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Critical cutting speed for onset of serrated chip ow in highspeed machining

G.G. Ye a,b, Y. Chen a, S.F. Xue b, L.H. Dai a,n

a State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, Chinab Department of Engineering Mechanics, College of Pipeline and Civil Engineering, China University of Petroleum, Shandong 266580, China

a r t i c l e i n f o

Article history:

Received 22 March 2014Received in revised form6 June 2014Accepted 16 June 2014Available online 23 June 2014

Keywords:

High speed machiningSerrated chip owDimensional analysisShear banding

a b s t r a c t

The transition of continuously smooth chip ow to periodically serrated chip ow as the cutting speed

increasing is one of the most fundamental and challenging problems in high speed machining. Here, anexplicit expression of the critical cutting speed for the onset of serrated chip ow, which is given interms of material properties, uncut chip thickness and tool rake angle, is achieved based on dimensionalanalysis and numerical simulations. It could give reasonable predictions of the critical cutting speeds atwhich chips change from continuous to serrated for various metallic materials over wide ranges of uncutchip thickness and tool rake angle. More interestingly, it is found that, as the turbulent ow is controlledby the Reynolds number, the transition of the serrated chip ow mode is dominated by a Reynoldsthermal number. Furthermore, the inuences of material properties on the emergence of serrated chipow are systematically investigated, the trends of which show good agreement with Rechtsclassical model.

&2014 Elsevier Ltd. All rights reserved.

1. Introduction

Cutting is a ubiquitous activity in daily life, science andtechnology[1,2]. The growing demand for enhancing productionefciency has stretched a rapid development of high speedmachining (HSM) technology, which has many advantages suchas high removal rates, low cutting forces, leading to excellentdimensional accuracy and surface nishing quality[3,4]. However,higher cutting speed usually renders the emergence of serratedchipow[5], which ties up with decreased tool life, degradation ofthe surface nish and less accuracy in the machined part[6]. So, topredict the critical condition and especially the critical cuttingspeed for the onset of serrated chip ow could be of signicantimportance.

The mechanism for the onset of serrated chip ow has beenextensively studied[712],and for most ductile metallic materials,the emergence of serrated chip ow is found be related to thethermoplastic shear instability occurred in the primary shear zone(PSZ)[8,9], which is often referred to the formation of adiabaticshear band [1316]. And thus, considerable efforts have beencarried out to focus on the adiabatic shear localization in theserrated chip formation process, and several classical theoretical

models have been developed to predict the onset of serratedchip ow.

The rst prediction for the emergence of serrated chip owwas provided by Recht [17]. He pointed out that when thetendency of the material in PSZ to harden with plastic deformationis overtaken by thermal softening effects, catastrophic shearoccurs, and thus the serrated chip forms. A similar approach wasproposed by von-Turkovich and Durham [18] to explain thetransition of chip ow from continuous to serrated. It wasassumed that such transition requires a maximum in the shearstressshear strain curve. Hou and Komanduri[19]and Komanduriand Hou[20]extended Rechts classical model to predict the onsetof shear instability. In their model, the possible sources of heatcontributing toward the temperature rise are identied based on

an analysis of the cyclic chip ow, and the temperature in theshear band was determined by using Jeagers classical methods.The shear stress in the shear band is calculated at the shear-bandtemperature and compared with the value of the shear strength ofthe bulk material at the preheating temperature. They stated that,once the shear stress in the shear band is less than or equal to theshear strength of the bulk material, shear localization is imminent.

The analytical model presented by Semiatin and Rao [21] isperhaps the rst to provide a quantitative prediction of the criticalspeed at which the serrated chips are produced. Using the dataavailable in the literature, the serrated ow is found to beimminent when the ow localization parameter (the ratio of the

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International Journal of Machine Tools & Manufacture

http://dx.doi.org/10.1016/j.ijmachtools.2014.06.0060890-6955/&2014 Elsevier Ltd. All rights reserved.

n Corresponding author. Tel.:86 10 82543958; fax:86 10 82543977.E-mail address:[email protected](L.H. Dai).

International Journal of Machine Tools &Manufacture 86 (2014) 1833
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normalized ow softening rate to the strain rate sensitivity) isequal to or greater than 5. This model could give reasonablepredictions of the critical speeds for the emergence of serratedchip ow in machining of AISI 4340 and 1045 steels, but thepredicted critical speeds for titanium were much higher than theexperimental ndings reported by Recht [17]. Later, Xie et al.[22,23] extended Semiatin and Raos model to investigate theeffect of cutting conditions on the onset of shear localization in

metal cutting. In their work, the power law relation was used todescribe the material plastic behavior, and Loewen and Shaw smodel was applied to estimate the shear band temperature. Andthus the ow localization parameter can be expressed in terms ofassociated cutting conditions and properties of the work material.Once the ow localization parameter surpasses the critical valuewhich should be determined experimentally, the shear localizationoccurs.

By applying ideas from the theory of the formation of adiabaticshear band in torsion, Molinari and Dudzinski [24] derived thecondition under which continuous chip ow becomes unstable.Soon after, Burns and Davies[25,26] introduced the concept of alocal deformation zone to treat the tool, chip and workpiece as acoupling system. They derived the critical condition for the onsetof serrated chip ow by solving the differential equations for theforce balance and heat balance inside PSZ. And they pointed outthat the emergence of serrated chip ow can be explained as asupercritical Hopf bifurcation phenomenon: the limit cycle of thenonlinear dynamic system of toolchipworkpiece.

With considering the effect of strain gradient which becomesimportant in the case of shear localization, Aifantis and his cow-orkers [27,28] presented a method for thermo-viscoplasticinstability in chip formation to describe the serrated chip ow.In their work, the shear deformation inside PSZ is treated as asimple shear. They carried out the perturbation analysis to predictthe onset of serrated chip ow, and the relations for the shearband width and spacing were also established. Similarly,also by using perturbation analysis, some other adiabatic shearcritical conditions were built by Li et al. [29], Ye et al. [30] and

Ma et al. [31]. In these works, some specic effects of HSM wereconsidered. Li et al.[29]considered the compressive stress appliedon the shear plane, and the adiabatic shear is found to be favoredby larger compression stress; In Ye et al.s work[30], the materialconvection coursed by the high speed chip ow was taken intoconsideration, and the material convection is proposed to benegative for the shear localization; Ma et al. [31] established ageneral criterion for predicting the material instability undercombined stresses loading, and applied it to the orthogonal cuttingprocess. They stated that, once the plastic work of shear deforma-tion is larger than one-third of that of stretching deformation, oris larger than four times of that of shrinking deformation, theshear located instability is imminent, and the serrated chip owemerges.

At recent, Childs [32] predicted the onset of serrated chipow by introducing a thermal number. He pointed out that oncethe thermal number achieves a critical number, the shearlocalization occurs. However, the critical thermal numberdepends on the material properties and tool rake angle, whichshould be determined by experimentations or numericalsimulations.

Besides the theoretical analysis, the nite element (FE) methodhas also been widely used to predict the onset of serrated chipow. Bker et al. [33]and Bker[34]predicted the serrated chipformation when cutting Ti6Al4V alloy by using ABAQUS. Thedistance criterion for chip separation was used in their model, andthe general trends concerning serrated chip ow were deducedrelated with the work material behavior. Rhim and Oh [35]pro-

posed a new ow stress model which takes into account dynamic

recrystallization to predict the adiabatic shear localization duringcutting AISI 1045 steel. It was found that the serrated chips can bepredicted by using the rigid plastic FE simulation together with thenew ow stress model. Later, Arrazola et al. [36,37]modeled the2D orthogonal cutting by using the Arbitrary Lagrangian Eulerianformulation proposed in ABAQUS/Explicit. The sensitivity of ser-rated chip prediction to the cutting speed and material inputparameters was systematically analyzed. More recently, an adap-

tive numerical methodology was developed by Issa et al. [38]topredict the thermo-mechanical eld localization in orthogonalcutting AISI 4340 stainless steel. In their work, the main thermo-mechanical phenomena such as the nonlinear isotropic and kine-matic hardening with thermal and ductile damage effects weretaken into account. And the effects of uncut chip thickness, initialtemperature, friction coefcient and work ductility on the adia-batic shear localization were investigated. Using the JohnsonCookdamage criterion for chip separation and the modied Zorevmodel for toolchip friction description, Duan and Zhang [39,40]developed a FE method to precisely predict the onset and theformation of serrated chip ow without articial assumptions. Andthe effects of the cutting conditions were also investigated.Migulez et al. [41]performed the FE simulations to predict theshear localization involved in high speed machining of Ti6Al4Vin a wide range of cutting speeds and feed rates. The effects ofsome material parameters on shear ow stability were investi-gated. It states that, the strain hardening exponent has a stabiliz-ing effect, and increasing the initial yield stress has a destabilizingeffect on the onset of serrated chip ow.

It should be pointed out that, all these fantastic pioneerworks give important clues for the understanding of the physicsand mechanics of serrated chip ow. And for most of thetheoretical instability criterions, they may give universaldescriptions for the onset of serrated chip ow, since they wereachieved based on the universal equations controlling the PSZdeformation. However, additional complex numerical calcula-tions are usually required to predict the critical cutting speed atwhich the chip ow changes from continuous to serrated. As for

the FE simulations, the onset of the serrated chip ow can beprecisely predicted. However, it should be pointed out that, incutting process the work materials differ widely in their abilityto deform plastically, to fracture and to sustain tensile/com-pressive stresses[42], thus the onset of serrated chip ow couldhave strong dependence on the work material. But for most ofthe FE analyses, they are usually focusing on a certain workmaterial. Moreover, though some fantastic pioneer FE analyseshave qualitatively investigated the effects of material propertiesand cutting conditions on the onset of serrated chip ow, thequantitative relationship has not been established. And theuniversal explicit expression of the critical cutting speed forthe onset of serrated chip ow is still unavailable.

In this work, high speed cuttings of various metallic materials

were carried out over wide ranges of cutting speeds. Based on theexperimental results, the dimensional analysis and numericalsimulations were applied to predict the critical cutting speed atwhich the serrated chip ow is produced. The universal expressionof the critical cutting speed for cutting metallic material by usingsharp tools is given in terms of the material properties, uncut chipthickness and tool rake angle. It is demonstrated here that oncethe Reynolds thermal number achieves a critical value thatdominated by the work material properties, the serrated chip owemerges. This shows striking parallels to the turbulent ow whichtakes place as the Reynolds number surpasses a critical valuedetermined by the uid properties. Furthermore, the inuences ofthe material properties on the onset of serrated chip ow areinvestigated systematically, the trends of which are in accordance

with Rechts classical criterion.

G.G. Ye et al. / International Journal of Machine Tools & Manufacture 86 (2014) 1833 19


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2. Experimental

To investigate the universal behavior existing in metal cutting,ve typical metallic materials, which are widely employed inautomotive, aerospace, and other industrial applications, are choseas work materials. They includes nickel-base superalloy (IN 718),titanium alloy (Ti6Al4V), steel (AlSI 4340), aluminum alloy(Al 7075) and copper. These ve materials, from easy to difcult-to-cut, have great differences in their thermo-physical properties.They cover a wide range of thermal diffusion, from 3.0 106 m2 s1 for IN 718 to 116 106 m2 s1 for copper.

Cutting experiments were carried out over a wide range ofcutting speeds from 0.05 m/s to 90 m/s by using computer-controlled lathe (0.055 m/s) and light-gas gun based device(590 m/s). The details of the light-gas gun based experimentaldevice can be found in Ref. [30]. Uncoated P10 carbide tools wereapplied, and new cutting inserts were used for each test to limitthe inuence of tool wear. Other test conditions can be found inTable 1.

After cutting, the chips were collected and embedded intoresin. The cross section was mechanically polished and thenetched. Microscopic observations were carried out to examinethe inuence of cutting speed on the chip ow mode.

3. Results

The ow pattern of chip ow evolves with cutting speed for

Al 7075, AISI 4340 steel, Ti6Al4V and IN 718 are shown inFig. 1.It should be pointed out that, the chip ow of copper isall continuously smooth in the applied cutting speed range(389 m/s), so is not shown here.

For the work materials Al 7075, AISI 4340 steel, IN 718 andTi6Al4V, there exists a distinct transition from continuouslysmooth ow to periodically serrated ow with cutting speedincreasing. And the critical cutting speed corresponding to suchtransition exhibits a strong material dependency. Moreover, bycomparing the critical cutting speeds for these four work materi-als, it is found that the transition from continuously smooth toperiodically serrated chip ow seems to be favored by decreasingin material thermal diffusion. About how the thermal diffusionand other material properties affect the onset of serrated chip ow

will be systematically discussed in the next section.The chipow is continuously smooth at lower speeds. The chip

ow is smooth, and the ow motion is homogenous as all crystalparticles are elongated uniformly in a same direction. However, asthe cutting speed increases, the continuously smooth chip owbecomes unsettled. Highly localized shear bands emerge becausethe smooth chip ow is not sufcient to dissipate the energythrough homogeneous plastic ow. The steady chip ow is brokenby the periodic emergence of shear bands, and the smooth freesurface turns out to be uctuant, thus a serrated chip ow forms(seeFig. 2a). FromFig. 2a it can be found that the serrated owmotion is quite inhomogenous since the crystal particles inside theshear bands are elongated seriously along the shear directionwhile those outside the shear bands remain almost undeformed.

The widely observed shear bands between the saw-teeth indicate

that the serrated chip ow in HSM is closely related to therepeated shear banding.

Moreover, the examination of the free surface of the serratedchipow reveals a ne distributed lamellar structure (seeFig. 2b).The shear surfaces of each adjacent lamella show severe elongateddimple structures. This dimple structure is the most signicantfeature of adiabatic shear fracture, which is formed under theeffect of shear stress when shear bands had been produced [43].

The obviously observed elongated dimple structure furtherdemonstrates that the serrated chip ow is ascribed to repeatedshear banding rather than periodic cracking. Therefore, we cantake the condition at which the shear bands just regularly emergein the chip as the critical condition for the onset of serratedchip ow.

4. Universal expression of the critical cutting speed

for the onset of serrated chip ow

From the experimental results we have known that the onset ofserrated chip ow has a strong dependency on the work material.

To clarify the link between the onset of serrated chip

ow and thematerial properties, the dimensional analysis is carried out.A special attention is accorded to the dependence of the critical

cutting speed for the onset of serrated chip ow (Vc) with respectto the material parameters and cutting conditions. Generally, Vcdepends on the following terms:

(a) The cutting conditions and toolchip interface characteristics:uncut chip thickness b; tool rake angle ; tool edge radius r;toolchip friction coefcient.

(b) The physical and mechanical properties of the work material:mass density , elastic modulus E, Poissons ratio , thermalparameters (thermal diffusion , heat capacity cand TaylorQuinney coefcient which denes the fraction of plasticwork converted into heat) and the parameters of the plasticconstitutive equation.

Usually, for most metal materials, the JohnsonCook (JC) lawis adopted to describe the coupling effects of strain hardening, ratehardening and thermal softening on plastic ow:

ABn 1Cln __0

1 TT0

Tm T0

m 1

where is the plastic stress, is strain, _ is strain rate, and Tistemperature. In Eq.(1),Ais the initial yield stress,Bthe hardeningmodulus, n the work-hardening exponent, C the strain ratedependency coefcient, _0the reference strain rate,mthe thermalsoftening coefcient, T0 the reference temperature and Tm is the

melting temperature.The values of JC parameters and other thermo-mechanical

properties used to describe the behavior of IN 718, Ti6Al4V, AISI4340 steel, Al 7075 and copper are specied inTables 2 and 3[3551].

Thus, the critical cutting speedVcis function ofb, ,r,,,E,,, c, , A, B, n, C, _0, m, T0 and Tm. Using the VashyBuckinghamtheorem, the following relationship is obtained:

Vc f; E;A; B; Tm;_0; C; m; n;; r;;; 2a

where

Vc Vc=cT01=2; 2=cT0b2; E E=cT0; A A=cT0; B B=cT0;

Tm Tn

m=T0; _

0 _

0b=cT01=2

2b

Table 1

Cutting parameters.

Rake angle

Clearanceangle

Tool edgeradius

Uncut chipthickness

Cuttingspeed

01 71 0.01 mm 100 m 0.0590 m/s

G.G. Ye et al. / International Journal of Machine Tools & Manufacture 86 (2014) 183320


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where Tnm Tm T0. Here, the dimensionless velocity Vc, whichcan be given as

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiV2c=cT0

q , reects the ratio of the kinetic energy

of external loading to the initial thermal energy. And the dimen-

sionless numbersand Ereect the ratio of the energy consumedin thermal diffusion and the energy stored in elastic deformationto the energy required for initial thermal heating, respectively.

A and B characterize respectively the internal heating due toplastic deformation in yielding and strain hardening process.

For simplicity, here Poissons ratio , tool edge radius r, toolchip friction coefcientand the TaylorQuinney coefcientarekept as constant (0.3; r01; 0.3; 0.9). Therefore, byomitting the parameters that are only dependent upon ,r,, and, Eq. (2) can be written as

Vc f; E;A; B; Tm; C;_0; m; n; 3

To determine the functional dependence, it is necessary tocapture the critical cutting speeds for any combination of thesedimensionless parameters. In this work, the experimentally-validated nite element model is developed to obtain the criti-

cal cutting speeds for given material parameters and cutting

conditions. The details of the numerical simulation can be foundin the Appendix A.

It should be pointed out that, for the continuous chip ow, thecutting force is almost constant after the cutting process stabilized.But for the serrated ow, a cyclic cutting force is produced, and theperturbation of the cutting force rises with increasing the cuttingspeed. Here, to dene the critical cutting speed, we assumed that,

when the uctuation of the cutting force (Fc/Faver) achieves 10%, thetransiton from continuous chip ow to serrated chip ow is regaredto be taken place, and the correspondind cutting speed is set asVc. Atthis condition, the shear bands just regularly emerge in the chip, andthe saw-teeth becomes visible, as shown in Fig. 3. From the HSMexperiments we have known that, the serrated chipow results fromrepeated shear banding. Thus we can take the condition at which theshear bands just regularly emerge in the chip as the critical conditionfor the onset of serrated chip ow. So, we have reasons to believethat the critical cutting speed dened above is reasonalbe.

For any combination of the dimensionless parameters, we canget the corresponding Vc by using FEM simulations. Thus, byvarying any one of the non-dimensional parameters while keepingthe others constant, we can get the evolution rule ofVcwith such

non-dimensional parameter.

Fig. 1. Chip ow pattern evolves with cutting speed for Al 7075, AISI 4340, Ti6Al4V and IN 718.



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For the non-dimensional parameters , E, A, B, Tm and _0, theycontain several variable parameters. It can be found that,E,A,B,Tmand _0 are the independent variables for , E, A, B, Tm and _0,respectively. And , c,T0 andb are their public variables. Here, wechanged the values of the independent variables,E,A,B,Tmand_0to vary respectively the ,E,A,B,Tmand _0. As thus, when varyingthese multi-variable dimensionless parameters, the other dimen-sionless parameters can be kept constant. Also, we can change thevalues of the public variables. But it should be noticed that, whenvarying any one of the multi-variable dimensionless parameters bychange the values of the public variables, it must change simulta-neously the value of the independent variables of the other multi-variable dimensionless parameters to keep them constant.

To investigate the changing tendencies ofVcwith,E,A,B,Tm

_0, C, n, m and , 10 sets of simulations were applied. Thecorresponding values of the independent/public variables for eachset are given inTable 4. Here, the room temperature T0is set to be300 K as constant for simplicity. Moreover, to achieve universalevolution rules ofVc, we investigate the changing tendencies ofVcwith each dimensionless parameter for 3 different combinations ofthe other dimensionless parameters, as shown inTable 4.

By investigating the evolution rules ofVcwith,E,A,B,Tm _0,C, n , m and , we get that

Vcpf1 e1:5 tan 453 1:5 4a

Vcpf2 0:5 4b

Vcpf3E E0:4

4c

Vcpf4n e8:5n 1 4d

Vcpf5A; B 4e

Vcpf6C;_0 4f

Vcpf7Tm; m 4gThe dimensionless cutting speedVcevolves with,,E, andn

for different combinations of other dimensionless parameters areshown inFig. 4.

It can be found that, the evolution rules ofVcwith ,,E, andnare independent on the other parameters, whileA andB,Cand _0,

Tm and m have coupling effects on the evolution rules of Vc.It should be noticed that, both A and B reect the internal heatingof the work material,Cand _0 control together the material strainrate hardening, and the material thermal softening is dominatedby bothTmandm. This may raise the possibility thatAandB,Cand_0, Tm andm are coupled with each other.

According to Eqs. (4a)-(4g), the dimensionless critical cuttingspeedVccan be given as

Vc C0f1f2f3Ef4nf5A; Bf6C;_0f7Tm; m 5where the expressions of f1, f2, f3 and f4 were given in Eqs. (4a)(4d),C0is a constant coefcient, and all the constant coefcients ofthe equations f5, f6and f7are equaled to 1.

To get the value ofC0and to achieve the expressions off5,f6and

f7, six additional sets of simulations were carried out (seeTable 5).

Fig. 2. Microstructure of (a) chip morphology and (b) chip free surface for Ti6Al4V ( V4.07 m/s).

Table 2

The values of the JCparameters.

Material A(MPa) B(MPa) C n m _0 (s1) Tm(K) T0(K)

Copper[44] 100 292 0.025 0.31 1.09 1 1356 300Al 7075[45] 546 678 0.024 0.71 1.56 1 893 300AISI 4340[46] 792 510 0.014 0.26 1.03 1 1793 300Ti6Al4V[47] 783 497 0.028 0.28 1.00 1 105 1880 300IN 718[48] 1350 1139 0.014 0.65 1.00 1 1570 300

Table 3

Mechanical properties and parameters.

Parameters Copper[44]

Al 7075[49]

AISI 4340[50]

Ti6Al4V[51]

IN 718[48]

E(GPa) 129 71 200 105 210(kg m3) 8960 2770 7860 4430 8200(106 m2 s1) 116 53 13 3 3(c) (J kg1 K1) 383 885 473 520 435



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the serrated chip ow occurs. This shows striking analogy to theturbulent ow which takes place as the ratio of external loading tothe viscous diffusion (Reynolds number Re) is up to a critical valuethat determined by the uid properties. It is demonstrated that thecontinuousserrated transition of the chip ow is controlled by theReynolds thermal number as the laminarturbulent transition of theuid is dominated by the Reynolds number. It should be pointed outthat, after the chip separates from the work material, it ows alongthe tool surface as the uidowing in a free surface water channel.The sticking friction takes place along the toolchip interface[54,55],making the chip ow velocity increase gradually in a thin layer nearthe tool surface, which is quite similar to that in the uid boundarylayer. This may raise the possibility that similar dimensionlessnumbers exist for describing the onset of serrated chip ow in HSM

and the emergence of turbulence in uid boundary layer.The evolution of Pe/with Pe/for various work materials

are plotted inFig. 8. In this gure, the solid and hollow patternsindicate that the chips obtained from corresponding cuttingexperiments are continuous and serrated, respectively. Some otherpublished experimental data[30,32,5670]are also given in thisgure to validate the criterion(9). It can be noticed from Fig. 8that, the serrated and continuous chip ow respectively fall in thezone of Pe=41 and Pe=o1. And the transition of the owpattern from continuous to serrated almost takes place aroundPe= 1. InFig. 8, the uncut chip thickness varies from 35 m to500 m, and the tool rake angel is in the range of 6117.51. Andthe work materials involve copper, aluminum alloys (Al 7075 andAl 2024), steels (AISI 4340 and AISI 4045), titanium alloy (Ti 6Al

4V) and nickel-base superalloy (IN 718). These materials have

great differences in their physical and mechanical properties.It implies that the explicit expression(7ac)and criterion(9) areuniversal, which can be used to predict the onset of serrated chipow for various metallic materials over wide ranges of uncut chipthickness and tool rake angle.

More interestingly, after the serrated chip forms, there exists ascaling law between the serration spacing and the Reynoldsthermal number, as shown in Fig. 9. Here, for the experimentalresults obtained inSection 3, we measured the total spacing of 10randomly selected adjacent serrations for each serrated chip, andthe average spacing is set to be the serration spacing. It can befound fromFig. 9that all the data for IN 718, Ti6Al4V, AISI 4340steel and Al 7075 can be tted by a universal straight line with aslope about

1/4. Thus, the serration spacing, which is one of the

most important parameters characterizing the serrated chip,follows a power low dependence on the Reynolds thermal numberas LpPe1=4. It shows clearly that the Reynolds thermal numbercontrols not only the initiation but also the evolution of theserrated chip ow. The Reynolds thermal number plays a majorimportant role in the high speed machining of metallic materials.

5. The inuence of material properties on the onset of serrated

chip ow

5.1. Rechts instability criterion

To better investigate and understand the inuence of material

properties on the onset of serrated chip ow, let us rst introduce

Table 4

Simulation conditions.

Setnumber

Variableparameter

The combination of other dimensionless parameters (deg)

Values of variables Datanumber

Material 106 E A B n C 102 _0 Tm m

1 Al 7075 1.1 97 0.7 0.9 0.71 2.4 1.9 107 2.0 1.56 (deg) 15,10,5,0,5,10,15. 3n721AISI 4340 1.2 179 0.7 0.5 0.26 1.4 2.7 107 5.0 1.03Ti6Al4V 5.8 152 1.1 0.7 0.28 2.8 2.5

1012 5.3 1.00

2 Al 7075 97 0.7 0.9 0.71 2.4 1.9 107 2.0 1.56 0 1, 5, 10, 50, 100, 200 106 m2 s1; orb50, 100, 200, 300, 400 m; orc200,600,1000 J kg1 K1.

3n1442AISI 4340 179 0.7 0.5 0.26 1.4 2.7 107 5.0 1.03Ti6Al4V 152 1.1 0.7 0.28 2.8 2.5 1012 5.3 1.00

3 E Al 7075 1.1 0.7 0.9 0.71 2.4 1.9 107 2.0 1.56 0 E50, 100, 150, 200, 250, 300 GPa; or2500, 5000, 9000 kg m3; or c200,600, 1000 J kg1 K1.

3n1236AISI 4340 1.2 0.7 0.5 0.26 1.4 2.7 107 5.0 1.03Ti6Al4V 5.8 1.1 0.7 0.28 2.8 2.5 1012 5.3 1.00

4 A Al 7075 1.1 97 - 0.9 0.71 2.4 1.9 107 2.0 1.56 0 A100,200,400,800,1400 MPa; or 2500,5000, 9000 kg m3; or c200, 600,1000 J kg1 K1.

3n1133AISI 4340 1.2 179 - 0.5 0.26 1.4 2.7 107 5.0 1.03Ti6Al4V 5.8 152 0.7 0.28 2.8 2.5 1012 5.3 1.00

5 B Al 7075 1.1 97 0.7 - 0.71 2.4 1.9 107 2.0 1.56 0 B100,200,400,800,1400 MPa; or 2500,5000, 9000 kg m3; or c200, 600,1000 J kg1 K1.

3n1133AISI 4340 1.2 179 0.7 - 0.26 1.4 2.7 107 5.0 1.03Ti6Al4V 5.8 152 1.1 - 0.28 2.8 2.5 1012 5.3 1.00

6 n Al 7075 1.1 97 0.7 0.9 2.4 1.9 107 2.0 1.56 0 n0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0. 3n1030AISI 4340 1.2 179 0.7 0.5 1.4 2.7 107 5.0 1.03Ti6Al4V 5.8 152 1.1 0.7 2.8 2.5

1012 5.3 1.00

7 C Al 7075 1.1 97 0.7 0.9 0.71 - 1.9 107 2.0 1.56 0 C0.005, 0.01, 0.015, 0.02, 0.025, 0.03, 0.035,0.04, 0.045, 0.05.

3n1030AISI 4340 1.2 179 0.7 0.5 0.26 - 2.7 107 5.0 1.03Ti6Al4V 5.8 152 1.1 0.7 0.28 - 2.5 1012 5.3 1.00

8 _0 Al 7075 1.1 97 0.7 0.9 0.71 2.4 2.0 1.56 0 _0 1 105, 1 103, 1, 1 103, 1 105; orb50, 200, 400 m; orc200,600,1000 J kg1K1.

3n1133AISI 4340 1.2 179 0.7 0.5 0.26 1.4 5.0 1.03Ti6Al4V 5.8 152 1.1 0.7 0.28 2.8 5.3 1.00

9 Tm Al 7075 1.1 97 0.7 0.9 0.71 2.4 1.9 107 1.56 0 Tm700, 900, 1100, 1300, 1500, 1700, 1900,2100, 2300 K.

3n927AISI 4340 1.2 179 0.7 0.5 0.26 1.4 2.7 107 1.03Ti6Al4V 5.8 152 1.1 0.7 0.28 2.8 2.5 1012 1.00

10 m Al 7075 1.1 97 0.7 0.9 0.71 2.4 1.9 107 2.0 0 m0.50, 0.75, 1.00, 1.25, 1.50, 1.75, 2.00. 3n721AISI 4340 1.2 179 0.7 0.5 0.26 1.4 2.7 107 5.0 Ti6Al4V 5.8 152 1.1 0.7 0.28 2.8 2.5 1012 5.3



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Rechts classical criterion for the onset of serrated chipow. In Rechtsmodel[17], it was assumed that the emergence of serrated chip owrequires a maximum in the shear stressshear strain curve, that is

d

dr0 10

where and are the shear stress and shear strain in the PSZ,respectively.

In general, the criterion(10)can be further written as

QRd_d

PdTdr0 11

where _ is the shear strain rate inside PSZ. Here Q =,R = _ and P =T reect the effect of strain hardening,strain rate hardening and thermal softening, respectively.

Fig. 4. Vcevolves with (a) , (b) , (c) Eand (d) n for different parameter combinations.

Table 5

The conditions for the additional simulations.

Setnumber

variableparameter

The combination of other dimensionless parameters (deg)

Values of variables Datanumber

Material 106 E A B n C 102 _0 1012 Tm m

11 A Ti6Al4V 5.77 152 0.28 2.8 2.5 5.27 1.0 0 A100,200,400,600,800,1000,1200,1400 MPa,whenB 100, 200, 400, 800, 1400 MPa.

8n540

12 B Ti6Al4V 5.77 152 0.28 2.8 2.5 5.27 1.0 0 B100,200,400,600,800,1000,1200,1400 MPa,whenB 100,200,400,800,1400 MPa.

8n540

13 C Ti6Al4V 5. 77 152 1.13 0.72 0.28 5.27 1.0 0 C0.005, 0.01, 0.015, 0.02, 0.025, 0.03, 0.035, 0.04,0.045, 0.05. when _0 1 105, 1, 1 105.

10n330

14 _0 Ti6Al4V 5. 77 152 1.13 0.72 0.28 5.27 1.0 0 _0 1 105, 1 103, 1, 1 103, 1 105; orb50,200,400 m; or c200,600,1000 J kg1 K1,whenC0.005, 0.025, 0.05.

11n333

15 Tm Ti6Al4V 5.77 152 1.13 0.72 0.28 2.8 2.5 0 Tm700, 900, 1100, 1300, 1500, 1700, 1900, 2100,2300 K, when m 0.50, 1.00, 1.50, 2.00.

9n436

16 m Ti6Al4V 5.77 152 1.13 0.72 0.28 2.8 2.5 0 m0.50, 0.75, 1.00, 1.25, 1.50, 1.75, 2.00. whenTm700, 1100, 1500, 1900, 2300 K.

7n535



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In HSM, the plastic deformation inside PSZ is usually treated asadiabatic[71], Thus dT=d in Eq.(11)can be given as

dT

dc

12

Moreover, prior to the onset of serrated chip ow, the plastic

deformation in PSZ is uniform, and the shear strain rate can be

treated as constant, that is

d_

d 0 13

Inserting Eqs.(12) and (13)into(11), and keep Q40 andP40in mind, Rechts criterion can be rewritten as

PcQ

Z1 14

Fig. 5. (a) Vcevolves with A for different B and (b) Vcevolves with B for different A.

Fig. 6. (a) Vcevolves with Cfor different _0 and (b) Vcevolves with _0 for different C.

Fig. 7. (a) Vcevolves with Tm for different m and (b) Vcevolves with m for different Tm.



10/16

This instability criterion is in accordance with the criterionproposed by Bai[72], which is derived based on the perturbationanalysis to characterize the onset of thermo-plastic shear band forsimple shearing. It indicates that when the tendency of thematerial in PSZ to harden with plastic deformation is overtakenby thermal softening effects, thermo-plastic shear instabilityoccurs, and the serrated chip ow forms.

The instability criterion (14) shows clearly that increase inshear stress and thermal softening effect P accelerate theinstability, whereas increasing the strain hardening effect Qretards the onset of serrated chip ow.

It should be pointed out that, the HSM process is much morecomplex than simple shearing, and the temperature rise inside PSZcould be affected by thermal diffusion and material convectionthat are caused by the rapid chip ow in HSM [26,30]. So, theinstability criterion(14), which is obtained based on the adiabatic

assumption, cannot be strictly applied to predict the criticalcondition for the onset of serrated chip ow. However, it givesclues to investigate the inuences of material parameters on thechip ow instability.

5.2. The inuence of the initial yield stress A and hardening

modulus B

The critical Reynolds thermal number Pec plotted with A forvarious B is shown inFig. 10a. There exists a scaling low betweenPecandAB=3 asPecpAB=34:8 15

It can be found that a higher initial yield stress A or hardeningmodulusBleads to a lower critical cutting speed at which the chipow changes from continuous to serrated. So, increasing the initialyield stress A or hardening modulus B promotes the onset ofserrated chip ow.

A higher initial yield stress usually indicates a higher hardness [73].And the serrated chip ow is usually favored by increasing thematerial hardness[74]. Thus the serrated chip ow could be facilitatedby increasing the material initial yield stress A.

For orthogonal cutting, the plane strain state is adopted, thusthe J-C law can be given in the form of shear stress as

1

ffiffiffi3p

A

B

ffiffiffi3p

n

1Cln

_

ffiffiffi3p _

0 1

TT0Tm T0

m

16

The JC law(16) indicates that a higher initial yield stress Aresults in a higher shear stress , leading to a higher energyconsuming and hence a higher temperature rise (see Eq.(12)) (theaverage shear strain inside PSZ can be regarded as constant beforeinstability occurs). This facilitates the shear banding and hencepromotes the emergence of serrated chip ow. Form Rechtsinstability criterion(14) it also can be found that a higher shearstressrenders a higherand thus promotes the instability. Thisis in accordance with the tendency described by Eq. (15).

On the other hand, a higher hardening modulus B indicates ahigher strain hardening, which seems to have a negative effect onthe instability initiation. However, it should be noticed that ahigher B also means a higher ow stress, which facilitates theserrated chip ow. Inserting the JC law into Rechts instabilitycriterion(14)we can get that

pAB=

ffiffiffi3

p n2B

17

This shows clearly that increasing the hardening modulus Balso accelerates the ow instability and thus promotes the onset ofserrated chip ow. Eq.(17)also implies that, increasing the initialyield stress promotes the instability much more obviously thanincreasing the hardening modulus. This shows a similar tendencywith Eq.(15), in which the hardening modulus is multiplied by asmaller coefcient (1/3) while the initial yield stress is multipliedby a bigger one (1).

5.3. The inuence of the hardening exponent n

The evolution of Pecas a function ofn is plotted inFig. 10b. Thecritical Reynolds thermal number Pec is linearly proportional toe8:5n 1. It is shown that increasing the hardening exponent nhinders the emergence of serrated chip ow.

A larger hardening exponentn usually implies a stronger effectof strain hardening, which retards the shear banding and thushinders the onset of serrated chip ow. Indeed, for the JC law thestrain hardening effect Q dependents on the strain hardeningexponent n as Qpn=

ffiffiffi3

p n 1. According to Oxley [75], the

average shear strain inside the primary shear zone can beestimated as

cos =2 sin cos 18where the shear angle can be given by =4 arctan

=2=2[76].

Fig. 8. Evolution of Pe= as a function of Pe=for various work materials.Fig. 9. Serration spacing plotted with the Reynolds thermal number ( b100 m;01).



11/16

Thus the average shear strain is usually in the range of 0.71.5(151rr151; 0rr0.3). So, in the investigated range of0.1rnr1, the strain hardening effect Q always increases withincreasing the hardening coefcientn(seeFig. 11). This retards thethermo-plastic shear instability (see Eq.(14)), and thus hinders theonset of serrated chip ow.

Moreover, to quantitatively compare the present model withRechts classical model,Fig. 12gives the evolutions of Pe= and

as functions of n for AISI 4340 steel (V10 m/s, b100 m,

01). Here, to work out the value of, the shear strain wasestimated by Eq. (18), and the temperature rise T and shearstrain rate _were approximately estimated as[26,75]

Tc

19

_

10V cos =b cos

20

Fig. 10. Evolutions of Pecas functions of (a) A , (b) n , (c) C, (d) Tm , (e) m and (f) E. The constant coefcients of the tted lines are in agrees with the values calculatedfrom Eq.(7).



12/16

It can be found fromFig. 12that, the present model has a samevarying tendency with Rechts classical model: when Pe= and are larger than one, both of them decrease rapidly withincreasingn; and when Pe= and become smaller than one,both of them decrease much more slowly with increasing n. Moreimportantly, Pe= 1 and 1 take place almost at a same n,which indicates that the critical condition for the onset of serratedchip ow predicted by the present model is in accordance withthat predicted by Rechts classical model.

5.4. The inuence of the strain rate dependency coefcient C

Fig. 10c shows the evolution of PecwithCfor various values of_0. The critical Reynolds thermal number for the onset of serratedchip ow follows a power low dependence on the strain rate

coefcientCas PecpC1:34 0:02 log _0 . It can be found that increas-

ing the strain rate dependency coefcient C facilitates the emer-gence of serrated chip ow.

A higher C indicates a higher ow stress due to strain ratehardening. This leads to a higher temperature rise (see Eq. (19))and thus accelerates the onset of serrated chip ow. Taking the JClaw into Rechts instability criterion (14) we can get that thedimensionless number is approximately proportional to1Cln _=

ffiffiffi3

p _0. Therefore, the instability criterion can be satis-

ed much more easily for a higher C, which is positive for the

emergence of serrated chip ow. Moreover, increasing the

reference strain rate _0 leads to a lower and thus hinders theonset of serrated chip ow. This is in accordance with that impliedinFig. 10c, in which a higher reference strain rate leads to a highercritical cutting speed.

5.5. The inuence of the melting temperature Tm and initial

temperature T0

Fig. 10d gives the variation of Pecwith respect to Tm. It showsthat the critical Reynolds thermal number Pecdepends linearly onT

4:2m . Indeed, from Eq. (7) it can be found that the critical cutting

speed for the onset of serrated chip ow is approximatelydependent on the melting and initial temperatures as VcpTm T04:2. Thus increasing the melting temperature Tm or redu-cing the initial temperature T0 hinders the onset of serratedchip ow.

HigherTmor lowerT0means the work material can be softenedby heating due to plastic deformation much harder. This retardsthe shear band initiation and hence hinders the emergence ofserrated chip ow. It should be noticed that, the thermal softeningeffect P in the instability criterion(14) is approximately propor-

tional toTm T0m

. Noticing that the thermal softening coef-cient m is positive. So, increasing the melting temperatureor reducing the initial temperature could weaken the thermalsoftening effect and thus stabilizes the thermo-plastic sheardeformation.

5.6. The inuence of the thermal softening coefcient m

The evolution of the critical Reynolds thermal number as afunction of the thermal softening coefcient m is shown inFig. 10e. The critical Reynolds thermal number Pecvaries with maccording to Pecpm, where 6cTmT0=1010 J1:5. Increasingthe thermal softening coefcientm has a stabilizing effect on the

thermo-plastic shear deformation which hinders the onset ofserrated chip ow.Similar to the effect of melting temperature Tm, the work

material is much harder to be softened by heating due to plasticdeformation for a larger m. For the JC law, the thermal softeningeffectPis approximately proportional to m as

PpmT=Tnmm 1 21

The temperature rise in the PSZ prior to shear banding can beroughly estimated from Eq. (19). And thus the temperature risefor the applied work materials (copper, Al 7075, AISI 4340 steel,Ti6Al4V and IN 718) can be worked out, as shown in Table 6(0.7oo1.5). It can be noticed that the nickel-base superalloy IN718 has a maximum temperature rise (295 K) at max

1.5, while

the copper has a minimum one (11 K) at min0.7. And T=Tnmhasa maximum value about 0.3 at max1.5 for the aluminum alloyAl 7075. It should be pointed out that, in the range of 0oT=Tnmo0:3, the term mT=Tnmm 1 decreases with increasing m , asshown inFig. 13. Thus, increasing the thermal softening coefcientmcould weaken the thermal softening effect, which stabilize thethermo-plastic shear deformation and hinders the onset of ser-rated chip ow. This trend is in accordance with that implied inFig. 10e.

Moreover, Fig. 14 gives the evolutions of Pe= and asfunctions ofm for AISI 4340 steel (V10 m/s, b 100 m,01).It is found that, Pe= and have same tendency with changingthe thermal softening coefcientm, and the Pe= 1 and 1almost take place at a same m. This shows clearly that the present

model has a same varying tendency with Rechts classical model.

Fig. 11. Evolution ofn=ffiffiffi

3p

n 1 as a function ofn.

Fig.12. Evolutions of Pe=and as functions ofnfor AISI 4340 steel (V10 m/s,b100 m, 01).



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5.7. The inuence of the elastic modulus E

The evolution of Pecas a function ofEis shown inFig. 10f. Thecritical Reynolds thermal number follows a power low dependenton the elastic modulus as PecpE

0:4. It shows that increasing the

elastic modulus has a negative effect on the onset of serratedchip ow.

A higher E means more energy could be stored in elasticdeformation while less energy could be divided to heating thework material through plastic ow. This retards the thermalsoftening and thus hinders the emergence of serrated chip ow.

Moreover, during cutting, the tool exerts a force on the chipover their contact surface, making the chip deform in a localcompressive deformation zone. The toolchip compressive stressinduces a gradient in the shear stress, leading to the large scaleshearing deformation that takes place in the PSZ. Thus the

thermo-plastic shear deformation and the energy input into the

PSZ are dominated by the toolchip compression. It should benoticed that, the elastic unloading of the toolchip compressioncould take place as the compressive stress reaches its yield limit[32].Therefore, increasing the elastic modulus E promotes the elasticunloading of the toolchip compression, leading to a reduction of theenergy input into the PSZ and thus retards the onset of serratedchip ow.

5.8. The inuence of the heat generation term c

According to Eq.(7), the critical cutting speed for the onset ofserrated chip ow depends on the material density and specicheat as Vcp c3:4. It shows that increasing the heat generationterm chinders the onset of serrated chip ow.

The heat generation termcdescribes the energy consumingfor unit temperature rise. According to(19), increasingcleads toa diminution of the temperature rise for a given value of shearstrain. As a consequence, the stress drop due to thermal softeningis weaker, which has a stabilized effect on the thermo-plasticshear deformation inside the PSZ. Indeed, from the instabilitycriterion(14)it also can be easily found that, highercretards thethermo-plastic shear instability and hence hinders the onset of

serrated chip ow.

6. Conclusions

HSM experiments of IN 718, Ti6Al4V, AISI 4340 steel, Al 7075and copper was undertaken with cutting speed ranging from 0.05to 90 m/s. The microscopic observations of chips reveal that thetransition from continuous chip ow to serrated chip ow can beattributed to a repeated shear band formation inside PSZ, and theonset of serrated chip ow has a strong dependence on the workmaterial. The dimensionless analysis and nite element simula-tions were carried out to obtain the critical cutting speed at whichthe serrated chip ow is produced. The universal expression of the

critical cutting speed for cutting metallic materials by using sharptools is achieved. It is given in terms of material properties, uncutchip thickness and tool rake angle. The predictions of the criticalcutting speeds show good agreements with the experimentalndings for various metal materials over wide ranges of uncutchip thickness and tool rake angle. Moreover, it is found that thereexist striking similarity between the serrated chip ow and theturbulent uid ow. As the laminarturbulent transition of theuid is dominated by the Reynolds number, the continuousserrated transition of the chip ow is controlled by a Reynoldsthermal number. And this Reynolds thermal number also controlsthe evolution of the serrated chip ow as the serration spacing isfollowed a power law dependence on the Reynolds thermalnumber. At last, the inuences of the material properties on the

onset of serrated chip ow are systematically investigated.It shows that increasing the work material density, specic heat,thermal conductivity, elastic modulus, melting temperature, refer-ence strain rate, work-hardening exponent and the thermal soft-ening coefcient hinders the onset of serrated chip ow, whileincreasing the material initial yield stress, hardening modulus,strain rate dependency coefcient and the reference temperaturepromotes the emergence of serrated chip ow. This shows goodagreement with Rechts classical criterion.

Acknowledgment

This work was supported by the Nature Science Foundation

of China (Grants nos. 11132011 and 11202221), the National Basic

Table 6

Temperature rise in the PSZ before shear banding.

Coppe r Al 7075 AISI 4340 Ti6Al4V IN 718

T(K) (0.7) 11 81 77 124 138T(K) (1.5) 23 174 166 265 295T=Tnm (0.7) 0.010 0.137 0.052 0.078 0.108T=Tnm (1.5) 0.022 0.293 0.111 0.168 0.232

Fig. 13. Evolution ofmT=Tnmm 1 as a function ofm.

Fig.14. Evolutions of Pe=andas functions ofmfor AISI 4340 steel (V10 m/s,b100 m, 01).



14/16

Research Program of China (Grant no. 2012CB937500) and theChina Postdoctoral Science Foundation (Grant no. 2013M540148).

Appendix A. Numerical simulation

A.1. Modeling

Based on the experimental

ndings, the

nite element simula-tions were applied to capture the critical cutting speed at whichthe chip ow transition from continuous to serrated takes place.

A plane strain model of orthogonal cutting is developed usingthe nite element code ABAQUS/Explicit with Lagrangian formula-tion. The basic geometry of the numerical model is presented inFig. A1. The work material is xed at the lowest contour and thecutting speed is applied to the tool. The tool is treated here forsimplicity as an analytical rigid body.

The mesh of the work material is divided into three parts: theuncut chip material (zone A), the fracture material (zone B) and

the leaving material (zone C). The upper boundary of zone Ccorresponds to the machined surface. The meshes in zones Band C are parallel to horizontal and vertical directions, whilethe meshes in the zone A are characterized by an inclinationangle with the tool surface. An optimal orientation 451is adopted here to facilitate the formation of segmented chipow[77].

A fully coupled thermalmechanical analysis is carried out by

considering CPE4RT elements, which are plane strain, quadrilat-eral, linearly interpolated, and thermally coupled elements withreduced integration and automatic hourglass control. The workmaterial is taken as elasticviscoplastic. And the plastic ow isgoverned by the J-C law.

The extended Coulomb friction model is chosen in this work tomodel the toolchip interaction, and the friction coefcient is setto be 0.3 as a constant.

The separation of the chip from the workpiece is modeled withthe help of a failure zone, see the zone B in Fig. A1. Up to failure,this zone behaves according to the JC model. The failure of thiszone takes place at a critical value pof the accumulated equiva-lent inelastic deformation, and hence the chip separates from thesurrounding workpiece in a dened distance from the tool tip. Inthis work, the

pis set to a value of 2.0 [78].

A.2. Validation of thenite element model

To validate the numerical model developed above, the niteelement simulations of high speed cutting of Ti6Al4V from0.05 m/s to 35 m/s were carried out. The uncut chip thickness andtool rake angle were set as 100 m and 01, respecctively. Theserrated chip morphology can be characterized by three para-meters, i.e., serration spacing, valley and peak (seeFig. A2a). Thecomparison of the simulated and experimental chip morphology ispresented in Fig. A2b. It can be seen that the simulated chipmorphologies agree well with the experimental ones. The good

agreements between the simulated and experimental resultsindicates that the nite element simulations employed in thiswork can give accurate predictions for the chip mophologies.

Fig. A2. (a) Simulated chip morphology for Ti6Al4V at V5 m/s and (b) comparison of simulated chip dimensions with experimental data.

Fig. A1. The schematic diagram of numerical model.



15/16

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Critical cutting speed for on set of serrated chip flow in high speed machining - VARIAS VIRUTAS Y...

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Transcript of Critical cutting speed for on set of serrated chip flow in high speed machining - VARIAS VIRUTAS Y...