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Fundamental study of nano-scale machining using bubble raft model
Elastohydrodynamics '96 / D. Dowson et al. (Editors) 0 1997 Elsevier Science B.V. All rights reserved.
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findmental study of nanc+scale machining using bubble raft model K. Maekawa, Y. Hojo and I. Ohshima Department of Mechanical Engineering, Ibaraki University, 4-12-1 Nakanarusawa, Hitachi 316, Japan The bubble raft model has been employed to investigate the cutting mechanism in nano-scale machining. The present paper first describes the instrumentation and measurement, then examines the influence of cutting conditions and tool geometry on chip formation and subsurface damage. Damage caused by edge dislocations increases with increasing depth of cut, or tool edge radius, or both. Atomistic defects, including vacancies and grain boundaries initially induced into the model, cause the damage to develop. These phenomena have been successfully visualized by means of the behaviour of soap bubbles. The experimental results are compared with those obtained by the molecular dynamics simulation of orthogonal machining of a copper single crystal. Qualitative agreement between the bubble raft model and the MD simulation can be seen with respect to basic cutting phenomena including chip formation and suhurface damage, in which a similar deformation mechanism through dislocations plays a primary role. Interaction between tool and workpiece is also a key factor in nano-scale machining.
1. INTRODUCTION Recent developments in the precision machining of X-ray mirrors and magnetic memory discs, by means of the diamond turning of copper and aluminium alloys using high-rigidity machine tools, generate surface accuracy of submicrometre order [l].There is a growing demand for developing more precise or ultra-precision machining in which a removal at an atomistic level is an ultimate goal. To establish nano-scale machining technologies including developments in micromachine devices, monitoring and machine control, and the optimisation of cutting conditions, it is vital to clarify cutting phenomena such as chip formation, cutting force, surface roughness and sub-surface damage at feeds of a few atomistic layers. Molecular dynamics (MD) simulations have been employed for this purpose, and the physical aspects are partially understood with respect to: the dependence of the specific energy on the depth of cut [2], the role of dislocations on chip formation [3], the minimum depth of cut for producing chips [4], tribological phenomena [5] and three-dimensional chip formation [6]. However, there remain problems of uncertainty of the po-
tentials used and spatia.l/time limitations in these computer experiments. MD simulations involve tracking the motion of atoms and molecules as a function of time. Typically, this motion is described by Newton's equations of motion and yields a set of 3N secondorder differential equations, where N is the number of particles. These can be solved with finitetimestep integration methods, typically tenths to a few femtoseconds [7]. Most current simulations then integrate for up to a total time from picoseconds to only a few nanoseconds for a system of N=lOOO-10000, despite the advent of much faster computers. The classical equations of motion require a method for calculating the forces between atoms. Currently there are two approaches: the first assumes that the potential energy of the system as a function of the relative atomic positions of the atoms can be represented in a mathematical form that contains some free parameters. The parameters are then chosen to describe some set of physical properties of the system of interest, and forces are obtained by taking the gradient of the potential energy with respect to atomic positions. The second approach involves the calculation of interatomic forces directly from an ab initio electronic structure calculation [8]. However,
5 80 there is no guarantee of the accuracy of either approach in obtaining the forces from a potential or a semiempirical electronic structure calculation; poorly chosen parameterisations and functional forms can yield nonphysical forces. It is clear that uncertainty of the calculation of forces as well as spatial/time limitations in current MD simulations necessitate an experimental verification of the simulation models. In the present study the bubble raft model [9]is employed to investigate nanescale cutting mechanisms as well as to make a comparison with the MD simulation [5]. Describing the experimentation, we demonstrate the influence of tool edge radius, depth of cut and crystal imperfection on chip formation and subsurface damage. The simulation experiments using soap bubbles assume that a (111) plane of an fcc crystal is cut using a rigid tool in a [lOi]direction. The experimental results are compared with those obtained by the MD calculation [5], where orthogonal machining of a (111) plane of a copper single crystal using a diamond-like tool at a cutting speed of 20 m/s is simulated, postulating the Morse potentials and a system of 2496 copper atoms and 120 carbon atoms.
2. EXPERIMENTATION According to Bragg’s instrumentation [9], a large population of soap bubbles can be formed on the surface of a soap solution by blowing compressed air into it through a narrow orifice of 0.05 mm diameter. The soap solution consists of 15.2 ml of oleic acid diluted by 50 ml of distilled water, 73 ml of 10%solution of tri-ethanolamine and 164 ml of pure glycerine. This is diluted in three times its volume of water to reduce viscosity. The orifice is set about 5 mm below the surface, and the air pressure, supplied by a small compressor, is controlled by a water manometer. Figure 1 shows a schematic diagram of the experimental apparatus. A cutting tool made of an acrylic board is driven by a step motor to yield a cutting action against the bubbles in a container. Cutting force is measured using two force sensors with a four-gauge measurement of the deflection of double cantilever springs positioned at the bottom and the front of the soap assemblage. The bottom of the container is blackened to show up
Compressor
Step motor
Fig. 1 Nano-scale machining simulation apparatus using bubble raft model. each bubble more clearly. During machining the behaviour of the bubbles is recorded by a 35 mm camera or an 8 mm videotape recorder. Assuming that a (111) close packed plane of an fcc copper single crystal whose lattice constant is 3.61 A is cut in a [lo11 direction, a bubble diameter of 1.2 mm is correspondent to a nearestneighbour distance of 2.55 A on the plane. This scale transformation is applied to the determination of tool edge radius. The cutting speed is set at 1.1 mm/s, whereas the MD simulation [5] assumes 20 m/s which corresponds to a speed of 6 . 6 5 ~ 1 0m/s ~ in the bubble model. The equivalent tool edge radius is set at 0, 3 and 5 nm, and the depth of cut at 1 and 2 nm. The influence of these parameters on chip formation and subsurface damage will be investigated for both perfect and imperfect crystals including vacancies and grain boundaries.
3. CHIP FORMATION AND SUBSURFACE DAMAGE 3.1. Influence of depth of c u t and tool edge
radius Figure 2 represents a snapshot of the behaviour of bubbles at a depth of cut of t = l nm with varying tool edge radius: (a) r=3 nm, (b) 5 nm and (c) 0. When the edge radius is small ((c) and (a)),
disorder of the bubble structure in the vicinity of the tool tip is light. In addition, the bubbles above an extension line of the bottom of the tool edge are removed as a chip by the cutting action. As a result, disorder of the machined surface and
581
Fig. 2 Behaviour of soap bubbles, showing the influence of depth of cut (t=l nm after scaling) on chip flow and subsurface damage: (a) tool edge radius r=3 nm, (b) 5 nm and (c) 0, when using acrylic tool at cutting speed of 1.1 mm/s.
Fig. 3 Behaviour of soap bubbles, showing the influence of depth of cut (t=2 nm after scaling) on chip flow and subsurface damage: (a) tool edge radius r=3 nm, (b) 5 nm and (c) 0, when using acrylic tool at cutting speed of 1.1 mm/s.
subsurface damage are negligibly small. In the case of (b) r=5 nm, on the contrary, the bubbles expected to be removed are indented below the bottom of the tool edge, edge dislocations propagating from the tool tip several depths of cut into
the workpiece. Figure 3 depicts a similar snapshot to Fig.2 but with the depth of cut doubled, t=2 nm. Compared with Fig.2, the indentation phenomenon becomes more apparent at r=3 nm and 5 nm.
582 Edge dislocations are frequently generated from the tool tip and propagate in the directions of 60' and 120' against the cutting direction. Thus lattice strain in the bubble structure caused by machining is not released by the elastic indentation of the layers but relieved by the rearrangement of bubbles through dislocations. Disorder of the bubbles is extended in front of the tool tip as the tool edge radius increases: in particular, an archshaped grain boundary can be seen at r=5 nm. An ideal tool of r=O, on the other hand, does not show such structural disorder, but generates a perfect chip; all the bubbles above the bottom of the tool edge are removed as a chip. 3.2. Influence of vacancies and grain boundaries Figure 4 represents a snapshot of the behaviour of bubbles at t=2 nm and r=3 nm where many vacancies and dislocations are introduced in the
Fig. 5 Behaviour of soap bubbles with existing grain boundaries, where the difference of cut distance between (a) and (b) is 24 mm.
-
Fig. 4 l3ehaviour of soap bubbles with existing vacancies, where the difference of cut distance between (a) and (b) is 12 mm.
workpiece before machining. The dark spots in the figure denote vacancies, and the grey line segments edge dislocations. With the tool movement, (a) to (b), edge dislocations frequently nucleate from the tool tip and penetrate into a deep portion within the workpiece via vacancies. Some vacancies close to the tool tip disappear to serve as the rearrangement of the bubble structure. As a result, deeper subsurface damage than in Fig.3 (a) can be seen. Figure 5 shows the influence of interfacial defects or grain boundaries on chip flow and subsurface damage at t=2 nm and r=3 nm. Although edge dislocations generated at the tool tip penetrate the workpiece, the grain boundary prevents them from propagating outside the grain; subsequent subsurface damage caused by machining is confined within the grain. In addition, another grain starts forming below the tool flank. Figure 5 (b) shows that the grain boundary ahead
583 of the tool edge as shown in Fig.5 (a) disappears after machining. With the advancement of the tool the other grain boundary ahead of the tool edge as shown in Fig.5 (b) changes its shape and a subgrain starts to generate by means of a rotation of the existing grain. There is deeper subsurface damage than in the cutting of a single crystal (Fig.3 (a)), though the chip shape is almost the same. 4. DISCUSSION
4.1. Cutting mechanism of soap bubbles The metal cutting mechanism at feeds in the nanometre range is largely affected by an atomistic interaction between tool and work atoms [5, lo]. In the cutting simulation using the soap bubbles, an acrylic board was used as the tool. Since i t has a high affinity for soap bubbles, it is observed that the bubbles removed as a chip or those generated as a machined surface adsorb on the tool rake face or the tool flank. The cutting experiment is therefore carried out using a tool made of Teflon whose affinity for soap bubbles is much lower. Figure 6 shows the chip formation and subsurface damage obtained using the Teflon tool at t=2 nm with various tool geometries: (a) r=3 nm, a=Oo, y=30", (b) r=O, a=Oo, y=3Oo, and (c) r=O, a=1O0, y=2Oo, where (Y is the rake angle and y is the clearance angle. In the comparisons of Fig.6 (a) with Fig.3 (a) and Fig.6 (b) with Fig.3 (c), the bubbles still adsorb on the tool faces, but the cutting action is enhanced; the Teflon tool produces more work bubbles as a chip. By setting a larger clearance angle, the machined surface is generated closer to the tool tip, leading to less subsurface damage. The level of the machined surface, however, is below the bottom of the tool edge due to the adsorbate on the tool flank. The increase of the rake angle (Fig.6 (c)) produces a thinner chip as compared with the zero rake-angle tool (Fig.6 (a)). Thus, chemical affinity as well as tool geometry influences the cutting mechanism of the soap bubbles. The generation and propagation of edge disle cations in the vicinity of the tool edge play a major role in nano-scale machining. It is interesting to note that the deformation pattern resembles a slip line field for the deformation of a perfect
Fig. 6 Behaviour of soap bubbles when using Teflon tool with various geometry: (a) tool edge radius r=3 nm, rake angle a=O0, clearance angle r=30", (b) r=O, a=Oo,y=3Oo, and (c) r=O, a=loo, y=2O0. plastic material caused by the sliding of a rigid twedimensional wedge. Figure 7 shows a steady state slip line field for the plastic deformation of a soft asperity by a hard asperity [ll],where no adhesion between the wedge and the substrate is postulated. As compared with Fig.3 (b), the ve-
5 84
Work material Tool Number of atoms Governing equations
Fig. 7 Slip line field for the deformation of a perfectly plastic material caused by the sliding of a rigid twedimensional wedge from right to left [111* locity discontinuity along ABCD coincides with an arch-shape grain boundary formed just ahead of the tool edge. This correspondence suggests a similarity in deformation mechanism between nano- (soap bubbles in a strict sense) and macroscale machining. 4.2. Correlation between bubble raft
model and MD simulation The results obtained by the bubble raft experiment are compared with those by the MD simulation [5]. The simulation model is outlined in Table 1, where a (111) plane of a copper single crystal is orthogonally machined in a [ 10x1 direction, postulating the Morse potentials: ( b ( ~ i j= )
D[exp{-2a(rij -r0)}-2 exp{a(ri,-~o)}] (1)
where (b is a pair potential energy function, rij is the relative distance between two atoms and D, a and TO correspond to the cohesion energy, the elastic modulus and the atomistic distance at equilibrium respectively. Table 2 lists the parameters of Morse type potentials. The cutting conditions, except cutting speed, correspond to those in Fig.2. Figure 8 represents a snapshot of the work a t o m at a total time step of 60,000, ie a cut distance of 12 nrn, in the cases of (a) r=3 nm, (b) 5 nm and (c) 0. The symbols o and 0 indicate respectively the instantaneous temperatures below and above 1,000 K which are simply converted from the kinetic energy of the atoms. Figure 9
Numerical procedures Initial temperature Time step Cutting speed Depth of cut Rake angle Edge radius Cut plane Cut direction
D, eV a, A-1 To,
A
cu-cu 0.3429 1.3588 2.6260
Cu single crystal Diamond (111) plane 2498 Cu, 120 C Newton’s equation Morse potential Verlet’s method 300 K 10 fs 20 m/s 1IUIl
O0 3 nm (111)
[ioi]
cu-C 0.100 1.700 2.200
c-c
2.423 2.555 2.522
shows the trajectories of the work atoms corresponding to Fig.8, where the translation of the straight parallel lines by one layer denotes the occurrence of shear deformation due to the prop agation of edge dislocations. A similarity in the structural disorder caused by machining can be seen between the bubble experiment (Fig.2) and the MD simulation (Figs.8 and 9). As the tool edge radius increases, the material removed as a chip decreases and subsurface damage becomes more severe; in particular, the indentation behaviour and an arch-shaped deformation boundary ahead of the tool tip can be also seen in Fig.9 (b). However, the movement of the work atoms in the deformation zone is more active in the MD simulation. This difference stems from the cutting speed used between the two models: 20 m/s vs 1.1 mm/s. Figure 10 compares the change of cutting force with time in the cases of (a) the bubble raft model (Fig.2 (a)) and (b) the MD simulation (Fig.8 (a)), where FH is the horizontal component and Fv
585
Fig. 8 Behaviour of work atoms and the distribution of temperature in machining (111) plane of perfect copper crystal with various tool edge radius: (a) r=3 nm, (b) 5 nm and (c) 0.
Fig. 9 Changes of atomic layers in [loll direction in machining (111) plane of perfect copper crystal with various tool edge radius: (a) r=3 nm, (b) 5 nm and ( c ) 0.
the vertical one. The time step in the MD simulation is 10 fs,and the force is monitored at every 50 steps. The bubble experiment gives a higher FH than Fv with fewer fluctuations, which arises from the adsorption of soap bubbles onto the tool flank and a quasi-static deformation at a cutting speed of 1.1 mm/s. In both models macroscopic shear in the workpiece caused by the movement of edge dislocations results in peaks in the cutting force. The role of atomistic defects introduced in the bubble raft model, such as the formation of subgrains and enhancement of structural disorder, is
also simulated in the MD calculations [4, 121. To make a quantitative comparison between the two models it is vital to determine the parameters in pair potentials of the soap bubbles, and of the soap bubbles and the tool. This will not be straightforward and needs sophisticated techniques undeveloped at present. Even though the potential shape may be identified, the difference in time-scale or cutting speed in both models is inevitable due to lack of computational power. These are the present limitations of the comparative approach.
586
-Horizontal (cutting) force FFf
..
-
-Vertical (normal) force Fv
E 0.08
e. 7. 0.06
U
3
-'
I
I
m
~
IZH'(Av. 1 . 7 5 ~ N/m) Fv (Av. 1 . 8 3 ~ 1 0 -N/mm) ~ I
I
4 m 5 m Number of time steps
-
60000
(b) Fig. 10 Variation of cutting force at t = l nm and r=3 nm: (a) bubble raft model and (b) MD simulation.
5. CONCLUSIONS In the present study the bubble raft method according to Bragg and Nye (91 has been employed to investigate the nanescale cutting mechanisms of soap bubbles as well as to make a comparison with molecular dynamics simulations of a copper single crystal. The major results obtained are summarised as follows: (1) Assuming that a (111) plane of an fcc crystal is machined using a rigid tool in a [ l O i ] direction, cutting conditions and tool geometry substantially affect chip formation and subsurface damage of the bubble workpiece. When the tool edge radius is small and/or the depth of cut is small, displacement of the bubbles is limited to be at or just below the machined surface, and more work bubbles are removed as a chip.
(2) Existing vacancies and edge dislocations in the soap bubbles result in further disorder of the bubble structure owing to the interaction between the defects and the dislocations propagated from the tool tip. (3) Qualitative agreement between the bubble raft model and the MD simulation can be seen with respect to basic cutting phenomena, including chip formation and subsurface damage in which a similar deformation mechanism through dislocations plays a primary role. The interaction between tool and workpiece is also a key factor in nanescale machining. (4) To make a quantitative comparison between the two models it is vital to determine a pair potential between soap bubbles. The introduction of appropriate interaction between the bubbles and the cutting tool is also essential. The advent of much faster computers is required for this comparative approach.
REFERENCES 1. N. Ikawa, R.R. Donaldson, R. Komanduri, W. Konig, P.A. McKeown, T. Moriwaki and I.F. Stowers, Ann. CIRP, 40, 2 (1991) 587. 2. J. Belak and I.F. Stowers, Proc. Am. Soc. Prec. Eng. (1990) 76. 3. S. Shimada, N. Ikawa, G. Ohmori and H. Tanaka, Ann. CIRP, 4 1 , f(1992) 117. 4. S. Shimada, N. Ikawa, H. Tanaka, G. Ohmori and J. Uchikoshi, Ann. CIRP, 42, 1 (1993) 91. 5. K. Maekawa and A. Itoh, Wear, 188 (1995) 115. 6. R. Rentsch and I. Inasaki, Ann. CIRP, 44, 1 (1995) 295. 7. D.W. Heermann, Computer Simulation Method, 2nd edn, Springer, Heidelberg (1990) 13-103. 8. R. Car and M. Parrinello, Phys. Rev. Lett, 55 (1985) 2471. 9. W.L. Bragg and J.F. Nye, Proc. Roy. SOC. London, A 190 (1949) 474. 10. K. Maekawa and Y. Hojo, P m . 8th ICPE, CompBgne, France (1995) 319. 11. J.M. Challen and P.L.B. Oxley, Wear, 53 (1979) 229. 12. K. Maekawa, J . SOC. Mat. Sci., Japan, 46 (1997) to appear. (in Japanese)
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findmental study of nanc+scale machining using bubble raft model K. Maekawa, Y. Hojo and I. Ohshima Department of Mechanical Engineering, Ibaraki University, 4-12-1 Nakanarusawa, Hitachi 316, Japan The bubble raft model has been employed to investigate the cutting mechanism in nano-scale machining. The present paper first describes the instrumentation and measurement, then examines the influence of cutting conditions and tool geometry on chip formation and subsurface damage. Damage caused by edge dislocations increases with increasing depth of cut, or tool edge radius, or both. Atomistic defects, including vacancies and grain boundaries initially induced into the model, cause the damage to develop. These phenomena have been successfully visualized by means of the behaviour of soap bubbles. The experimental results are compared with those obtained by the molecular dynamics simulation of orthogonal machining of a copper single crystal. Qualitative agreement between the bubble raft model and the MD simulation can be seen with respect to basic cutting phenomena including chip formation and suhurface damage, in which a similar deformation mechanism through dislocations plays a primary role. Interaction between tool and workpiece is also a key factor in nano-scale machining.
1. INTRODUCTION Recent developments in the precision machining of X-ray mirrors and magnetic memory discs, by means of the diamond turning of copper and aluminium alloys using high-rigidity machine tools, generate surface accuracy of submicrometre order [l].There is a growing demand for developing more precise or ultra-precision machining in which a removal at an atomistic level is an ultimate goal. To establish nano-scale machining technologies including developments in micromachine devices, monitoring and machine control, and the optimisation of cutting conditions, it is vital to clarify cutting phenomena such as chip formation, cutting force, surface roughness and sub-surface damage at feeds of a few atomistic layers. Molecular dynamics (MD) simulations have been employed for this purpose, and the physical aspects are partially understood with respect to: the dependence of the specific energy on the depth of cut [2], the role of dislocations on chip formation [3], the minimum depth of cut for producing chips [4], tribological phenomena [5] and three-dimensional chip formation [6]. However, there remain problems of uncertainty of the po-
tentials used and spatia.l/time limitations in these computer experiments. MD simulations involve tracking the motion of atoms and molecules as a function of time. Typically, this motion is described by Newton's equations of motion and yields a set of 3N secondorder differential equations, where N is the number of particles. These can be solved with finitetimestep integration methods, typically tenths to a few femtoseconds [7]. Most current simulations then integrate for up to a total time from picoseconds to only a few nanoseconds for a system of N=lOOO-10000, despite the advent of much faster computers. The classical equations of motion require a method for calculating the forces between atoms. Currently there are two approaches: the first assumes that the potential energy of the system as a function of the relative atomic positions of the atoms can be represented in a mathematical form that contains some free parameters. The parameters are then chosen to describe some set of physical properties of the system of interest, and forces are obtained by taking the gradient of the potential energy with respect to atomic positions. The second approach involves the calculation of interatomic forces directly from an ab initio electronic structure calculation [8]. However,
5 80 there is no guarantee of the accuracy of either approach in obtaining the forces from a potential or a semiempirical electronic structure calculation; poorly chosen parameterisations and functional forms can yield nonphysical forces. It is clear that uncertainty of the calculation of forces as well as spatial/time limitations in current MD simulations necessitate an experimental verification of the simulation models. In the present study the bubble raft model [9]is employed to investigate nanescale cutting mechanisms as well as to make a comparison with the MD simulation [5]. Describing the experimentation, we demonstrate the influence of tool edge radius, depth of cut and crystal imperfection on chip formation and subsurface damage. The simulation experiments using soap bubbles assume that a (111) plane of an fcc crystal is cut using a rigid tool in a [lOi]direction. The experimental results are compared with those obtained by the MD calculation [5], where orthogonal machining of a (111) plane of a copper single crystal using a diamond-like tool at a cutting speed of 20 m/s is simulated, postulating the Morse potentials and a system of 2496 copper atoms and 120 carbon atoms.
2. EXPERIMENTATION According to Bragg’s instrumentation [9], a large population of soap bubbles can be formed on the surface of a soap solution by blowing compressed air into it through a narrow orifice of 0.05 mm diameter. The soap solution consists of 15.2 ml of oleic acid diluted by 50 ml of distilled water, 73 ml of 10%solution of tri-ethanolamine and 164 ml of pure glycerine. This is diluted in three times its volume of water to reduce viscosity. The orifice is set about 5 mm below the surface, and the air pressure, supplied by a small compressor, is controlled by a water manometer. Figure 1 shows a schematic diagram of the experimental apparatus. A cutting tool made of an acrylic board is driven by a step motor to yield a cutting action against the bubbles in a container. Cutting force is measured using two force sensors with a four-gauge measurement of the deflection of double cantilever springs positioned at the bottom and the front of the soap assemblage. The bottom of the container is blackened to show up
Compressor
Step motor
Fig. 1 Nano-scale machining simulation apparatus using bubble raft model. each bubble more clearly. During machining the behaviour of the bubbles is recorded by a 35 mm camera or an 8 mm videotape recorder. Assuming that a (111) close packed plane of an fcc copper single crystal whose lattice constant is 3.61 A is cut in a [lo11 direction, a bubble diameter of 1.2 mm is correspondent to a nearestneighbour distance of 2.55 A on the plane. This scale transformation is applied to the determination of tool edge radius. The cutting speed is set at 1.1 mm/s, whereas the MD simulation [5] assumes 20 m/s which corresponds to a speed of 6 . 6 5 ~ 1 0m/s ~ in the bubble model. The equivalent tool edge radius is set at 0, 3 and 5 nm, and the depth of cut at 1 and 2 nm. The influence of these parameters on chip formation and subsurface damage will be investigated for both perfect and imperfect crystals including vacancies and grain boundaries.
3. CHIP FORMATION AND SUBSURFACE DAMAGE 3.1. Influence of depth of c u t and tool edge
radius Figure 2 represents a snapshot of the behaviour of bubbles at a depth of cut of t = l nm with varying tool edge radius: (a) r=3 nm, (b) 5 nm and (c) 0. When the edge radius is small ((c) and (a)),
disorder of the bubble structure in the vicinity of the tool tip is light. In addition, the bubbles above an extension line of the bottom of the tool edge are removed as a chip by the cutting action. As a result, disorder of the machined surface and
581
Fig. 2 Behaviour of soap bubbles, showing the influence of depth of cut (t=l nm after scaling) on chip flow and subsurface damage: (a) tool edge radius r=3 nm, (b) 5 nm and (c) 0, when using acrylic tool at cutting speed of 1.1 mm/s.
Fig. 3 Behaviour of soap bubbles, showing the influence of depth of cut (t=2 nm after scaling) on chip flow and subsurface damage: (a) tool edge radius r=3 nm, (b) 5 nm and (c) 0, when using acrylic tool at cutting speed of 1.1 mm/s.
subsurface damage are negligibly small. In the case of (b) r=5 nm, on the contrary, the bubbles expected to be removed are indented below the bottom of the tool edge, edge dislocations propagating from the tool tip several depths of cut into
the workpiece. Figure 3 depicts a similar snapshot to Fig.2 but with the depth of cut doubled, t=2 nm. Compared with Fig.2, the indentation phenomenon becomes more apparent at r=3 nm and 5 nm.
582 Edge dislocations are frequently generated from the tool tip and propagate in the directions of 60' and 120' against the cutting direction. Thus lattice strain in the bubble structure caused by machining is not released by the elastic indentation of the layers but relieved by the rearrangement of bubbles through dislocations. Disorder of the bubbles is extended in front of the tool tip as the tool edge radius increases: in particular, an archshaped grain boundary can be seen at r=5 nm. An ideal tool of r=O, on the other hand, does not show such structural disorder, but generates a perfect chip; all the bubbles above the bottom of the tool edge are removed as a chip. 3.2. Influence of vacancies and grain boundaries Figure 4 represents a snapshot of the behaviour of bubbles at t=2 nm and r=3 nm where many vacancies and dislocations are introduced in the
Fig. 5 Behaviour of soap bubbles with existing grain boundaries, where the difference of cut distance between (a) and (b) is 24 mm.
-
Fig. 4 l3ehaviour of soap bubbles with existing vacancies, where the difference of cut distance between (a) and (b) is 12 mm.
workpiece before machining. The dark spots in the figure denote vacancies, and the grey line segments edge dislocations. With the tool movement, (a) to (b), edge dislocations frequently nucleate from the tool tip and penetrate into a deep portion within the workpiece via vacancies. Some vacancies close to the tool tip disappear to serve as the rearrangement of the bubble structure. As a result, deeper subsurface damage than in Fig.3 (a) can be seen. Figure 5 shows the influence of interfacial defects or grain boundaries on chip flow and subsurface damage at t=2 nm and r=3 nm. Although edge dislocations generated at the tool tip penetrate the workpiece, the grain boundary prevents them from propagating outside the grain; subsequent subsurface damage caused by machining is confined within the grain. In addition, another grain starts forming below the tool flank. Figure 5 (b) shows that the grain boundary ahead
583 of the tool edge as shown in Fig.5 (a) disappears after machining. With the advancement of the tool the other grain boundary ahead of the tool edge as shown in Fig.5 (b) changes its shape and a subgrain starts to generate by means of a rotation of the existing grain. There is deeper subsurface damage than in the cutting of a single crystal (Fig.3 (a)), though the chip shape is almost the same. 4. DISCUSSION
4.1. Cutting mechanism of soap bubbles The metal cutting mechanism at feeds in the nanometre range is largely affected by an atomistic interaction between tool and work atoms [5, lo]. In the cutting simulation using the soap bubbles, an acrylic board was used as the tool. Since i t has a high affinity for soap bubbles, it is observed that the bubbles removed as a chip or those generated as a machined surface adsorb on the tool rake face or the tool flank. The cutting experiment is therefore carried out using a tool made of Teflon whose affinity for soap bubbles is much lower. Figure 6 shows the chip formation and subsurface damage obtained using the Teflon tool at t=2 nm with various tool geometries: (a) r=3 nm, a=Oo, y=30", (b) r=O, a=Oo, y=3Oo, and (c) r=O, a=1O0, y=2Oo, where (Y is the rake angle and y is the clearance angle. In the comparisons of Fig.6 (a) with Fig.3 (a) and Fig.6 (b) with Fig.3 (c), the bubbles still adsorb on the tool faces, but the cutting action is enhanced; the Teflon tool produces more work bubbles as a chip. By setting a larger clearance angle, the machined surface is generated closer to the tool tip, leading to less subsurface damage. The level of the machined surface, however, is below the bottom of the tool edge due to the adsorbate on the tool flank. The increase of the rake angle (Fig.6 (c)) produces a thinner chip as compared with the zero rake-angle tool (Fig.6 (a)). Thus, chemical affinity as well as tool geometry influences the cutting mechanism of the soap bubbles. The generation and propagation of edge disle cations in the vicinity of the tool edge play a major role in nano-scale machining. It is interesting to note that the deformation pattern resembles a slip line field for the deformation of a perfect
Fig. 6 Behaviour of soap bubbles when using Teflon tool with various geometry: (a) tool edge radius r=3 nm, rake angle a=O0, clearance angle r=30", (b) r=O, a=Oo,y=3Oo, and (c) r=O, a=loo, y=2O0. plastic material caused by the sliding of a rigid twedimensional wedge. Figure 7 shows a steady state slip line field for the plastic deformation of a soft asperity by a hard asperity [ll],where no adhesion between the wedge and the substrate is postulated. As compared with Fig.3 (b), the ve-
5 84
Work material Tool Number of atoms Governing equations
Fig. 7 Slip line field for the deformation of a perfectly plastic material caused by the sliding of a rigid twedimensional wedge from right to left [111* locity discontinuity along ABCD coincides with an arch-shape grain boundary formed just ahead of the tool edge. This correspondence suggests a similarity in deformation mechanism between nano- (soap bubbles in a strict sense) and macroscale machining. 4.2. Correlation between bubble raft
model and MD simulation The results obtained by the bubble raft experiment are compared with those by the MD simulation [5]. The simulation model is outlined in Table 1, where a (111) plane of a copper single crystal is orthogonally machined in a [ 10x1 direction, postulating the Morse potentials: ( b ( ~ i j= )
D[exp{-2a(rij -r0)}-2 exp{a(ri,-~o)}] (1)
where (b is a pair potential energy function, rij is the relative distance between two atoms and D, a and TO correspond to the cohesion energy, the elastic modulus and the atomistic distance at equilibrium respectively. Table 2 lists the parameters of Morse type potentials. The cutting conditions, except cutting speed, correspond to those in Fig.2. Figure 8 represents a snapshot of the work a t o m at a total time step of 60,000, ie a cut distance of 12 nrn, in the cases of (a) r=3 nm, (b) 5 nm and (c) 0. The symbols o and 0 indicate respectively the instantaneous temperatures below and above 1,000 K which are simply converted from the kinetic energy of the atoms. Figure 9
Numerical procedures Initial temperature Time step Cutting speed Depth of cut Rake angle Edge radius Cut plane Cut direction
D, eV a, A-1 To,
A
cu-cu 0.3429 1.3588 2.6260
Cu single crystal Diamond (111) plane 2498 Cu, 120 C Newton’s equation Morse potential Verlet’s method 300 K 10 fs 20 m/s 1IUIl
O0 3 nm (111)
[ioi]
cu-C 0.100 1.700 2.200
c-c
2.423 2.555 2.522
shows the trajectories of the work atoms corresponding to Fig.8, where the translation of the straight parallel lines by one layer denotes the occurrence of shear deformation due to the prop agation of edge dislocations. A similarity in the structural disorder caused by machining can be seen between the bubble experiment (Fig.2) and the MD simulation (Figs.8 and 9). As the tool edge radius increases, the material removed as a chip decreases and subsurface damage becomes more severe; in particular, the indentation behaviour and an arch-shaped deformation boundary ahead of the tool tip can be also seen in Fig.9 (b). However, the movement of the work atoms in the deformation zone is more active in the MD simulation. This difference stems from the cutting speed used between the two models: 20 m/s vs 1.1 mm/s. Figure 10 compares the change of cutting force with time in the cases of (a) the bubble raft model (Fig.2 (a)) and (b) the MD simulation (Fig.8 (a)), where FH is the horizontal component and Fv
585
Fig. 8 Behaviour of work atoms and the distribution of temperature in machining (111) plane of perfect copper crystal with various tool edge radius: (a) r=3 nm, (b) 5 nm and (c) 0.
Fig. 9 Changes of atomic layers in [loll direction in machining (111) plane of perfect copper crystal with various tool edge radius: (a) r=3 nm, (b) 5 nm and ( c ) 0.
the vertical one. The time step in the MD simulation is 10 fs,and the force is monitored at every 50 steps. The bubble experiment gives a higher FH than Fv with fewer fluctuations, which arises from the adsorption of soap bubbles onto the tool flank and a quasi-static deformation at a cutting speed of 1.1 mm/s. In both models macroscopic shear in the workpiece caused by the movement of edge dislocations results in peaks in the cutting force. The role of atomistic defects introduced in the bubble raft model, such as the formation of subgrains and enhancement of structural disorder, is
also simulated in the MD calculations [4, 121. To make a quantitative comparison between the two models it is vital to determine the parameters in pair potentials of the soap bubbles, and of the soap bubbles and the tool. This will not be straightforward and needs sophisticated techniques undeveloped at present. Even though the potential shape may be identified, the difference in time-scale or cutting speed in both models is inevitable due to lack of computational power. These are the present limitations of the comparative approach.
586
-Horizontal (cutting) force FFf
..
-
-Vertical (normal) force Fv
E 0.08
e. 7. 0.06
U
3
-'
I
I
m
~
IZH'(Av. 1 . 7 5 ~ N/m) Fv (Av. 1 . 8 3 ~ 1 0 -N/mm) ~ I
I
4 m 5 m Number of time steps
-
60000
(b) Fig. 10 Variation of cutting force at t = l nm and r=3 nm: (a) bubble raft model and (b) MD simulation.
5. CONCLUSIONS In the present study the bubble raft method according to Bragg and Nye (91 has been employed to investigate the nanescale cutting mechanisms of soap bubbles as well as to make a comparison with molecular dynamics simulations of a copper single crystal. The major results obtained are summarised as follows: (1) Assuming that a (111) plane of an fcc crystal is machined using a rigid tool in a [ l O i ] direction, cutting conditions and tool geometry substantially affect chip formation and subsurface damage of the bubble workpiece. When the tool edge radius is small and/or the depth of cut is small, displacement of the bubbles is limited to be at or just below the machined surface, and more work bubbles are removed as a chip.
(2) Existing vacancies and edge dislocations in the soap bubbles result in further disorder of the bubble structure owing to the interaction between the defects and the dislocations propagated from the tool tip. (3) Qualitative agreement between the bubble raft model and the MD simulation can be seen with respect to basic cutting phenomena, including chip formation and subsurface damage in which a similar deformation mechanism through dislocations plays a primary role. The interaction between tool and workpiece is also a key factor in nanescale machining. (4) To make a quantitative comparison between the two models it is vital to determine a pair potential between soap bubbles. The introduction of appropriate interaction between the bubbles and the cutting tool is also essential. The advent of much faster computers is required for this comparative approach.
REFERENCES 1. N. Ikawa, R.R. Donaldson, R. Komanduri, W. Konig, P.A. McKeown, T. Moriwaki and I.F. Stowers, Ann. CIRP, 40, 2 (1991) 587. 2. J. Belak and I.F. Stowers, Proc. Am. Soc. Prec. Eng. (1990) 76. 3. S. Shimada, N. Ikawa, G. Ohmori and H. Tanaka, Ann. CIRP, 4 1 , f(1992) 117. 4. S. Shimada, N. Ikawa, H. Tanaka, G. Ohmori and J. Uchikoshi, Ann. CIRP, 42, 1 (1993) 91. 5. K. Maekawa and A. Itoh, Wear, 188 (1995) 115. 6. R. Rentsch and I. Inasaki, Ann. CIRP, 44, 1 (1995) 295. 7. D.W. Heermann, Computer Simulation Method, 2nd edn, Springer, Heidelberg (1990) 13-103. 8. R. Car and M. Parrinello, Phys. Rev. Lett, 55 (1985) 2471. 9. W.L. Bragg and J.F. Nye, Proc. Roy. SOC. London, A 190 (1949) 474. 10. K. Maekawa and Y. Hojo, P m . 8th ICPE, CompBgne, France (1995) 319. 11. J.M. Challen and P.L.B. Oxley, Wear, 53 (1979) 229. 12. K. Maekawa, J . SOC. Mat. Sci., Japan, 46 (1997) to appear. (in Japanese)