Computational Materials Science 65 (2012) 29–36

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Computational Materials Science

journal homepage: www.elsevier .com/locate /commatsci

Modeling the effect of tool edge radius on contact zone in nanomachining

Seyed Vahid Hosseini ⇑, Mehrdad VahdatiMechanical Engineering, K.N. Toosi University of Technology, Tehran, Iran

a r t i c l e i n f o a b s t r a c t

Article history:Received 13 May 2012Received in revised form 24 June 2012Accepted 25 June 2012Available online 31 July 2012

Keywords:Nanometric cuttingTool edge radiusContact zoneMD simulation

0927-0256/$ - see front matter � 2012 Elsevier B.V. Ahttp://dx.doi.org/10.1016/j.commatsci.2012.06.037

⇑ Corresponding author. Address: Mechanical EnginUniversity of Technology, Pardis Ave., Molasadra St.43344, Tehran, Iran. Tel.: +98 9125217940; fax: +98 2

E-mail addresses: mscmechanic@hotmail.com (S.V.(M. Vahdati).

The contact between tool and workpiece during nanomachining is a complicated phenomenon due tocomparable tool edge radius, R, with cutting depth, a. This paper presents an investigation into the effectsof tool edge radius on contact zone, chip formation mechanism, stagnation zone, tool forces and hydro-static stress distributions. Molecular dynamics simulations of the nanometric cutting on single crystalcopper were performed using EAM potential function with wide range from a/R =1 to tools with variousrounded tip. Results showed that although at a/R P 1, both tool tip and rake edge participate in chip for-mation, at a/R < 1 chip is formed only by rounded edge. Also, at a/R < 1, a small fraction of atoms com-pared with a sharper tool are separated as chip and larger fraction is pressurized to pass beneath thetool edge. Indeed, in rounded edge tools, the stable stagnation zone is located in tool curvature tip thatacts as the first effective cutting edge. The height of stagnation point from the bottom edge of toolincreases with edge radius, where it is independent from undeformed chip thickness. In addition, cuttingforce is slightly increased at smaller a/R; however, the trust force is raised remarkably especially whencutting depth approaches to critical depth of cut. Smaller a/R, similarly, induced higher compressivehydrostatic stress in wider contact length. Finally, if cutting depth is lower than the height of stagnationzone, the cutting mechanism will change to sliding mechanism.

� 2012 Elsevier B.V. All rights reserved.

1. Introduction Ikawa et al. [4] conducted atomistic analysis of nanometric

Nanomachining of non ferrous metals with single crystaldiamond tool has become increasingly important to produce microand nanometallic components with intricate structures [1]. Tooledge geometry has a significant effect on almost all nano-cuttingparameters such as cutting forces, tool life, surface finish and resid-ual stresses [2]. Therefore, understanding the effects of differentedge preparations and predicting them is crucially important.

Unlike conventional cutting with fine depth of cut, the machin-ing characteristics are influenced by the tool edge radius, R,especially when undeformed chip thickness, a, is comparablysmall. For single crystal diamond tools, R is governed by technolog-ical limitations where production of perfectly sharp cutters is prac-tically impossible. Even if cutting starts with a sharp tool, the tooltip will eventually wear out or break off and machining will becontinued with a worn edge. Tool geometry is usually neglectedin modeling of conventional machining such as the famous shearplane model which is based on the assumption of perfectly sharptools [3]. Such crucial assumption is acceptable in the modelingof conventional machining as the undeformed chip thickness ismuch larger than the tool edge radius.

ll rights reserved.

eering Department, K.N. Toosi, Vanak Sq, P.O. Box 19991-188864748.Hosseini), vahdati@kntu.ac.ir

cutting to investigate the minimum chip thickness of cut for agiven edge radius. It was concluded that while the minimumthickness is affected by the tool-work material interaction to acertain degree, it is strongly affected by the sharpness of the cut-ting edge. Shimada et al. [5] worked on molecular dynamics sim-ulation to investigate the ultimate accuracy that can be obtainedin ultra precision machining of aluminum and copper using ahypothetically perfect machine tool. They expected the mini-mum thickness of cut to be about 1 nm or less. Also, they esti-mated the ultimate roughness and depth of deformed layer inthe machined surface as �0.5 and �5 nm respectively. Yuanet al. [6] studied the effect of diamond tool sharpness on mini-mum cutting thickness and cutting surface integrity in ultra pre-cision machining experimentally. Their results showed that thesurface roughness, micro hardness, residual stress and the dislo-cation density of the machined surface vary with cutting edgeradius. Komanduri et al. studied the effect of tool geometry innanometric cutting in terms of rake angle and tool edge radiususing pair-wise Morse potential function [7,8]. They observedthat the negative rake angle and/or large edge radius providehigh hydrostatic pressure underneath the tool required for theformation of a small plastic deformation zone immediately be-neath the tool instead initiating brittle fracture in brittle mate-rial like silicon. Komanduri et al. [9] also investigated theeffect of different tool rake angles on nanoscale cutting of mono-crystalline silicon with perfectly sharp tool edge.

30 S.V. Hosseini, M. Vahdati / Computational Materials Science 65 (2012) 29–36

Pei et al. [10] studied the effect of tool rake angle on cutting pro-cess of copper single crystal. They observed as the rake angle chan-ged from �45 to 45, the machined surface became smoother. Inaddition, a comparison between pair-wise Morse and metallicEAM potential was done that showed there was no big differencein the simulated chip formation and machined surface under thesedifferent potentials. However using EAM potential could predicttool forces precisely. Pei et al. [11] also performed large scale MDsimulation of copper nanomachining with rounded tool edge invarious cutting depths, speeds and crystal orientation. They illus-trated that dislocations and other lattice defects were generatedin cutting region near the tool edge and some of them glided deepinto the workpiece. Lucca et al. [12] investigated the effect of singlecrystal diamond tools with negative rake angles on tool forces forGermanium. Also, tool edge geometry and the new machined sur-faces were characterized with atomic force microscopy. Theyobserved a significant increase in trust force to the cutting force ra-tio for decreasing depth of cut and for increasing negative rake an-gle. Cheng et al. simulated tool wear in nanometric cutting ofsilicon workpiece [13]. They investigated the wear mechanism bycalculating temperature and stress in the diamond tool. Indeed,they analyzed relationship between temperature and sublimationenergy of diamond and workpiece atoms. Han et al. [14] studiedthe effect of tool geometry on atomic displacement in nanoma-chining of Si with various tool edge radii. In this study they mod-eled a non realistic sharp tool and rounded edge tool with 1.5, 2and 2.67 nm radius and 0.6 nm depth of cut using MD simulation.They observed that in case of nanometric cutting, the edge radiuscannot be ignored compared with the depth of cut. When the cut-ting depth fall into the nanometer domain, the mechanism ofnano-cutting can be described by an indentation-sliding model.Cai et al. [15] used molecular dynamics method to simulate crackinitiation in the ductile–brittle mode of cutting for depths of cutranging from smaller than tool cutting edge radius to larger in Simaterial. They found when the undeformed chip thickness be-comes larger than the tool edge radius, crack may be initializedue to a peak deformation. As the undeformed chip thickness issmaller than the cutting edge radius, there is no peak in the chipformation zone, and thus there is no crack initiation zone in theundeformed workpiece material. Han and Hu [16] investigate theeffect of rake angle on bur formation. The results showed that inductile materials, the cracks propagate parallel to the cutting direc-tion and form positive burrs; while cutting brittle materials, thecracks propagate into the workpiece and formed negative burrs.

In the nanomachining process, the influence of tool edge radiuson the chip formation and material deformation require more fun-damental investigations. Previous studies on the effects of tooledge radius were mainly focused on the chip formation mechanismand its mechanics but the underlying contact phenomenon andstagnation zone was not investigated. In reality, the effects of tooledge radius on the contact phenomenon can be seen from theatoms flow around the nanometric tool edge when the work mate-rial is compressed and piled up ahead of the cutting tool. Consider-ing the above literature, the main objective of this study was toinvestigate the effect of tool geometry (a/R) on contact phenomenaand its corresponding stress states for single crystal of copper withmolecular dynamics (MD). Also, the relation of a transition modefrom sliding to cutting in critical depth of cut was studied.

1 For interpretation of color in Figs. 1–9, the reader is referred to the web version ofthis article.

2. Simulation methodology

2.1. Geometry and boundary conditions

In this paper copper was chosen as workpiece because of itsimportance to nanoscale processing applications. Changes in the

mechanism of chip formation due to tool edge radius effect are dri-ven by the combination of a and R. Thus, the study was carried outby performing molecular dynamics simulation at R = 0, 1.09, 2.53and 4.9 nm that yield a wide range of a/R. However, only four dis-tinct cases of a/R =1, 1, 0.46 and 0.23 were included in the discus-sions to illustrate the tool edge radius effect where a/R =1represents the sharp tool. In addition, eight different depths ofcut were modeled for a round edge tool with R = 4.9 nm to studythe effect of depth of cut on contact phenomenon.

In this modeling, a soft copper was machined by a considerablyharder diamond tool. The hardness of diamond is considerablyhigher than copper [17]. Under such conditions, it is a goodapproximation to consider the tool as a rigid body in these simula-tions. The tool consists of 4000–5500 atoms of carbon, dependingon their geometries. The MD nano-cutting model with definedboundary conditions is illustrated in Fig. 1.

For simulating nano machining of (001) plane copper, a slab of3.62 � 14.48 � 10.86 nm dimensions was utilized, consisting of58020 atoms. The nano-cutting was investigated along the [010]direction of the (001) surface. Periodic boundary conditions weremaintained only along x direction to eliminate the effect of freesurface. In order to study the effect of tool geometry on contactphenomenon, the tool was fixed and cutting velocity had to be ap-plied to the workpiece. So, three layers of workpiece atoms in theboundary faces of xy and xz plane (green1 color in Fig. 1) were fedhorizontally into the rigidly fixed cutting tool at 100 m/s cuttingspeed. All other atoms were allowed to move with the MDalgorithm.

Also, three layers in xy and xz plane, nearby the fixed layers,were considered as thermostatic boundary which the temperatureof these atoms was maintained at 300 K with a standard nose ther-mostatic algorithm (red color in Fig. 1). So, rescaling of atom veloc-ities is performed in these layers if the temperature grows morethan 5 K from the specified temperature. This algorithm allowsthe transfer of heat from the machined region on the surface tothe bulk of the workpiece, similar to real condition. It is importantnot to rescale the atom velocities within the active Newtonianzone (white color in Fig. 1). Both the thermostatic atoms andNewtonian atom’s motion followed the Newton’s second law,and were determined by the direct integration of the classicalHamiltonian equations of motion using Velocity-Verlet method[18]. The Computational parameters, machining condition, tooland workpiece properties were summarized in Table 1.

2.2. Potential model

A pair-wise Morse potential was applied between the toolatoms and workpiece atoms (C–Cu interaction). Also, EAM poten-tial model was used for the Cu–Cu interaction between the work-piece atoms. The basic approach of the EAM, which evolved fromthe density-functional theory, is that the total potential energy(Umetal) for an atomic system is the sum of the embedding energy(F) and short-range repulsive pair potential (Vij) energy (Eq. (1)).

Umetal ¼12

XN

i¼1

XN

j–1

VijðrijÞ þXN

i¼1

FðqiÞ ð1Þ

The embedding energy is the energy to place an atom i in a hostelectron density (qi) at the site of that atom. The electron density(qi) at any point is well described by a sum of the individual atomicdensities. The embedding function (F) incorporates quantummechanical contributions to the cohesion of the solid. EAM poten-tial has been very successful in modeling the elastic properties, de-fect formation energies and fracture mechanisms of various bulk

Fig. 1. Schematic of nano-cutting model and boundary conditions.

Table 1Nanomachining condition, computational parameters, tool and workpiece properties.

Nanomachiningcondition

Cutting direction [010] on (001) surfaceUndeformed chip

thickness1.09 nm for various R

0.36, 0.72, 1.09, 1.45, 1.81, 2.17, 2.53, 2.90 nm forR = 4.9 nm

Cutting speed 100 m/s

Computationalparameters

Potential type for Cu–Cu

EAM; Cut off distance = 5 Å

Potential type for Cu–C Morse; Cut off distance = 6.5 ÅBoundary temperature 300 KTime step 1 fs

WorkpieceLattice properties FCC; Lattice constant = 3.62 ÅSubstrate material Single crystal of copper

39960 Newtonian atoms +Number of atoms 8610 thermostatic atoms +

9450 fixed atomsTool propertiesAtom type Rigid atomsRake angle 15�Clearance angle 10�Tool edge radius 0, 1.09, 2.53, 4.9 nmNumber of atoms 4122, 3944, 3161, 5423

S.V. Hosseini, M. Vahdati / Computational Materials Science 65 (2012) 29–36 31

metals [19,20]. The EAM has also been widely applied to surfaceproperties as well, successfully describing surface energies, surfacereconstructions and adsorption on metal surfaces.

3. Results and discussion

3.1. Chip formation mechanism

Atomic displacement plots in Fig. 2 illustrate chip formationand material deformation for different a/R at initial cutting stage(cutting distance = 1.2 nm). The arrow indicates the direction ofdisplacement vector while its size represents the relative magni-tude of displacement. Near the tip of sharp tool (a/R =1), atomsof workpiece were divided into two distinct regions: A regionwhich transferred to chip and a remaining part that generated

new machined surface. Also, chip was first formed on the rake faceof the cutting tools as shown in Fig. 2a.

Using round edge tool, atoms of workpiece were divided intothree zones: The first region was ahead of tool edge in which dis-placement of atoms became zero. The second zone covered theupper atoms and was converted to chip. Atoms of the third zonewere pressed by tool edge to generate new machined surface. Ata/R = 1, both rounded tool edge and rake edge participated in chipformation (Fig. 2b). As shown in Fig. 2c, in case of larger tool radius(a/R = 0.46), a small fraction of atoms were separated as chip andlarge fraction passed through beneath the tool edge. At a/R = 0.23, the behavior of material deformation was similar to thatof a/R = 0.46, but the material flow around tool edge became moregradual. In addition, the chip layers could not reach the positiverake edge due to large edge radius and small depth of cut (Fig. 2d).

3.2. Position of stagnation point

Fig. 3 shows the distribution of workpiece atoms around thetool tip during steady state cutting (cutting distance = 6 nm),where the tool is displayed in black spheres.

When the velocity tends to be zero, the material cannot be mov-ing anymore and form a region known as stagnated zone. The stag-nation zone is simply formed due to the entrapment of some atomsunderneath the rounded tip of the tool. This zone is shown withblue atoms in Fig. 4 for sharp tools and rounded edge tools withvarious a/R. At sharp tool (a/R =1), a small unstable stagnated re-gion was noticed on tip of the tool. In round edge tool, the stagna-tion zone started to form in the early beginning of cutting then itsshape stabilized when steady state cutting was reached. In general,unsharp tools usually develop such phenomenon which has beenreported earlier for blunt and chamfered tools in conventionalmachining [21,22]. The stagnation zone acts as the first effectivecutting edge during cutting [22], which adds to the complexity ofthe cutting process especially when a/R 6 1. Since the stagnationzone acts as the first effective cutting edge, it is believed to playan important role in controlling and explaining the current results.The stagnation zone tip shows an interesting behavior; its heightfrom the bottom edge of tool is increased with edge radius. Table2 shows the height (h) for different cases that experienced stagna-tion-zone formation. The stagnation-zone tip is where the work-piece material starts to split into two parts, one forming the chip

Fig. 2. Initial stages of chip formation at (a) a/R =1; (b) a/R = 1; (c) a/R = 0.46; and (d) a/R = 0.23.

32 S.V. Hosseini, M. Vahdati / Computational Materials Science 65 (2012) 29–36

and the other forming the workpiece new surface; therefore, whenit moves upwards (h increases) more material is pressed into thenew machined surface which tends to increase the thickness ofthe plastically deformed region with edge radius.

3.3. Effect of tool edge radius on tool contact forces

Fig. 4 shows the history of tool forces versus cutting distance forsharp tool and tool with three types of edge radius. Although cut-ting force was slightly increased at larger a/R, the trust force israised remarkably. Based on MD results, the steady state time aver-aged cutting force and trust force for a/R =1, 1, 0.46, 0.23 were12.3, 34.5, 44.9, 45.3 nN and �30.5, 14.9, 57.4, 63.8 nNrespectively.

As shown in Fig. 4, the trust force was strongly dependant ontool edge radius. At sharp tool, cutting process was performed bylower force compared with other cases. In addition, atomic pres-sure on positive rake edge made tool trust force in Z� direction.This means that sharp tool tended to penetrate inside workpiece.At a/R = 1 both the tool tip and tool rake edge had contact withworkpiece material, which in turn results in two contradictingphenomena on trust force: First, an increase trust force in Z+ direc-tion since atoms were pressed ahead of the tip and clearance edge;second, a decrease trust force in Z+ direction due to atoms pressureon positive rake edge. The overall result of these two contradictingphenomena made trust force of tool near zero.

Reduction of undeformed chip thickness ratio to tool edge ra-dius to a/R = 0.46, atomic pressure either in chip area or in material

beneath tool tended to create trust force in Z+ direction. In this casethe values of trust and cutting were approximately equal to eachother. At a/R = 0.23, since a larger number of atomic layers werecompressed, the trust force increased significantly and becamemore than cutting force.

3.4. Hydrostatic stress distribution

During nanomachining, workpiece atoms were faced with highcompressive stress under the tool. Hydrostatic stress is the averageof three normal stress components in the three principal axes,P = (S11 + S22 + S33)/3. The snapshots that indicate distributionthe direction and magnitude of hydrostatic stress of workpiecesat different a/R are shown in Fig. 5.

In case of sharp tool (a/R =1), high hydrostatic pressure hap-pened in rake edge near the tool tip. Also, plastic deformationwas most intense at the chip root and extended towards the turn-ing point of the chip free boundary, known as primary deformationzone. Such plastic deformation behavior for a/R value of 1 wassimilar to conventional machining model that is shown in Fig. 5a.The value of hydrostatic pressure was lower than round tool edge.In addition, in new machined surface a hydrostatic tensile stresswas created at the free edge of the workpiece. In other cases,hydrostatic stress occurred at the rounded edge of tool. At a/R = 1as shown in Fig. 5b, the hydrostatic stress direction started fromthe tip and continued toward the free-surface that chips had beenformed. At this state, the position of maximum hydrostatic stressand stagnation point were located at the same zone. It is necessary

Fig. 3. Stagnation zone for various tools edge radius.

Fig. 4. Tool forces history during nano-cutting at (a) a/R =1; (b) a/R = 1; (c) a/R = 0.46; and (d) a/R = 0.23.

S.V. Hosseini, M. Vahdati / Computational Materials Science 65 (2012) 29–36 33

Table 2Height of stagnation zone from the bottom of tool.

Tool edge radius (nm) R = 0 R = 1.1 R = 2.5 R = 4.7Height (nm) – 0.40 0.53 0.90

34 S.V. Hosseini, M. Vahdati / Computational Materials Science 65 (2012) 29–36

to mention that the hydrostatic pressure compared with a/R < 1occupied smaller area.

During chip formation, the work was subject to great compres-sive hydrostatic stress during chip formation at a/R = 0.46 and 0.23as shown in Fig. 5c and d. With decreasing undeformed chip thick-ness to tool edge radius, compressive hydrostatic stress in greaterquantities and in wider length was applied to workpiece. In thesecases, the location of the maximum hydrostatic stress point wasshifted under the stagnation point. The reason is that a large frac-tion of atoms located in cutting zone, should be pressed to passthrough the tool edge. The bigger height of stagnation zone tip (Ta-ble 2), the more atom layers to pressurize which finally increasedtrust force. Existence of high hydrostatic pressure at a/R < 1, in-creases plastic deformation zone in large depths of atomic layersand consequently increases the residual stress at new machinedsurface of the workpiece that can affect surface integrity. Yuan

Fig. 5. Hydrostatic stress distributions at (a) a/R =1

Fig. 6. Effect of tool edge radiu

and Zhou took some TEM photographs of the machined surfacethat was machined with two different tool edge radii. Their resultshowed residual stress and dislocation density were increased bytool edge radius that confirms the current simulation results [6].

3.5. Effective rake angle

At a/R P 0.46, the effective rake angle ceff was approximated asthe positive tool rake because the chip flows along the rake edgeduring chip growth. At a/R = 0.46, the ceff became highly negativein initial stages of chip growth as shown in Fig. 2c. By developmentof nano-cutting process, the chip is located on the rake face of tooland effective rake angle ceff transforms from negative to positiveangles (Fig. 6a). At a/R < 0.23, illustrated in Fig. 6b, the effectiverake angle formed negative due to large tool edge radius. Indeed,since the undeformed chip thickness is too small according tothe tool edge radius, effective rake angle still remained negativein developed state.

3.6. Critical depth of cut

Fig. 7 shows the position of stagnation point zone of tool withedge radius of 4.9 nm with blue atoms for different cutting

; (b) a/R = 1; (c) a/R = 0.46; and (d) a/R = 0.23.

s on effective rake angle.

S.V. Hosseini, M. Vahdati / Computational Materials Science 65 (2012) 29–36 35

depths a = 0.36–2.9 nm. Except at very low a/R (a = 0.36, 0.72 nm),the position of stagnation zone was approximately constant inother cases. This indicates that undeformed chip thickness has noeffect on position of stagnation zone.

Fig. 8 shows the transition mode from sliding to cutting for a toolwith edge radius R = 4.9 nm in small depths of cut. At a = 0.36 nm,the depth of cut was not big enough to cut workpiece with roundededge tool as indicated in Fig. 8a. This means at a/R = 0.07, a tool withlarge negative rake angle only compressed work material and slid onits surface. So, no chip was formed and only the trace of tool move-ment remained on workpiece surface. As the height of stagnationpoint for this tool edge radius is 0.9 nm (Table 2), only small amountof atoms reached stagnation point at a = 0.72 nm. But, in this casenanometric cutting did not occur. However, transition mode fromsliding to cutting can be identified in this cutting depth. Withincreasing depth of cut to 1.09 nm, that was more than critical depthof cut, nano chip formation happened perfectly (Fig. 8c). Ikawa et al.experimentally reported critical l nm cutting depth in ultra precisioncutting of copper with a ground diamond tool [23]. He declared thatthe tool was too sharp to be measured by available instruments but

Fig. 7. Constant stagnation point angle for undeformed chip thickness: (a) 0.36 nm; (b)2.90 nm.

Fig. 8. Transitional mechanism from sliding to cutting for a tool with 4.7 nm ed

the cutting edge radius of this tool was estimated to be 2.5–5 nm thatis comparable to current MD simulation results.

3.7. Relation between ratio of trust force to the cutting force and a/R

Fig. 9 shows diagram of the ratio of trust force to the cutting forcefor various a/R that indicates when a/R is reduced, Ftrust/Fcut ratio is in-creased significantly. Circle symbols represent results of a constanttool edge radius (4.9 nm) with various depths of cut between 0.36and 2.9 nm. In this case, when a/R < 0.18, cutting process convertedinto sliding mechanism. So, cutting force was reduced and Ftrust/Fcut

is increased significantly. In critical depth of cut for tool edge radiusof 4.9 nm, trust force was approximately twice the cut-ting force. Indeed, in the interval of a/R between 0.2 nm and0.6 nm, Ftrust/Fcut reduced from 1.5 to 1. In addition, square symbolindicates Ftrust/Fcut for a constant undeformed chip thick-ness (a = 1.09 nm) and various tool edge radius that shows simi-lar behavior with the circular diagram. Therefore, the ratio ofundeformed chip thickness to tool edge radius is a governing parame-ter in nanomachining in which tool forces ratio are greatly influenced.

0.72 nm; (c) 1.09 nm; (d) 1.45 nm; (e) 1.81 nm; (f) 2.17 nm; (g) 2.53 nm; and (h)

ge radius in small depths of cut, (a) 0.36 nm; (b) 0.72 nm; and (c) 1.09 nm.

Fig. 9. Ratio of trust force to the cutting force versus a/R.

36 S.V. Hosseini, M. Vahdati / Computational Materials Science 65 (2012) 29–36

4. Conclusions

Changes in the contact phenomenon due to tool edge radius ef-fect are driven by the combination of a and R. Wide range of a/Rfrom a sharp tool (a/R =1) to tools with various rounded tips wereinvestigated in this paper. Based on molecular dynamic simulation,findings were summarized as follows:

1. Although at a/R P 1 both tool tip and rake edge participated inchip formation, at a/R < 1 chip was formed by rounded edge oftool. Indeed, at a/R < 1, a small fraction of atoms, compared witha sharper tool, were separated as a chip and a large fraction ofatoms was compressed to pass through beneath the tool edge.

2. For a perfect sharp tool, a small unstable stagnated region wasnoticed on tip of the tool. In rounded edge tools, the stable stag-nation zone was located in rounded tool edge that acted as thefirst effective cutting edge. Indeed, its height from the bottomedge of tool was increased with edge radius.

3. Results showed that cutting force was slightly increased at smal-ler a/R; however, the trust force was raised remarkably espe-cially when approached to critical depth of cut. So, Ftrust/Fcut ratio was increased significantly at small a/R.

4. Smaller a/R induced higher compressive hydrostatic stress inwider contact length. In these cases, the location of the maxi-mum hydrostatic stress point was shifted under the stagnationpoint.

5. For a specific tool edge radius, the position of stagnation zone isapproximately constant in various depths of cut. In addition, ifthe cutting depth is lower than height of stagnation zone tipfrom the bottom of tool, the cutting mechanism is transformto the sliding mechanism.

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