Numerical Cutting Modeling with Abaqus/Explicit 6

15 Pages·2002·0.79 MB·English

Numerical Cutting Modeling with Abaqus/Explicit 6.1
P.J.Arrazola*/ **, F.Meslin*, J-C.Hamann* and F.Le Maître*
* École Centrale de Nantes-Laboratoire Mécanique et Matériaux, 44320 Nantes, France
** Escuela Politécnica Superior de Mondragon Unibertsitatea, Departamento de Fabricación, 20500
Mondragón, Spain. E-mail: [email protected]
Abstract: Numerical cutting modeling gives access to thermo-mechanical variables values such as stress,
strain and temperature, that in some cases are not easily measurable through experimental tests, so it
offers a new way to improve several fields related to the machining process: cutting tools manufacturing,
parts manufacturing and tool and workpiece materials among other. In this paper a 2D and a 2D 1/2
models developed with Abaqus/Explicit 6.1 and the problems encountered while trying to model the chip
formation process are showed. As an example of what can be achieved with numerical cutting modeling,
tool rake angle influence while machining AISI 4140 steel, is analyzed.
1. Introduction
Numerical cutting modeling provides understanding and prediction of cutting process variables such as
stress, strain, temperature, cutting forces, and unlike experimental tests, calculates at least an approximate
value of some of them. Basically, some of these variables are not measurable through conventional
machining tests.

Unlike analytical models (Merchant, 1944) (Lee, 1951), finite element method allows including effects of
the cutting process such as friction at the tool-chip interface, work-hardening, straining rate and
temperature dependencies of the workpiece material responses. Three kinds of mechanical formulation can
be used. Eulerian formulation (Strenkowski, 1990), in which the grid is not attached to the material, is
computationally efficient but needs to update the free chip geometry (Leopold, 1999). Lagrangian
formulation, in which the grid is attached to the material, requires to update the mesh (remeshing
algorithm) or to use a chip separation criterion to form a chip from the workpiece (Ceretti, 1996) (Grolleau,
1996). An alternative method is to use Arbitrary Lagrangian Eulerian (ALE) formulation (Movahhedy,
2000) (Pantale, 1996). In this case, the grid is not attached to the material and it can move to avoid
distortion and update the free chip geometry. However, whatever formulation is used, numerical cutting
modeling requires: (i) numerical model definition, (ii) material flow characteristics at high temperature,
strain-rate and strain as encountered during cutting process, (iii) a tool-chip contact friction model.

The main objective of this paper is to show the possibilities of using Abaqus for numerical cutting
modeling purpose, as well as to show the major drawbacks encountered in the model set up.

The paper starts with an explanation of what the cutting process is about. Afterwards, the 2D numerical
model set up in Abaqus will be explained and some numerical cutting modeling examples in 2D ½ will be
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showed. Then the major drawbacks found in numerical cutting modeling until now and how they are
expected to be overcome are pointed out. Finally the conclusions of this work will be discussed.

2. Numerical cutting modeling of chip formation process
Machining or cutting process is employed when good tolerances, surface finish and special forms are
needed in manufactured parts. Although it has been used for a long time and much progress has been
achieved, there are still many aspects that could be improved in order to cut down costs and get better
manufacturing parts quality.
In the cutting process, the interaction of a specially designed tool with the part to be manufactured makes
the chip to be removed from the part (see Figure 1). The cutting conditions (cutting speed, uncut chip
thickness, depth of cut…) and the tool geometry among other parameters, have great influence in the
process results. Basically, in most of the cases, the process parameters optimization is done considering
past experience and experimental tests. This approach can lead to high costs and, even worse not
necessarily to the best solution.
When a new cutting tool needs to be developed, for example a cutting mill, even if we analyze it in a 2D
plan there are several parameters that need to be defined: rake angle, clearance angle, cutting edge radius...
(see Figure 2).
Cutting tools and parts manufacturers are interested in tool life variable, i.e., the time in which the cutting
tool is able to cut the part material without reaching an established criterion. This criterion could be tool
wear on the rake or clearance face, or others: part surface finish, part tolerance, cutting forces or cutting
power… We must point out that numerical modeling, at this stage, is not able to predict these variables.
Instead, it can give values of other thermo-mechanical variables as temperature, pressure, chip speed, etc.
that cannot be measured easily by experimental tests. Basically, the dimension, where the chip formation
takes place is so small that the sensors usually used to measure theses variables cannot be used. In fact, tool
life will be longer or shorter depending on the values of these variables. Thus, within the next future it
could be possible to predict tool life using models that will take into account these variables values. At this
stage, the manufacturer will have to choose the best solution taking into account only these thermo-
mechanical variables values and his knowledge. Cutting modeling approach combined with past experience
can help to reduce time consuming experimental tests.
3. Numerical cutting modeling in 2D
Using general-purpose software as Abaqus for numerical cutting modeling allows having a flexible model.
This way, the final user is able to study some cutting process matters, like the material and friction behavior
and numerical aspects influence.
In Figure 3 we show the procedure to set up numerical simulation with Abaqus. In order to reduce
computational time, in most cases a 2D numerical modeling is done. Furthermore, this kind of modeling
could be enough to study several aspects of the cutting process.
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Depending on the formulation used, there are several approaches to model the process. When using the
Lagrangian formulation proposed in Abaqus Standard and in order to avoid large deformations and separate
the chip from the part two solutions can be forecasted. A remeshing algorithm (Madhavan, 2000) can be
used or we can set up geometrical or mechanical criteria to separate a stuck chip to the part from which it is
going to be removed (Behrens, 1999). In the last approach, the results depend on these criteria, and the
material quantity that is removed from the part is decided from the beginning.
Another solution could be to use an Arbitrarian Lagrangian Eulerian formulation or the adaptive meshing
option proposed in Abaqus Explicit (Abaqus, 00). In this case, there are several possibilities. Two of them
are showed in this paper.
In Figure 4 our first approach is showed. An example of one of the models set up in Abaqus and the final
geometry of the model after 3 milliseconds of machining time can be viewed. That is 15 mm length of cut
at 300 m /min cutting speed.
The element type used in both the workpiece and the tool is a four node bilinear displacement and
temperature, reduced integration with hourglass control: CPE4RT. The number of elements in the part is
897 and in the tool 97. The element dimension varies from 0.005 to 0.200 mm depending on the model
zone considered. The calculation time was of 24 hours in a computer with 1 Gb of RAM memory and 1400
Mhz.
We define the part or workpiece as an adaptive mesh domain, while the tool is considered rigid. The
material moves from the left to the right at the cutting speed and the user does not impose the material that
goes by the chip and by the workpiece itself. The tool is fixed in 1 and 2 directions. After the calculus, the
chip takes the stationary geometry.
Adaptive mesh constraints, boundary conditions and parameters that control the intensity of the adaptive
meshing are applied according to the manual (Abaqus, 00).
Numerical simulation of chip formation requires a thermo-visco-plastic law for the workpiece material
behavior. In the case of large plastic deformation and large strain rate, the well-known Johnson-Cook
formulation is often used. This formulation is proposed in Abaqus Explicit. So the flow stress σ is given
eq
by:
σeq = (A + B ⋅εenq )⋅ [1 + C ⋅ Log (ε&eq 0,001 )]× 1 − T -Tamb T - T m  (1)
  fus amb  
Above expression, εeq is the plastic strain, ε&eq is the strain rate, T the temperature, Tamb the room
temperature, T the melting temperature. A, B, C, n and m are rheological parameters. The workpiece
fus
material is AISI 4140 and the rheological parameters for the Johnson-Cook law have been taken from
bibliography (Grolleau, 1996). Rheological parameters values for AISI 4140, can be seen in Table 1. Its
physical and elastic properties can be seen in Table 2. They have been taken from bibliography (Metals
Handbook, 78)

The tool material is cemented carbide with 90WC-10Co as a nominal composition. Its cutting edge radius
is 50 µm, a usual value encountered in the industry. Tool material physical and elastic properties can be
seen in Table 3. They have been taken from bibliography (Metals Handbook, 80).
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The friction between the tool and the chip is assumed to follow a Coulomb law. The Coulomb friction
coefficient has been 0.32, according to some authors (Grolleau, 1996).

Another approach to model chip formation process with Abaqus explicit is showed in Figure 5.
Calculations are run in 2 steps. In the first one, we will consider the exit chip surface as a lagrangian one in
order to lengthen the chip. In a second step, we will consider the exit surface as an eulerian one. We choose
the first one for the better mesh control and because we do not need to stop the calculation.
4. Numerical cutting modeling analysis/results in 2D
A numerical study of the rake angle influence has been done in order to show what can be reached with
numerical cutting modeling. We ran two test where the rake angle value was + 6º (Test 1) and – 6º (Test 2).
Data of cutting parameters are collected in Table 4. In Figure 6, we can observe numerical results obtained
for temperature, Von Mises stress, plastic strain and the cutting and feed forces after 5 milliseconds of
machining time, for the two examples. Variables results of this numerical analysis can be seen in Table 5.
After these results, we can notice the great rake angle influence over the temperature, chip thickness, tool-
chip contact length, shear angle, cutting and feed forces. Negative rake angle raises the temperature in 72 K
(7%), the chip thickness in 0.08 mm (13%), the tool-chip contact length in 0.15 mm (30%), the cutting
force in 125 N (18%) and the feed force in 165 N (60%). Cutting and feed forces, and chip thickness are
close to those found in experimental tests (Grolleau, 96).
5. Numerical cutting modeling in 2D ½
In Figure 7 we show an example of the 2D ½ model set up in Abaqus, and the final geometry of the model
after 1 millisecond of machining time. That is 5 mm. of length of cut at 300m. /min. cutting speed. The
element type used in both the workpiece and the tool is an eight node trilinear displacement and
temperature, reduced integration with hourglass control: C3D8RT. The number of elements in the part is
2104 and in the tool 495. The element dimension varies from 0.05 to 0.100 mm. depending on the model
zone considered. The calculation was of nearly 72 hours in a computer with 1Gb of RAM memory and
1400 Mhz for 1 milliseconds of machining time.
The procedure and considerations to set up the model, was quite similar to the 2D model one. As in the 2D
model, we define the part or workpiece as an adaptive mesh domain, while the tool is considered rigid.
Adaptive mesh constraints, boundary constraints and adaptive meshing parameters are applied in the same
way as we did for the 2D model as well.
As we can see we have access to the temperature variable, in an area that cannot be easily measured by
other means. To do so, the tool has been removed.
6. General numerical cutting modeling drawbacks
We must not forget that, generally, numerical modeling deals with material and friction behavior from a
macroscopic point of view. Apart form that, some shortcomings found in cutting modeling that have been
detailed in a previous paper (Arrazola, 2001) are pointed out in next sections.
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6.1 Material law behavior
As we have mentioned in section 3, numerical cutting modeling needs a thermo-visco-plastic law, as the
Johnson-Cook one. The rheological parameters A, B, C, n and m are usually obtained by Split Hopkinson
pressure bar bench equipped with a high energy heating device, or impact tests, associated to tensile or
compression tests. Unfortunately, these devices cannot provide, in the same time, more than 5.103 s-1 as
strain rate and 0.5 as plastic deformation (Maekawa, 1983) (Meslin, 2000). It means that for the
constitutive equation to be evaluated an extrapolation will be necessary. With this extrapolation of the
constitutive relation, it is impossible to have an accurate estimation of tool forces, temperatures and
stresses, especially in some cases (stainless steel...).
6.2 Friction law
The friction parameters at the tool-chip contact are hardly identified. Only few methods are available and,
in all cases, experimental conditions are not conducted in similar conditions as encountered in cutting
process. Pion-on disc friction tests give values usually overestimated. The modified pion-on disc device
proposed by Olsson (Olsson, 1989), allows refreshing the working material like in the cutting process.
However, the pressures applied on the pion-on disc device are still low comparing to the mechanical
conditions during machining. In the test proposed by Joyot (Joyot, 1994), even if the loading system is high
enough to impose a high pressure, the temperature at the interface between the frictional tool and the
working material is not similar to that supposed during cutting process. As a result of that, the chemical
diffusion at tool-chip interface is not taken into account. A different approach is to use machining tests to
obtain an approximation of Coulomb friction coefficient. An example of this idea is Albrecht’s method
(Albrecht, 1960), but with this approach a hypothetical friction coefficient is obtained after machining
through different cutting conditions (uncut chip thickness).
6.3 Inverse Identification of material and friction law
To overcome these problems, one solution is to obtain a good identification of the constitutive relation by
using inverse methods. The aim of these methods is to identify the rheological parameters of the
constitutive equation with orthogonal cutting experiments associated to Finite Element Methods
simulations. This technique requires a lot of experiments and cutting tests and, what is more, it is difficult
to make a distinction between the effects of workpiece material flow, the effects of tool-chip contact
interface and the numerical approximations. Moreover, several coupled solutions of material behavior low
and friction law can be found if few parameters are compared in the identification, for example only cutting
forces. However, the use of special cutting tools could help to overcome this problem. Here again, Abaqus
can be used as a tool for inverse identification of friction law and material behavior.
7. Numerical cutting modeling drawbacks encountered in Abaqus 6.1-1.
Although modeling of chip formation process has been possible using Abaqus Explicit 6.1-1, the major
weakness that were found will be pointed out:
- Adaptive mesh restrictions normal to eulerian surfaces
Chip exit surface is considered as an eulerian surface and as result of that, normal mesh restrictions must to
be imposed. When modeling a long chip, elements that are close to the exit surface tend to distort too much
and the adaptive meshing algorithm is not able to update the mesh properly, as can be seen in Figure 8.
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Thus, the initial chip length needs to be shorten after several trials. A normal mesh restriction that could
“turn” and follow the chip curling movement, will be a good solution.
- Adaptive meshing algorithm
The initial model geometry is defined, considering the acquired experience in machining. When a new
study case needs to be analyzed, the best model geometry is unknown. A good meshing algorithm is needed
in order to allow chip geometry to adapt itself. As showed in Figure 9, problems were found when the chip
tended to shrink or to swell up too much from the initial geometry.

Moreover, differences in numerical results were found for equal machining cases studies when initial
model chip thickness was different. In Figure 10, temperature results of two different tests are showed. The
only difference between them was the initial chip thickness of the model. Comparing with rake angle study
showed previously, the differences are the cutting edge radius (40µm. in this case) and the uncut chip
thickness (0.2 mm. in this case). In case a) it was twice times the uncut chip thickness and in case b) it was
one and a half times the uncut chip thickness. After 3 milliseconds of machining time a difference of 25 º is
found.
- Cutting Edge Meshing
Cutting edge radii can vary from values of 5 µm to 50 µm as can be seen in Figure 11. However, cutting
edge radius plays a decisive roll when machining with small uncut chip thickness, as it is the case when
finishing operations are done. Meshing radii of 20 µm in 3D geometries with C3D8RT elements was not
possible in Abaqus CAE.
- Adiabatic Shear Banding
Segmented or serrated chips should be predicted if an appropriate answer to the industry is searched (see
Figure 12). At this stage is not possible to do so with Abaqus Explicit without setting up arbitrary criteria.
8. Conclusions
The numerical study of the rake angle influence made with Abaqus Explicit has showed that cutting
modeling can be used as a complementary approach to reduce time consuming and expensive experimental
tests. The most important point to obtain a reliable modeling of the chip formation process is to use
material and friction laws identified in similar conditions to those found in machining process. In this case,
as well, Abaqus offers the possibility of being used as a tool for inverse identification.
Although some improvements need to be done, Abaqus Explicit offers an easy way to model chip
formation process. Several shortcomings or drawbacks, related to the software itself, should be overcome in
order to give a reliable answer to the industry: adaptive mesh restrictions, adaptivity mesh algorithm,
meshing capabilities…
9. References
1. Abaqus/Explicit User’s manual Vol I. Version 6.1. Hibbit, Karlsson and Sorensen, Inc., 2000.
2. Albrecht, P., New developments in the theory of the metal-cutting process, Part 1, Journal of
Engineering for Industry, 348-358,1960.
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3. Arrazola, P.J., Meslin, F., Hamann, J-C, “Simulation numèrique de la coupe: effets des paramètres
rhéologiques”, Xvème Congrès Français de la Mecanique, pp.147-152, 2001.
4. Behrens, A., Westhoff, B., “Finite Element Modeling of High Speed Machining Processes”, High
Speed Cutting, 2nd International German and French Conference, pp.185-190, 1999.
5. Ceretti, E., Fallbohmer P., Wu W.T., Altan T., “Application of 2D FEM to chip formation in
orthogonal cutting”, Journal of Material Processing Technology, 59:169-180, 1996.
6. Grolleau, V., “Approche de la validation expérimentale des simulations numériques de la coupe avec
prise en compte des phénomènes locaux à l'arête de l'outil”, Phd Thesis, Ecole Centrale de Nantes,
1996.
7. Joyot, P., “Modélisation numérique et expérimentale de l’enlèvement de matière”, Phd Thesis
Université de Bordeaux, 1994.
8. Lee, E.H., B.W. Shaffer B.W., “The theory of plasticity applied to a problem of machining”, ASME
Journal of Applied Mechanics, 73:404-413, 1951.
9. Leopold, J., Schmidt G., “Challenge and problems with Hybrid Systems for the modelling of
machining operations”, II CIRP international Workshop on Modeling of Machining Operations, 298-
311, 1999.
10. Madhavan, V., Gandikota, V.A., and Agarwal, R., “Nonlinear Finite Element Analysis of Machining
and Sheet Metal Forming”, AIAA Journal, vol.38, No. 11,2000.
11. Maekawa, K., Shirakashi T., Usui E.,”Flow stress of low carbon steel at high temperature and strain
rate (Part 2)”, Bull. Japan. Soc. Of Prec. Engr., 17/3:167-172, 1983.
12. Merchant, E., “Basic mechanics of the metal-cutting process”, Transaction of the ASME, Journal of
Applied Mechanics, 66:168-175, 1944.
13. Meslin, F., Hamann J.C., “Definition of constitutive equations and friction by inverse method and
machining tests”, International Workshop on friction and Flow Stress in Cutting and Forming, 112-
137, 2000.
14. Metals Handbook, Properties and selection: Irons and steels. Vol. 1, ASM, 1978.
15. Metals Handbook, Properties and selection: stainless Steels, Tool Materials and special purpose
metals. Vol. 3, ASM, 1980.
16. Movahhedy, M.R., Gadala M.S., Altintas Y., “Simulation of chip formation in orthogonal metal
cutting process: an ALE finite element approach”, Machining Science and Technology, 4/1:15-42,
2000.
17. Olsson, M., Simulation of cutting tool wear by a modified pion-on disc test, Int. J. Mach. Tools
Manufact. 38/1-2:113-130, 1989.
18. Pantale, O., Rakotomalala R., Touratier M., Hakem N.,”A three dimensional Numerical Model of
orthogonal and oblique metal cutting processes”, Engineering Systems Design and Analysis, ASME-
PD, 75:199-205, 1996.
19. Strenkowski, J.S., Moon K., “Finite Element Prediction of Chip Geometry and Tool/Workpiece
Temperature Distributions in Orthogonal Metal Cutting”, Journal of Engineering for Industry,
112:313-318, 1990.
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10. Tables
Table 1. Workpiece AISI 4140 steel rheological parameters.
A B
Materials n C m
(MPa) (Mpa)
42CrMo4 598 768 0.2092 0.0137 0.807
Table 2. Workpiece AISI 4140 steel physical and elastic properties.
Density kg.m-3 7800
Young modulus Gpa. 210
Poisson’s ratio 0.3
Specific heat J.kg-1.K-1 473. at 473 K
519. at 673 K
561. at 873 K
Melting temperature K 1793
Inelastic heat fraction 0,9
Conductivity W/mºC 42.6 at 373.
42.3 at 473.
37.7 at 673.
33. at 873.
Expansion 0 at 293.
1.46 x 10-6 at 673.
Table 3. Tool cemented carbide physical and elastic properties.
Density kg.m-3 14500
Young modulus Gpa. 580 at 293 K
570 at 473 K
560 at 673 K
540 at 873 K
Poisson’s ratio 0.3
Specific heat J.kg-1.K-1 220
Conductivity W/mºC 112
Expansion 5.4 x 10-6 at 293 K.
5.3 x 10-6 at 473 K
5.4 x 10-6 at 673 K
5.6 x 10-6 at 873 K

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Table 4. Variable values set up in the numerical modeling study of the rake angle
influence.
Parameter Value
Test1 Test2
Cutting conditions Cutting Speed (m. /min.) 300 300
Uncut Chip Thickness (mm.) 0,3 0,3
Tool geometry Rake angle (º) 6 -6
Clearance angle (º) 6 6
Cutting edge radius (µm.) 50 50

Table 5. Numerical results obtained in the numerical modeling study of the rake angle
influence.
TEST γ Τ (κ) σp (Mpa) ε () σt(Mpa) t2(mm) h (mm) φ(°) Fv (N) Ff (N)
TEST1 6 915 1318 2,5 4886 0,58 0,49 29 675 275
TEST2 -6 987 1264 3,2 2339 0,66 0,64 25 800 440

11. Figures
SSUURRFFAACCEE T TOO B BEE M MAACCHHININEEDD: :
NNOOTT M MOODDEELLEEDD I NIN 2 2DD
SSUURRFFAACCEE B BEEININGG M MAACCHHININEEDD::
MMOODDEELLEEDD I NIN 2 2DD
CHIP
TOOL PART
Vc

Figure 1. Cutting process.
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RRAAKKEE AANNGGLLEE
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GGEEOOMMEETTRRYY??
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Figure 2. Cutting tools parameters to be defined.

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Figure 3. Numerical cutting modeling procedure when using general-purpose software
like Abaqus.

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