jo ur nal ho me p age: www.elsev ier .com/ locate /prec is ion
evelopment of metal cutting process accompanied by a localizedompressive hydrostatic stress field formation: Examination byolecular dynamics simulation
eito Uezakia, Jun Shimizub,∗, Libo Zhoub
Graduate School of Science and Engineering, Ibaraki University, Nakanarusawa 4-12-1, Hitachi 316-8511, JapanDepartment of Intelligent Systems Engineering, Ibaraki University, Nakanarusawa 4-12-1, Hitachi 316-8511, Japan
r t i c l e i n f o
rticle history:eceived 19 August 2013eceived in revised form 22 October 2013ccepted 20 November 2013vailable online 12 December 2013
eywords:
a b s t r a c t
Improving machined surface integrity is important for precision machining. The aim of this work is todevelop a cutting tool, which enables to generate a localized compressive hydrostatic stress field inthe vicinity of cutting point to suppress unnecessary plastic flow and to improve the surface integrity ofworkpiece. In this paper, as the first step a simple cutting tool attached with a laminar jig equipped with asmall rectangular hole for cutting chip elimination was proposed, and a molecular dynamics simulation ofnano-cutting of monocrystalline aluminum was performed in order to verify and reveal the effectiveness
uttingolecular dynamics
imulationydrostatic stresslastic flow
and issues, respectively, of proposed method for improving machined surface integrity. The obtainedsimulation results were also compared to those using a normal cutting tool in order to clarify the cuttingmechanism. As a result, it was clarified that a high compressive hydrostatic stress field was successfullyintroduced in the vicinity of cutting point. Consequently, the burr formation and elimination of cuttingchip were remarkably suppressed and smoothened, respectively by using proposed cutting tool.
urrhip
. Introduction
The machining process represented by cutting can lead to dam-ge of the machined surface and subsurface, such as burr, residualtress and so on. It is because the material removal in such a processs mainly carried out by the plastic deformation and subsequentracture. Therefore, the suppression of unnecessary plastic flow isf considerable importance in the precision machining.
It is commonly known that the hydrostatic pressure causes thelastic deformation [1], even though it affects the deformationehaviors of materials. For example, the yield stress and ductil-
ty of many kinds of metals increase under a high compressiveydrostatic pressure [2]. At an atomic level, a high compressiveydrostatic pressure reduces the density of lattice defect such asoids and cracks, and also works to inactivate the mobility of work-iece atoms [3]. Such characteristics are expected to be applicableo higher quality surface machining. It has been reported in someapers that an improvement in the machined surface integrity can
e realized when the cutting is conducted under a high compres-ive hydrostatic pressure condition [4,5]. However, relatively largequipment utilizing the hydraulic pressure is needed to give such
a high compressive hydrostatic pressure to the workpiece, and thishas been a big issue for practical use.
As a practical method, grinding is effective to give such a highcompressive hydrostatic stress field in the vicinity of the machiningpoint due to a usage of abrasive grains with negative rake angles,even though the sharpness in the chip elimination tends to be dete-riorated. Therefore, an alternative method for introducing such ahigh compressive hydrostatic stress field, even if a tool with posi-tive rake angle is used, is considered of value.
The present study aims to develop a cutting tool, which enablesto generate a localized compressive hydrostatic stress field in thevicinity of the cutting point to suppress unnecessary plastic flowand to improve the surface integrity of workpiece. In this paper,as the first step a simple cutting tool attached with a laminar jigequipped with a small rectangular hole for cutting chip eliminationwas proposed, and a molecular dynamics [6] (MD) simulation ofnano-cutting of monocrystalline aluminum was performed in orderto verify and reveal the effectiveness and issues, respectively, ofproposed method for improving machined surface integrity, as wellas to clarify the cutting mechanism.
2. Hydrostatic stress and yield condition
The stress at any point in an isotropic material, assumed tobehave as a continuum, is completely defined by nine stress
372 K. Uezaki et al. / Precision Engineering 38 (2014) 371–378
cf
�
ss
�
enac
s
�
wsr
a
o
wVvaus
� 6(�
wiot
Fig. 1. Proposed cutting tool model.
omponents and can be expressed as a second-order tensor asollows:
ij =
⎛⎜⎝
�11 �12 �13
�21 �22 �23
�31 �32 �33
⎞⎟⎠ (1)
The stress tensor is decomposed into a hydrostatic and deviatortresses. The hydrostatic stress is defined as the average normaltress
m = 13
�ii = �11 + �22 + �33
3(2)
Hydrostatic stress means the stress components which actsqually in all directions. Even at very high level of hydrostatic stress,o plastic deformation occurs because no shear stress exerts onny crystal plane. The hydrostatic stress only causes the volumetrichange in the material.
The deviator stress is obtained by subtracting the hydrostatictress from the full stress tensor as follows:
devij = �ij − �m · ıij =
⎛⎜⎝
�11 − �m �12 �13
�21 �22 − �m �23
�31 �32 �33 − �m
⎞⎟⎠ (3)
here ıij is identity tensor. Only the deviator stress produces sheartress and can lead to plastic flow when it exceeds the yield crite-ion.
The yield criterion by using von Mises yield model is expresseds:
12
�devij �dev
ij − C = 0 (4)
r as a function of the stress tensor components:
16
[(�11 − �22)2 + (�22 − �33)2 + (�33 − �11)2
+ 6(�212 + �2
23 + �231)] − C = 0 (5)
here C is a constant depending on the yield point of the material.on Mises yield criterion is isotropic criterion. However, that is inery good agreement with the experimental results of various met-ls and most commonly used today. From Eqs. (4) and (5), it is alsonderstood that the yield criterion only depends on the deviatortress.
Equivalent stress (von Mises equivalent stress) is defined as:
� =
√3�dev
ij�dev
ij
2=√
(�11 − �22)2 + (�22 − �33)2 + (�11 − �33)2 +2
hich is used to predict yielding of materials under multiaxial load-ng conditions using results from simple uniaxial tensile. Yieldingccurs when the equivalent stress, �� , reaches the yield stress ofhe material in uniaxial tension.
212 + �2
23 + �231)
(6)
Fig. 2. Schematic drawing of cutting process and stress distribution in proposedcutting method.
Note that, in the latter part, 1, 2 and 3-axis directions arereplaced by x, y and z-axis ones, respectively, for clarification ofdiscussion.
3. Proposed cutting model
Fig. 1 shows the schematic drawing of proposed cutting tool. Alaminar jig equipped with a small rectangular hole for cutting chipelimination is attached to the cutting tool in order to introduce alocalized compressive hydrostatic stress in the vicinity of cuttingpoint.
Fig. 2(a) and (b) illustrates the cross-sectional view of cuttingprocess and the Mohr’s stress circle describing inner stress condi-tion when using the proposed cutting tool, respectively. The cuttingtool shown in Fig. 2(a) is intended to introduce a high compressivehydrostatic stress field in the vicinity of the cutting point easily byjust applying a pressure from the attached jig, even when a positiverake angle is utilized. By using such a cutting tool, the unnecessaryplastic flow would be decreased due to an increase in the shearstrength (or yield stress) of workpiece [7] as shown in Fig. 2(b), andthe plastic deformation would be most likely to occur just under therectangular hole due to the imbalance in stresses. The most mate-rial plastically deformed would be eliminated from the hole as a
cutting chip. As a result, the propagation of plastic flow is expectedto be decreased as compared to that by the normal cutting.
K. Uezaki et al. / Precision Engineering 38 (2014) 371–378 373
4
uctiobatpatallelb
te
m
a
F
wbit
iah
Table 1Simulation conditions.
Cutting edge Diamond (rigid body)
Rake angle 0◦
Flank angle 10◦
Nose radius 1.5 nmJig for hydrostatic pressure Diamond (rigid body)Workpiece Pure aluminum (Al(1 0 0))Model 3DInteratomic potential Morse (Al–Al, Al–C)Integral calculation Leap-frog methodTime step 3 fsNumber of workpiece
atoms107,123 atoms
Environment In vacuumInitial temperature 300 KCutting speed 50 m/sLubrication between
workpiece and cuttingtool
Cohesive energy D is reduced by 10% (Al–C)
Fig. 3. Molecular dynamics simulation model for nano-cutting.
. Simulation model and conditions
The proposed MD simulation model is shown in Fig. 3. In the sim-lation, both the cutting tool tip and attached jig are assumed toonsist of rigid diamond. The difference between the proposed andraditional cutting models is only whether it is equipped with a lam-nar jig with a small rectangular hole for cutting chip eliminationr not. The dimensions of the rectangular hole were determinedy considering the expansion of the cutting chip in both the thicknd width directions. The rake and flank angles and nose radius ofhe cutting tool are 0◦ and 10◦, and 1.5 nm, respectively. The work-iece is assumed to consist of monocrystalline aluminum and have
perfectly smooth (1 0 0) surface at an atomic level. Other thanhe uppermost surface, the analysis layer composed of Newtoniantoms is boxed by a thermostat (controlled constant temperature)ayer where atoms are arrayed in a lattice of constant length. Thisayer allows energy dissipation when the mechanical energy is gen-rated inside the analysis layer. The layer outside the thermostatayer is assumed to be a boundary layer composed of perfect rigidody atoms.
In the molecular dynamics method, by taking the mass of atom io be m and its position vector at the time t to be ri(t), the followingquation of motion is obtained:
d2ri(t)dt2
= F i(t) (7)
nd Fi(t) is calculated using the following equation:
i(t) =∑j=i
grad �(rij) (8)
here � is interatomic potential depending on the distanceetween atoms, and the index j indicates atoms except for atoms
. Eq. (7) is applied to all the atoms of interest and solved by usinghe leap frog method [8] with a proper time step.
An existing Morse potential is applied for the description ofnteraction between a pair of aluminum atoms [9]. Because thectual potential between an aluminum atom and a carbon atomas not been clarified, the Morse potential proposed by Ikawa et al.
Depth of cut (extrusion) 2 nmCutting distance 15 nm
[10] is applied here. The expression of the Morse potential functionis as follows:
where r is the atomic distance between pair atoms, D is the dissocia-tion energy, ̨ is the potential coefficient, and r0 is the equilibrationdistance.
Table 1 shows the molecular dynamics simulation conditions.The cutting tool is slid horizontally on the surface of workpiece atthe speed of 50 m/s after indenting into the workpiece surface tothe depth of 2 nm. The broken arrows in Fig. 3 show the cuttingtool trajectories. In this simulation, a constant 2 nm depth of cut(distance between the workpiece surface and jig) is given to applya high compressive pressure from the jig. As the first step, the sizeof the rectangular hole in the jig is determined by estimating thechip thickness, of course it needs further examinations. For refer-ence, the average pressure from the jig during a cutting processwas almost 2.2 GPa in this trial. The pressure is calculated from thethrust force acting on the jig. In order to give a lubrication effect, theatomic force between a pair of aluminum atom and carbon atomsis reduced by 10% by lowering the cohesive energy D in Eq. (9). Forthe sake of simplicity, the simulations are conducted in the vac-uum, and no chemical reaction and no surface reconstruction areconsidered here, respectively.
The internal stress was calculated by dividing the workpieceinto 1 nm long cubic blocks with using the virial theorem [11,12]as follows:
P = 13V
(∑i∈V
mv2i
+∑i∈V
F i · ri
)(10)
where V is the volume of divided individual block, vi is the velocityof atom i. Eq. (10) is applied to all the atoms belonging in eachdivided block.
In this simulation, the centro-symmetry parameter (CSP)defined by Kelchner et al. [13] is used to identify the dislocationsand other lattice defects. The CSP is computed as follows:
CSP =6∑
i=1
|ri + ri+6|2 (11)
where ri and ri+6 are the vectors corresponding to the six pairs ofopposite neighbors in the FCC lattice. The CSP takes zero for theatoms in a perfect FCC lattice. On the other hand, it takes a positive
374 K. Uezaki et al. / Precision Engineering 38 (2014) 371–378
vv
5
w
5
1pssxg
psrhfhFv
5
t1pc
red around the cutting groove shoulders.
Fig. 4. Hydrostatic stress distribution (x–y cross-section).
alue for the atoms located near a defect such as dislocation andacancy as well as a surface.
. Simulation results and discussion
The simulation results by the proposed cutting tool (with jig)ere compared with those by the normal one (without jig).
.1. Hydrostatic stress distribution
Fig. 4 shows the snapshots of cross-sectional atomic arrays after5 nm long cutting and hydrostatic stress distribution in the work-iece, which is shown by a gray scale. The variation in hydrostatictress of aforementioned each 1 nm long cubic block from initialtate is shown here. Furthermore, all the following snapshots on–y cross-section show the half space beyond the center of cuttingroove.
In Fig. 4(a), the region which is subject to relatively high com-ressive hydrostatic stress around 2 GPa (atoms in blue) widelypreads beneath the cutting tool while such a trend is hardlyecognized in Fig. 4(b). This indicates that the quasi-compressiveydrostatic state in the vicinity of the cutting tool tip is success-
ully supplied by using the proposed cutting tool. Also, the tensileydrostatic stress just under the cutting groove becomes lower inig. 4(a) than that in Fig. 4(b). Such a trend is preferable from theiew point of the residual stress in machined subsurface.
.2. Deformation and chip removal
Fig. 5 shows the snapshots of cross-sectional atomic arrays andraveling distance of workpiece atoms from initial position after
5 nm long cutting. The color other than white is given to the work-iece atoms moved longer than the Burgers vector. Hence, it can beonsidered that the atoms in gray are subject to plastic deformation.
Fig. 5. Traveling distance of workpiece atoms (x–y cross-section).
The magnitude of the Burgers vector of the FCC crystal is definedby the following equation:
|b| =√
2a
2(12)
where a is the lattice constant. a and |b| of aluminum are 0.405and 0.286 nm, respectively. For reference, the two different brokenlines drawn in each figure indicate the initial surface and the cuttingdepth, respectively.
Relatively large number of atoms in red can be recognizedaround the cutting groove shoulder in Fig. 5(b). These atoms consti-tute a burr (or pile-up). Such a trend is hardly observed in Fig. 5(a).Also, the amount of atoms in the cutting chip in Fig. 5(a) is muchlarger than that in Fig. 5(b). This indicates that the proposed cut-ting tool have an advantage in the smooth chip formation. On theother hand, relatively large number of atoms in gray are seen underthe machined groove bottom in Fig. 5(a). It is considered that theplastic flow extends deep into the workpiece.
For evaluating the transcription of cutting tool locus, Fig. 6shows the snapshots of cross-section of cutting grooves and trav-eling distance of workpiece atoms. For reference, the cutting toolpassed is also shown in Fig. 6. The depth of the groove is about0.3 nm shallower in Fig. 6(a) than that in Fig. 6(b), and this can bethought that a higher elastic recovery occurs after releasing highercompressive hydrostatic stress as mentioned before. The entranceof the groove is about 0.8 nm wider in Fig. 6(a) than that in Fig. 6(b).This is thought to be because of the abrupt direction change in theplastic deformation due to the effect of the attached jig. On theother hand, Fig. 6(b) shows a good transcription at first glance.However, the actual situation is different. In Fig. 6(a), the atomslocated around the groove shoulders were simply removed as apart of the cutting chip, while the previously removed workpieceatoms were just embedded in the clearance gap formed around thegroove shoulders in Fig. 6(b) as there can be seen some atoms in
The number of workpiece atoms at various traveling distancesfrom initial arrays is categorized and shown in Fig. 7. Atoms arecategorized into different three ranges: traveling distance td is (a)
K. Uezaki et al. / Precision Engineering 38 (2014) 371–378 375
lamra
-20
0
20
40
60
80
100
120
140
0 50 100 150 200 250 300 330
258ps
Indenting CuttingTime ps
Cutt
ing
fo
rce
nN
:Principal force :Thrust force
(a) Proposed tool
-20
0
20
40
60
80
100
120
140
0 50 100 150 200 250 300 330Inde nting Cutting
Time ps
Cutt
ing
fo
rce
nN
:Principal force :Thrust force
(b) Normal tool
Fig. 8. Time variation of cutting forces.
Fig. 6. Cross-sectional view of cutting grooves (z–y cross-section).
ess than Burgers vector,√
2a/2, (b)√
2a/2 to a and (c) larger than
. These different three ranges are defined as: (a) elastic defor-ation range, (b) plastic deformation range and (c) cutting chip
ange, respectively. By using proposed cutting tool, the number oftoms classified into elastic deformation range becomes greater,
Fig. 7. Classification of deformed workpiece atoms by traveling distance.
while that classified into plastic deformation range becomes lower.From this result, the plastic deformation including burr formationdecrease by using proposed method. The number of atoms classi-fied into cutting chip range increase by using proposed cutting. Thisis consistent with the results shown in Fig. 5. From these results, itis confirmed that the suppression of plastic deformation includingburrs formation, and a smooth cutting chip formation are achievedby proposed cutting method.
5.3. Cutting force
The time variations of principal and thrust cutting forces aredepicted in Fig. 8. The cutting forces exerted on the proposed cut-ting tool (Fig. 8(a)) were calculated from the resultant force due tothe tool and jig. In Fig. 8, both of the principal forces are stable ataround 70 nN. It can be understood that the frictional force betweenthe additional jig and the workpiece surface is relatively small andalmost negligible, while the thrust force by proposed cutting toolbecomes larger than that by normal one. This indicates that theadditional jig successfully supplies a high-pressure to the work-piece surface and gives a high compressive hydrostatic stress fieldin the vicinity of cutting point.
The variations of cutting forces in Fig. 8(a) are comparativelylarger than that in Fig. 8(b). This reason will be discussed later.
376 K. Uezaki et al. / Precision Engineering 38 (2014) 371–378
Fig. 9. CSP distribution (x–y cross-section).
Fig. 10. CSP distribution seen from beneath workpiece surface.
Fig. 11. Equivalent stress distribution (x–y cross-section).
5.4. Slip deformation and stress distribution
Figs. 9 and 10 show the CSP distributions in cross-section andviews from beneath the workpiece surface after 15 nm long cutting,respectively. In order to eliminate the uncertainty due to the latticevibration, the atoms having the CSP smaller than 3 are removed fora clear visualization, since such atoms are assumed to have a perfectcrystal structure.
In Figs. 9(a) and 10(a), four different slip planes spread to theobliquely downward can be observed along with {1 1 1} plane in<1 1 0> direction. However, no slip planes are recognized aroundthe cutting tool tip, even though a shear plane is clearly observedjust under the rectangular hole of jig as surrounded by a solidcircle in Fig. 10(a). This indicates that the plastic deformation
only occurs just under the hole as expected with the exception ofabove mentioned four different slip planes. On the other hand, inFigs. 9(b) and 10(b), many narrow slip planes are generated around
Fig. 12. Equivalent stress distribution (z–y cross-section).
K. Uezaki et al. / Precision Engineering 38 (2014) 371–378 377
Fig. 13. Variation in CSP distribution seen from beneath workpiece surface whenp
ta
pct
otFwmtpnbbei
further improvement in the surface integrity. On the other hand, in
roposed cutting tool is utilized.
he cutting tool tip although the number of plastically deformedtoms located below the cutting depth is relatively few.
Figs. 11 and 12 show the equivalent stress distribution in work-iece after 15 nm long cutting. Those figures show the x–y and z–yross-sections, respectively, and Fig. 12 is seen from 1 nm ahead ofhe rake face as indicated by broken lines in Fig. 11.
Relatively higher equivalent stress larger than 4 GPa can bebserved almost only around the shear plane located just underhe rectangular hole of jig in the case of proposed cutting (seeigs. 11(a) and 12(a)), while such high equivalent stresses areidely dispersed in both x and y directions in the case of nor-al one (see Figs. 11(b) and 12(b)). The equivalent stress needed
o initiate the slip deformation is around 6.2 GPa in the case ofroposed cutting, while it becomes around 5.8 GPa in the case oformal one. Therefore, it can be considered that the yield stressy proposed cutting method becomes about 7% higher than thaty normal one. Such a trend agrees well with the aforementioned
xpectation [2]. Additionally, the ideal critical resolved shear stresss 5.1 GPa for monocrystalline aluminum. In the nano-scale cutting
Fig. 14. Comparison of behavior of uppermost surface atoms (t = 262.5 ps).
processes of monocrystal, the shear stress takes such extremelyhigh values.
From these results, the proposed cutting tool is advantageous torestrict the plastic flow around the shear plane located just underthe rectangular hole and to increase the shear strength of work-piece, although it is accompanied by aforementioned slip planesformation.
5.5. Mechanism of slip planes formation
As an example, Fig. 13 shows the CSP distribution seen from theobliquely downward when t = 247.5 and 262.5 ps, respectively, inthe case of proposed cutting. During the period between t = 247.5and 262.5 ps, the principal cutting force showed a significant sud-den decrease (see t = 258 ps in Fig. 7(a)). In Fig. 13, it can be seena newly generated slip plane surrounded by a solid circle. Hence,aforementioned sudden decrease in the principal cutting force iscaused by the internal stress release due to the generation and rapidmovement of dislocation. It can be also observed that the newlygenerated slip plane starts from just under the jig rather than theshear plane.
Fig. 14 shows the snapshots of the uppermost surface atomswhen t = 262.5 ps in the case of proposed and normal cutting,respectively. In Fig. 14(a), a step can be observed at the point A,and this resulted in the generation of new slip plane shown inFig. 13(b). Such a step is originating from the friction accompaniedby stick-slip like motion between the jig and workpiece surface,and this should be solved by improving the jig shape or else for
Fig. 14(b), almost all the removed uppermost surface atoms con-tribute to the burr (or pile-up) formation.
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78 K. Uezaki et al. / Precision
. Conclusions
In order to develop a cutting tool, which enables to generate aocalized compressive hydrostatic stress field in the vicinity of cut-ing point to suppress unnecessary plastic flow and to improve theurface integrity of workpiece, a simple cutting tool attached with
laminar jig equipped with a small rectangular hole for cuttinghip elimination was proposed. And a molecular dynamics simula-ion of nano-cutting of monocrystalline aluminum was performednd the results were compared to those using a normal cutting toolo verify and reveal the effectiveness and issues, respectively, ofroposed method, as well as to clarify the cutting mechanism. Theesults obtained are summarized as follows:
. A high compressive hydrostatic stress field around 2 GPa is suc-cessfully generated in the vicinity of cutting point when a 2.2 GPacompressive pressure is given by jig. In that case, the averagethrust force is about five times as high as that in the normalcutting.
. The yield stress becomes 6.2 GPa and about 7% higher than thatby normal cutting (5.8 GPa).
. The number of plastically deformed atoms is decreased andparticularly, the burr (or pile-up) formation is remarkably sup-pressed.
. The elimination of cutting chip becomes remarkably smooth.
. The transcription of cutting tool locus becomes worse becauseof the slightly larger elastic recovery when releasing the highercompressive hydrostatic stress in the depth direction, and theabrupt change in the plastic deformation in the width direction.
. The plastic flow and shear strength are restricted and increased
around the shear plane located just under the rectangular holeof jig, respectively, even though it is occasionally accompaniedby the slip planes generation originating from friction betweenthe jig and workpiece surface.
[
[
ering 38 (2014) 371–378
From the conclusions, the following improvements can be listedas the future tasks for better machined surface integrity: By improv-ing the jig shape, e.g., by giving an inclination or a curved surfaceshape, the thrust force would be decreased and the hydrostaticcompressive stress field would be more localized. These lead to thedecrease in both the friction between the jig and workpiece andthe residual stress caused by the slip deformation. Furthermore,by giving the roundness around the rectangular hole of the jig, thedirection change in the plastic deformation would be relaxed, andthe width of the cutting groove entrance would come close to thedesirable one.
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