Numerical modelling of 3D hard turning using arbitrary Lagrangian

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Int. J. Machining and Machinability of Materials, Vol. 3, No. 3, 2008
Numerical modelling of 3D hard turning using
arbitrary Lagrangian Eulerian finite element method
P.J. Arrazola*
Mondragón University,
Loramendi 4, Mondragón 20500, Spain
E-mail: pjarrazola@eps.mondragon.edu
*Corresponding author
T. Özel
Department of Industrial and Systems Engineering,
Rutgers University,
Piscataway, NJ 08854-8018, USA
E-mail: ozel@rci.rutgers.edu
Abstract: In this paper, 3D Finite Element Method (FEM)-based numerical
modelling of precision hard turning has been studied to investigate the effects
of chamfered edge geometry on tool forces, temperatures and stresses in
machining of AISI 52100 steel using low-grade Polycrystalline Cubic
Boron Nitrite (PCBN) inserts. An Arbitrary Lagrangian Eulerian (ALE)-based
numerical modelling is employed for 3D precision hard turning.
The Johnson-Cook plasticity model is used to describe the work material
behaviour. A detailed friction modelling at the tool-chip and tool-work
interfaces is also carried. Work material flow around the chamfer geometry of
the cutting edge is carefully modelled with adaptive meshing simulation
capability. In process simulations, feed rate and cutting speed were kept
constant and analysis was focused on forces, temperatures and tool stresses.
Results revealed good agreements between FEM results and those reported in
literature about experimental ones.
Keywords: cutting; hard turning; finite element modelling; arbitrary
Lagrangian Eulerian method.
Reference to this paper should be made as follows: Arrazola, P.J. and Özel, T.
(2008) ‘Numerical modelling of 3D hard turning using arbitrary Eulerian
Lagrangian finite element method’, Int. J. Machining and Machinability of
Materials, Vol. 3, No. 3, pp.238–249.
Biographical notes: P.J. Arrazola received a PhD in Mechanical Engineering
from Ecole Centrale of Nantes in 2003. He is a Professor of Mechanical
Engineering at Mondragon University. His research interest includes modelling
of machining processes, chip formation study, machinability, high speed
cutting and micromachining. He has over 15 years of experience in
manufacturing research. He has been a Reviewer and Organiser for several
journals and conferences. He has published over 40 refereed articles in journals
and congresses.
T. Özel received a PhD in Mechanical Engineering from The Ohio State
University in 1998. He is an Assistant Professor of Industrial and Systems
Engineering at Rutgers University. His research interest includes modelling of
Copyright © 2008 Inderscience Enterprises Ltd.
Numerical modelling of 3D hard turning using ALE FEM
239
machining processes, automation and process control, optimisation of
processes and systems, and micro/nano manufacturing. He has over 10 years of
experience about manufacturing research. He has been a Reviewer, Organiser,
Guest Editor and Editorial Board Member for several journals and conferences.
He has published over 50 refereed articles.
1 Introduction
Hard turning is a popular manufacturing process in producing finished components that
are typically machined from alloy steels with hardness between 50 and 70 HRc (Koenig
et al., 1984). Polycrystalline Cubic Boron Nitrite (PCBN) cutting tools are widely used in
hard turning. PCBN tools are designed with a certain micro edge geometry with a
process called edge preparation. Microgeometry of a cutting edge plays a pivotal role on
the workpiece surface properties and the performance of the cutting tool (Toenshoff
et al., 1995). In order to improve the overall quality of the finished component, tool edge
geometry should be carefully designed.
Design of cutting edge may affect the chip formation mechanism and therefore, help
reducing cutting forces and increasing tool life. It is known that sharp tools are not
durable enough for most of the machining operations; therefore, tool manufacturers
introduced different types of tool edge preparations such as chamfer, double chamfer,
chamfer + hone, hone, and waterfall hone (also referred to as oval or parabolic) edge
designs (Karpat and Ozel, 2007) as shown in Figure 1.
Figure 1
Microgeometry edge preparations for a triangular insert with nose radius
Source: Karpat et al. (2007).
Numerical modelling of machining processes is continuously attracting researchers for
better understanding of chip formation mechanisms, heat generation in cutting zone,
tool-chip interfacial frictional characteristics and quality and integrity of the machined
surfaces. In predictive process engineering for machining processes, prediction of
physics related process field variables such as temperature and stress fields becomes
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P.J. Arrazola and T. Özel
highly important. Tool edge microgeometry influences tool life and process viability as
well as surface quality and integrity in hard turning. Finite element modelling is a
process design tool to investigate the influence of tool edge microgeometry for
hard turning.
This paper introduces a new way of modelling 3D precision hard turning by using
finite element modelling with Arbitrary Lagrangian Eulerian (ALE) technique. The aim
of this paper is to demonstrate the possibilities of using Finite Element Method (FEM) as
a reliable tool for improving tool insert design for 3D hard turning and predicting the
superficial state of the machined workpiece. Firstly, finite element modelling is
described. Then the results of process simulations will be provided and compared with
those obtained in literature. Finally overall conclusions are pointed out and future
research direction is discussed.
1.1 Numerical modelling of machining
In finite element modelling, there are two types of analysis in which a continuous
medium can be described: Eulerian and Lagrangian. In a Lagrangian analysis, the
computational grid deforms with the material, where as in a Eulerian analysis, this is
fixed in space. The Lagrangian calculation embeds a computational mesh in the material
domain and solves for the position of the mesh at discrete points in time. Updated
Lagrangian formulation with continuous remeshing has been used in simulation of
continuous and segmented chip formation in machining processes (Ceretti et al., 1996;
Klocke et al., 2001; Leopold et al., 1999; Madhavan et al., 2000; Marusich and Ortiz,
1995; Özel and Altan, 2000; Sekhon and Chenot, 1992). ALE technique combines the
features of pure Lagrangian and Eulerian analyses. ALE formulation is also utilised in
simulating machining to avoid frequent remeshing for chip separation (Adibi-Sedeh and
Madhavan, 2003; Arrazola et al., 2007; Haglund et al., 2005; Movahhedy et al., 2000;
Olovsson et al., 1999; Özel and Zeren, 2005; Rakotomalala et al., 1993).
Numerical modelling of 3D hard turning is essential in order to predict accurate tool
forces, stress, temperature, strain and strain rate fields. It also allows the estimation of the
superficial state of the machined surface, that is, the residual stresses induced in the
workpiece. Finite element model for 3D turning has also been introduced in earlier
studies. In 3D FEM studies for modelling machining processes, Guo and Dornfeld
(1998) presented a model to simulate burr formation when drilling stainless steel. Ceretti
et al. (2000) used 3D FEM to model in turning of aluminium alloys and low-carbon
steels under orthogonal and oblique cutting conditions. Guo and Liu (2002) proposed
3D FEM for hard turning of AISI 52100 steel using PCBN tools. The model was used to
predict the cutting forces, temperature distribution over the cutting edge and the residual
stress distribution on the machined surface. They also presented a basic sensitivity
analysis for flow stress and friction. Effects of edge preparation in cutting tools for hard
turning have been studied using FEM simulations by Yen et al. (2004) and Chen et al.
(2006). Klocke and Kratz (2005) used 3D FEM to calculate the temperate on the
chamfered edge design PCBN tool. Aurich and Bil (2006) proposed a 3D FEM model for
serrated chip formation. More recently, Arrazola et al. (2007b) proposed a 3D FEM
model for predicting residual stresses.
Numerical modelling of 3D hard turning using ALE FEM
2
241
Finite element modelling of 3D hard turning
The 3D finite element model for hard turning has been developed under the general
purpose FEA software Abaqus/Explicit© (v6.6-1). Figure 3 shows a scheme of the
boundary conditions assumed for the model, as well as the shape and mesh employed for
the cutting tool and the workpiece material.
One of the main disadvantages of ALE models with Eulerian boundaries is that an
initial chip must be defined. The complex tool geometries and negative rake angles
usually employed in hard turning result in complicated chip shapes, which are
usually difficult to be predicted previously. In this paper, a new hybrid approach
is presented, where initially a manual remeshing stage is performed and finally
a well known ALE step with Eulerian boundaries is used to reach the steady state
condition.
The first remeshing stage allows a simple workpiece to be initially meshed, since
there is no need to have an initial chip. In this phase, several remeshing steps are
performed in order to ensure that the mesh does not get highly distorted. Once the final
contact length is ensured, a final remeshing is made to start the last step, where the steady
state is reached eventually. In the final stage, Eulerian boundaries are employed for the
Entry_Material and Exit_Material surfaces, and the ALE formulation is used. The
difference between the initial and final stages is that in the first stage there is not an
Eulerian surface for the Exit_Chip, while in the final step there is. This provides that in
the first stage the chip behaves like a balloon that is being inflated. Figure 2 shows the
initial mesh, three steps for the initial remeshing stage, and the final step with full
Eulerian boundaries.
A remeshing stage is completed as follows. Firstly, after an Abaqus Explicit step is
finished, the model is imported into Abaqus Standard. Once the import is completed, a
new mesh is designed taking into account the deformed state of the previous mesh.
For this task, a high-performance finite element preprocessor is employed, Altair
Hypermesh 8.0, which permits to create surfaces from a previous mesh. After the desired
mesh is created, a mapping calculation is made in Abaqus Standard, in order to
interpolate the solution onto the new mesh from the output databases generated with
the old mesh. Finally, the analysis is imported into Abaqus Explicit and a new
step is performed. This procedure is repeated until desired steady-sate solution has
been reached.
The ALE formulation employed for the the final step (see Figure 3) makes the
material enter the workpiece mesh and exit it via different Eulerian boundary surfaces:
Entry_Material, Exit_Chip and Exit_Material.
Thanks to this new hybrid formulation employed, artificial criterion (physical or
geometrical) to generate the chip or an initial chip design are not needed. Only a
short initial remeshing stage is needed to obtain the final chip shape. Such features,
probably the major advantages of the presented model over the ones reported in literature
(Guo and Liu, 2002 and Karpat and Özel, 2007), avoids the introduction of arbitrary
effects on the obtained results, making the simulation more robust. This point gets
special relevance when trying to forecast the state of the machined surface and
residual stresses.
242
Figure 2
P.J. Arrazola and T. Özel
Initial mesh, remeshing steps and final steady state step for the ALE finite element
model for 3D hard turning (see online version for colours)
243
Numerical modelling of 3D hard turning using ALE FEM
Figure 3
Mechanical boundaries used in the final step of the ALE model for 3D
hard turning
Both tool and workpiece are considered as deformable, in order to analyse the stresses
that appear in the tool. Only elastic properties are used for the tool. Although the
limitations reported in literature (Warnecke and Oh, 2002) the thermo-visco plastic
behaviour of the workpiece is modelled by the Johnson and Cook (1983) constitutive
equation:
m
⎡
⎛ ε ⎞ ⎤ ⎡ ⎛ θ − θ ⎞ ⎤
n
σ = ⎡ A + B × ( ε ) ⎤ × ⎢1 + C × ln ⎜ ⎟ ⎥ × ⎢1 − ⎜ w 0 ⎟ ⎥
⎣
⎦ ⎢
⎝ ε 0 ⎠ ⎥⎦ ⎢ ⎝ θ m − θ 0 ⎠ ⎥
⎣
⎣
(1)
⎦
In the Johnson-Cook model, ε is the plastic strain, ε is the plastic strain rate, ε 0 is the
reference plastic strain rate (0.001s–1), θw is the temperature of the workpiece, θm is
the melting temperature of the workpiece material and θ0 (293 K) is the room
temperature. Material constant A is the yield strength, B is the hardening modulus,
C is the strain rate sensitivity, n is the strain-hardening exponent and m the thermal
softening exponent. Although a more realistic simulation model for the machining
process should also take into account the state of the work material due to a previous
machining pass or manufacturing process, in our model the material enters the workpiece
without any strain or stress history.
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P.J. Arrazola and T. Özel
Due to the limitations imposed by the importing options in Abaqus Standard, the
Johnson-Cook law has been discretised into tabular data. The number of points employed
to describe the material behaviour is 15525, with 25 levels for the strain, 23 for the strain
rate and 27 for the temperature.
Coulomb friction law has been selected for the modelling of the tool-chip interface
contact. Heat transfer is allowed on the tool-chip contact area.
The elements employed are C3D8RT, eight node bricks with tri-linear displacement,
temperature calculation and hourglass control. Their size varies from 2 to 30 µm
depending on the zone. Table 1 gives the input parameters for the Hard Turning
simulation (Guo and Liu, 2002).
Table 1
Material properties and cutting condition for the process simulations
Material properties
Plasticity
Johnson-Cook Law
Inelastic heat fraction (β)
Density
(ρ)
(kgm–3)
Elasticity
(E) (GPa)
Conductivity (k)
–1
–1
(Wm K )
Specific heat
–1
–1
(c) (JKg K )
Expansion (K–1)
A [MPa]
2482.4
B [MPa]
n
C
m
1498.5
0.19
0.027
0.66
0.9
7827
Workpiece
(AISI 52100 62HRC)
Tool (PCBN)
Workpiece
3120
201.33 f(T)
Tool
Workpiece
680
43
Tool
Workpiece
100
458
Tool
Workpiece
Tool
960
11.5 × 10–6 f(T)
–6
4.9·10
Contact
Thermal conductance, (Ki ) [W m–2 K–1]
Heat Partition coefficient (Γ)
Friction coefficient (µ)
Friction energy transformed into heat (η)
Process
Cutting speed (V) [m/min]
Feed rate [mm/rev]
Depth of cut (p) [mm]
Cutting edge microgeometry
Nose radius (rp) [mm]
Rake angle (γ) [º]
Clearance angle (α) [º]
Cutting edge inclination angle (λs) [º]
Cutting edge angle (κs) [º]
1 × 108
0.5
0.35 (Guo)
1
120
0.1
0.2
Chamfer 20º × 0.1mm
0.8
–5
5
0
0
Numerical modelling of 3D hard turning using ALE FEM
3
245
Results and discussions
A unique simulation has been run in the cutting conditions explained in Table 1, that is,
a Cutting speed (V) of 120 m/min., a Feed rate of 0.1 mm/rev and a Depth of cut (p) of
0.2 mm.
Simulation was run until the steady state was reached: 0.133 ms.
Figure 4 shows the temperature fields for the hard turning simulation in the tool
and workpiece. As it can be observed, a temperature of 1558 K has been achieved in the
tool, while the maximum temperature in the workpiece is 1483 K. Both maximum
temperatures are located at the zone where the chip thickness is minimum.
It is observed that two hot points are obtained as has been claimed in the past from
other authors (Karpat et al., 2007; Klocke et al., 2005) when using a variable chamfered
microedge geometry.
Figure 4
Temperature (K) contour maps in the workpiece and tool for the hard turning
simulation, and the path (in red) used for the residual stresses extraction (see online
version for colours)
One of the main advantages of 3D simulations is that it is possible to analyse the variable
state of the chip formation process along the cutting edge. This way, Figure 5 shows the
plastic strain and Von Mises equivalent stress contour maps for different cutting planes
shown in Figure 2 (perpendicular to the cutting edge). As it can be observed, the
maximum plastic strain reaches the value of 4, and is generated where the undeformed
chip thickness is minimum. This issue matches with the maximum tool temperature
found at the same zone.
On the other hand, the maximum stress appears in the tool, in the central zone of the
chip width.
Figure 6 shows the contact pressure field that appears in the tool. As it can be
observed, the contact length varies with the undeformed chip thickness. Moreover, it can
be observed that a pressure zone appears in the flank surface, which could be the cause
of the flank wear.
The cutting force obtained from this hard turning simulation has been 154 N, while
the feed force has a value of 58 N. The radial force has a value 138 N, which is almost as
big as the cutting force.
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P.J. Arrazola and T. Özel
Figure 5
Plastic strain and Von Mises equivalent stress for three different cross sections along
the cutting edge (see online version for colours)
Figure 6
Contact pressure on the tool for the Hard Turning simulation (see online version
for colours)
As explained earlier, an important advantage of this model is that it does not delete any
element from the model, so the superficial state of the workpiece can be estimated.
Figure 7 shows the residual stress components corresponding to the ones which would be
measured on a Hole-Drilling test. That is, only the planar stress state corresponding to
Numerical modelling of 3D hard turning using ALE FEM
247
the machined surface will be analysed. For this task, stress values from a path
(see Figure 4) have been extracted, corresponding to the material that would not be
removed in the next revolution. The component S11 would correspond to the stress in the
feed direction, component S33 to the cutting direction and component S13 to the shear
stress in the plane. Their values vary form −400 Mpa for S13 to −1200 Mpa for S33.
That is, all of them are negative (compressive) in the machined surface, which matches
roughly with experimental data found in Liu et al. (2004). As it can be observed in
Figure 8, according to experimental measures found in Liu et al. (2004), a slightly
compressive stress can be found at the machined surface, while the compressive stress
becomes higher with the depth, until 15 µm are reached. On the other hand, the
compressive residual stresses found in the simulation are maximum in the machined
surface. This could be due to the high temperature found on this surface (570 K) which
could generate compressive stresses due to the thermal expansion. This fact suggests that
a cooling and stress relaxation step should be carried out in order to obtain more realistic
residual stresses.
Figure 7
Stress components along the depth of the workpiece (see online version for colours)
Figure 8
Residual stress found by Lin et al. (2004) in the cutting direction for the same
cutting conditions
4 Conclusions
A 3D finite element model for hard turning has been developed under the general
purpose FEA software Abaqus/Explicit© (v6.6-1) using the ALE formulation.
A chamfered geometry PCBN cutting tool for hard turning of AISI 4340 steel has been
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P.J. Arrazola and T. Özel
utilised. This FEA technique allows predicting the fields of temperature, Von Mises
stresses and contact pressure over the cutting tool and workpiece surfaces. Predicted
machining-induced stress fields were compared with an experimental work and good
agreement was observed. Predicted temperature and stress fields possibility can help
understanding the cutting tool wear in hard turning, thus reducing costly and time
consuming experimental approaches.
References
Adibi-Sedeh, A.H. and Madhavan, V. (2003) ‘Understanding of finite element analysis results
under the framework of Oxley’s machining model’, Proceedings of the 6th CIRP International
Workshop on Modeling of Machining Operations, Hamilton, Canada.
Arrazola, P.J. (2003) ‘Modélisation Numérique de la Coupe: Étude de Sensibilité des Paramètres
d’Entrée et Identification du Frottement entre Outil-Copeau’, PhD Thesis, E.C. Nantes,
France.
Arrazola, P.J., Llanos, I., Villar, J.A., Ugarte, D. and Marya, S. (2007) ‘3D finite element modelling
of chip formation process’, Proceedings of the 10th CIRP International Workshop on
Modeling of Machining Operations, Regio-Calabria, Italia.
Arrazola, P.J., Villar, A., Ugarte, D. and Marya, S. (2007) ‘Serrated chip prediction in finite
element modeling of the chip formation process’, Machining Science and Technology,Vol. 11,
No. 3, pp.367–390.
Aurich, J.C. and Bil, H. (2006) ‘3D finite element modelling of segmented chip formation’, Annals
of the CIRP, Vol. 55, No. 1, pp.47–50.
Ceretti, E., Fallböhmer, P., Wu, W.T. and Altan, T. (1996) ‘Application of 2-D FEM to chip
formation in orthogonal cutting’, Journal of Materials Processing Technology, Vol. 59,
pp.169–181.
Ceretti, E., Lazzaroni, C., Menegardo, L. and Altan, T. (2000) ‘Turning simulations using a
three-dimensional FEM code’, Journal of Materials Processing Technology, Vol. 98,
pp.99–103.
Chen, L., El-Wardany, T.I., Nasr, M. and Elbestawi, M.A. (2006) ‘Effects of edge preparation and
feed when hard turning a hot work die steel with polycrystalline cubic boron nitride tools’,
Annals of the CIRP, Vol. 55, No. 1, pp.89–92.
Guo, Y. and Dornfeld, D.A. (1998) ‘Finite element analysis of drilling burr minimization with a
backup material’, Transactions of NAMRI/SME, Vol. XXVI, pp.207–212.
Guo, Y.B. and Liu, C.R. (2002) ‘3D FEA modeling of hard turning’, ASME Journal of
Manufacturing Science and Engineering, Vol. 124, pp.189–199.
Haglund, A.J., Kishawy, H.A. and Rogers, R.J. (2005) ‘On friction modeling in orthogonal
machining: an arbitrary Lagrangian-Eulerian finite element model’, Transactions of
NAMRI/SME, Vol. 33, pp.589–596.
Johnson, G.R. and Cook, W.H. (1983) ‘A constitutive model and data for metals subjected to large
strains, high strain rates and high temperatures’, Proceedings of the 7th International
Symposium on Ballistics, The Hague, The Netherlands, pp.541–547.
Karpat, Y. and Özel, T. (2007) ‘3D FEA of hard turning: investigation of PCBN cutting tool
micro-geometry effects’, Transactions of NAMRI/SME, Vol. 35, pp.9–16.
Karpat, Y., Özel, T., Sockman, J. and Shaffer, W. (2007) ‘Design and analysis of variable
micro-geometry tooling for machining using 3D process simulations’, Proceedings of
International Conference on Smart Machining Systems, 13–15 March, National Institute of
Standards and Technology, Gaithersburg, Maryland, USA.
Klocke, F. and Kratz, H. (2005) ‘Advanced tool edge geometry for high precision hard turning’,
Annals of the CIRP, Vol. 54, No. 1, pp.47–50.
Numerical modelling of 3D hard turning using ALE FEM
249
Klocke F., Raedt, H-W. and Hoppe, S. (2001) ‘2D-FEM simulation of the orthogonal high speed
cutting process’, Machining Science and Technology, Vol. 5, No. 3, pp.323–340.
Koenig, W.A., Komanduri, R., Toenshoff, H.K. and Ackeshott, G. (1984) ‘Machining of hard
metals’, Annals of the CIRP, Vol. 33, No. 2, pp.417–427.
Leopold, J., Semmler, U. and Hoyer, K. (1999) ‘Applicability, robustness and stability of the finite
element analysis in metal cutting operations’, Proceedings of the 2nd CIRP International
Workshop on Modeling of Machining Operations, Nantes, France, pp.81–94.
Liu, M., Takagi, J. and Tsukuda, A. (2004) ‘Effect of tool nose radius and tool wear on residual
stress distribution in hard turning of bearing steel’, Journal of Materials Processing
Technology, Vol. 150, pp.234–241.
Madhavan, V., Chandrasekar, S. and Farris, T.N. (2000) ‘Machining as a wedge indentation’,
Journal of Applied Mechanics, Vol. 67, pp.128–139.
Marusich, T.D. and Ortiz, M. (1995) ‘Modeling and simulation of high-speed machining’,
International Journal for Numerical Methods in Engineering, Vol. 38, pp.3675–3694.
Movahhedy, M.R., Gadala, M.S. and Altintas, Y. (2000) ‘FE modeling of chip formation in
orthogonal metal cutting process: an ALE approach’, Machining Science and Technology,
Vol. 4, pp.15–47.
Olovsson, L., Nilsson, L. and Simonsson, K. (1999) ‘An ALE formulation for the solution of
two-dimensional metal cutting problems’, Computers and Structures, Vol. 72, pp.497–507.
Özel, T. and Altan, T. (2000) ‘Determination of workpiece flow stress and friction at the chip-tool
contact for high-speed cutting’, International Journal of Machine Tools and Manufacture,
Vol. 40, No. 1, pp.133–152.
Özel, T. and Zeren, E. (2005) ‘Finite element modeling of stresses induced by high speed
machining with round edge cutting tools’, Proceedings of IMECE’05, 2005 ASME
International Mechanical Engineering Congress and Exposition, Paper No. 81046, Orlando,
Florida, 5–11 November.
Rakotomalala, R., Joyot, P. and Touratier, M. (1993) ‘Arbitrary Lagrangian-Eulerian
thermomechanical finite element model of material cutting’, Communications in Numerical
Methods in Engineering, Vol. 9, pp.975–987.
Sekhon, G.S. and Chenot, J.L. (1992) ‘Some simulation experiments in orthogonal cutting’,
Numerical Methods in Industrial Forming Processes, pp.901–906.
Toenshoff, H., Wobeker, H-G. and Brandt, D. (1995) ‘Hard turning – influences on the workpiece
properties’, Transactions of North American Manufacturing Research Institute, Vol. 13,
pp.215–220.
Warnecke, G. and Oh, J-D. (2002) ‘A new thermo-viscoplastic material model for
finite-element-analysis of the chip formation process’, Annals of the CIRP, Vol. 51, No. 1,
pp.79–82.
Yen, Y-C., Jain, A. and Altan, T. (2004) ‘A finite element analysis of orthogonal machining using
different tool edge geometries’, Journal of Material Processing Technology, Vol. 146, No. 1,
pp.72–81.