Journal of Materials Processing Technology 128 (2002) 256±265
Some phenomenological and computational aspects
of sheet metal blanking simulation
M. Rachika,*, J.M. Roelandta, A. Maillardb
a
Universite de Technologie de CompieÁgne, GSM, Lab. Roberval, BP 20529, 60205 CompieÁgne, France
CETIM, Service MeÂtaux en Feuilles, 52 avenue FeÂlix Louat, BP. 80067, 60304 Senlis Cedex, France
b
Received 17 April 2001; received in revised form 27 February 2002; accepted 28 June 2002
Abstract
In this paper, we present a comprehensive experimental and numerical study of the sheet metal blanking process. Various blanking tests
involving different materials and geometry are investigated and the numerical results are compared with experimental data. For the numerical
aspects of this study, the main topics discussed are sheet metal constitutive model, the numerical integration algorithm and mesh adaptivity.
Taking into account the complexity of the blanking process, we chose an explicit ®nite element code to overcome the convergence problems.
Our numerical model is thus based on a dynamic explicit scheme associated with the ALE formulation for mesh adaptivity. Since the choice of
the sheet metal constitutive model is important to achieve the product shape prediction and the burr height estimation, we compare the
Parndtl±Reuss plasticity model with Gurson±Tvergaard±Needleman coupled plasticity-damage model. The comparisons between numerical
results and measurements show that the maximum punch force is strongly related to the plastic ¯ow but that the burr height estimation requires
damage modelling. In addition, Gurson's modi®ed model greatly improves the punch force prediction.
# 2002 Elsevier Science B.V. All rights reserved.
Keywords: Blanking; Forming process simulation; Ductile fracture; Explicit dynamic; ALE
1. Introduction
Sheet metal blanking is an industrial process widely used
in automotive, electronic and several other industrial applications. It consists in separating a blank from a sheet by
means of a high-localised shear deformation due to the
action of a punch. The pioneering work of Johnson and
Slater [1] shows that the phenomena involved in the blanking operation have been well known for a long time. The
authors gave an interesting schematic representation of
punch force versus punch penetration diagram where the
phases associated with the different phenomena are well
identi®ed. They clearly show that the maximum punch force
is strongly related to the plastic ¯ow and that it does not
depend on the initiation and the propagation of a fracture.
It should be pointed out that amongst several existing
sheet metal forming processes, the blanking process stands
apart since it leads to plastic shearing followed by the
creation and the propagation of cracks (Fig. 1).
Despite its widespread use, the design of the metal
blanking is often based on trial and error tests, that is a
*
Corresponding author.
E-mail address: [email protected] (M. Rachik).
time consuming procedure. Over the last few decades,
several researches have been devoted to the modelling of
the blanking process. The earlier work of Atkins [2] and
Zhou and Wierzbicki [3] concerned the development of
some analytical models. These simple models can be used
to estimate the punch force but they are not able to investigate all the phenomena involved. Moreover, they are
limited to plane strain problems. In this sense, the ®nite
element method seems to be a powerful tool that can
improve the knowledge of sheet metal blanking since it is
more adapted to the complex constitutive models and the
general boundary conditions. For these reasons, the numerical simulation of sheet metal blanking has gained a widespread interest within the computational mechanics
community. In this way, several ®nite element approaches
have been put forward to model the blanking process. These
models deal with different aspects of the shearing process
and are more or less able to describe all the phenomena
involved. They are mainly characterised by the way that the
material behaviour is modelled (with or without ductile
fracture assessment) and the mesh adaptivity is handled.
Maiti et al. [4] performed the assessment of the in¯uence
of some process parameters like clearance and friction on
the punch force. They used an elastoplastic model with the
0924-0136/02/$ ± see front matter # 2002 Elsevier Science B.V. All rights reserved.
PII: S 0 9 2 4 - 0 1 3 6 ( 0 2 ) 0 0 4 6 0 - 0
M. Rachik et al. / Journal of Materials Processing Technology 128 (2002) 256±265
257
The assessment of the influence of some relevant process
parameters such as clearance, friction, etc.
The prediction of the cut edge shape and the burr height
that greatly affects the quality of the parts.
Fig. 1. Blanking process description.
small strain assumption. Consequently, the validity of this
approach is limited to weak punch penetration (less than
30% of the sheet thickness). Goijaerts et al. [5] have developed a ®nite element procedure based on an elastoplastic
model with ®nite deformations theory. The mesh adaptivity
is handled by the combination of automatic global remeshing and the arbitrary Lagrangian±Eulerian (ALE) approach.
Using such a procedure enables the punch force to be
estimated for large penetrations.
The simulations performed in the previously described
pieces of research only deal with the shearing operation and
are not able to predict the cut surface shape which is a
signi®cant criteria for the blanked part quality. In order to
improve these models, recent ®nite element approaches
have been presented, in which the material fracture is
implemented.
Taupin et al. [6] used the McClintock [7] criterion to
handle the ductile fracture in the blanking process. Element
removal and global remeshing of the blanked sheet were
used to simulate the material separation. The authors successfully simulated some axisymetric blanking tests; however, the computational cost seems to be quite signi®cant. To
take into account the material failure, Hambli and Potiron
[8] used a continuum damage model proposed by LemaõÃtre
[9] coupled with an elastoplastic model. To handle the
material separation, the authors used crack propagation,
simulated by the rigidity loss of the concerned elements.
Brokken et al. [10] proposed a ®nite element procedure in
which the ductile fracture is modelled using a discrete
fracture approach. The propagation criteria they used, is
based on Rice and Tracey's model [11]. In their approach,
the authors proposed an elaborate procedure for adapting the
mesh to ensure the crack propagation. The previously
described pieces of research are not exhaustive and the
reader can refer to the excellent work of Wisselink [12]
for a recent and complete literature review on the subject.
In this paper, we present a comprehensive experimental
and numerical study of the sheet metal blanking process.
Our work is mainly devoted to the development and the
validation of a ®nite element procedure for numerical
simulation of this process. The main objective of such a
procedure concerns:
The punch force prediction that is important for the tool
dimensioning and the punch wear prediction.
To achieve these objectives, the previously cited procedure must take into account all the involved physical phenomena with the help of robust and reliable numerical
algorithms. We describe the development and the validation
of our simulation procedure as follows.
In Section 2, we present the experimental aspects of the
study. In Section 3, we describe the ®nite element approach
and discuss three important topics, namely the load stepping
algorithm that ensures the procedure reliability, mesh adaptivity and the sheet metal constitutive model in particular the
ductile fracture handling which is vital for the product shape
prediction. Section 4 is devoted to the comparison between
numerical and experimental results. First we investigate the
assessment of the in¯uence of some process parameters on
the punch force. Next we examine the ability of our numerical procedure to predict the product shape with particular
attention paid to the burr height prediction.
This work leads to some useful guidelines for numerical
simulation of the blanking process. The most relevant key
®ndings concern the cut edge shape prediction since we can
give a good estimation of the burr height without crack
propagation handling. This is important because the crack
propagation modelling is a dif®cult and unreliable task.
2. Experimental aspects
In order to validate the simulation assumptions, different
blanking tests were carried out using one of Cetim's mechanical presses (200 t, 80 SPM) and an instrumented circular
punching tool. A piezo sensor is placed just above the punch
(see Fig. 2) so that only the cutting force (excluding the blank
holder) is measured for each stroke. The tool is connected to a
signal acquisition and processing system which produces
a curve for each blanking operation, displaying the force as
a function of the real punch travel along the sheet (Fig. 3).
Fig. 2. Schematic representation of the blanking tool used.
258
M. Rachik et al. / Journal of Materials Processing Technology 128 (2002) 256±265
When analysing the punch force versus the punch
penetration curve, ®ve main phases can be distinguished
(Fig. 3):
elastic phase;
sheet indentation and plastic shearing;
reduction of the sheared section overriding strain-hardening of the sheet;
crack initiation and propagation between the cutting
edges;
expulsion of the blanked part.
As the clearance increases, the following phenomena can
be observed:
Fig. 3. Diagrammatic representation of punch force/punch penetration
diagram.
The punching tests were carried out under the following
conditions:
Die diameter (dm) equal to 9 mm and radial blanking
clearance of 1.5±16% of the sheet thickness (use of
different punch diameters). If the thickness of the punched
sheets is taken into account (Table 1), it can be seen that
the ratio of the punch diameter dm to the sheet thickness t
is relatively small (<10). We know from experience that
this ratio considerably changes the shape of the punch
force versus punch penetration curve.
Sharp punch and die, which corresponds to a cutting edge
radius of about 0.02 mm.
Linear speed of punch in contact with the sheet: 55 mm/s.
Lubrication with a full-strength oil.
Application of a blank holder with a sheet contact force of
about 4000 N.
Blanking tests were carried out using both a mild steel
sheet and a stainless steel sheet. The EN 10111 DD13 steel is
a hot rolled steel also designed for drawing, while the EN
10088 X6Cr17 steel is a ferritic stainless steel used for
metalworking. The mechanical and geometrical properties
of these sheets are given in Table 1.
Table 1
Characteristics of blanked materialsa
Steel grade
0 (MPa)
s
ˆ k…p0 ‡ ep †n
s
h (mm)
DD13
X6Cr17
226
282
k ˆ 556, n ˆ 0:189
k ˆ 739, n ˆ 0:200
2.5
1.92
a
0 : initial yielding stress; s
: current yielding stress; ep : equivalent
s
plastic strain; k, p0 and n: material parameters; h: sheet metal thickness.
a reduction in the maximum blanking force (only to a
small extent);
an increase in the punch penetration at fracture and
consequently an increase in the burnished depth of the cut;
a sudden drop in the force curve during the fracture phase
(4) that is caused by a rapid crack propagation mechanism;
a lower and virtually nil expulsion force on the blanked
part (phase 5).
3. Numerical aspects
When dealing with numerical simulation of the sheet
metal blanking process, particular attention must be paid
to three signi®cant topics, namely: (i) the load stepping
algorithm for solving the non-linear global equilibrium
equation, (ii) the mesh adaptivity that ensures the solution
reliability for high strain level, and (iii) the sheet metal
constitutive model. In this work, the ABAQUS explicit code
is used [13].
3.1. Load stepping algorithm
In the numerical simulation of the sheet metal blanking
process, a quasi-static approach is usually adopted. The
®nite element discretisation of the virtual work leads to a
strongly non-linear equation:
r…u; t† ˆ fext …u; t†
fint …u; t† ˆ 0
(1)
where r is the residual vector, fext the external force vector,m
fint the internal force vector, u the nodal displacement vector
and t the time.
The vast majority of approaches for solving Eq. (1) are
based on the Newton±Raphson iterative scheme or its
variants. The main drawback of these algorithms is the
convergence problem that becomes critical when dealing
with large deformation and frictional contact. In contrast to
these procedures, we focus upon non-iterative algorithms
like the explicit dynamic [14] or high order load stepping
algorithm [15].
M. Rachik et al. / Journal of Materials Processing Technology 128 (2002) 256±265
In this work, an explicit dynamic approach is adopted.
Eq. (1) is rewritten with the inertial efforts taken into
account:
r…u; t† ˆ fext …u; t†
fint …u; t†
M
uˆ0
(2)
 the nodal acceleration
where M is the mass matrix and u
vector.
The time integration of Eq. (2) is performed by means of
the central difference integration scheme. For a typical time
step ‰tn ; tn‡1 Š…tn‡1 ˆ tn ‡ Dt†, the solution is advanced
according to the following procedure:
u_ n‡1=2 ˆ u_ n
1=2
‡ Dt
un ;
un‡1 ˆ un ‡ Dtu_ n‡1=2
(3)
where u_ is the nodal velocity vector.
The nodal acceleration 
un is computed from Eq. (2) by

un ˆ M 1 …fext …un ; tn †
fint …un ; tn ††
(4)
A diagonal mass matrix is used in order to ensure the
procedure effectiveness in terms of computational cost.
The previously described integration algorithm is conditionally stable and the time step size is generally very small,
particularly in the case of blanking process simulation.
3.2. Mesh adaptivity
In the ®nite element simulation of the blanking process
using the Lagrangian formulation, an additional problem
that one can encounter concerns large element distortions.
These distortions lead to strain localisation, element degradation and important errors that make the solution unreliable. In order to overcome this dif®culty, frequent updating
of the mesh is needed. Schematically, two approaches can be
used to update the mesh:
The global remeshing technique where the element topology is changed. The deformed configuration is rediscretised at certain load steps and the solution dependant state
variables are properly transformed from the distorted
mesh to the new (regular) mesh. The main drawback of
this technique is the rapid increase in the total number of
degrees of freedom that leads to a prohibitive computational cost. In addition, the whole domain is remeshed and
an additional computational effort is required to handle
the boundary conditions and the contact state.
The ALE formulation where the element topology is
preserved. The evolutions of the mesh and material
particles are uncoupled and the mesh is moved during
the incremental process in such a manner that excessive
distortion of the elements is avoided. For a detailed
description of the ALE basic mathematical concepts,
the reader can refer to Donea [16].
The ALE approach was successfully used in the numerical simulation of various forming processes and seems to
be well adapted to sheet metal blanking simulation
[10]. Depending on the problem formulation and the load
259
stepping algorithm, different variants of the ALE formulation can be used (coupled, uncoupled or semi-coupled ALE).
For a detailed discussion of these aspects, the reader can
refer to Wisselink [12].
In our work, the global equilibrium is solved by means of
an explicit dynamic scheme that is conditionally stable. This
stability requirement limits the amount of material motion
within a time increment. For this reason, the ALE approach
is used in an operator split (uncoupled) way where the
Lagrangian motion (material) and the mesh motion are fully
uncoupled. For a typical time step, the solution is advanced
according to the following procedure:
(i) A Lagrangian step is performed where the nodal
displacements are computed by means of the explicit
scheme described in Section 3.1 and the state variables
are updated.
(ii) A mesh adaptation is performed to move the nodes to
appropriate positions that limit the element distortion.
The state variables are then transported to follow this
mesh motion.
3.2.1. Mesh smoothing
After the Lagrangian step, the nodes are moved to limit
the element distortion. The node positions are determined by
using a volume smoothing algorithm. Each node is relocated
by computing a volume weighted average of the element
centres in the elements surrounding the node as illustrated in
Fig. 4.
This so called Kikuchi's algorithm is iterative and the
location of node n at the …i ‡ 1†th iteration is determined as
follows:
xie ˆ
nne
1 X
xi
nne kˆ1 k
(5)
where xie is the position vector of the eth element centre, xik
the position vector of the kth node of the eth element and nne
the node number of the eth element:
Pnsel i i
Ve xe
xi‡1
ˆ
(6)
Peˆ1
n
nsel i
eˆ1 Ve
i
where xi‡1
n is the position vector of node n, Ve the volume of
the surrounding eth element and nsel the number of surrounding elements.
Fig. 4. Node relocation.
260
M. Rachik et al. / Journal of Materials Processing Technology 128 (2002) 256±265
3.2.2. Advection
After the mesh smoothing, the state variables at the
integration points fn‡1 on the new mesh at time tn‡1 has
to be determined from their values at the integration point
on the old mesh. The mapping procedure must guarantee
the state variable conservation during the mesh motion. Each
state variable must remain unchanged during the advection
step:
Df @f
@f
ˆ
‡ wi
ˆ 0 …summation on i†
Dt
@t
@xi
(7)
where w is the velocity of the mesh motion and x the material
co-ordinates.
A good algorithm for solving Eq. (7) must be stable,
conservative, accurate and monotonic. The vast majority of
existing algorithms were originally developed by the computational ¯uid mechanics community [17]. In the ®nite
element codes devoted to non-linear mechanical problems,
the ALE is often used in an operator split way and the widely
used advection algorithm is based on van Leer's work [18].
This algorithm is brie¯y presented in the following section
but, for reasons of clarity, we present it here for one
dimension. In this case, Eq. (7) can be rewritten as
@f
@f
‡w
ˆ0
@t
@x
(8)
Using the ®nite difference notation, Eq. (8) is solved by
means of the following scheme:
n
fn‡1
j‡1=2 ˆ fj‡1=2 ‡
cj ˆ
wj n
…f
2 j
1=2
Dt
…c
Dx j
‡ fnj‡1=2 † ‡
cj‡1=2 †;
jwj j n
…fj
2
1=2
fnj‡1=2 †
(9)
If fnj‡1=2 is chosen to be constant over the interval ‰xj ; xj‡1 Š
the algorithm supplied by Eq. (9) is a ®rst-order algorithm.
The second-order van Leer algorithm is obtained by replacing fnj‡1=2 by the average value over the interval of a nonconstant distribution fnj‡1=2 (x):
Z xj‡1
n
fj‡1=2 ˆ
fnj‡1=2 …x† dx
(10)
xj
The distribution fnj‡1=2 (x), or more precisely its range
(minimum and maximum values), must guarantee the algorithm monotonicity. There are different ways of imposing
this condition.
The previously described algorithm can easily be extended
to two- or three-dimensional problems [19].
3.3. Sheet metal constitutive model
In numerical simulation of metal forming processes, the
choice of the material constitutive model is a crucial stage.
This depends on the physical phenomena involved in the
process and the simulation goal. In the case of the sheet
metal blanking process, the straining mechanisms
involved are well known [1]. This suggests a constitutive
model that can properly describe large elastoplastic strain
and failure.
3.3.1. Ductile fracture
To understand the failure mechanism in sheet metal
blanking, several experimental studies were carried out
[5]. All these studies con®rmed that the material separation
is related to the ductile fracture. It is now well established
that ductile fracture in metals is mainly caused by the growth
and coalescence of micro cavities. This consists of three
different stages:
Void initiation at imperfection and second phase particles.
Void growth caused by plastic deformation. It should be
noted that the growth rate is strongly related to the
hydrostatic stress.
Void coalescence that leads to crack initiation and propagation.
For ductile fracture handling in the numerical simulation
of the sheet metal blanking process, several pieces of
research have been carried out using local criteria. The
majority of these use uncoupled criteria [6,10,20] that can
be stated as follows.
The failure occurs when
Z ef
f …s; ep † dep ˆ Cc
(11)
0
where ef is the equivalent plastic strain at failure, s the
Cauchy stress, ep the equivalent plastic strain, Cc the critical
value of a material parameter and f a function that depends
on the chosen criteria.
Gouveia et al. [21] presented different variants of this
criteria applied to different forming processes, among them
blanking. Goijaert et al. [22] compared and evaluated four
different fracture criteria based on Eq. (11) for ductile
fracture prediction in metal blanking.
According to the various research studies on the subject,
an ef®cient constitutive model for the ductile fracture prediction in metal blanking has to take into account the
hydrostatic stress and the equivalent plastic strain. In addition, the continuous evolution of damage during the straining process (graded material degradation) suggests the use of
a coupled plasticity-damage model. Hambli [23] successfully used LemaõÃtre's model [9] to treat ductile fracture in
blanking.
The majority of the previously described pieces of
research use a discrete crack propagation model to predict
the material separation and the product shape near the cut
edge. The main drawback of such an approach is the error
arising from several sources that deteriorates the numerical
solution and makes the prediction quality quite poor concerning the burr height estimation. In our work, the ductile
fracture is taken into account by means of the Gurson±
Tvergaard±Needleman model [24,25]. Contrary to the previously cited works, the crack propagation is deduced from
the material failure whose evolution is included in the
M. Rachik et al. / Journal of Materials Processing Technology 128 (2002) 256±265
261
coupled plasticity-damage model. Comparisons between
experiments and numerical results (Section 4) show that
this model gives a good estimation of the punch force versus
punch penetration, particularly for the punch penetration at
failure. It also realistically predicts the product shape near
the cut edge (rollover, sheared zone and burr height).
In this section, we brie¯y recall the constitutive equations
associated with the Gurson±Tvergaard±Needleman model
that can be considered as a generalisation of the Prandtl±
Reuss plasticity for porous materials.
Yielding surface
seq
3sm
Fˆ
‡ 2q1 f cosh
q2
…1 ‡ q3 f 2 † ˆ 0
2s
s
while the void nucleation fnucl is described by a normal
distribution around a mean value:
"
2 #
e
e
f
1
p
N
N
e_ p
f_ nucl ˆ p exp
(19)
2
S
S 2p
(12)
q
where F is the yielding function, seq ˆ 3=2s0ij s0ij the von
the
Mises equivalent stress, s0 the effective stress deviator, s
yielding stress, sm the hydrostatic stress, q1, q2 and q3 the
adjustable material parameters.
f is related to the volume void fraction f in a such way
that the model describes the three stages of ductile fracture
(void initiation, void growth and void coalescence) and the
rapid loss of the material capacity when void coalescence
occurs:
8
f
si f fc ;
>
>
>
<
f F fc
… f fc † si fc f fF ;
(13)
f ˆ fc ‡
>
fF fc
>
>
:
f F
si f fF ;
4. Applications
where f is the void volume fraction, fc the critical void
volume fraction and fF the void volume fraction at failure:
f F ˆ 1
q1
when q3 ˆ q21
(14)
The plastic strain is given by the normality ¯ow rule:
@F
e_ p ˆ l_
@s
(15)
where ep is the plastic strain, l the plastic ¯ow multiplier and
s the Cauchy stress.
The equivalent plastic strain evolution is governed by the
following relation:
e_ p ˆ
…1
s : e_ p
f †seq
where fN is the volume fraction of nucleating void, eN the
mean strain for void nucleation and S the standard deviation.
It should be noted that when the void volume fraction is
zero the previously described model simpli®es into the
classical Prandtl±Reuss plasticity model with the von Mises
yielding surface.
To validate the previously discussed topics, several blanking tests are simulated and the numerical results obtained are
compared with experimental data. These validations are
carried out separately for two main aspects. The ®rst part
concerns the validation of our numerical procedure ability to
predict the maximum punch force and the assessment of the
in¯uence of certain parameters such as clearance and material parameters. The second part is devoted to the validation
of the product shape prediction with particular attention paid
to the burr height estimation.
4.1. Punch force prediction
The blanking tests described in Section 2 are simulated
using an axisymmetric ®nite element model that is schematically described in Fig. 5.
It should be noted that the punch, the die and the blank
holder are modelled using rigid bodies. For the sheet metal
constitutive model, a simple elastoplastic model with isotropic hardening is compared to a coupled plasticity-damage
model (Gurson). The physical parameters and the plasticity
model parameters for the two steels investigated, are given in
Table 1 (Section 2) while the parameters of the damage
model are summarised in Table 2.
In this paragraph, we give a comparison between the
elastoplastic model, modi®ed Gurson's model and the
(16)
The evolution of void volume fraction f comes from the
growth of the existing void and the nucleation of the new
void:
f_ ˆ f_ gr ‡ f_ nucl
(17)
The void growth fgr is related to the compressibility of the
surrounding material. It depends on the volumetric part of
the plastic strain rate:
f_ gr ˆ …1
f †_epkk
(18)
Fig. 5. Schematic description of the blanking test.
262
M. Rachik et al. / Journal of Materials Processing Technology 128 (2002) 256±265
Table 2
Gurson's model parameters for steels
Yielding multiplier
q1
q2
q3
1.5
1
2.25
Void nucleation
S
eN
fN
0.1
0.3
0.04
Void at failure
fc (%)
fF (%)
10
10.1
Fig. 6. Punch penetration at fractureÐmaterial DD13.
Table 3
Maximum punch force versus clearanceÐmaterial DD13
Clearance (%)
3
8
12
Fmax (kN)
Gurson model
Plasticity model
Experiments
18.849
17.779
17.214
18.899
17.815
17.281
19.007
18.252
17.198
experiments with clearance values ranging from 3 to 12%.
The results are summarised in Table 3 for the DD13 steel and
Table 4 for the X6Cr17 steel. In light of these results, the
following remarks can be formulated:
The numerical results are in good agreement with the
experimental data.
The maximum punch force is strongly related to the
plastic behaviour and the damage occurs after the plastic
instability.
The clearance influence on the maximum punch force can
be assessed as well by the elastoplastic model as by the
Gurson's model.
Based on the full curve of the punch force versus the
punch penetration, we can note that the punch penetration
at fracture can be predicted by Gurson's model. In addition it is clearly shown that the punch penetration at
fracture is strongly related to the critical void volume
fraction fc since this is the only parameter we have to
adjust in order to improve the results.
To examine the punch penetration at fracture, ®rst the
potential crack site is located (point where the void volume
Table 4
Maximum punch force versus clearanceÐmaterial X6Cr17
Clearance (%)
3
11
Fmax (kN)
Gurson model
Plasticity model
Experiments
19.306
17.85
19.221
18.069
18.765
18.01
Table 5
Punch penetration at fracture (material DD13)
Clearance (%)
Numerical results (mm)
Measurements (mm)
12
8
3
1.44
1.45
1.47
1.53
1.72
1.74
fraction is maximum). The evolution of the void volume
fraction at this point with the punch penetration is then
plotted. Fig. 6 illustrates this evolution for different clearance values (material DD13).
For the sake of clarity, the punch penetrations at fracture
deduced from Fig. 6 are summarised in Table 5. These
results agree with experiments.
4.2. Burr height prediction
While the punch force and the punch penetration at
fracture are important for tool and machine dimensioning,
the shape of the cut edge and the burr height are crucial for
the ®nal product quality. The prediction of these parameters
by numerical simulation may be very helpful in blanked part
design. In this section, we show the ability of our numerical
procedure to predict the shape of the cut surface and the burr
height. To validate these aspects, we compare our numerical
results with measurements performed by Li [26] on trimming of aluminium autobody sheets. The trimming tests are
simulated using a plane strain ®nite element model with a
coupled elastoplastic-damage model. For the isotropic hardening of the aluminium, the yielding stress is given by
ˆ k…p0 ‡ ep †n .
s
The material parameters are summarised in Table 6.
The simulations were carried out for clearance values
ranging from 5 to 25% of the sheet metal thickness and blade
with an edge radius of 0.254 mm.
As has been pointed out before, the ductile fracture is
related to the hydrostatic stress. A contour plot of this
M. Rachik et al. / Journal of Materials Processing Technology 128 (2002) 256±265
263
Table 6
Material parameters of the aluminium sheet
Plasticity
k (MPa)
p0
n
576.79
0.01658
0.3593
Damage
Yielding
q1
q2
q3
1.5
1
2.25
Nucleation
S
eN
fN
0.1
0.3
0.04
Failure
fc (%)
fF (%)
Fig. 8. Rollover measurement.
12
12.1
quantity is presented in Fig. 7. This clearly shows that the
hydrostatic stress is at its maximum in the fracture zone.
In the majority of the research work carried out on the
numerical simulation of the blanking process, the prediction
of the shape of the cut edge is based on discrete crack
propagation. Contrary to this approach, we use the void
volume fraction evolution to predict as well the different
zones of the cut edge as the burr height.
The rollover is determined from the deformed mesh. Fig. 8
shows the rollover for a clearance of 15%.
The other cut surface zones are deduced from the void
volume fraction evolution along the cut edge. Fig. 9 shows
this evolution for a clearance of 15%:
The shear zone is located between points A and B where
the void volume fraction is lower than its failure value.
The fracture zone is located between points B and C
where the void volume fraction reaches its failure value.
Fig. 9. Void volume fraction evolution along the cut edge.
We use the following procedure for the burr height
prediction:
Fig. 7. Hydrostatic stress contour plot.
Fig. 10. Void volume fraction evolution used to measure the burr height.
264
M. Rachik et al. / Journal of Materials Processing Technology 128 (2002) 256±265
punch penetration at fracture and the burr height requires
a constitutive model that takes into account the ductile
fracture. For this purpose, we use the coupled model of
Gurson±Tvergaard±Needleman. The comparisons between
experiments and numerical results show that this model
improves the punch force prediction for the whole process.
In addition, it gives a satisfactory burr height prediction. It
should be noted that the most important parameter for the
damage model is the critical void volume fraction. In
the present work this parameter was adjusted to improve
the results, but in the future we would like to identify it by
means of the inverse method that combines measurements
and blanking tests simulation.
References
Fig. 11. Burr height evolution with clearance for a 0.245 mm blade radius.
Localisation of the maximum void volume fraction on the
top of the blanked sheet. This point is associated with
crack initiation.
Determination of the punch penetration at fracture.
Localisation of the maximum void volume fraction on the
deformed shape that corresponds to the punch penetration
at fracture.
The burr height is given by the distance between the flat
side of the sheet and the location of the maximum void
volume fraction.
As illustrated in Fig. 10, the burr height is given by the
distance along the y-axis between points A and B.
Fig. 11 shows a comparison between measurements (Li
[26]) and simulation results. The comparison concerns the
burr height evolution with clearance for a given blade edge
radius. The predicted results are in good agreement with
those of experiments.
5. Conclusion
In this work, some signi®cant aspects of numerical simulation of the sheet metal blanking process are discussed. All
the numerical results are compared with experiments in
order to examine their validity. The comparisons concern
the punch force prediction, the punch penetration at fracture
and the prediction of the cut edge shape.
Our ®nite element procedure is based on the dynamic
explicit scheme associated with the ALE method for mesh
adaptivity. This procedure is very ef®cient from the point of
view of computational cost since the performed simulations
take less than 30 min on a Compaq XP100 work station
(500 MHz).
For the sheet metal constitutive model we show that the
maximum punch force is reached during the plastic straining
phase and consequently, it can be well predicted by means of
a standard plasticity model. However, the prediction of the
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