author's personal copy - rutgers school of engineeringcoe · author's personal copy...

This article appeared in a journal published by Elsevier. The attachedcopy is furnished to the author for internal non-commercial researchand education use, including for instruction at the authors institution

and sharing with colleagues.

Other uses, including reproduction and distribution, or selling orlicensing copies, or posting to personal, institutional or third party

websites are prohibited.

In most cases authors are permitted to post their version of thearticle (e.g. in Word or Tex form) to their personal website orinstitutional repository. Authors requiring further information

regarding Elsevier’s archiving and manuscript policies areencouraged to visit:

http://www.elsevier.com/copyright

http://www.elsevier.com/copyright

Author's personal copy

Investigations on the effects of friction modeling in finite element simulationof machining

Pedro J. Arrazola a, Tugrul Ozel b,�

a Escuela Politecnica Superior de Mondragon Unibertsitatea, Loramendi 4, 20500 Mondragon, Spainb Manufacturing Automation Research Laboratory, Department of Industrial and Systems Engineering, Rutgers University, Piscataway, NJ 08854, USA

a r t i c l e i n f o

Article history:

Received 29 October 2008

Received in revised form

2 October 2009

Accepted 6 October 2009Available online 13 October 2009

Keywords:

Finite element modeling

Arbitrary Lagrangian Eulerian method

Friction laws

Limit shear stress

a b s t r a c t

Accurately predicting the physical cutting process variables, e.g. temperature, velocity, strain and stress

fields, plays a pivotal role for predictive process engineering for machining processes. These predicted

field variables, however, are highly influenced by workpiece constitutive material model (i.e. flow

stress), thermo-mechanical properties and contact friction law at the tool–chip–workpiece interfaces.

This paper aims to investigate effects of friction modeling at the tool–chip–workpiece interfaces on chip

formation process in predicting forces, temperatures and other field variables such as normal stress and

shear stress on the tool by using advanced finite element (FE) simulation techniques.

For this purpose, two distinct FE models with Arbitrary Lagrangian Eulerian (ALE) fully coupled

thermal-stress analyses are employed to study not only the effects of FE modeling with different ALE

techniques but also to investigate the influence of limiting shear stress at the tool–chip contact on

frictional conditions, which was never done before. A detailed friction modeling at the tool–chip and

tool–work interfaces is also carried by coupling sticking and sliding frictions. Experiments and

simulations have been performed for machining of AISI 4340 steel using tungsten carbide tooling and

the simulation results under increasing limit shear stress have been compared to experiments. The

influence of limiting shear stress on the tool–chip contact friction was explored and validity of friction

modeling approaches was examined. The results presented in this work not only provide a clear

understanding of friction in FEM modeling of machining but also advance the process knowledge in

machining.

& 2009 Elsevier Ltd. All rights reserved.

1. Introduction

Machining is a popular technology to produce discrete metalparts at high production rates. However, machining at highcutting speeds results in high chip sliding velocities, low frictionbut high heat generation on the tool surfaces, especially on rakeface, and leads to excessive crater wear and short tool life. It alsoinduces a small amount of heat and plastic deformation on themachined workpiece which may be advantageous for bettersurface integrity once selections of tool edge geometry andmachining parameters are optimized. Specifically, cutting edgeroundness may induce stress and temperature fields on themachined subsurface and influences finished surface properties aswell as tool life. Finite element (FE) simulations can be utilized tooptimize tool geometry and predict optimum cutting conditions,tool life and surface integrity. However, accurate predictions offorces and field variables largely depend on modeling approach,work material flow stress data and thermal properties, heat

transfer and friction laws implemented at tool–chip-workpieceinterfaces.

From the historical perspective, research on finite elementmodeling (FEM) of chip formation process has been centeredaround two-dimensional orthogonal cutting based plain strainmodels with workpiece materials ranging from low carbon steels,copper, aluminum, stainless steel, hardened steels to titanium andlately on nickel alloys. First FE modeling studies appeared in early1980s. After more than two decades of research, the fact remainsunchanged that chip formation process in cutting is difficult toanalyze, even by using finite element modeling. However, manyadvances have been made on numerical and computational FEmodeling techniques. This paper aims to investigate some aspectsof tool–chip contact friction modeling and implementation into FEmodeling of chip formation process using advanced numericalsolution techniques. First, these FE modeling techniques will bediscussed and then the friction modeling will be investigated.

As commonly known, there are two types of analysis in whicha continuous medium can be described, i.e. Eulerian andLagrangian, in FE modeling of chip formation process. In aLagrangian analysis, the computational grid deforms with thematerial whereas in an Eulerian analysis it is fixed in space. The

ARTICLE IN PRESS

Contents lists available at ScienceDirect

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

International Journal of Mechanical Sciences

0020-7403/$ - see front matter & 2009 Elsevier Ltd. All rights reserved.

doi:10.1016/j.ijmecsci.2009.10.001

� Corresponding author. Tel.: +1732 4451099; fax: +1732 445 5467.

E-mail address: [email protected] (T. Ozel).

International Journal of Mechanical Sciences 52 (2010) 31–42

Author's personal copyARTICLE IN PRESS

Lagrangian calculation embeds a computational mesh in thematerial domain and solves for the position of the mesh atdiscrete points in time. In those analyses, two distinct methods,implicit and explicit time integration techniques, can be utilized.The implicit technique is more applicable for solving linear staticproblems while the explicit method is more suitable for non-linear dynamic problems such as metal cutting.

First numerical approaches for chip formation appeared inliterature used a pre-defined chip geometry and iterativesolutions lead by Usui and Shirakashi [1]. Those models werefound inadequate since incipient chip formation was not ob-servable. A majority of earlier chip formation finite elementmodels have relied on the Lagrangian formulation for non-steadystate plane-strain analysis (including incipient chip formation)pioneered by Strenkowski and Carroll [2] and later followed byKomvopoulos and Erpenbeck [3], Lin and Lin [4], Zhang andBagchi [5] and Shih [6], whereas very few utilized the Eulerianformulation [7]. However, it was evident that Lagrangianformulation required a criterion for separation of the undeformedchip from the workpiece. For this purpose, several chip separationcriteria such as strain energy density, effective strain and fracturemechanics based criteria were implemented in chip formationsimulations as reported by Black and Huang [8]. Later, updatedLagrangian implicit formulation with automatic remeshing hasbeen offered to simulate material plastic flow around the tool tipfor continuous and segmented chip formation to avoid using amaterial separation criterion by Sekhon and Chenot [9], Marusichand Ortiz [10], Ceretti et al. [11], Leopold et al. [12], Ozel and Altan[13], Madhavan et al. [14], Klocke et al. [15] and Baeker et al. [16].

Later, the Arbitrary Lagrangian Eulerian (ALE) technique, whichcombines features of pure Lagrangian and Eulerian analyses, hasbeen utilized in chip formation simulations by Rakotomalala et al.[17] and Olovsson et al. [18], which was followed by Movahhedyet al. [19,20], Adibi-Sedeh and Madhavan [21], Ozel and Zeren[22], Haglund et al. [23] and Arrazola et al. [24]. ALE formulationis utilized mostly to reduce frequent remeshing of workpiecegeometry due to mesh distortions during material separationaround the tool tip, which then results in extrapolation of fieldvariables from previous mesh topography. Explicit dynamic ALEformulation is very efficient for simulating highly non-linearproblems involving large localized deformations and changingcontact conditions such as those experienced in machining. Theexplicit dynamic procedure performs a large number of small timeincrements efficiently. The adaptive meshing technique does notalter elements and connectivity of the mesh. This techniqueallows free boundary conditions, whereby only a small part of theworkpiece in the vicinity of the tool tip needs to be remeshedfrequently.

Undoubtedly mechanics of machining involves some sort ofmaterial separation during chip and surface formation with severeplastic flow of bulk work material along the cutting zone. As adistinct advantage of ALE formulation framework, termination ofthe analysis due to excessive mesh distortions in the chip, acrossdeformation zones and the machined surface can be avoidedusing suitable mesh densities and control parameters throughadaptive meshing. During adaptive meshing, a smooth computa-tional mesh within the ALE domain is first regenerated andsubsequently, solution variables such as energy, density, thermaland mechanical variables, etc. from the previous distorted meshare mapped to the new mesh. Through continual meshing andadvection, quality of the mesh is maintained while the finiteelement solution is advanced readily throughout the course ofchip formation.

In more recent literature, FE simulation of chip formation hasbeen utilized to investigate the influence of tool edge radius andmicro-geometry on predicting forces, stress and temperaturefields. Ng et al. [25] investigated the influence of flow stress inhigh speed machining of steels. Ozel [26] showed the difference instress and temperature fields around edge micro-geometry forhoned and chamfered tools. Yen et al. [27] studied the influence oftool chamfer angle on stress and temperature fields; Guo and Wen[28] looked into the effects of stagnation and round edgegeometry on chip morphology. Ozel and Zeren [29,30] investi-gated the effect of tool edge radius on machined surfacetemperature and stress fields and compared with experimentalresults. Liu and Melkote [31] studied size effect in micro-cuttingusing chip formation simulations.

Prediction of machining induced residual stress fields with FEsimulation of chip formation especially in hardened steelapplications is carried out by a number of works including Liuand Guo [32], Yang and Liu [33], Guo and Liu [34], Umbrello et al.[35], Ee et al. [36], Outeiro et al. [37] and Nasr et al. [38]. Mostrecently, 3D FE modeling of chip formation has been offered tostudy the effects of micro-edge geometry on field variables andtool wear by Attanasio et al. [39], Ozel et al. [40] and Ozel [41].

2. Orthogonal machining experiments

Plunge turning of thin webs with average thickness wwork=2.8mm has been performed on annealed AISI 4340 steel usinguncoated carbide (K313 grade) cutting tool inserts (TPG-432) with0.040 mm edge radius in a rigid CNC turning center at RutgersUniversity as illustrated in Fig. 1. The tool holder (CTCPN644)provided a positive 31 rake angle and 81 clearance angle. In theexperiments, straight edges of triangular inserts (wtool=20 mm

Nomenclature

A plastic equivalent strain in Johnson–Cook constitutivemodel (MPa)

B strain related constant in Johnson–Cook constitutivemodel (MPa)

C strain rate sensitivity constant in Johnson–Cookconstitutive model

Fc, Ft cutting and thrust force components (N/mm)N, Fn normal force (N)N, FR frictional force (N)k shear flow stress (N/mm2)m shear friction factorn strain-hardening parameter in Johnson–Cook consti-

tutive model

rb edge radius of the tool (mm)Tmelt melting temperature of the work material (1C)Troom room temperature (1C)t

u , tc uncut and cut chip thicknesses (mm)V cutting velocity (m/s)go rake angle (deg)e effective strain (-)_e effective strain rate (1/s)_e 0 reference strain rate (1/s)f shear angle (deg)t frictional shear stress (N/mm2)tlimit limiting shear stress (N/mm2)tp maximum shear stress in sticking region along the

tool–chip interface (N/mm2)sn normal stress (N/mm2)

P.J. Arrazola, T. Ozel / International Journal of Mechanical Sciences 52 (2010) 31–4232


wide) were used to create an orthogonal cutting condition (wtool/wwork=7.14). In each test, a new thin web was cut for about 20 susing fresh inserts to eliminate effects of tool wear. Theexperiments were replicated five times. Forces were measuredwith a Kistlers turret type force dynamometer, a PC-based DAQsystem and Kistlers DynoWare software, and cut chipthicknesses were measured using a toolmaker’s microscope. Inorthogonal cutting tests, constant speed V=300 m min�1 and feedtu=0.2 mm/rev were applied. Mean cutting force Fc=514 N with

10.2 N standard deviation and mean thrust force Ft=204 N with6.0 N standard deviation were measured per unit width of cut(w=1 mm). Measured forces and chip thickness are summarizedin Table 1.

3. Finite element modeling of chip formation process

In this study, FEM simulations in orthogonal cutting of AISI4340 steel are investigated. In machining of AISI 4340 steel,uncoated tungsten carbide tool with edge roundness rb=0.040mm, 31 rake angle and an 81 clearance angles are used. Constantchip thickness tu=0.2 mm and cutting speed V=300 m min�1 areselected. All the cutting conditions are assumed to revealcontinuous chip formation.

The essential and desired attributes of continuum-based finiteelement models for machining are: (1) the work material modelshould satisfactorily represent elastic, plastic and thermo-me-chanical behavior of work material deformations observed duringthe machining process, (2) FE model should not require chipseparation criteria that highly deteriorate the physical processsimulation around the tool cutting edge especially in the presenceof a dominant tool edge geometry such as a round edge and/or achamfered edge design and (3) Interfacial friction characteristicson tool–chip and tool–work contacts should be modeled fairlyaccurately in order to account for additional heat generation andstress developments due to friction.

3.1. Work material constitutive model

In numerical analysis, accurate flow stress models areconsidered highly necessary to represent work material constitu-tive behavior under high strain rate deformation conditions.Orthogonal cutting tests and inverse analysis of machining areoffered to determine flow stress at machining regimes [13,25,42].Johnson–Cook (J–C) material model [43] is often used to representthe thermo-visco-plastic behavior of workpiece material despiteits limitations reported with regard to dynamic strain aging, i.e.blue-brittleness effect during a certain range of temperaturevariations in the plastic deformation of carbon steels [44].

This constitutive model describes the flow stress of a materialwith the product of strain, strain rate and temperature effects thatare individually determined as given in Eq. (1). In the Johnson–Cook model, the constant A is in fact the initial yield strength ofthe material at room temperature and a strain rate of 1/s, and erepresents the plastic equivalent strain. The strain rate _e isnormalized with a reference strain rate _e0. The temperature termin the J–C model reduces the flow stress to zero at the meltingtemperature of the work material, leaving the constitutive modelwith no temperature effect. In this study, FE simulation ofmachining AISI 4340 steel in annealed condition is investigatedand its J–C material model constants are adapted from Ng et al.[25] as given in Table 2.

s ¼ ½AþBðeÞn� 1þC ln_e_e 0

!" #1�

T � Troom

Tmelt � Troom

� �m� �ð1Þ

3.2. Friction modeling

In order to simulate machining, it would be desirable to be ableto model both the form of frictional and normal stress distribu-tions along the tool rake face in terms of friction coefficient m andshear friction factor m [44]. Frictional stress follows Coulomb lawt=msn closely at low stress variations; however shear frictionmodeltp=mk becomes more suitable at high stress variations,

Table 1Input parameters for the FE models, contact and cutting conditions.

Parameter AISI 4340+carbide

tool

Material properties

AISI 4340 steel plasticity

Johnson–Cook model

A coefficient (MPa) 792

B coefficient (MPa) 510

n coefficient (-) 0.26

C coefficient (-) 0.014

m coefficient (-) 1.03

Melting temperature (K) 1793

Ref. room temperature

(K)

293

_e Reference strain

rate (-)

0.001

Inelastic heat fraction b (-) 0.9

Density r (kg m�3) AISI 4340 steel 7850

Carbide 15000

Elasticity E (N m�2) AISI 4340 steel 208

Carbide 800

Poisson ratio n (-) AISI 4340 steel 0.22

Carbide 0.2

Conductivity l(W m�1 K�1)

AISI 4340 steel 44.5

Carbide 46

Specific heat c (J kg�1 K�1) AISI 4340 steel 477

Carbide 203

Expansion aw (K�1) AISI 4340 steel 1.23�10�6

Carbide 4.7�10�6

Conv. heat tr. coefficient hcon (W m�2 K�1) -

Emissivity e (-) -

Contact conditions

Thermal conductance Ki (W m�2 K�1) 1�108

Heat Partition coefficient G (-) 0.5

Friction coefficient m (-) 0.5

Shear stress limit tp (MPa) Unlimited–200–300–

400–500–600–700

Friction energy tran. into heat Z (-) 1

Cutting conditions

Cutting speed V (m min�1) 300

Uncut chip thickness tu (mm) 0.2

Depth of cut—d.o.c. d (mm) 1

Cutting edge roundness rb (mm) 40

Rake angle go (deg) 3

Clearance angle an (deg) 8

Carbide insert TPG432

Dynamometer AISI 4340 steel Workpiece with thin webs

Fig. 1. Experimental set-up for orthogonal turning.

P.J. Arrazola, T. Ozel / International Journal of Mechanical Sciences 52 (2010) 31–42 33


where plastic contact takes place. As commonly accepted, alongthe tool–chip contact area near the cutting edge a sticking regionforms and the frictional shearing stress at the sticking regionbecomes equal to the average shear flow stress at tool–chipinterface in the chip, kchip [44]. Over the remainder of the tool–chip contact area a sliding region forms and the frictional stresscan be determined using a coefficient of friction (m) as shown inFig. 2.

When the normal stress (sn) distribution over the rake face isfully defined and the coefficient of friction (m) is known, thefrictional stress t can be determined. Hence, frictional stressdistribution on the tool rake face can be represented in twodistinct regions: a) In the sticking region along the tool–chipinterface where plastic contact occurs

tðxÞ ¼ kchip when msnðxÞZmk and 0oxr lp ð2aÞ

b) In the sliding region along the tool–chip interface, where elasticcontact occurs

t¼ msnðxÞ when msnðxÞomk and lpoxr lc ð2bÞ

On the other hand, the mean coefficient of friction betweentool and chip in orthogonal cutting is usually calculated from the

measured cutting and thrust forces as given by Eq. (4).

m¼ FtþFc tan aFc � Ft tan a

ð3Þ

Friction characteristics that include parameters of the normaland frictional stress distributions on the tool rake face, the lengthof sticking region (lp) and chip–tool contact length (lc) are not easyto implement with the contact and friction modeling in FEsimulations. It is often difficult to obtain these frictionalconditions, which depend on tool and work material pair inmetal cutting, without measuring stress distributions along thetool rake face [44]. Some experimental values for these stressdistributions have been given by Childs et al. [44,45]. In addition,friction models that combine friction coefficient m and shearfriction factor m are also given. Usui and Shirakashi [1] derived anempirical stress characteristic equation as a friction model at thetool–chip interface. Dirikolu et al. [46] made a further modifica-tions to this model by multiplying k with a friction factor m,where 0omo1 and introducing an exponent n.

t¼mk 1� exp �msn

mk

� �a� �� 1=a

ð4Þ

However, implementation of these experimental frictionalobservations into finite element based simulation models is stillnot exploited as evident from the many studies reporting uses of amean friction coefficient. As has been repeatedly stated, frictionwith stick–slip behavior is vastly ignored in FE simulations ofmachining studies due to unavailability of such friction models inmost commercially available FEA software.

In recent years, researchers investigated the influence offriction modeling in FE simulations [23,47–49]. A limiting shearstress to the maximum shear stress is suggested by Haglund et al.[23]. Variable friction models such as pressure dependentcoefficient of friction (m(p)) or shear friction as a function ofcontact pressure (m(p)) have been offered by Ozel [41,47]. Filiceet al. [48] presented a critical analysis comparing mean frictioncoefficient and shear friction model. Arrazola et al. [49] proposeda friction determination method from machining experiments forFE simulations.

In this work, friction modeling with two distinct FE modelingapproaches has been investigated. A mean friction coefficient of0.48 with a standard deviation of 0.04 was calculated from fivereplications of orthogonal cutting experiments and it was roundedup and implemented as m=0.5 for simplicity in FE simulations.Use of this mean friction coefficient with and without limiting

Table 2FE simulation conditions and comparison of the results with experiments. (V=300 m min�1, tu=0.2 mm/rev, 1 mm width of cut).

Test no. FE modeling

technique

Simulated Experimental

Limit shear

stress (tlimit)

Model

boundaries

Ttool (K) Tchip (K) sn (MPa) t (MPa) Fc (N/mm) Ft (N/mm) tc (mm) Fc (N) Ft (N) tc (mm)

1 Unlimited Eulerian 1503 1543 2720 1005 500 204 0.39 514 204 0.33

2 200 Eulerian 1200 1222 2727 222 455 133 0.37

3 300 Eulerian 1399 1429 2703 373 473 165 0.38

4 400 Eulerian 1501 1543 2551 476 491 197 0.38

5 500 Eulerian 1504 1545 2481 500 497 209 0.39

6 600 Eulerian 1504 1544 2396 601 499 207 0.39

7 700 Eulerian 1503 1543 2514 766 500 205 0.39

8 Unlimited Lagrangian 1579 1608 1880 211 529 178 0.24

9 200 Lagrangian 1381 1437 1533 210 455 122 0.27

10 300 Lagrangian 1561 1617 1619 210 507 176 0.28

11 400 Lagrangian 1534 1595 1574 227 514 174 0.27

12 500 Lagrangian 1572 1633 2272 226 525 210 0.29

13 600 Lagrangian 1501 1574 1920 220 532 192 0.30

14 700 Lagrangian 1527 1583 1679 213 584 200 0.31

Normal stress at the rake

Frictional stress at the rakeτ = kchip

WO

RK

PIE

CE σn, τ

σn, (x)

τ = μ σn (x)

lp lc

TOOL

x

Fig. 2. Normal and frictional stress distributions on the tool rake face.



shear stress has been studied, since the maximum frictional stress(tp) cannot be greater than the chip material shear flow stresskchip.

Throughout this work, penalty contact method with finitesliding is employed to represent friction conditions. Contact pairinteraction is defined by a friction coefficient m. In order tounderstand the influence of stick–slip contact conditions, wherethe maximum shear stress reaches a limit (tlimit=tp), a limitingshear stress model is also implemented. Various values of theshear stress limit (200–700 MPa) are also tested and computedcontact normal pressure and shear stress fields are compared witheach other.

It should be noted that, in this study, sliding friction model isimplemented using only friction coefficient with finite sliding andsticking–sliding friction model is implemented using frictioncoefficient with finite sliding and shear stress limit.

The results presented in this work will not only provide a clearunderstanding of friction modeling in finite element modeling ofmachining but will also advance the process knowledge in highspeed machining especially about the accuracy of predictedphysical variables such as tool temperatures and stresses in aparticular cutting condition. Experimentally, it is very costly anddifficult to measure stresses and temperatures in machiningprocesses.

3.3. Finite element modeling techniques

In this paper, ABAQUS/Explicit software with ALE modelingapproach is used to conduct FE simulations for orthogonal cuttingconsidering round tool edge geometry and all of the aboveattributes are successfully implemented in the model. The chipformation process is simulated via adaptive meshing and plasticflow of work material in the vicinity of the tool round edge.Therefore, there is no need for a chip separation criterion in theproposed FE models.

The explicit dynamic method is used mainly because it hasadvantages of computational efficiency for large deformation andhighly non-linear problems as experienced during chip formationin machining. As a coupled thermal-mechanical process, chipformation can generate heat to cause thermal effects, whichinfluence mechanical effects strongly. Simultaneously workmaterial properties may change significantly as strain rate andtemperature increase. Thus, a fully coupled thermal-stressanalysis in which the temperature solution and stress solutionare carried out concurrently must be applied.

Therefore, a thermo-mechanical FE simulation scheme iscreated by including tool and workpiece thermal and mechanicalproperties as summarized in Table 2. Both workpiece and toolmodels utilize four-node bilinear displacement and temperature

INFLOW

CHIPFLOW

OUTFLOW

TO O L

WORKPIECE

V = V

Euleriany

x

x c

Lagrangian

CHIP

ToolPositionAtIncipientState

WORKPIECE

y

x

Lagrangian

Vx = Vc

T = T0

Ux = Uy = 0, T = T0

ToolPositionAtSteady-State

Vx = Vc

Ts = Ts

Fig. 3. FE simulation model for ALE formulation with: (a) Eulerian and Lagrangian boundary conditions, and (b) pure Lagrangian boundary conditions.



(CPE4RT) quadrilateral elements and a plane-strain assumptionfor deformations that occur during the orthogonal cutting process.Element size has a significant influence on predicted temperatureresults. Thus, this parameter was carefully controlled in bothmodels and an element size varying between 1.5�10�6 and10�10�6 m depending on the model zone (smaller at the tool-chip interface) was chosen in this study.

3.4. ALE FE model with Eulerian and Lagrangian boundaries

Initially an ALE model has been designed in which theworkpiece is also modeled with Eulerian boundaries from theinflow, chip-flow and outflow ends and with Lagrangian bound-aries at top and bottom surfaces of the workpiece as shown inFig. 3a. Top surface of the workpiece with free boundaries reachesthe final deformed shape at steady-state cutting and it is allowedto deform without restraint.

In this particular ALE approach, the general governingequations are solved for both Lagrangian boundaries and Eulerianboundaries in the same fashion. This technique exclusivelycombines features of pure Lagrangian analysis and Euleriananalysis in which the mesh is fixed spatially and the materialflows through the mesh as explained earlier. However, this FEMmodel requires a pre-defined chip geometry. The chip surfaces aredefined with Lagrangian boundary conditions and the chip uppersurface is defined with Eulerian boundary conditions. Therefore,the chip flow is bound at a vertical position. However, the chipthickness and chip–tool contact length gradually settle to theirfinal values with a change in deformation conditions as thecutting reaches its steady state.

The major drawback of this particular ALE approach is that thepre-defined chip shape must be determined before hand andentered into the FE simulation model. Similar ALE models werepresented by Adibi-Sedeh and Madhavan [21], Ozel and Zeren[22], Haglund et al. [23] and Arrazola et al. [24].

3.5. ALE FE model with pure Lagrangian boundaries

An FEM simulation model with ALE scheme with pureLagrangian boundaries is designed and kinematic penalty contactconditions between the tool and the workpiece are defined asshown in Fig. 3b. This model allows an FE simulation scheme tosimulate chip formation from the incipient to steady state. In thisFE scheme, the explicit dynamic procedure performs a largenumber of small time increments efficiently. The adaptivemeshing technique does not alter elements and connectivity ofthe mesh. This technique combines the features of pureLagrangian analysis in which the mesh follows the material andEulerian analysis, when it is needed as part of the adaptivemeshing, in which the mesh is fixed spatially and the materialflows through the mesh. The cutting process as a dynamic eventcauses large deformations in a few numbers of increments,resulting in massive mesh distortion and termination of the FEsimulation. It is highly critical to use adaptive meshing with finetuned parameters in order to simulate plastic flow over thetoolround edge. Therefore the intensity, frequency and sweepingof adaptive meshing are adjusted to the most optimum setting formaintaining a successful mesh during the simulation of theorthogonal cutting process.

4. Simulation results and discussions

In order to test the influence of friction modeling with limit-ing shear stress values on FE simulations, a set of simulation

experiments has been conducted. All input parameters used in theFE simulations are summarized in Table 1. The simulation experi-ments as well as results obtained from each simulation are given inTable 2. As can be seen, seven simulations have been carried outwith each FE ALE solution technique, one simulation with theCoulomb friction law (without a shear stress limitation) and the restwith a sticking–sliding model (with a limiting shear stress), wherethe maximum shear stress has been limited to 200, 300, 400, 500,600 and 700 MPa. In all simulations, cutting conditions as well as themean friction coefficient have been kept the same.

FE simulations of chip formation process with the ALEtechnique using Eulerian boundaries (Tests 1–7) and Lagrangianboundaries (Tests 8–14) have been conducted separately. Cuttingforces, temperature, stress and velocity fields are predicted usinga mean coefficient of friction (m=0.5) with no limiting shear stressand with limiting shear stresses (tlimit) of 200, 300, 400, 500, 600and 700 MPa. Fig. 4a depicts the evolution for the maximumtemperature on the tool and the chip. Fig. 4b shows the predictedcutting forces from the test models with increasing shear stresslimit (tlimit). As can be observed, for tlimit values higher than400–500 MPa, results for temperatures and forces are almostequal to those obtained with the Coulomb friction law, wherethere is no limit shear stress utilized.

The predicted forces and experimental forces presented inTable 2 showed some differences as well as good agreementswhen different ALE modeling techniques with various limit shearstress values are applied.

In ALE FE model with Lagrangian boundaries, simulated forcesincrease when the limit shear stress is increased. Predicted cuttingand thrust forces are found closer to the experimental ones for a

1100

1200

1300

1400

1500

1600

1700

200Maximun Shear Stress (MPa)

Tem

pera

ture

(K)

Max. Chip Temperature Eulerian BoundariesMax. Tool Temperature Eulerian BoundariesMax. Chip Temperature Coulomb Eulerian BoundariesMax. Tool Temperature Coulomb Eulerian BoundariesMax. Chip Temperature Lagrangian BoundariesMax. Tool Temperature Lagrangian BoundariesMax. Chip Temperature Coulomb Lagrangian BoundariesMax. Tool Temperature Coulomb Lagrangian Boundaries

0

100

200

300

400

500

600

700

200

Forc

e (N

)

Maximum Shear Stress (MPa)

Cutting Force (Fc)Feed Force (Ff)Cutting Force CoulombFeed Force CoulombCutting Force Lagrangian Boundaries (Fc)Feed Force Lagrangian Boundaries (Ff)Cutting Force Coulomb Lagrangian BoundariesReed Force Coulomb Lagrangian BoundariesExperimental Cutting ForceExperimental Feed Force

300 400 500 600 700 800

300 400 500 600 700 800

Fig. 4. (a) Variation of maximum temperature on the tool and the chip, and

(b) cutting forces with increasing maximum shear stress.



limiting shear stress value between 400 and 500 MPa as shownTable 2.

However, comparing the forces of Coulomb friction andsticking–sliding friction revealed an important difference, whichcan be seen for a maximum shear stress of 200 MPa in Fig. 4. Theinfluence is larger for the thrust force since it decreases by 35%,while the cutting force decreases by only 11%.

Fig. 5 shows simulated temperature fields for Tests 1,2, 5 and 7.As can be observed in Test 1, where the shear stress is not limited,a second hot spot below the cutting edge appears in the tool and amaximum temperature of 1543 K has been achieved. On the otherhand, the shear stress limit of 200 MPa (Test 2) decreases themaximum temperature to 1222 K and the hot spot disappears.Fig. 6 shows simulated temperature fields for Tests 8, 9, 12 and 14.Similar trends are observed in those testing conditions. However,predicted temperature values are found to be larger with ALE FEmodel with Lagrangian boundaries.

Figs. 7 and 8 show the contact normal pressures sn and theshear stresses t for Tests 1–2 and 8–9, respectively. The scale forthe numerical values has been kept constant for both tests, inorder to make a visual comparison. It can be observed thatthe normal pressure sn indicates hardly any changes between thesimulation with Coulomb friction and the ones with limiting shearstress friction. However the shear stress values obviously aresmaller as the maximum shear stress limitation is decreased.

Attention has also been paid to predicted velocity fields.Figs. 9 and 10 show simulated velocity fields for Tests 1–2 and8–9, respectively. There exist stagnation points along the roundcutting edge, where work material below the stagnation pointflows underneath the tool along the flank face and work materialabove the stagnation point begins to flow along the rake face andbecomes the chip. This is evident in simulated velocity fields,indicating a very low velocity around the stagnation point.Velocity fields for Tests 1 and 2 showing the stagnation pointand material flow direction around the round cutting edge aregiven in Fig. 9. As can be seen, when the maximum stress is notlimited (Test 1) a stagnant zone is clearly formed where thevelocity is lower than 0.05 m/s. For Test 2, where the maximumshear stress tp is limited to 200 MPa, this stagnant zone vanishes.

After comparing chip thicknesses, it is observed that lower chipthickness values than the experimental ones are found whenusing the ALE FE model with Lagrangian boundaries. However, inthe case of the ALE FE model with Eulerian chip boundaries,higher values than the experimental ones are obtained.

It must be noted that for sticking–sliding contact conditions, adifficulty in identifying friction parameters exists as the max-imum shear stress tp varies with temperature, plastic strain andstrain rate. On the other hand, a simple Coulomb friction law doesnot limit the maximum shear stress and unrealistic values, higherthan the material shear stress limit, could occur for high contactpressures. As will be explained latter, this may not pose a seriousproblem if a FE model with plastic yield and ALE formulation isused, since the shear stress applied will never be higher than theone that the material can withstand plastically.

A limit to shear stress can be calculated with the Johnson–Cookconstitutive model. For example, let us assume an average plasticstrain of 4 for the secondary shear zone, a temperature of 1000 1C anda strain rate of 105. With these values, a flow stress of 680 MPa isobtained using the J–C model for AISI 4340 steel with parametersgiven in Table 1, so the maximum shear stress with Von Mises yieldcriterion should be around tp ¼ kchip ¼ s=

ffiffiffi3p¼ 393 MPa.

The Coulomb friction model offered in ABAQUS establishes thetangential force and sliding condition. The program calculates thesticking force at each node, based on the mass and accelerationassociated to each node. This tangential force is compared tofriction force on Coulomb law (mFn) and the minimum value is

TEMP (K)

154314391335123011261022

918814710606501397293

Test 1 (Max. 1543 K) �p = unlimited

TEMP (K)

122211441067

989912835757680603525448370293

Test 2 (Max. 1222 K) �p = 200 MPa

TEMP (K)

154514401336123211281023

919814710606502397293

Test 5 (Max. 1545 K) �p = 500 MPa

TEMP (K)

154314391335123011261022

918814710606501397293

Test 7 (Max. 1543 K) �p = 700 MPa

Fig. 5. Simulated temperature fields for Tests 1, 2, 5 and 7.



Fig. 6. Simulated temperature fields for Tests 8, 9, 12 and 14.

CPRESS (MPa)28002567233321001867163314001167

933700467233

0

CPRESS (MPa)28002567233321001867163314001167

933700467233

0

CSHEAR (MPa)1000

917833750667583500417333250167

830

-968

CSHEAR (MPa)1000

917833750667583500417333250167

830

-228

2 �p = 200 MPa tseTTest 1 �p = detimilnu

Fig. 7. Contact normal pressure rn and shear stress s fields for Tests 1 and 2.



Fig. 8. Contact normal pressure rn and contact shear stress s fields for Tests 8 and 9.

Location of the stagnation point and flow direction

Velocity (m/s)5.14.74.33.83.43.02.62.11.71.30.90.40.1

0

Velocity (m/s)5.14.74.33.83.43.02.62.11.71.30.90.40.1

0

Test 1 �p = unlimited Test 2 �p = 200 MPa

Location of the stagnation point and flow direction

Fig. 9. Stagnation point and flow direction in velocity fields for Tests 1 and 2.



applied to this node. If the minimum value is the friction force(mFn) a sliding condition exists, where as if the minimum value isthe tangential force at the node, the sticking condition exists(Table 3).

Fig. 11 shows the normal pressure (sn), shear stress applied (t)and the shear stress predicted by Coulomb’s law for a stickingnode (a) and a sliding node (b) in Test 1 condition (without shearstress limit). As can be observed in Fig. 11a, the shear stress thatABAQUS software applies to a certain node is not the stress fromCoulomb’s law, but the sticking force, which is smaller. If the sameanalysis is made for a sliding node (Fig. 11b) it can be seen that theshear stress applied is the same as the one from Coulomb’s law.

5. Conclusions

This study stresses the importance of detailed friction model-ing studies to improve predictions made with FE simulations of

the chip formation process. While predicted and experimentalforces show differences, comparing the forces between theCoulomb friction and the sticking–sliding friction reveals im-portant findings that the influence is larger over the thrust forcesince it decreases by 35%, while the cutting force decreases onlyby 11%. The results presented in this work not only provide a clearunderstanding of friction modeling in finite element modeling ofmachining but also advances the process knowledge in machiningespecially about the relation between predicted physical variablessuch as tool temperatures and stresses and the friction modelimplemented. Experimentally, it is very costly and difficult tomeasure stresses and temperatures in high speed machining.From the results of this study, the following conclusions can bedrawn and recommendations can be made:

� When the FE simulation model of ALE with Eulerian bound-aries is used, same results are obtained when a Coulomb

Fig. 10. Simulated velocity fields for Tests 8 and 9.

Table 3Comparison of friction models.

Shear stress not limited Maximum shear stress (tp) Conclusion

Elastic body For very high normal forces, the friction force would be

very high and the body would never slip, even if the

material’s maximum shear stress was overcome. In this

case the body should slip in reality but it would not in

the simulation

For very high normal forces, the friction force will be

limited to tp, and the body would slip in the simulation,

as should happen in reality

It makes sense to limit the

shear stress, since one cannot

simulate the failure straight

away with an elastic

simulation

Plastic body+

Lagrangian

For very high normal forces, the friction force would be

very high and the body would plastically deform. In this

case the body should slip in reality but it would not in

the simulation. The elements in contact would deform

and distort greatly that the simulation would stop

For very high normal forces, the friction force would be

very high and the body would plastically deform. When

the shear stress limit is achieved the body would slip in

the simulation as it should in reality

In this case, it may not make

much sense to limit the shear

stress

Plastic

body+ALE

Since the material flows through the mesh, the mesh

does not distort and the shear stress applied at each

node cannot be higher than the stress that the material

can withstand

If the shear stress is limited, a value smaller than the one

that the material needs to yield plastic deformations is

applied

It does not make much sense

to limit the shear stress, since

we are simulating material

failure and FEA software will

never apply a higher value



friction and a sticking–sliding friction are utilized, if themaximum shear stress is higher than 500 MPa. For limitingshear stress values of 200, 300 and 400 MPa, lower tempera-tures and cutting forces are predicted with the FE simulations.� When using FE model of ALE with Lagrangian chip boundaries,

predicted forces increase with increasing limiting shear stressvalue. In this case the influence of limiting shear stress on thefriction model becomes apparent.� A major shortcoming of stick–slip friction models is the

uncertainty about the limiting shear stress value as it isdependent on local deformation conditions and temperatures.� These investigations reveal that stick–slip friction models

should be used with caution and limiting shear stress valuesmust be determined for each cutting condition to predictforces, stresses and temperatures more accurately in FEsimulations of chip formation processes.

References

[1] Usui E, Shirakashi T. Mechanics of machining—from descriptive to predictivetheory. In: On the art of cutting metals—75 years later, ASME Publication PED,vol. 7, 1982. p. 13–35.

[2] Strenkowski JS, Carroll JT. A finite element model of orthogonal metal cutting.ASME Journal of Engineering for Industry 1985;107:346–54.

[3] Komvopoulos K, Erpenbeck SA. Finite element modeling of orthogonal metalcutting. ASME Journal of Engineering for Industry 1991;113:253–67.

[4] Lin ZC, Lin SY. A couple finite element model of thermo-elastic-plastic largedeformation for orthogonal cutting. ASME Journal of Engineering for Industry1992;114:218–26.

[5] Zhang B, Bagchi A. Finite element simulation of chip formation andcomparison with machining experiment. ASME Journal of Engineering forIndustry 1994;116:289–97.

[6] Shih AJ. Finite element simulation of orthogonal metal cutting. ASME Journalof Engineering for Industry 1995;117:84–93.

[7] Strenkowski JS, Carroll JT. Finite element models of orthogonal cutting withapplication to single point diamond turning. International Journal ofMechanical Sciences 1986;30:899–920.

[8] Black JT, Huang JM. An evaluation of chip separation criteria for the FEMsimulation of machining. ASME Journal of Manufacturing Science andEngineering 1996;118:545–53.

[9] Sekhon GS, Chenot JL. Some simulation experiments in orthogonal cutting.Numerical Methods in Industrial Forming Processes 1992;901–906.

[10] Marusich TD, Ortiz M. Modeling and simulation of high-speed machining.International Journal for Numerical Methods in Engineering 1995;38:3675–94.

[11] Ceretti E, Fallbohmer P, Wu WT, Altan T. Application of 2-D FEM to chipformation in orthogonal cutting. Journal of Materials Processing Technology1996;59:169–81.

[12] Leopold J, Semmler U, Hoyer K. 1999. Applicability, robustness and stability ofthe finite element analysis in metal cutting operations. In: Proceedings of thesecond CIRP international workshop on modeling of machining operations,Nantes, France, January 1999. p. 81–94.

[13] Ozel T, Altan T. Determination of workpiece flow stress and friction at thechip–tool contact for high-speed cutting. International Journal of MachineTools and Manufacture 2000;40(1):133–52.

[14] Madhavan V, Chandrasekar S, Farris TN. Machining as a wedge indentation.Journal of Applied Mechanics 2000;67:128–39.

[15] Klocke F, Raedt H-W, Hoppe S. 2D-FEM simulation of the orthogonalhigh speed cutting process. Machining Science and Technology2001;5(3):323–40.

[16] Baeker M, Rosler J, Siemers C. A finite element model of high speed metalcutting with adiabatic shearing. Computers and Structures 2002;80:495–513.

[17] Rakotomalala R, Joyot P, Touratier M. Arbitrary Lagrangian–Eulerian thermo-mechanical finite element model of material cutting. Communications inNumerical Methods in Engineering 1993;9:975–87.

[18] Olovsson L, Nilsson L, Simonsson K. An ALE formulation for the solution oftwo-dimensional metal cutting problems. Computers and Structures1999;72:497–507.

[19] Movahhedy MR, Gadala MS, Altintas Y. FE modeling of chip formation inorthogonal metal cutting process: an ALE approach. Machining Science andTechnology 2000;4:15–47.

[20] Movahhedy MR, Altintas Y, Gadala MS. Numerical analysis of metal cuttingwith chamfered and blunt tools. ASME Journal of Manufacturing Science andEngineering 2002;124:178–88.

[21] Adibi-Sedeh AH, Madhavan V. Understanding of finite element analysisresults under the framework of Oxley’s machining model. In: Proceedings ofthe sixth CIRP international workshop on modeling of machining operations,Hamilton, Canada, 2003.

[22] Ozel T, Zeren E. 2005. Finite element method simulation of machining of AISI1045 steel with a round edge cutting tool. In: Proceedings of the eighth CIRPinternational workshop on modeling of machining operations, Chemnitz,Germany, April 10–11, 2005. p. 533–42.

[23] Haglund AJ, Kishawy HA, Rogers RJ. On friction modeling in orthogonalmachining: an arbitrary Lagrangian–Eulerian finite element model. Transac-tions of NAMRI/SME 2005;33:589–96.

[24] Arrazola PJ, Villar A, Ugarte D, Meslin F, Le Maıtre F, Marya S. 2005. Serratedchip prediction in numerical cutting models. In: Proceedings of the eighthCIRP international congress workshop on modelling of machining operations,Chemnitz, Germany, April 10–11, 2005. p. 115–22.

[25] Ng E-G, Tahany IEW, Dumitrescu M, Elbastawi MA. Physics-based simulationof high speed machining. Machining Science and Technology 2002;6/3:301–29.

[26] Ozel T. Modeling of hard part machining: effect of insert edge preparationfor CBN cutting tools. Journal of Materials Processing Technology2003;141:284–93.

[27] Yen Y-C, Jain A, Altan T. A finite element analysis of orthogonal machiningusing different toll edge geometries. Journal of Material Processing Technol-ogy 2004;146(1):72–81.

[28] Guo YB, Wen Q. A hybrid modeling approach to investigate chip morphologytransition with the stagnation effect by cutting edge geometry. Transactionsof NAMRI/SME 2005;33:469–76.

[29] Ozel T, Zeren E. Numerical modeling of meso-scale finish machining withfinite edge radius tools. International Journal of Machining and Machinabilityof Materials 2007;2(3/4):451–68.

[30] Ozel T, Zeren E. Finite element analysis of the influence of edge roundness onthe stress and temperature fields induced by high speed machining.International Journal of Advanced Manufacturing Technology 2007;35(3–4):255–67.

Fig. 11. Time varying contact normal pressure rn, shear stress s and Coulomb’s shear stress for (a) sticking node and (b) sliding node in the ALE FEmodel with Eulerian

boundaries.



[31] Liu K, Melkote SN. Finite element analysis of the influence of tool edge radiuson size effect in orthogonal micro-cutting process. International Journal ofMechanical Sciences 2007;49(5):650–60.

[32] Liu CR, Guo YB. Finite element analysis of the effect of sequential cuts andtool–chip friction on residual stresses in a machined layer. InternationalJournal of Mechanical Sciences 2000;42:1069–86.

[33] Yang X, Liu CR. A new stress-based model of friction behavior in machiningand its significant impact on residual stresses computed by finite elementmethod. International Journal of Mechanical Sciences 2002;44/4:703–23.

[34] Guo YB, Liu CR. 3D FEA modeling of hard turning. ASME Journal ofManufacturing Science and Engineering 2002;124:189–99.

[35] Umbrello D, Hua J, Shivpuri R. Hardness-based flow stress and fracturemodels for numerical simulation of hard machining AISI 52100 bearing steel.Materials Science and Engineering A 2004;374(1–2):90–100.

[36] Ee KC, Dillon Jr. OW, Jawahir IS. Finite element modeling of residual stressesin machining induced by cutting using a tool with finite edge radius.International Journal of Mechanical Sciences 2005;47(10):1611–28.

[37] Outeiro JC, Umbrello D, Saoubi RM’. Experimental and numerical modelling ofthe residual stresses induced in orthogonal cutting of AISI 316L steel.International Journal of Machine Tools and Manufacture 2006;46(14):1786–94.

[38] Nasr MNA, Ng E-G, Elbestawi MA. Modelling the effects of tool-edge radius onresidual stresses when orthogonal cutting AISI 316L. International Journal ofMachine Tools and Manufacture 2007;47(2):401–11.

[39] Attanasio A, Ceretti E, Rizzuti S, Umbrello D, Micari F. 3D finite elementanalysis of tool wear in machining. CIRP Annals—Manufacturing Technology2008;57(1):61–4.

[40] Ozel T, Karpat Y, Srivastava AK. Hard turning with variable micro-geometryPcBN tools. CIRP Annals—Manufacturing Technology 2008;57(1):73–6.

[41] Ozel T. Computational modelling of 3D turning: influence of edge micro-geometry on forces, stresses, friction and tool wear in PcBN tooling. Journal ofMaterials Processing Technology 2009;209(11):5167–77.

[42] Ozel T, Zeren E. A methodology to determine work material flow stressand tool–chip interfacial friction properties by using analysis of machin-ing. ASME Journal of Manufacturing Science and Engineering 2006;128:119–129.

[43] Johnson GR, Cook WH. A constitutive model and data for metals subjected tolarge strains, high strain rates and high temperatures. In: Proceedings of theseventh international symposium on ballistics, The Hague, The Netherlands,1983. p. 541–7.

[44] Childs THC, Maekawa K, Obikawa T, Yamane Y. Metal machining: theory andapplications. London, UK: Arnold Publishers; 2000.

[45] Childs THC, Dirikolu MH, Maekawa K. Modelling of friction in the simulationof metal machining. Tribology Series 1998;34:337–46.

[46] Dirikolu MH, Childs THC, Maekawa K. Finite element simulation of chip flowin metal machining. International Journal of Mechanical Sciences2001;43(11):2699–713.

[47] Ozel T. The influence of friction models on finite element simulationsof machining. International Journal of Machine Tools and Manufacture2006;46(5):518–30.

[48] Filice L, Micari F, Rizzuti S, Umbrello D. A critical analysis on the frictionmodelling in orthogonal machining. International Journal of Machine Toolsand Manufacture 2007;47(3–4):709–14.

[49] Arrazola PJ, Ugarte D, Domınguez X. A new approach for the frictionidentification during machining through the use of finite element modeling.International Journal of Machine Tools and Manufacture 2008;48(2):173–183.


author's personal copy - rutgers school of engineeringcoe · author's personal copy...

Documents