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INFLUENCE OF THE JOHNSON COOK MATERIAL MODEL PARAMETERS AND

FRICTION MODELS ON SIMULATION OF ORTHOGONAL CUTTING PROCESS

Amrita Priyadarshini, Surjya K. Pal and Arun K. SamantarayDepartment of Mechanical Engineering, Indian Institute of Technology Kharagpur,

Kharagpur 721302, West Bengal, India

ABSTRACT

In the recent past, Finite Element (FE) modeling has emerged as one of the most effective tools

that could substitute the conventional time consuming and expensive experimental tests to a great

extent. This work deals with FE model-based analysis of the two critical factors during

orthogonal cutting, namely the flow stress characterization of work material and the frictional

boundary conditions at the tool-chip interface. We exploit the new set of Johnson-Cook constants

reported recently along with two other sets of data that are commonly used in finite element

modeling for orthogonal cutting of AISI 4340 steel. The new set of Johnson-Cook material data

has not been used yet in any reported work on the orthogonal cutting process simulation. Besides,

a comparative study has been made by considering seven most relevant friction models among

various models proposed by researchers, including a relatively newer one. Though few works are

already available related to friction modeling, the uniqueness of the presented results lies in the

consideration of several friction models where friction coefficients are functions of temperature,

stress and sliding velocity, etc. Results show that the cutting conditions are the critical parameters

which decide the type of friction encountered in the chip formation process and, therefore, the

friction model has to be selected based on the cutting conditions for best results.

Keywords:Orthogonal cutting, Finite element simulation, Friction modeling, Johnson-Cook

material model

Corresponding author: Phone: +91-3222-282996, Fax: +91-3222-255303; E-mail: [email protected]


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1.INTRODUCTION

Machining process is one of the commonly used manufacturing processes. Because of its broad

use and complexity, continuous effort is being made to solve practical problems associated with

efficient material removal. This is achieved primarily through detailed study of the chip formation

process. Although experimental and analytical studies have contributed significantly to the

improvement of the machining process, researcher is now more focused in developing accurate

models based on numerical techniques. Finite element method is one such promising tool. These

simulations not only substitute the expensive and time consuming experimental tests for

predicting some of the difficult to measure variables (stress, strain and machining temperature),

but also determine results with higher accuracy as compared to the analytical models.

One of the first FE models developed for metal cutting process was by Klamecki (1973) in the

year 1972. Since then many works have been found to use FEM for gaining better understanding

of the machining process. Numerous FE codes such as DEFORM, FORGE2, ABAQUS/Standard,

ABAQUS/Explicit, Ansys/LS-DYNA have come up that are being used by the researchers; thus

giving results closer to the experimental ones. However, it should be noted that the accuracy of

FE modeling is determined by how adequately the characterization of selected input parameters

reflect the deformation behaviour undergoing during the chip formation in the actual practice. In

general, application of finite element modeling to cutting process involves consideration of

certain key features such as type of formulation (Eulerian, Lagarangian or Arbitary Lagrangian

Eulerian), material models, friction models and chip separation criterion. Lagrangian formulation

is easy to implement, efficient and fast converging but unable to handle large deformation

problems involving high mesh distortion. This necessitates the incorporation of chip separation

criterion to simulate the cutting action at the cutting zone (Strenkowski and Moon, 1990).

Eulerian approach, on other hand, permits simulation of machining process without the use of any


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mesh separation criterion. But the main drawback of Eulerian formulation is that it is unable to

model the free boundaries and may only be used when boundaries of the deformed material are

known a priori. While Arbitrary Lagrangian Eulerian (ALE) formulation is the one which takes

the best part of both Lagrangian and Eulerian formulations and combines them into one. ALE

reduces to a Lagrangian form on free boundaries of the chip while maintains an Eulerian form at

locations where significant deformation occurs, as found during the deformation of material in

front of the tool tip (Rakotomalala, Joyot and Touratier, 1993). ALE formulation is utilized

mostly to eliminate the termination of analysis due to excessive mesh distortion that is likely to

occur in the vicinity of the tool tip.

Many chip separation criteria have been used in the literature which can be broadly categorized as

geometrical (based on distance tolerance from the tool tip) and physical types (based on stress,

strain or strain energy density). Strenkowski and Carrol (1985) introduced the chip separation

criterion based on the effective plastic strain and found that chip geometry and forces are

unaffected by varying the threshold of the effective plastic strain. The simulation results of Huang

and Black (1996) showed that the type of chip separation criterion did not greatly affect chip

geometry and the distributions of stress and strain but it did affect the distribution of residual

stresses on the machined surface. Some researchers tried to introduce ductile failure in chip

separation. Rosa et al. (2007) evaluated two fracture modes, namely, specific distortional energy

criterion and tensile cracking criterion (Cockroft-Latham ductile failure) and concluded that

former is an appropriate criterion to evaluate ductile damage. The Johnson-Cook damage model

is an extension of specific distortion energy criterion which has come up as an efficient model to

simulate the chip separation and thus, is being widely used in machining problems. Though the

energy required for the separation of work material and chip is recognized, it is usually neglected

when compared to shearing and friction energies (Shaw, 2003). It is found that mostly the chip

separation criterion is considered as a mere computation fix in order to permit the tool movement


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into the work material (Atkins, 2003). While incorporating damage models, generally a thin

sacrificial layer is implemented and chip is formed due to failure/deletion of these elements

(Vaziri, Salimi and Mashayekhi, 2010).

The right type of formulation and chip separation criterion are undoubtedly essential for

simulating the cutting process but they do not affect the chip formation process, in terms of chip

morphology and cutting forces significantly. According to Ng et al. (2002), the difficulties in

accurate FE modeling of cutting process arise basically from two critical factors, namely,

dependence of the chip formation process on the material models describing the flow stress

property of the workpiece material and the friction conditions between the tool rake face and the

chip.

1.1.Material models

Several classical plasticity models have been widely employed that represent, with varying

degrees of accuracy, the material flow stresses as a function of strain, strain rate and temperature.

These models include the Oxley model (Oxley, 1989), the Johnson-Cook model (Johnson and

Cook, 1983), Zerilli-Armstrong model (Zerilli and Armstrong, 1987), Usui model (Usui and

Shirakashi, 1982), Mechanical Threshold Stress (MTS) model (Banerjee, 2007), Litonski-Batra

model (Litonski, 1977; Batra, 1988), Maekawa model (Maekawa, Shirakashi and Usui, 1983),

etc. Davies et al. (2003) compared the experimental results for machining of AISI 1045 steel to

the predictions of three different material models, namely, Johnson-Cook model, Zerilli-

Armstrong model and Power law rate dependent model. Adibi-Sedeh et al. (2005) have presented

a detailed comparison of various process variables using Oxley model, Johnson Cook model and

Maekawa history dependent model for AISI 1045 steel and found that Johnson-Cook model

predicts chip thickness better when compared with other models as well as experimental results.

Shi and Liu (2004) found that the predicted residual stresses and the chip curl varied for the type


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of models selected, namely, Litonski-Batra, Power law, Johnson-Cook and Bodner-Partom

models while machining Hy-100 steel. They found that the forces predicted by Johnson-Cook

model deviate by less than 13% and the chip thickness and shear angle do not deviate from the

measurement by more than 9%. It is noted that Johnson-Cook model is the most popular model

and often found to be used as the benchmark for comparison of different other models. This could

be attributed to the fact that it not only shows less discrepancy between the predicted and the

experimentally found chip morphology and cutting forces but also, the basic form of the model is

readily acceptable to most computer codes, since it uses variables which are available in the codes

(Johnson and Cook, 1983). This material model defines the flow stress as a function of strain,

strain-rate and temperature such that, it not only considers the strain rates over a large range but

also temperature changes due to thermal softening by large plastic deformation. Johnson-Cook

model is not restricted to the continuous chip formation only; it is equally efficient in simulating

the formation of segmented or saw teeth type chip which are found while machining hardened

steels such as AISI 4340, AISI H13 as well as Titanium alloys based on adiabatic shearing

(Mabrouki and Rigal, 2006; Ng and Apsinwall, 2002; Baker, Rosler and Seimers, 2002).

However, every model has its own limitations and hence, it is not always true that Johnson-Cook

model gives better results than any other models in all cases (Fang, 2003). Recently, researchers

are working on temperature dependent flow softening based modified Johnson-Cook material

where flow softening, strain hardening and thermal softening effects and their interactions are

coupled in order to simulate segmented chip formation while machining Titanium alloy (Sima

and Ozel, 2010; Calamaz, Coupord and Girot, 2008).

Majority of these constitutive material models do not adequately represent the flow stress

property of the workpiece that is usually heat treated to hardness levels ranging from 50-62 HRC

as in the case of hard machining (Umbrello, Hua and Shivpuri, 2004). Gradually, researchers are

attempting to develop innovative models that include the effect of hardness in the flow stress


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models to reflect the heat treatment on the selected material. Umbrello, Hua and Shivpuri (2004)

and Umbrello et al., (2008) have proposed hardness based flow stress models for AISI 52100 and

AISI H13 tool steel by taking Johnson Cook model as the reference flow stress curve for hardness

46 HRC as well as including an additional component that takes into account the variation of

workpiece hardness on flow stress. It has been reported that the value of JohnsonCook constant,

A, varies with the temper of the steel. Banerjee (2007) fitted the yield stress versus Rockwell C

(Rc) hardness curve for AISI 4340 steel to determine the value of A for various tempers. In

addition to the selection of suitable material model, selection of correct values of constants used

in the material models are also critical for predicting the forces, chip morphology and cutting

temperatures with reasonable accuracy. Umbrello, Saoubi and Outeiro (2007) studied the effects

of five different sets of work material constants available in the literature by using them in the

JohnsonCook constitutive equation for orthogonal cutting of AISI 316L and predicted the

cutting forces, chip morphology, temperature distribution and residual stresses. Lesuer (200)

defined a new set of material constants to be used in the JohnsonCook model for Ti6Al4V and

2024-T3 aluminium based on the performed experiments and additional data from past literature.

Similarly, Ozel and Karpat (2007) utilized the evolutionary computational methods of classical

particle swarm optimization and cooperative swarm optimization to identify the JohnsonCook

constants for AISI 1045, AISI 4340, AA6082 aluminium and Ti6Al4V titanium alloy. The

present paper aims to exploit the new set of Johnson-Cook constants found by Ozel and Karpat

(2007) along with two other sets of data that are commonly used in FE modeling of orthogonal

cutting of AISI 4340 steel.

1.2.

Friction models

Another important aspect while simulating the chip formation process is identification of the

frictional parameters at the tool chip interface. Accuracy of the developed model depends on the

frictional boundary conditions because of its direct effect on the forces and distribution of stresses


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and temperatures over the rake surface. The tool-chip interfacial conditions are hard to evaluate

experimentally due to high strain and temperature occurring in a localized region. As a

consequence, frictional parameters are assumed based on the experimental tests conducted on

much lower strain and temperature.

It is known that the simplest way of characterizing tool-chip friction is to assume Coulombs

friction law where coefficient of friction is considered constant over the entire rake surface. The

coefficient of friction () is defined as the ratio of the cutting force parallel to the tool rake face to

the force normal to the rake face. In past, researchers have evaluated the value of

experimentally and found it to be ranging from 0.2 to as high as 1.8 (Zorev, 1966; Kronenberg,

1966; Usui and Takeyama, 1960); whereas, the value of used in reported FE models is found to

lie in a range of 0.0-0.5 (Strenkowski and Moon, 1990; Komvopoulos and Erpenbeck, 1991;

Strenkowski and Carroll, 1985). The idea of using values below the limiting values not only suit

the sliding conditions but also produce results that are in good agreement with the experimental

ones. However, few researchers strictly pointed out that the concept of coefficient of friction is

not adequate to define the tool-chip interfacial conditions. Still the concept is being widely used

by the researchers even today because it makes the problem simpler. Besides coefficient of

friction, constant shear friction factor mhas also been utilized as an input into the FE simulations

to represent the friction at entire tool-chip interface in some of the works (Filice et al., 2007). This

law again neglects altogether the low stress variation of frictional stress with normal stress n .

But, experimental investigations carried by Zorev (1963), Childs (1998) and Lee, Liu and Lam

(1995) suggested that the normal and frictional stresses are not uniform over the tool rake face.

The tool-chip contact consists of two distinct regions, namely, a sticking zone near the cutting

edge and a sliding zone away from the cutting edge. In the sticking region, very high values of

normal stress occur while the frictional stress is assumed to be equal to the equivalent shear stress

limit of the workpiece material. No relative motion exists between the tool and the chip. On the


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contrary, in the sliding region normal stress is small and relative sliding of chip on the rake

surface occurs that is assumed to obey the Coulombs friction law. A modified Coulombs law as

reported by Shi, Deng and Shet (2002) is one such model that takes care of the stick-slip zones

along the tool-chip interface.

Literature suggests that none of the friction models is perfect. Therefore, newer varieties of

friction models are being developed by incorporating suitable modifications to the basic friction

laws. Wu, Dillon and Lu (1996) extended the Zorev friction model where they assumed sticking

and sliding regions to be of equal lengths such that the frictional stress is the function of the

equivalent stress in the sliding region, while in the sliding region it decreases linearly to zero.

Usui and Shirakashi (1982) described the frictional force behaviour as a function of normal force

depending on the workpiece-tool material combination. Recently, relevant values of friction

coefficients have been obtained under high velocity, high temperatures and high pressures by

using a newly designed tribometer (Zemzemi et al., 2008). This system has helped to identify new

friction models for different workpiece materials based on the average local sliding velocity. It

has been found that the most relevant parameter affecting the adhesive friction coefficient is the

local sliding of the workpiece material against the cutting tool (Zemzemi et al., 2009; Rech et al.,

2009; Bonnet et al., 2008). Few researchers have suggested that the friction coefficient may vary

with temperature (Ng et al., 2003; Guo and Liu 2002). Generally speaking, friction coefficients

decrease with increasing relative sliding speed and as the speed increases, contact temperature

increases due to greater frictional work being done. Hence, decrease of friction coefficient with

increasing temperature logically follows. Besides, extreme temperature variation occurs in the

case of machining process. Moufki, Molinari and Dudzinski (1998) have considered that the

interface temperature has the primary role; and they used Coulomb law in which the friction

coefficient is a monotonically decreasing function of temperature. Ozlu, Budak and Molinari

(2009) demonstrated that true representation of the friction behaviour should involve both


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sticking and sliding zones on the rake face for the accurate predictions. They stated that the total

contact length on the rake face is 3-5 times the feed rate such that for high cutting speeds the

contact is mainly sliding. While in one of the recent works, Arrazola and Ozel (2010) investigated

the effect of limiting shear stress at the tool-chip interface on frictional conditions by coupling

sticking and sliding friction. The investigations revealed that the stick-slip friction models should

be used with caution since limiting shear stress value is dependent on local deformation

conditions and temperatures. Brocail et al. (2010) proposed a friction law according to variables

like contact pressure, interfacial temperature, sliding velocity and Coulombs friction coefficient

and derived the constants with the help of a numerical model of upsetting sliding test. In few of

the recent works, comparison of some selected friction models has been presented showing their

effect on FE simulations for orthogonal cutting of AISI 1045, low carbon free cutting steel

(LCFCS) and AISI 4140 (Filice et al., 2007; Ozel, 2006; Haglund, Kishawy and Rogers, 2008). It

is suggested that the examined models are insufficient and further investigation is needed. Hence,

the present work makes an attempt to give some insight in the friction modeling problem by

considering seven most relevant friction models among various models proposed by past

researchers, including a relatively newer one, in the FE modeling of orthogonal cutting.

From the critical review of literature, it can be stated that the selection of appropriate material

models and friction models is a critical issue in FE simulation of machining process. The main

objective of the research reported here is to study the effects of three different set of material

constants used in Johnson-Cook material model and the effects of seven different types of friction

models on the process variables in finite element modeling of orthogonal cutting of AISI 4340 by

using a carbide tool.


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2.SIMULATION PROCEDURE

2.1. Model features

The present work focuses on the developing a 2D FE model of chip formation process based on

orthogonal cutting conditions. A plane strain condition was assumed because the feed value is

generally very less as compared to the depth of cut. A fully coupled thermal-stress analysis

module of finite element software ABAQUS/Explicit version 6.7 has been employed to perform

the study of chip formation process. This makes use of elements possessing both temperature and

displacement degrees of freedom. It is necessary because metal cutting is considered as a coupled

thermo-mechanical process, wherein, the mechanical and thermal solutions affect each other

strongly. The explicit dynamics procedure used is computationally efficient for the analysis of

metal cutting process that involve very large deformations and complicated contact conditions.

Furthermore, Arbitrary Lagrangian Eulerian (ALE) adaptive meshing technique is more generally

applicable in ABAQUS/Explicit. This approach provides control of mesh distortion which is

again very much possible in the case of cutting process undergoing large deformations (Abaqus

version 6.7 analysis users manual, 2007).

The 2D model comprises a portion of cutting tool which participates in the cutting and a

rectangular block representing the workpiece. The cutting tool is considered to be perfectly sharp

based on the fact that the effect of tool edge radius hardly plays any role once a steady state is

reached in cutting. Such assumption has been taken for the simplicity of problem by many of the

researchers (Shi, Deng and Shet, 2002; Mabrouki et al., 2008b).The cutting tool includes the

following geometrical angles: inclination angle 90= , rake angle 6 = and flank angle

5= . Both the tool and the workpiece are modeled as deformable bodies and discretized with

four-node plane strain thermally coupled quadrilateral, bilinear displacement and temperature

(CPE4RT) type elements. As boundary conditions, the cutting tool movement is constrained in


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both vertical and horizontal directions and the workpiece block was given the cutting velocity.

The geometric details and the boundary conditions of the FE model are shown in Fig. 1. The tool

and the workpiece are initially at the room temperature. Heat transfer from the chip surface to

cutting tool is allowed by defining the conductive heat transfer coefficient (h) equal to 500

2kW m K (Coelho, Ng and Elbestawi, 2007). Thermal radiation from the free surface of the

chip to the surrounding as well as heat transfer between the boundaries of the machined surface

and air are considered insignificant and are thus, neglected. Johnson-Cook shear failure model is

employed as the damage model to the damage zone (Mabrouki and Rigal, 2006). This model

along with the ELEMENT DELETION = YES module of the software allow the separation of the

chip from the workpiece (Abaqus version 6.7 analysis users manual, 2007; Mabrouki et al.,

2008a). The INELASTIC HEAT FRACTION and the GAP HEAT GENERATION modules of

the software are used to incorporate heat generation rate due to plastic deformation (pq )and heat

generation rate due to friction on the toolchip interface ( fq ) by introducing (fraction of the

inelastic heat) andf (fraction of the frictional work), respectively (Abaqus version 6.7 analysis

users manual, 2007; Mabrouki et al., 2008b).

2.2.Physical properties of the cutting tool and workpiece materials

The present work considers machining of AISI 4340 using tungsten carbide cutting tool. The

Table 1 lists the properties of both cutting tool and the workpiece material used in simulation of

the chip formation process (Mabrouki and Rigal, 2006).

2.3. Material model

Several material constitutive models have been used in FE analysis of metal cutting processes.

Johnson-Cook model, being most widely used, is employed to describe the flow stress property of

workpiece material AISI 4340 in this study. This material model defines the flow stress as a


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function of strain, strain-rate and temperature such that, it not only considers the strain rates over

a large range but also temperature changes due to thermal softening by large plastic deformation.

According to Johnson-Cook constitutive material model, von Mises tensile flow stress of the

workpiece is described as follows:

( )

cos

1 ln 1

m

n room

o melt roomelasto plasicterm vis ity softening

term term

T TA B C

T T

= + +

(1)

where, is the equivalent stress, Ais the initial yield stress (MPa), Bis the hardening modulus

(MPa), n is the work-hardening exponent, C is the strain rate dependency coefficient, m is the

thermal softening coefficient, is the equivalent plastic strain, is the plastic strain rate, o is

the reference strain rate (1.0 s1), roomT is room temperature, meltT is the melting temperature,

These work material constants have been found by various researchers by applications of several

methods, thus producing different values of data sets for a specific material. As a result, selection

of suitable data sets along with appropriate material model becomes equally important. The

present study selects three sets of Johnson-cook material constants, including a relatively new

data set explored by an evolutionary computational method, namely, M1, M2 and M3 from the

available literature. A brief description of each of the sets of data is given below, while the values

are listed in the Table 2.

M1: The data for the material constants of M1 were obtained by performing torsion tests over a

wide range of strain rates (quasi-static to about 400/s); dynamic Hopkinson bar tensile tests over a

wide range of temperatures as well as the static tensile tests. The data were then evaluated by

comparing computation results with data from cylinder impact tests (Johnson and Cook, 1983).

The values obtained are found to be used widely in the literature.


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M2: Ozel and Karpat (Ozel and Karpat, 2007) developed a new methodology that utilizes an

evolutionary computational method with the aim of minimizing error in identifying the Johnson-

Cook constitutive model parameters. The material constants of M2 were explored and

recalculated by cooperative particle swarm optimization (CPSO).

M3: The M3 set of material constants were identified by conducting Split Hopkinson pressure bar

compression tests over a wide range of temperatures (-196C to 600C) and strain rates (quasi-

static to about 7000/s). A computer program was used to perform optimization to fit the

experimental data (Gray et al., 1994).

2.4. Friction models

Friction modeling plays a significant role as it is known to considerably influence the accuracy in

simulation of the chip formation process. Several models have already been proposed with the

aim of achieving results closer to the experimental data. In this study, seven friction models

developed by the researchers in the past were selected to study their effect on the process

variables. This section briefly discusses the selected friction models.

F1: Constant friction coefficient model

This model simply considers the coulombs friction law on the entire contact zone (Strenkowski

and Moon, 1990). The software defines this model by introducing a constant value of coefficient

of friction which, in the present case, is equal to 0.2 (Komvopoulos and Erpenbeck, 1991;

Mabrouki et al., 2008b).

F2: Constant friction coefficient with limited shear stress model

This model allows introduction of stick-slip conditions at the tool chip interface by defining the

equivalent shear stress limit from the beginning for sticking zone and a constant value of


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coefficient of friction () for the sliding zone (Shi, Deng and Shet, 2002; Mabrouki et al., 2008b).

The constitutive mathematical model is given as:

max maxn

maxn n

, for ( Sticking zone)

, for ( Sliding zone)

=

(2)

In the sticking zone, the normal stress ( n ) is very large and frictional stress ( ) is assumed to

be equal to the equivalent shear stress limit, max . The value of max can be approximated

as 3A , where A is the initial yield stress (Mabrouki et al., 2008). In the sliding zone, the

normal stress is small and the frictional stress follows the simple Coulombs law with =0.2

(Komvopoulos and Erpenbeck, 1991; Mabrouki et al., 2008b).

F3: Variable friction coefficient as a function of temperature

The friction law in this model accounts for the temperature effects. The model postulates the

Coulombs law with a mean coefficient of friction ( ) in terms of mean interface temperature

(Tint) as defined below (Moufki, Molinari and Dudzinski, 1998):

int( )T = (3)

It is assumed that coefficient of friction is a decreasing function of temperature i.e. decreases

linearly to zero as the average temperature reaches the melting point of the workpiece material.

F4: Variable friction coefficient as a function of normal stress

This model defines the coefficient of friction as a function of the average normal stress ( n ) over

the entire tool chip contact surface. This is expressed as follows:


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n

= . (4)

The normal stress and shear stress ( ) values used for the evaluation of are taken from the

experimentally found stress distributions by Buryta, Sowerby and Yellowley (1994).

F5: Variable friction coefficient as a function of sliding velocity

This model considers a variable friction coefficient as a function of the average local sliding

velocity at the tool-chip contact. Zemzemi et al. (2009) identified a new empirical friction model

based on the local sliding velocity lsV as follows:

057.0)ln(07.0 += lsV (5)

This friction relates the friction coefficient and the local sliding velocity in the range of 2-170

m/min corresponding to the cutting velocity up to 200 m/min.

F6: Rate dependent friction coefficient model

This recent friction model developed by Tawfiq (2007) is expressed by the following relation:

+= eksk )( (6)

where, k is the coefficient of kinetic friction, s is coefficient of static friction, is the

exponential decay coefficient and v is the relative sliding velocity of the slave and master

surfaces. The optimum values of coefficients, s = 0.4 and k = 0.2 were determined through

trial and error approach (Tawfiq, 2007).


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F7: Two friction coefficients model

In this model, basic Coulombs law is implemented with two different coefficients for specified

portions of the contact length ( cL ), namely sticking region ( stickingL ) and sliding region. On the

basis of past research, the length of the sticking region was assumed equal to the uncut chip

thickness (Ozel, 2006). In order to apply this at the tool-chip interface, the tool rake surface was

split into two sections such that

23.0= when stickingLx0 and 15.0= when csticking LxL ,

wherexis the distance measured from the tool tip along the tool rake face. The constant values of

were taken based on the existing literatures (Komvopoulos and Erpenbeck, 1991; Ozel, 2006).

3. RESULTS AND DISCUSSION

In this section, numerical results obtained from FE simulations with different types of Johnson-

Cook material constants and the friction models are presented.

3.1. Johnson-Cook material constants

Since chip morphology affects the stress, strain and temperature distributions, prediction of the

right kind of chip morphology through finite element simulations is an important aspect in the

study of metal cutting. This motivates us to carefully select the material model as well as the

corresponding material constants to be used in the flow stress equation of the chosen material

model. The results dealing with three different sets of Johnson-Cook material constants, namely,

M1, M2 and M3 (see Table 1) are presented in this section. The friction model for each of the

three cases are kept same i.e. constant friction model with limited shear stress, so that the results

can be compared on the same conditions. Fig. 2 shows the predicted chip morphology and the


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cutting force ( cF ) variation over a simulation time of 2 ms at cutting velocity of 100 m/min and

uncut chip thickness of 0.2mm for different values of material constants (M1, M2 and M3). The

chip morphology may be described in terms of the average values of segmented chip geometry

such as distance between two saw-teeth (D), peak (a) and valley (b). In addition, the

corresponding cutting force profiles are presented which not only show the predicted values of

cutting forces but also aid in deriving the segmentation frequency. The segmentation frequency

(fSN in Hz) can be calculated as:

( )1000

N

=

initialfinalSN

TTf (7)

where, N = number of saw teeth produced between a given time interval of initialT to finalT .

The results in Figure 1 show too much variation in the predicted chip morphology, cutting force

values and the segmentation frequency with the change in the values of material constants. When

the sets M2 and M3 are compared with M1, cutting forces showed a deviation of as high as 68%.

While 63% of deviation in chip geometry and almost 50% of deviation in segmentation frequency

were observed. As discussed earlier, the constantA used in the Johnson-Cook model is known to

vary with the temper of steel and hence can be correlated to the hardness of the work material

(Banerjee, 2007). It is also evident from literature that as the hardness changes, there is a change

in the flow stress of the work material (Umbrello et al., 2007). That the value ofAaffects the chip

morphology, segmentation frequency as well as cutting force values is therefore, a logical

conclusion. Generally, harder the workpiece material, higher is the tendency for the deformation

to localize and thus produce more prominent segmented chips even at low cutting speeds

(Umbrello, Hua and Shivpuri, 2004). This can be figured out in the case of M3 where the value of

Ais highest. Not only the saw teeth are well defined for M3 but also the segmentation frequency

is higher. Furthermore, as the material hardness increases, more deformation energy is required


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for the chip formation (Qian and Hossan, 2007). This explains the increasing trend of cutting

forces from M1 to M3. In addition, mand n are also considered as the critical parameters that

influence the segmentation of chip (Baker, 2003). Baker (2003) suggested increase in mleads to

increase in chip segmentation and decrease in cutting forces, while increase in n causes lesser

tendency to undergo chip segmentation keeping cutting force nearly constant. This could be the

reason possibly for higher value of segmentation frequency ( SNf = 3663 Hz) for M1 as compared

to the other two values. In the former case, greater value of mand lower value of n(see Eq. (1))

increases the number of saw teeth or segmentation frequency, but comparatively lesser distinct

and smaller chips are produced due to lower value ofA.

To give a clear insight, the temperature distributions, being the most important factor responsible

for the varied chip morphology, are presented for all the three cases in Fig. 3 at a cutting velocity

( cV ) of 120 m/min and uncut chip thickness ( f ) of 0.2 mm for a simulation time of 2 ms. As

expected, the distribution patterns of temperatures are different from each other, reflecting

difference in the chip morphology. It is known that the chip segmentation basically results from

the thermal softening due to very high temperatures in highly localized regions of the shear plane

during the cutting of hardened steels. The temperature distribution of M1 is not as localized as the

other two, in the shear zone. While in case of M2 and M3, higher values of temperatures are

attained in a highly localized region in the form of a band extending from tool tip towards the

back of the chip. Consequently, highly pronounced saw teeth are produced due to the thermal

softening caused by very high temperatures at the back of the chip. The maximum temperature at

the rake face ( rakeT ) of the tool and shear zone ( shearT ) of the workpiece can also be determined

from the simulated results presented in Fig. 3. In Fig. 3 (c), the chip appears to penetrate the

workpiece. But in actual sense, the chip flows out at the side of the workpiece and it is simply the

overlapping of the images of chip and workpiece (hidden boundary shown by dashed lines). The

predicted results conform well to the existing ones which have concluded that greater hardness,


19/35

which in the present context is higher value of A, yields higher cutting temperatures (Matsumoto

and Hsu, 1987). This, as stated earlier, can be attributed to the higher energy involved during the

cutting of the harder steels (Qian and Hossan, 2007).

The predicted results show that material constants significantly affect various aspects of the

simulation of the chip formation process. As far as the chip morphology is concerned, the

distance between the two consecutive saw-teeth in case of M2 (D=0.326 mm) is fairly closer to

the experimental one (D=0.3 mm) found by Belhadi et al. (2005). But at the same time, M2

underestimates the segmentation frequency to some extent. When cutting forces were considered,

experimental values were taken from the work of Lima, Avila and Abrao (2005). Tests were

conducted for machining AISI 4340 steel of hardness varying from 23 to 42 HRC with coated

carbide tool and the corresponding cutting forces measured were around 475 N and 575 N,

respectively. It is found that the M2 gives a cutting force value that is closer to the one obtained

by Lima, Avila and Abrao (2005) for 42 HRC steel, while M1 gives a cutting force of 408.19 N

comparable with the value obtained in the case of 23 HRC, (though an underestimated value) and

M3 yields cutting force of 687.7 N which of course is a much higher value. Hence, this work

demonstrates the importance of choosing optimum values of material constants that may prove as

a satisfactory compromise between the hardness of the workpiece material and the cutting

variables such as chip morphology, cutting forces and cutting temperatures.

3.2. Influence of friction models

This section aims to investigate the importance of implementing the right kind of frictional

boundary conditions in the FE simulation. Seven different friction models (F1 to F7) are selected

from the review of past research and are incorporated into a finite element model by keeping all

the other factors constant, say, the workpiece material model, tool geometry and the cutting

conditions. The Johnson-Cook material model, with M1 set of parameters, was considered for the

workpiece material AISI 4340 of hardness 48 HRC (Mabrouki and Rigal, 2006). Table 3 shows


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the predicted values of various process variables such as the cutting force ( cF ), thrust force ( tF ),

tool chip interface temperature ( intT ), contact length ( cL ) and chip thickness ( 2a ) for the seven

cases by varying the cutting velocity from 60 to 180 m/min for uncut chip thickness of 0.2 mm.

The predicted values show the trend that accord well with the basic theory. The forces, contact

length and chip thickness tend to decrease while the interface temperature increases with the

increase in the cutting velocity in all the seven cases. However, percentage change in the

variables varies with the type of friction model used. The predicted cutting force and thrust force

are compared with the experimental values obtained by Lima et al. (2005)and Lima, Avila and

Abrao (2007) for machining AISI 4340 of hardness 42 HRC and 50 HRC using negative rake

( 6 = ) carbide tool under equivalent cutting conditions. Although the workpiece hardness

considered in this work is marginally different from those considered in Lima et al. (2005) and

Lima, Avila and Abrao (2007), the forces can be assumed to lie in the range identified in these

cited sources and thus, a qualitative assessment of the correlation between the published

experimental results and our numerical results can be made. Experimental findings of Lima et al.

(2005) show a percentage decrease of 30.78% and 21.88% for cutting forces when machining

AISI 4340 of hardness 42 HRC and 50 HRC, respectively as the cV is increased from 60 m/min

to 180 m/min. The numerical results show a maximum decrease of 15% in the cutting force and

27.8 % decrease in the thrust force (both observed in the case of F3) for the same variation in

cutting speed. The friction model F4 showed 11.8 % decrease in the cutting force while the rest of

the models, except F5, show a percentage decrease of 8-10% in cutting force. In case of F5,

variation in force is found to be lowest, i.e. 5 %. Lima, Avila and Abrao (2007) observed an

increase in the cutting and thrust forces with the increase in hardness (23 to 42 HRC) while

cutting AISI 4340. In their research (Lima, Avila and Abrao, 2007), cutting force and thrust force

came out to be around 550 and 240 N, respectively, while machining AISI 4340 of hardness 42

HRC at cV = 120 m/min and f = 0.2 mm/rev. However, lower forces were observed when


21/35

machining work material AISI 4340 hardened to 50 HRC in comparison with 42 HRC, i.e. cF =

425 N and tF= 100 N in the work of Lima et al. (2005). Since the present work deals with a

work material having hardness 48 HRC, the values of cutting and thrust forces ought to lie in

between the mentioned values (450550 N for cF and 150250 N for tF at cV = 120 m/min and f

= 0.2 mm/rev). It can be seen from Table 3 that the predicted values of the cutting and thrust

forces appear to fall in the concerned range; thrust force being slightly underestimated. The

model F5 seems to give one of the best values of cutting force ( cF = 500.5 N) with tF =187.9 N,

while F4 gives a better value for thrust force ( tF = 192.6 N) with a corresponding value of cutting

force ( cF = 486.8 N) slightly lower than the value obtained from F5.

The percentage increase in the interface temperature is found to be as high as 40-45 % in case of

F1, F2, F6 and F7, while the friction models F5, F3 and F4 showed a percentage increase of 30,

29 and 23%, respectively. However, the predicted values of average interface temperatures for all

the cases are found to be underestimated when compared with the experimental results by Dhar,

Kamruzzaman and Ahmed (2006). The average interface temperatures for cutting velocities of 63

and 128 m/min were found to be 737.5 C and 788 C, respectively, when measured

experimentally while machining AISI 4340. Though the frictions models F1, F2, F6 and F7

exhibit large temperature increase with the increase in the cutting velocity, the intT values are

much lower especially at cV = 60 m/min. Hence, F5 and F4 can be considered as models showing

fairly better results for intT because not only they show higher values as compared to others but

also they exhibit temperature increase fairly well. Since temperature at interface is directly

influenced by the relative velocity, velocity dependent friction model F5 could possibly predict

the value of intT better. Fig. 4 shows the variation in the temperature distribution over the rake

face for friction models F4, F5 (that showed better results in terms of intT ) and F2 (one of the


22/35

commonly used friction model) at cV = 120 m/min and f = 0.2 mm/rev. As expected, all three

models show that the temperature is non-uniformly distributed along the rake face with peak

interface temperature occurring at some distance away from the cutting edge. The difference is

mainly observed in the position and the value of the peak interface temperature in models F2, F4

and F5. This may be attributed to the distribution of frictional stress along the tool chip contact

length. Fig. 5 presents the normal and frictional stress distribution along the tool chip interface. It

can be seen that F5 has the highest value of frictional stress followed by F4 and F2. This reflects

the trend observed in the case of temperature distribution in Figure 4. It is also noted that there is

almost no change in the stress distribution for model F1 (constant friction coefficient) and F2

(constant friction coefficient with limited shear stress model). Hence, it may be inferred that the

ABAQUS-Explicit software is unable to simulate the stick-slip zones based upon the equivalent

shear stress value effectively in case of F2.

Chip reduction coefficient (), one of the most important process output (in terms of process

evaluation and optimization) is defined as the ratio of chip thickness (a 2) to uncut chip thickness

(f). This has been calculated and plotted forc

V = 60180 m/min, as shown in Fig. 6 for each of

the seven models. The reason to determine chip reduction coefficient is that it is an important

machinability index giving much idea about the nature of the tool-chip interaction, chip contact

length, and chip form. As expected, decreases with the increasing cutting velocity for all the

cases. But it is observed that the decrease in is more prominent in F5 followed by F4 and F3.

Note that all the three models are variable friction models, F5 as a function of sliding velocity, F4

based on experimentally measured normal and frictional stresses and F3 being temperature

dependent model. Interestingly, similar type of behaviour was observed by Ozel (2006), who

suggested that the predicted process variables are clearly found to be most accurate when utilizing

variable friction models based on the experimentally measured normal and frictional stresses on

the tool rake surface.


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In general, it is observed that the predicted values tend to vary with the change in the friction

model. The constant Coulomb friction coefficient model (F1) is one of the most widely used

models as it is considered to be a fair compromise from simplicity and accuracy point of view of

the problem. When rest of the models are compared with the model F1, the variable friction

models F4 (stress dependent) followed by F5 (sliding velocity dependent) and F3 (temperature

dependent) showed significant deviations in cutting force, thrust force and interface temperature,

while F2, F6 and F7 produced nearly same values for all the three variables. F4 showed a

deviation of 6 % in cF , 37 % in tF and 20 % in intT . Such observation is in agreement with the

results predicted by Filice et al. (2007) and Ozel (2006). Filice et al. (2007) found tF to differ by

29 %, intT by 24 % and cF by 12 % among different friction models for machining AISI 1045.

Similarly, Ozel observed the thrust force varying by 8 % and cutting force by not more than 3 %

with the friction models while machining Low Carbon Free Cutting steel (LCFCS). It can be said

that influence of friction models is larger over the thrust force followed by temperature as

compared to cutting force (Arrazola and Ozel, 2010). However, variation in contact length and chip

thickness are found to be less among all the models as compared to the variation in the contact

length with higher predicted values for models F4 and F5. Likewise, Filice et al. (2007) and Ozel

(2006) have also found out that the main mechanical results such as cutting forces, contact length

etc. are not as sensitive to the friction models as compared to the cutting temperatures.

From the predicted results, it is reasonable to state that the friction modeling is not very critical at

higher cutting speeds but it is fairly prominent in case of low cutting speed ( cV = 60 m/min)

showing a difference of 37% in thrust force and 20% in interface temperature by model F4. The

model F4, being the function of average normal stress over the rake face, reflects the stick-slip

zone in a much realistic way. This could be a probable reason for which F4 comes out to be one

of best models when compared with the rest of the models as well as with the existing


24/35

experimental results. The friction models tend to be crucial at low cutting speeds can be attributed

to the fact that sliding contact strongly depends on the cutting speed. At low cutting speeds

sticking zone can be up to 30% of the total contact while for high cutting speeds the contact is

mainly sliding (Ozlu, Budak and Molinari, 2009). Consequently, at higher cutting speeds all the

friction models behave like constant Coulomb friction coefficient model, thus showing similar

kind of results.

4. CONCLUSIONS

Incorporation of different friction models were used in an FE model to predict cutting force and

thrust force within a satisfactory range during orthogonal machining. It is observed that cutting

temperatures followed by thrust force seem to be affected more by the type of frictional

conditions implemented as compared to the cutting forces. In the present work, the overall values

of cutting temperatures for all the seven considered friction models are found to be lower than the

experimental ones. The one possible reason could be the inability to include the effect of hardness

in the flow stress models which properly include the effect of the heat treatment on the selected

work material in the simulation. This necessitates the incorporation of the right kind of material

models and their corresponding material constant values depending upon the hardness along with

the appropriate friction model in the FE simulation. Therefore, the first part of this work dealt

with the variation of chip morphology, forces and temperatures with three different sets of

material constants used in the Johnson-Cook model. Significant differences were observed in the

values of cutting forces and chip geometry. The deviation in cutting force value was found to be

as high as 68%. The chip geometry and segmentation frequency were found to differ by 63% and

50%, respectively. The new set of material parameters developed by Ozel and Karpat (2007)

through evolutionary computational method, M2, gives values of cutting force and chip geometry

that are closer to the existing experimental results (Lima, Avila and Abrao, 2005). The results


25/35

indicate that suitable selection of the material constants incorporates the effect of hardness of the

workpeice material on the flow stress behaviour of the work material.

The models F4 followed by F5 gave the best results in terms of cutting force, thrust force and

interface temperature when compared with the existing experimental findings. The decrease in

with the increase in cutting speeds is also more prominent in F4 and F5. Interestingly, both the

models are variable friction models, F4 based on normal and frictional stresses and F5 as a

function of sliding velocity. F4 showed the maximum deviation in the values of thrust force

(37%) and interface temperature (20%) when compared with the commonly used model F1.

However, the cutting forces, contact length and chip thickness are not as sensitive to the friction

models as compared to the thrust force and cutting temperatures. It is also noted that there is

almost no change in the stress distribution for model F1 (constant friction coefficient) and F2

(constant friction coefficient with limited shear stress model) reflecting the inadequacy of the

software to model stick-slip zones based upon the equivalent shear stress value effectively in case

of F2.

The effect of friction model is not very significant at higher cutting speeds but it is reasonably

significant in case of low cutting speed showing a difference of 37% in thrust force and 20% in

interface temperature by model F4. The present investigation points out that the selected friction

models does not affect the chip formation process at high cutting speeds which may be attributed

to the fact that chip-tool contact is mostly sliding type, i.e, governed by Coulomb friction law, at

high cutting speed. But at low cutting speeds, it is observed that the friction modeling plays a

crucial role in predicting the correct thrust force and the temperature. Though the chip thickness

prediction accuracy is inadequate, as far as other results are concerned, F4 friction model may be

considered as most suitable friction model among the selected models.


26/35

Most of the works so far, including the present study consider the effect of material modeling and

the friction modeling individually on the simulation of chip formation process. It is, however felt

that emphasis should be given to the combining of the friction models with suitable material

models or at least the material constant values depending upon the hardness of the work material,

instead of considering the friction models or material models alone to overcome the inadequacies.

This will definitely characterize the metal cutting process in a more realistic way that may

possibly lead to results closer to the experimental ones.

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FIGURES

Fig. 1 Geometric details and boundary conditions of the model

X

Y

Z

Chip surface

Work piece

Damage zone

Vc

Cutting tool


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Model Chip morphology Cutting force

M1

D =0.199 mm

a = 0.309 mm

b = 0.272 mm

0.0 0.3 0.5 0.8 1.0 1.3 1.5 1.8 2.0

0

100

200

300

400

500

Tfinal

Tinitial

Cuttingforce(N)

Time (ms)

cF = 408.19 N

SNf = 3663.3 Hz

M2

D =0.326 mm

a = 0.368 mm

b = 0.217 mm

0.0 0.3 0.5 0.8 1.0 1.3 1.5 1.8 2.0

0

100

200

300

400

500

600

700

800

Tfinal

Tinitial

Cuttingforce(N)

Time (ms)

cF = 597.25 N

SNf = 1855Hz

M3

D=0.217 mm

a= 0.313 mm

b= 0.222 mm

0.0 0.3 0.5 0.8 1.0 1.3 1.5 1.8 2.0

100

200

300

400

500

600

700

800

900

Tfinal

Tinitial

Cuttingforce(N)

Time (ms)

cF = 687.73 N

SNf = 2798.5 Hz

Fig.2Predicted chip morphology and cutting force for M1, M2 and M3 at cV = 120 m/min and

f = 0.2 mm for t = 2 ms


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(a)

(b)

(c)

Fig. 3Temperature distributions (C) for (a) M1, (b) M2 and (c) M3 at cV = 120 m/min and f =

0.2 mm


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0.2 0.4 0.6 0.8 1.0

0

100

200

300

400

500

600

700

Temperature(C)

Distance from the cutting edge (mm)

F5

F4

F2

Fig. 4Temperature distributions along the rake surface of the tool predicted by using friction

models F2, F4 and F5 at t = 2 ms

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Stress(GPa)

Distance from the cutting edge (mm)

Normal Stress (F1)

Normal Stress (F2)

Normal Stress (F4)

Normal Stress (F5)

Frictional Stress (F1)Frictional Stress (F2)

Frictional Stress (F4)

Frictional Stress (F5)

Fig. 5Stress distributions along the rake surface of the tool predicted by using different friction

models at t = 2 ms

60 90 120 150 180

1.80

1.95

2.10

2.25

2.40

2.55

2.70

2.85

3.00

Chipreductioncoefficient

Cutting velocity (m/min)

F1 F5

F2 F6

F3 F7

F4

Fig. 6Variation of chip reduction coefficient with cutting velocity with different friction models


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Table 1 Physical properties of cutting tool and workpiece

Parameter Work piece

(AISI 4340)

Tool

(Tungsten carbide)

Thermal Conductivity, k 44.5W/m/oC 50 W/m/ oC

Density, 7850 kg/m3 11900 kg/m3

Youngs modulus, E 205 GPa 534 GPa

Poissons ratio, 0.3 0.22

Specific heat, Cp 475 J/kg/oC 400 J/kg/ oC

Expansion coefficient, (10-5) 1.37

Table 2Johnson-Cook Constants for AISI 4340

Model A(MPa) B(MPa) C n m

M1(Johnson and Cook, 1983) 792 510 0.014 0.26 1.03

M2 (Ozel and Karpat, 2007) 1523.3 1022.6 0.001512 0.5358 0.89438

M3 (Gray et al., 1994) 2100 1750 0.0028 0.65 0.75


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Table 3 Predicted values from FE simulations at cV = 120m/min and f = 0.2 mm

ModelcV (m/min) cF (N) tF(N) intT (C) cL (mm) 2a (mm)

60 503.29 163.19 558.84 0.59 0.526

120 471.28 152.7 651.01 0.487 0.484

F1

180 448.9 146.34 778.4 0.428 0.423

60 503.07 163.34 558.8 0.570 0.517

120 471.28 152.7 651.01 0.448 0.47

F2

180 448.9 146.34 778.403 0.408 0.414

60 520.40 176.38 561.01 0.448 0.548

120 463.0 139.76 617.12 0.415 0.461

F3

180 441.15 127.22 721.16 0.407 0.409

60 532.41 223.66 667.07 0.530 0.590

120 486.88 192.687 683.16 0.489 0.501

F4

180 469.22 187.31 820.68 0.448 0.416

60 514.39 191.54 653.66 0.529 0.518

120 500.5 187.99 709.968 0.448 0.486

F5

180 486.34 179.97 847.19 0.407 0.461

60 502.88 162.64 526.85 0.448 0.507

120 470.15 152.25 646.15 0.428 0.464

F6

180 450.35 147.02 778.18 0.407 0.464

60 500.13 169.92 550.0 0.467 0.511

120 477.24 168.19 683.82 0.457 0.464

F7

180 457.52 163.15 800.71 0.416 0.424