A COMPARATIVE STUDY OF DIFFERENT CHIP SEPARATION
APPROACHES FOR NUMERICAL MODELING OF
ORTHOGONAL CUTTING
Bo Hou
1
, Yong-fu Wu
1
, Shu-hui Li
1,2
, Zhong-qin Lin
1,2
and Zhong-qi Yu
1,2
1
Shanghai Key Laboratory of Digital Autobody Engineering, Shanghai Jiao Tong University
800 Dongchuan RD., Shanghai, China
2
State Key Laboratory of Mechanical System and Vibration, Shanghai, China
Keywords: Dry cutting, Modelling, ALE, Damage evolution, Residual stress.
Abstract: Numerical cutting modelling gives access to thermo-mechanical field such as stress, strain and temperature
that are difficult to obtain through experiments, thus provides a unique insight and helps to improve design
quality and shorten design cycle. Chip separation is one of the most important issues in cutting simulation
because of its significant influence on chip formation, stress and temperature predictions. Modelling of an
orthogonal cutting process using ABAQUS/explicit is presented. Two kinds of chip separation approaches
are compared, a partial damage zone (PDZ) and an Arbitrary-Lagrangian-Eulerian (ALE) based approach,
with the aim to characterize the effect on chip formation, cutting force, temperature and residual stress. ALE
and PDZ methods predict the similar cutting force and temperature results, and they also predict different
chip formations and residual stress profiles. The predictions are analysed and possible reasons are discussed.
1 INTRODUCTION
Numerical cutting modelling are more and more
essential in predicting chip formation, cutting forces,
distributions of strain, strain rate, stress, and cutting
temperature. Therefore, it provides a unique insight
for fundamental understanding of the machining
process, which leads to proper choice or design of
cutting tools, fixture, spindle, feed, and reduction of
lengthy and costly design iterations experimentation
required for process optimization.
Reliable cutting simulation heavily depends on
the chip separation approaches, which are based on
three main formulations. The first one is the
Lagrangian formulation, in which the elements are
attached to the material. Shet and Deng (2003:573-
583) applied Lagrangian model for orthogonal
cutting simulation, in which the chip separation was
modelled by nodal release based on critical stress
criterion. In the study of Hortig and Svendsen
(2007:66-76), the continuous chip was formed along
a predefined separation path based on the fracture
criterion and element deletion. Ng et al (2002:301-
329) and Mabrouki et al (2008:1187-1197) studied
saw-tooth chip formation with a predefined
separation path, as well as a damage law for
modelling fragmented chip behaviour. The chip
separation approaches based on Lagrangian
formulation are generally base on partial damage
zone (PDZ) corresponding to the trajectory of the
tool-tip. However, the PDZ must be predefined
which is difficult for 3D milling modelling.
Furthermore, the global damage zone (GDZ)
approach is applied for chip separation, in which
each element is assessed for damage over the mesh
and all time increments. Pantalé et al (2004:4383-
4399) and Anurag et al (2009:303-317) studied
orthogonal and 3D milling process using GDZ
approach with no pre-defined sacrificial element or
zipped nodes to be split.
The Eulerian formulation, in which the element
is not attached to the material, handles material flow
around tool tip without the need to define a failure
criterion (Nasr, Ng and Elbestawi, 2007:401-411).
However, the chip shape has to be known a priori,
which represents a huge drawback. Furthermore,
residual stress cannot be estimated because the
material elastic behaviour is not considered
(Movahhedy, Gadala and Altintas, 2000:267-275).
Studies using Eulerian formulation for chip
separation are reported by Kim et al (1999:45-55)
458
Hou B., Wu Y., Li S., Lin Z. and Yu Z..
A COMPARATIVE STUDY OF DIFFERENT CHIP SEPARATION APPROACHES FOR NUMERICAL MODELING OF ORTHOGONAL CUTTING.
DOI: 10.5220/0003646004580464
In Proceedings of 1st International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SDDOM-2011), pages
458-464
ISBN: 978-989-8425-78-2
Copyright
c
2011 SCITEPRESS (Science and Technology Publications, Lda.)
and Strenkowski et al (2002:723-731).
The Arbitrary-Lagrangian-Eulerian (ALE)
formulation combines the features of Lagrangian
and Eulerian analysis. The Eulerian technique is
perfect for modelling the material flow around tool
tip, while the Lagrangian technique is suitable for
modelling the unconstrained material flow at the free
boundaries. Therefore, the thermo-mechanical field
surrounding the tool tip can be analysed more
reliably, together with the absence of separation
criterion, which is always necessary in Lagrangian
model. As a result, the residual stress can be
calculated with enough accuracy which is
impossible in Eulerian models (Nasr, Ng and
Elbestawi, 2008:149-161). However, serrated chip
cannot be modelled with this technique. Another
drawback is the necessity to precisely define the
previous geometry of the chip.
Different chip separation approaches are adopted
in cutting simulations for different purposes, such as
prediction of chip formation, cutting force and
residual stress. However, a systematic comparison of
them has not been reported yet. It is difficult to
estimate the practical effects of different approaches
for the same material and cutting process. This paper
aims to estimate PDZ and ALE based chip
separation approaches in terms of chip formation,
stress, temperature distribution and cutting force
prediction during orthogonal cutting of an aeronautic
aluminium alloy Al7050-T7451, which is generally
used as the structural material of aircraft.
2 NUMERICAL MODEL
2.1 Material Constitutive Model
The Johnson-Cook material model is utilized.
Assuming a von Mises type yield criterion and an
isotropic strain hardening rule, the flow stress is
given by
()
0
0melt0
1ln 1
m
n
TT
AB C
TT
ε
σε
ε
⎡⎤
⎛⎞
⎢⎥
=+ +
⎜⎟
⎢⎥
⎝⎠
⎣⎦
(1)
where
ε
is the equivalent plastic strain.
ε
and
0
ε
are the equivalent plastic strain rate and a reference
strain rate, respectively. T, T
0
and T
melt
stand for
temperature, reference temperature and melting
temperature, respectively. A, B, C, m and n are
material parameters.
There are two popular experimental methods to
obtain the flow stress data under cutting condition:
Split Hopkinson pressure bar (SHPB) (Lennon and
Ramesh, 1998:1279-1292) and Orthogonal cutting
(OC) (Sartkulvanich, Koppka and Altan, 2004:61-
71). Fu (2007:30) combined the SHPB and OC
methods to determine the material parameters of Eq.
1. For Al7050-T7451, the physical properties and
Johnson-Cook model parameters are shown in Table
1 and Table 2, respectively.
Table 1: Physical properties of workpiece (Al7050-T7451)
and Tool material (YG6).
Physical
parameter
Workpiece
(Al7050-T7451)
Tool
(YG6)
Density, ρ
(kg/m3)
2800 14600
Elastic modulus,
E (GPa)
69.35(20),
63(100),
57.09(200),
44.57(300)
630
Poisson’s ratio, v 0.33 0.21
Specific heat, C
p
(J/kg)
888(50),
904(100),
988(150),
1004(204),
1047(260)
400
Thermal
conductivity,
λ(W/m)
134(50),
142(100),
147(125),
176(200)
79.6
Linear Expansion
coefficient,
α (10
-6
/)
23.6(100),
23.3(125),
23.5(150),
24(200)
-
T
melt
() 630
-
T
0
() 25
-
Table 2: Johnson-Cook constitutive model parameters of
Al 7050-T7451 (Fu, X.L., 2007).
A (MPa) B (MPa) C n m
0
ε
463.4 319.5 0.027 0.32 0.99 1
2.2 ALE Chip Separation Approach
The ALE model is divided in several zones, and uses
sliding, Lagrangian and Eulerian contours allowing
the material to flow across an internal Eulerian zone
surrounding the tool tip.
As shown in Figure 1, Zones 1, 2 and 3 combine
Lagrangian/Eulerian boundaries with sliding
boundaries, where the material is allowed to flow
tangentially to the contour and not allowed to go
across this boundary. At Eulerian zone 4, it is
considered as a tube with one entrance and two
exits, and the material enters on the left-hand
A COMPARATIVE STUDY OF DIFFERENT CHIP SEPARATION APPROACHES FOR NUMERICAL MODELING
OF ORTHOGONAL CUTTING
459
boundary and exits at the right-hand boundary and at
the top surface. In order to retain the Eulerian
boundaries, adaptive mesh constraints are endowed
with both the X and Y direction of the zone 4.
The geometry of the baseline model with zero
rake angle and cutting edge radius 0.02mm of tool,
cutting depth 0.1mm and cutting width 1.5mm of
workpiece is established. The tool is fixed and the
cutting speed is applied to the workpiece.
Continuous chip formation is assumed. The material
flowed around the tool tip as if it is a fluid. In other
words, there is no need to define a failure criterion.
Figure 1: Illustration of ALE model.
2.3 PDZ Chip Separation Approach
Figure 2 illustrates the geometry of the orthogonal
cutting model with a predefined cutting path, which
is composed of four parts: (1) tool, (2) chip, (3) tool-
tip passage zone and (4) workpiece. A chamfer is
designed on part 2 to avoid distortion problems at
the beginning of calculation. The centre of the tool
tip is placed exactly at the middle height of part 3.
The length and width of parallelogram mesh are set
less than 20μm due to high shear localization.
Figure 2: Illustration of ALE model.
The separation of the chip from the workpiece is
based on a shear failure module which is applied to
part 3. The shear failure module is based on the
effective plastic strain
ε
. When any element
reaches the failure plastic strain value
f
ε
, the
damage parameter D, in Eq. 2 equals to one. When
this occurs, the corresponding element will be
deleted. The workpiece is fixed and the cutting
speed is applied to the tool. Continuous chip
formation is assumed. The tool geometry, cutting
depth and cutting width of the workpiece is exactly
the same as that used in ALE model.
1
f
D
ε
ε
==
(2)
2.4 Contact Modelling
The modified Coulomb friction model is adopted to
describe the sliding and sticking phenomenon on the
tool rake face. Figure 3 shows the characteristic of
the model. Sticking or sliding friction conditions
along the tool-chip interface are dependent on the
shear stress magnitude. Sticking will occur at high
contact pressure, as shown in the shaded region.
When the contact pressure is low, as is the case
away from the tool cutting edge, sliding friction will
dominate (as shown in the unshaded region).
Figure 3: Stick-Slip region for the coulomb friction.
The following expression has been applied:
τ = μp when μp < τ
max
(sliding) (3)
τ = τ
max
when μp τ
max
(sticking) (4)
where τ, p are the friction stress and the contact
pressure on the tool rake face, respectively. τ
max
, is
the maximum shear stress of the material, and μ is
the friction coefficient. In this study, the tendency of
friction coefficient μ with cutting speed is obtained
by the orthogonal cutting tests (Fu, 2007:50).
2.5 Heat Generation
Heat generation during metal cutting is important in
tool wear and plays an important role in surface
integrity and chip formation. The majority of the
heat generated comes from plastic deformation and
friction. The temperature increment associated with
the heat generation are expressed by
12
p
ff
T
C
σ
ε
ρ
⋅∂
Δ=
(5)
Sliding
Eulerian
Tool
Workpiece
Lagrangian
Lagrangian
Lagrangian
Cutting velocity
Cutting velocity
20μm
Part 3
Part 4
Part 2
Part 1
SIMULTECH 2011 - 1st International Conference on Simulation and Modeling Methodologies, Technologies and
Applications
460
Where ΔT is temperature increment, f
1
is work-heat
convection factor; f
2
is the conversion efficiency
factor. f
1
and f
2
are taken as 0.9.
ε
is the effective
plastic strain increment. ρ and C
p
are material
density and specific heat. Heat transfer between tool
and workpiece is not considered.
2.6 Analysis
Plane strain conditions are considered (as the
workpiece width is at least ten times the chip
thickness). An explicit resolution method with
dynamic and coupled thermo-mechanical analysis is
performed with CPE4RT element type.
Analysis is carried out in two steps. In the first
step, cutting is modelled at constant cutting speed
and steady state conditions are reached. In the
second step, the workpiece is unloaded and cooled,
and the residual stress profile is obtained.
3 RESULTS AND DISSCUSSION
3.1 Chip Formation
The comparison of the predicted chip and Mises
stress at t=0.075ms and t=0.15ms for ALE and PDZ
methods is shown in Figure 4. The chip curl of the
PDZ method has larger radius than that of ALE
method. Generally, the chip with a longer contact
length with the tool produces a larger curl radius
than that with a shorter contact. As the calculation
time increases, the number of elements of ALE
model in contact with the tool decreases because
they are enlarged as well as the excessive distortion
at the curvature zone of the chip, thus diminishing
the accuracy of the calculation. Indeed, the chip
from the PDZ model has twice longer contact length
than that of ALE model. The chip curl is a key issue
for the design of chip breakers, and good tool
performance from the correct design.
3.2 Cutting Force
Figure 5 illustrates the predicted cutting force and
feed force under different cutting speeds. It is clear
that the predicted cutting force almost yield a similar
pattern that the force magnitude decreases with the
cutting speed. Small discrepancy is found between
the predicted cutting force of the ALE and PDZ
methods, which is less than 30N.
It is found that the predicted feed force of the
ALE model is below that of PDZ model. Larger
(a)
(b)
Figure 4: Chip formation process of (a) ALE, (b) PDZ
method at v=800m/min.
discrepancy between the predicted feed forces is
found when the cutting speed over 800m/min. In
PDZ model, the elements of the separation path are
enlarged to failure which will apply an extra force
perpendicular to the machined surface around the
too-tip. As the cutting speed increases, the feed force
is influenced significantly.
Φ
1
t=0.075ms
t=0.15ms
Φ
2
t=0.075ms
t=0.15ms
A COMPARATIVE STUDY OF DIFFERENT CHIP SEPARATION APPROACHES FOR NUMERICAL MODELING
OF ORTHOGONAL CUTTING
461
(a)
(b)
Figure 5: Predicted (a) cutting force and (b) feed force
results under different cutting speeds.
(a)
(b)
Figure 6: Predicted temperature distributions of (a) ALE,
(b) PDZ, at v=800m/min.
3.3 Stress and Temperature Field
Figure 6 shows the instantaneous temperature fields
at t=0.075ms. The predictions of ALE and PDZ
model have a similar temperature distribution
pattern. The highest temperature region occurs at the
tool-chip interface, i.e., secondary shear zone. The
maximum temperatures are 534.5°C and 493.7°C for
ALE and PDZ model predictions, respectively,
while the average temperature in the shear zone are
131.6°C and 122.6°C for the ALE and PDZ model.
In Figure 7, the stress distributions in the cutting
direction S
11
at t=0.075ms are depicted. In each case,
the highest stress level is found in the first shear
zone with the peak compressive stress in contact
with the tool tip. The highest value of S
11
, 1400MPa
is found in the prediction using ALE method, while
1085MPa is found in the prediction using PDZ
method. Moreover, strong stress fields exist in the
zones in front of and behind the tool tip, in which
compressive stress (green zone) dominates the front
zone while tensile stress dominates the back zone
(red zone) due to the effect of tool flank.
However, the stress distribution patterns on the
produced new surface are quite different for ALE
and PDZ methods, which are tensile stress
dominated and compressive stress dominated
respectively.
(a)
(b)
Figure 7: Predicted S
11
distributions of (a) ALE, (b) PDZ,
at v=800m/min.
3.4 Residual Stress
The effect of chip separation and cutting speeds on
140
160
180
200
220
240
260
280
0 200 400 600 800 1000 1200 1400
Cutting speed V (m/min)
PDZ model
Cutting force (N)
ALE model
0 200 400 600 800 1000 1200 1400
15
30
45
60
75
90
105
Feed force (N)
Cutting speed V (m/min)
PDZ model
ALE model
SIMULTECH 2011 - 1st International Conference on Simulation and Modeling Methodologies, Technologies and
Applications
462
the predicted residual stresses in cutting direction
(RS
11
) is shown in Figure 8.
For each cutting speed, ALE method produces
tensile stress on the surface, and the magnitude of
RS11 decreases within the depth of 100 μm below
the machined surface. Then, the RS
11
tends to be
constant as the depth over 100μm. This pattern
agrees well with the computed residual stress results
of Nasr (2008:149-161) using ALE method, which
are also verified by the experiments. On the other
hand, PDZ method produces compressive stress on
the surface, and the RS
11
increases within depth of
100 μm below the machined surface. Then, the RS
11
tends to be constant as the depth over 100μm.
The effect of cutting speeds on the predicted
RS
11
is also different for ALE and PDZ methods.
The predicted peak magnitude of RS
11
by ALE
method decreases as the cutting speed increases,
which is generally reported in literature. On the
other hand, the predicted peak magnitude of RS
11
by
PDZ method increases proportionally as the cutting
speed increases.
(a)
(b)
Figure 8: Predicted residual stress profiles of (a) ALE, (b)
PDZ method under different cutting speeds.
The primary cause of residual stress generation is
plastic deformation. In order to explain the different
residual stress predictions, the plastic strain in the
cutting direction (PE11) of the machined surface
around the tool-tip are shown in Figure 9. It is clear
that ALE method produces the compressive strain on
the surface and near-surface layers, with the peak
value of 0.06. But PDZ method produces the tensile
strain with the peak value of 0.01. After the
workpiece is unloaded and cooled, the residual stress
will becomes tensile and compressive dominated,
respectively.
(a)
(b)
Figure 9: Predicted strain distributions of (a) ALE, (b)
PDZ method, at v=800m/min.
The combination of mechanical and thermal
loading produces the strain results, and it is noticed
the cutting force and temperature predictions are
similar for ALE and PDZ methods. It is interesting
that the same thermo-mechanical loading produces
different strain results.
It is noticed that the elements of the separation
path in PDZ model are enlarged to failure which will
drag the element on the new produced surface. As a
result, the tensile dominated strain state is formed.
On the other hand, ALE method handles the material
flow surrounding the tool-tip perfectly, thus the
material exiting at the right-hand boundary of
Eulerian zone is merely affected by the tool flank.
As a result, the compressive dominated strain state is
formed in the prediction of ALE model.
4 CONCLUSIONS
Based on the prediction results and discussions, the
following conclusions are obtained:
0 50 100 150 200 250 300
-100
-50
0
50
100
150
200
250
300
V=200m/min
Depth below machined surface (μm)
Residual stress RS
11
(MPa)
V=400m/min
V=600m/min
V=800m/min
-500
-400
-300
-200
-100
0
100
200
V=200m/min
V=400m/min
V=600m/min
V=800m/min
Depth below machined surface (μm)
Residual stress RS
11
(MPa)
0 50 100 150 200 250 300
A COMPARATIVE STUDY OF DIFFERENT CHIP SEPARATION APPROACHES FOR NUMERICAL MODELING
OF ORTHOGONAL CUTTING
463
¾ Chip formation predicted by ALE and PDZ
methods is quite different. ALE method is
difficult to predict reasonable chip formation.
¾ ALE and PDZ methods predict similar cutting
force and temperature predictions.
¾ ALE and PDZ methods predict different
residual stress profiles, and the possible reasons
are discussed through the strain results around
the tool-tip.
ACKNOWLEDGEMENTS
The authors acknowledge the support from the
National Basic Research Program of China
(No.2010CB731703) and National Natural Science
Foundation of China (No.51075267).
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