, the effect of dif-224ferent copper structures can be revealed. By comparing cases C3,225C5, C6, and C9, insights about the role of depth of cut in machin-226ing polycrystalline coppers can be obtained. Also, the effect of227cutting speed can be analyzed by comparing cases C5 and C7, and228the effect of tool rake angle can be illustrated by comparing cases229C3 and C8.

230Results and Discussion

231Chip Formation. The snapshots of cases C1 and C3 are shown232in Figs. 3 and 4, respectively. For the purpose of brevity, the233machining processes for other cutting conditions are not provided234here. It can be seen that there are pronounced differences among235the results while cutting different copper structures. This indicates236that the copper structure affects the chip formation and subsurface237deformation of the machined surface. This can be attributed to the238change of dominant deformation mode from dislocation move-239ment to other mechanisms such as grain boundary sliding [27,28].240By measuring the contact length of tool/chip shown in the sim-241ulation snapshots for cases C1–C6, the comparison can be made242in Fig. 5. It can be observed that the contact length of tool/chip243interface (at the tool travel distance of 25 nm) increases with the244increase of the grain size, as well as depth of cut.

245Total Cutting Forces. The total cutting forces of all atom246groups along the tool/chip interface during the cutting processes247are obtained. The tangential and thrust forces are the two248force components of interest in the orthogonal machining.249Figures 6(a)–6(d) show the evolution of the two force components250during the atomistic machining processes for cases C1–C4,251respectively. The results from machining both polycrystalline and252monocrystalline structures reveal the similar stick-slip phenomena253as reported by Shimizu et al. [10]. Also, the ratio of tangential254force and thrust force in cutting processes mostly varied from 0.7255to 1.85.256It can be seen that the total cutting forces vary to a great extent257for different copper structures. The average cutting forces are

Fig. 2 Tool atom grouping on rake face for obtaining normaland friction stress distributions

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258 obtained by averaging the fluctuating force values in the relatively259 stable cutting stage, and the results are shown in Fig. 7. As the260 grain size decreases from 12.25 nm to 6.26 nm, both the average261 thrust and tangential forces decrease substantially. The similar262 phenomenon was obtained by Shi et al. [27] while analyzing the263 cutting force exerted on all the tool atoms by the polycrystalline264 copper atoms. However, the cutting forces in polycrystalline265 machining at cases C2–C3 are all smaller than those in monocrys-266 talline machining. Shi and Verma [28] confirmed that higher cut-267 ting forces are required to machine a monocrystalline structure268 than a polycrystalline structure. It also can be seen that the

269average ratio of tangential force to thrust force decreases from2701.33 to 1.25 with the reduction in grain size.

271Effect of Grain Size on Friction. Figures 8(a) and 8(b),272respectively, show the friction and normal force profiles along the273tool/chip interface under cases C1–C4, when the cutting travel274distance is 25 nm. As mentioned previously, cases C1–C4 have a275monocrystalline structure, and grain sizes of 12.25, 7.72, and2766.26 nm, respectively. It can be seen in Fig. 8(a) that the profiles277of normal forces under cases C1–C4 starts from a peak value near

Table 2 Parameters for atomistic machining conditions

Cutting condition Copper structures Depth of cut (nm) Cutting speed (m/s) Rake angle (deg)

C1 Monocrystalline 2.0 500 �15C2 Polycrystalline (grain size: 12.25 nm) 2.0 500 �15C3 Polycrystalline (grain size: 7.72 nm) 2.0 500 �15C4 Polycrystalline (grain size: 6.26 nm) 2.0 500 �15C5 Polycrystalline (grain size: 7.72 nm) 1.5 500 �15C6 Polycrystalline (grain size: 7.72 nm) 2.5 500 �15C7 Polycrystalline (grain size: 7.72 nm) 1.5 200 �15C8 Polycrystalline (grain size: 7.72 nm) 2.0 500 �30C9 Polycrystalline (grain size: 7.72 nm) 8.0 500 �15

Fig. 3 Snapshots of atomistic machining for case C1 at tool travel distance 5 (a) 15 nm and(b) 25 nm

Fig. 4 Snapshots of atomistic machining for case C3 at tool travel distance 5 (a) 15 nm and(b) 25 nm

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278the tool cutting edge, sharply decreases, and then gradually279decreases to zero at the point where the tool/chip contact no lon-280ger exists. The similar pattern was obtained at macroscale by Usui281and Takeyama [33] in machining of lead with a photoelastic tool282at 0.018 m/min. Also, it can be found that the magnitudes of nor-283mal forces are not significantly dependent on the grain size, but284the reduction in grain size overall decreases the normal force285along the tool/chip interface with only a few exceptions.286Figure 8(b) reveals the friction force profile along the tool/chip287interface. For each case, the friction force starts a negative value288near the cutting edge, increases to the maximum value at a small289distance from the cutting edge, and decreases to zero as the con-290tact between tool and chip ceases to exist. Interestingly, the simi-291lar patterns are found in macromachining results of literature,292such as Baqgchi and Wright [34] in machining of steel tubes with293a single crystal sapphire tool, and Chandrasekaran and Kapoor294[35] in machining of lead with �10 deg rake angle tool at cutting295speed of 0.0254 m/min. In the first atom group of the tool/chip

Fig. 5 Contact length of tool/chip interface, (a) with variousgrain sizes of copper crystal for cases C1–C4 and (b) using dif-ferent depths of cut for cases C5, C3, and C6

Fig. 6 Cutting force evolution for cases (a) C1, (b) C2, (c) C3, and (d) C4

Fig. 7 Average cutting forces for cases C1–C4

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296 interface as shown in Fig. 2, the friction force profiles for the297 monocrystalline and polycrystalline structures all exhibit negative298 values. This is because the material atoms below the cutting tool299 undergo extremely high pressure, the deformed chip atoms near300 the cutting edge have a tendency to move downward along the301 rake face due to the higher compression ahead of the tool. Mean-302 while, in the first section of interface which is close to the cutting303 edge, both the friction and normal forces in monocrystalline304 machining are higher than that in polycrystalline machining.305 Figure 9 shows that the profiles of the friction coefficient are306 also affected by grain size. The overall trends are still similar.307 With the increase of the distance from the cutting edge, the fric-308 tion coefficient steadily increases, reaches the maximum in the309 middle part of the contact length, and then fluctuates around 0.8 to310 the point where tool/chip contact no longer exists.

311 Effect of Depth of Cut on Friction. Figure 10 depicts the312 effect of depth of cut on the normal and friction force distributions313 by comparing cases C5, C3, C6, and C9, which have the depths of314 cut of 1.5, 2.0, 2.5, and 8.0 nm, respectively. In particular, case C9315 is simulated to study the tool/chip force distribution pattern when316 the depth of cut is higher than the average grain size, which is317 7.72 nm in this case. The four cases adopt the identical cutting318 parameters except for the depth of cut. The results are obtained at319 the tool travel distance of 15 nm. It is observed that in general the320 change of depth of cut does not bring significant differences to the321 patterns of normal or friction stress profile. For the normal force322 profiles, the trends are similar, which all exhibit a peak near the323 tool tip, and decrease gradually toward zero at the end of tool/chip324 contact. Meanwhile, the magnitude of normal force over the entire325 contact length increases with the depth of cut. It should be noted326 that the increase of depth of cut to 8 nm does raise the entire pro-327 file of normal force to a much higher level. In terms of friction328 force patterns, the increase of depth of cut makes the friction force329 lower for the initial portion of contact length, while it makes the330 friction force higher for the later portion of tool/chip contact.331 Meanwhile, the increase of depth of cut does not bring significant

332increase to the peak friction force (compared with the normal333force). Therefore, the depth of cut effect is more complicated for334the interfacial friction force. The observation that the friction335force is less sensitive to the change of depth of cut needs to be fur-336ther investigated in the future.337Figure 11 compares the distributions of the friction coefficient338under the three levels of depth of cut. The general trends of fric-339tion coefficient are similar under different depths of cut. The fric-340tion coefficient in the stable stage for all four cases varies in the341range of 0.7–2.0. However, in the first half contact area, the fric-342tion coefficient appears to be higher when a smaller depth of cut is343applied. It should also be noted that when the depth of cut reaches3448.0 nm, the friction coefficient is overall smaller than the other345cases.

346Evolution of Friction With the Progress of Machining.347Figure 12 depicts the friction analysis results at the tool travel dis-348tances of 15, 20, and 25 nm for case C3. It can be observed that349the normal force distributions at all three travel distances follow350the same pattern, but the normal force overall becomes higher

Fig. 8 Tool/chip friction analysis for copper crystals with vari-ous grain sizes, (a) normal force and (b) friction force

Fig. 9 Friction coefficient distributions for copper crystalswith various grain sizes

Fig. 10 Tool/chip stress profiles with four levels of depth ofcut: (a) normal force and (b) friction force

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351 with the progress of machining. Also, the shapes of friction force352 curves are similarly shaped and the magnitudes of friction forces353 near the cutting edge are surprisingly identical. Figure 13 shows354 the friction coefficient distributions along the interface with the355 progress of machining. The shapes of curves of friction coefficient356 distributions are not strongly influenced by the travel distance357 and all reach the maximum at a distance of 4.4 nm from the tool358 cutting edge.

359 Effects of Machining Speed and Tool Rake Angle. Figure 14360 compares the friction behaviors along the tool/chip interface in361 polycrystalline machining for cases C5 and C7, which have the362 cutting speeds of 500 and 200 m/s, respectively. It can be seen363 from Fig. 14(a) that as the cutting speed reduces from 500 to364 200 m/s, the normal force becomes smaller when the distance365 from the cutting edge below 3.6 nm in polycrystalline machining,366 but it reverses the trend beyond that distance. The same observa-367 tion can be made for the friction force profiles in Fig. 14(b). How-368 ever, it is clear that the overall machining force for case C5 is still369 much higher than that of case C7. This is because the major

370contributor of overall cutting force is the first half of normal force371profile, in which the force magnitude is significantly higher than372the latter half of normal force profile, as well as the entire range373of friction force profile.374Figure 15 illustrates the effect of tool rake angle on friction dis-375tribution by comparing cases C3 and C8, which adopt the rake376angles of �15 deg and �30 deg, respectively. It can be seen that377the shape of normal force distribution is not significantly affected378by the tool rake angle in polycrystalline machining. The value of379normal force near the tool edge slightly increases as the rake angle380changes from �15 deg to �30 deg. The same phenomenon can be381found in the friction force distributions even though more varia-382tions exist among friction force distributions obtained using the383rake angle tools.

384Further Discussion

385It is well known that a number of friction models for tool/chip386interface in machining operations have been developed in

Fig. 11 Friction coefficient profiles with four levels of depth ofcut

Fig. 12 Friction analysis along tool/chip interface with the pro-gress of machining for a polycrystalline copper: (a) normalforce and (b) friction force

Fig. 13 Friction coefficient distributions with the progress ofmachining for a polycrystalline copper

Fig. 14 Comparison of tool/chip force distributions for casesC5 and C7: (a) normal force and (b) friction force

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387 literature. These models are usually obtained for some particular388 machining conditions (e.g., work and tool materials and cutting389 parameters). The famous ones include the constant Coulomb fric-390 tion model, sticking–sliding model, constant shear friction model,391 and variable shear friction model [36]. In the traditional numerical392 simulation of machining (e.g., finite element analysis), some par-393 ticular friction model needs to be assumed so that the simulation394 can be carried out. Nevertheless, the assumption of friction model395 could be problematic without enough consideration. MD simula-396 tion demonstrates its advantage in this aspect—it does not assume397 the friction model, and the computation results directly reveal the398 friction phenomena. Furthermore, it is clear that none of the above399 mainstream friction models for macromachining can provide a400 good fit for the friction distribution patterns obtained for atomistic401 machining of polycrystalline coppers.402 It should be noted that the machining speeds adopted in this403 study are significantly higher than the speed range for high speed404 machining. This is certainly the limitation of most MD simulation405 studies. The 200 m/s cases take more than 40 h to finish the com-406 putation using a cluster of 16 central processing unit (CPU) cores.AQ4407 The reduction of machining speed to the range of 1–10 m/s408 requires will have to use hundreds of CPU cores so that the com-409 putation can be completed within a reasonable amount of time. In410 the future efforts, we plan to explore the opportunities of graphics411 processing unit computing, which is believed to be effective for412 MD simulation with a much lower cost figure.413 Also, in this study, a negative rake angle is chosen for all the414 cutting conditions. It is because at nanometric or atomistic scale,415 the rake angle is usually negative due to the tool edge radius.416 However, it will be beneficial to investigate the positive rake417 angle situation so that a more complete picture about friction418 mechanisms of nanometric or atomistic machining can be419 obtained. Finally, the validation of MD simulation results should420 be addressed. This experimental validation of any nanometric or421 atomistic machining has been a major challenge [26]. With the

422increase of simulation problem size, AFM scratching, AFM nano-423indentation, and TEM in situ indentation are the possible techni-424ques that can be adopted to verify the MD simulation models.

425Conclusions

426This paper investigates the friction behaviors along tool/chip427interface in atomistic machining of polycrystalline copper struc-428tures. Besides the grain size, the cutting parameters of depth of429cut and cutting speed are considered as well. Based on the simula-430tion results, the following points can be summarized.

• 431The normal stress profiles in both polycrystalline and mono-432crystalline machining at atomistic scale are all similarly433shaped. The normal stress always starts from the maximum434around the tool cutting edge, but it continuously decreases to435zero at the end of tool/chip contact.

• 436The shear stress profiles follow a similar pattern for all the437simulation cases. The shear stress always starts from a nega-438tive value near the cutting edge. This is because the material439atoms below the cutting tool undergo extremely high pres-440sure, and the deformed chip atoms near the cutting edge have441a tendency to move downward along the rake face. The shear442stress increases along the rake face and reaches a peak value.443After that, it gradually falls to zero as the tool/chip contact444ceases.

• 445The trends of normal force and friction force profiles are not446significantly affected by the grain size of polycrystalline cop-447per. However, the reduction in grain size increases the magni-448tude of the normal force along the tool/chip interface.

• 449In polycrystalline machining, the increase of depth of cut450consistently increases the normal force along the entire con-451tact area, and tends to increase the friction force for the ma-452jority of the tool/chip contact area. This is mainly because the453cutting forces usually increase with increase of depth of cut.

• 454In polycrystalline machining, the normal and friction forces455generally increase as the cutting speed and the magnitude of456negative tool rake angle increase within the investigation457range of this study.

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