Prediction of Ductile Fracture in

A. M. Goijaerts
Metal Blanking
e-mail: ad@wfw.wtb.tue.nl
This study is focused on the description of ductile fracture initiation, which is needed to
predict product shapes in the blanking process. Two approaches are elaborated using a
L. E. Govaert local ductile fracture model. According to literature, characterization of such a model
should take place under loading conditions, comparable to the application. Therefore, the
F. P. T. Baaijens first approach incorporates the characterization of a ductile fracture model in a blanking
experiment. The second approach is more favorable for industry. In this approach a
Materials Technology,
tensile test is used to characterize the fracture model, instead of a complex and elaborate
Eindhoven University of Technology,
blanking experiment. Finite element simulations and blanking experiments are performed
P.O. Box 513,
for five different clearances to validate both approaches. In conclusion it can be stated
5600 MB Eindhoven, The Netherlands
that for the investigated material, the first approach gives very good results within the
experimental error. The second approach, the more favorable one for industry, yields
results within 6 percent of the experiments over a wide, industrial range of clearances,
when a newly proposed criterion is used. 关S1087-1357共00兲02202-4兴

1 Introduction triaxiality 共triaxiality is defined as hydrostatic stress over equiva-

lent Von Mises stress: ␴ h / ¯␴ 兲. A larger hydrostatic pressure post-
Blanking is a common technique in high volume production.
pones the initiation of voids and slows down the growth of voids.
Since the beginning of this century, researchers have been analyz-
Therefore, triaxiality is often represented in f ( ␴ ). Large plastic
ing the blanking process. Blanking experiments on either planar
strains permit voids to grow and coalesce. This justifies the inte-
关1,2兴 or axisymmetric 关3–5兴 configurations have led to empirical
gration over plastic strain.
guidelines for process variables such as punch and die radius,
In the formulation of Eq. 共1兲, C is stated to be a material con-
speed and clearance. Nevertheless, the blanking process is not yet
stant and has to be determined experimentally. However, in litera-
fully understood.
ture no example is found, where C is determined in an experiment
Nowadays, it can be observed that product specifications are
which is in a very different loading condition from the verification
getting more severe, since high-tech products are becoming
configuration. These kinds of criteria are only found successful
smaller and smaller. This can lead to lengthy trial and error pro-
when applied in similar loading conditions, which suggests that
cedures in developing industrial blanking applications and a
some information of the loading path is represented in the param-
proper model of the blanking process is desired. Because of the
eter C. Therefore, the approach where C is determined in the
constantly changing loading situations in the material, the process
blanking process is expected to be the most successful. However,
is too complex for an analytical approach 关6–8兴. Instead, the finite
for industrial applications this is a rather complicated and difficult
element method has been used to simulate the blanking process,
with varying success 关9–11兴. One major difficulty in the numeri-
cal analysis is the description of ductile fracture. This is important
because ductile fracture initiation determines the fracture zone and
shear zone and thus the product shape 共Fig. 1兲.
The physical background for ductile fracture in metals is known
to be the initiation, growth and coalescence of voids 关12–14兴.
Voids can initiate at inclusions, secondary phase particles or at
dislocation pile-ups. Growth and coalescence of voids are driven
by plastic deformation. Therefore, it seems evident to incorporate
the deformation history in a ductile fracture model. Because the
numerical implementation of a fracture growth model, using a
local ductile fracture model, is present in our research group 关11兴,
this category of criteria will be utilized for this purpose.
The class of local ductile fracture criteria that incorporate the
stress and strain history 共a short overview is given by Clift et al.,
关15兴兲 can be written as an integral over plastic strain 共␧ p 兲 up to
fracture of a certain function of the actual stress state 共reflected by
the Cauchy stress tensor ␴兲 reaching a threshold value C:

冕 ␧p
f 共 ␴ 兲 d␧ p ⫽C (1)

If the integral on the left-hand side reaches the critical value C

during the process, ductile fracture is supposed to initiate. In the
formulations for the different criteria, some parameters that influ-
ence ductile fracture are expected to appear: plastic strain and

Contributed by the Manufacturing Engineering Division for publication in the

JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript received Fig. 1 The blanking process with an indication of the different
April 1999; revised Oct 1999. Associate Technical Editor: K. Stelson zones determining the product shape

476 Õ Vol. 122, AUGUST 2000 Copyright © 2000 by ASME Transactions of the ASME
 Table 1 Material properties of X30Cr13 equivalent plastic strain, by fitting a master-curve through the
maxima of the stress-strain curves of these tensile tests 共Fig. 2兲.
This fitting procedure yields the following master-curve:
␴ y ⫽420⫹133• 共 1⫺e ⫺␧ p /0.0567兲 ⫹406• 共 ␧ p 兲 0.5⫹70.7•␧ p (2)
where ␴ y is the Von Mises yield stress and ␧ p ⫽(2/3•(␧ 21 ⫹␧ 22
⫹␧ 23 )) 0.5 is the equivalent logarithmic plastic strain, with ␧ 1 ,␧ 2 ,
␧ 3 the principal strains.
approach. An industrially favorable approach would be to deter-
mine the C in an easier test, e.g., a tensile test. Both approaches 2.1.2 Blanking Experiments. An axisymmetric blanking
will be elaborated in this paper. setup with a die-hole diameter of 10.00 mm, including a
In section 2 we discuss the experimental methods and the nu- blankholder with constant pressure, was built with five different
merical model. In section 3 we determine the parameter C in a punches 共diameters: 9.98, 9.94, 9.88, 9.80 and 9.70 mm兲 resulting
blanking experiment. In section 4 we try the other approach, in five different clearances, covering the industrially used range of
where we attempt to predict ductile fracture initiation in the blank- clearances 共1, 3, 6, 10 and 15 percent of the sheet thickness of 1
ing process by determining the parameter C in a tensile test. Fi- mm兲. To avoid exorbitant simulation times, the punch and die
nally, we discuss the results and conclude in section 5. radii are enlarged to approximately 0.1 mm. The punch radii are
somewhat smaller and the die radius is a bit larger, to make sure
2 Methods fracture will initiate at the punch and grow to the die radius. We
want to determine the punch displacements at fracture initiation
2.1 Experimental. In order to obtain a satisfying material (a⫹b⫹c, Fig. 3兲 experimentally, to have reference points in the
description, also for large plastic strains, we used a material char- numerical simulations for the initiation of ductile fracture. In our
acterization technique, that had already been presented 关16,17兴 blanking setup, six experiments were performed for every clear-
and is briefly explained in subsection 2.1.1. ance. The shear zone or burnish共b兲 and the burr共c兲 are measured
To characterize and verify ductile fracture initiation criteria of afterwards at eight positions over the circumference of the
the form of Eq. 共1兲, experiments are needed. For the first approach blanked products, and averaged to justify for the misalignment of
we need an axisymmetric blanking setup with different geometries the punch. Then, the values are averaged over the six experiments
共subsection 2.1.2兲. We chose to vary the clearance, because the and the standard-deviation is calculated 共Fig. 3兲.
effect on the product shape of a change in clearance is known to It was shown by Stegeman et al. 关18兴 that the roll-over or draw-
be large 关3–5兴. in共a兲 could be accurately predicted for this material, with the men-
For the second approach a universal tensile testing machine is tioned, validated model. Because it is difficult to account for the
required to characterize ductile fracture criteria in tensile tests. To spring-back of the specimen, the roll-over is taken from the nu-
verify the validity of fracture models in tensile tests for different merical simulations and not from an experimental measurement.
levels of triaxiality, an additional setup is needed to perform ten- Such determination of the roll-over applies for other materials as
sile tests under hydrostatic pressure 共subsection 2.1.3兲. well, if the numerical finite element model describes the roll-over
accurately. The element size near the transition of roll-over and
2.1.1 Material Characterization. We used a 13 percent Cr.
shear zone is taken as the standard-deviation. The results are in
ferritic stainless steel 共X30Cr13, DIN 17006兲, that was assumed to
agreement with the trend found in literature 关1兴 and depicted in
plastically deform according the Von Mises yield condition with
Fig. 3.
isotropic hardening 关18兴. 共Some material properties are given in
The roll-over height is very low for small clearances and be-
Table 1.兲 In formulating this plastic deformation, the yield stress
comes larger for wider clearances because the broader deforma-
increases with increasing equivalent plastic strain. The relation-
tion zone allows more bending. The shear zone is getting smaller
ship between the yield stress and the equivalent plastic strain is
for larger clearances and this is caused by the hydrostatic stress
difficult to obtain experimentally for large strains, using conven-
state; for small clearances the hydrostatic pressure is larger and
tional test such as tensile or shear experiments. This was achieved
this postpones ductile fracture initiation, despite of the fact that
by performing 20 tensile tests with each tensile specimen being
the deformation is more localized and that the strains are larger.
subjected to a different amount of rolling to obtain different initial
plastic deformations. The assumption of isotropic hardening al-
lows addition of the rolling and tensile equivalent plastic strains.
We determined the relationship between the yield stress and the

Fig. 3 Experimental results for ductile fracture initiation for

Fig. 2 Strain hardening behavior varying clearance

Journal of Manufacturing Science and Engineering AUGUST 2000, Vol. 122 Õ 477
The burr height is very small 共in the order of 5 ␮m兲 and is largely nitude as the equivalent Von Mises stresses. A larger hydrostatic
determined by the punch radius. The average punch displacements pressure, or a more negative hydrostatic stress, makes the triaxi-
at fracture (a⫹b⫹c) is firstly plotted in Fig. 6 共later兲, along with ality more negative and postpones ductile fracture initiation. One
twice the standard deviations 共95 percent interval兲. The combina- can imagine that voids inside the material will not initiate or grow
tion of the trend for roll-over height and shear height 共plus burr兲 that fast if there is a large hydrostatic pressure. Thus, there will be
explains the minimum in the curve. There is a small experimental more plastic deformation in the neck, and thus larger local strains,
deviation for the clearance of 10 percent. This is a result of the for lower triaxialities 共higher hydrostatic pressures兲.
larger punch radius for the specific 10 percent clearance punch. A
larger punch radius postpones ductile fracture initiation because 2.2 Numerical. We simulated the blanking process using a
the deformation becomes less localized. two-dimensional, axisymmetric finite element model, described
by Brokken et al. 关17兴 and Stegeman et al. 关18兴. Quasi-static
2.1.3 Tensile Tests Under Different Pressures. An experi- analyses are performed on the model geometries that match the
mental setup is used, with which it is possible to perform a tensile experimental setup for the five different clearances. We modelled
test under a superposed hydrostatic stress. The tensile test is per- the specimen with an isotropic elasto-plastic material, using the
formed in an oil chamber and the oil pressure is maintained during material properties as specified in subsection 2.1.1. The plastic
the entire tensile test. Measurements are performed at three dif- material behavior is described by the Von Mises yield condition,
ferent levels of superposed hydrostatic pressure: 0, 250 and 500 by isotropic hardening and by the Prandtl-Reuss representation of
MPa. Clamp force and displacement are measured. The dimen- the flow rule 关19兴. The mesh, used for the 15 percent clearance, is
sions of the tensile specimens are chosen according to the require- shown in Fig. 8. The left boundary at the top 共specimen center兲 is
ments of the pressurized tensile apparatus and shown in Fig. 4. the axis of symmetry. The other boundaries are either free sur-
The measured force displacement curves were identical within faces or in interaction with a contacting body 共punch, die or
the experimental error for all different hydrostatic pressures. This blankholder兲.
means that the hydrostatic pressure has no influence on the plastic Linear quadrilateral elements are used, which become smaller
yielding and hardening behavior. This is an experimental approval as they approach either the die radius or the punch radius. Near
for the use of a yield condition without pressure dependence. those radii, which are between 0.05 and 0.15 mm, the element
However, a closer investigation of the broken tensile specimens proportions need to be in the range of 5 ␮m, resulting in up to
showed a significant difference; the thickness of the material at 3000 elements in the entire mesh. This element size is not neces-
the neck after fracture was smaller for larger hydrostatic pres- sary to predict the process force correctly, but it will be vital to
sures. This means that the process of necking was interrupted by accurately describe the field variables, needed to predict ductile
ductile fracture in an earlier stage under a smaller hydrostatic fracture initiation. The punch moves down and penetrates the
pressure. Results are shown in Fig. 5 along with twice the specimen, resulting in constantly changing boundary conditions.
standard-deviations 共95 percent interval兲 for three measurements To deal with these difficult boundary conditions and the localized
at every hydrostatic pressure. This can be explained by consider- large deformations, the finite element application that we used,
ing the influence of the triaxiality ( ␴ h / ¯␴ ) on the physical mecha- combines three numerical procedures: the commercial implicit fi-
nism of ductile fracture initiation, being the initiation, growth and nite element package MARC 关19兴 共using an updated Lagrange
coalescence of voids. The triaxiality is greatly influenced by the formulation兲, an arbitrary Lagrange-Euler approach 关20,21兴 and
hydrostatic pressures because they are in the same order of mag- an automatic remeshing algorithm 关17兴, to overcome severe mesh
distortion problems. This model was experimentally validated up
to fracture on both deformation fields—using Digital Image
Correlation—and process forces, using a planar blanking setup
关18,22兴. Therefore, the deformation history in the blanking pro-
cess can be calculated adequately, which is a prerequisite for the
local modelling of ductile fracture.

3 Characterization of a Ductile Fracture Model in

Fig. 4 Dimensions of the tensile specimens in mm, thickness
is 1 mm Blanking
In subsection 3.1 the strategy to characterize a ductile fracture
model in the blanking process and subsequently predict ductile
fracture initiation over a wide range of clearances is explained.
Next, some ductile fracture criteria, found in literature, are evalu-
ated and some adaptations are made to make two models valid for
the blanking process.
3.1 Strategy. We consider ductile fracture initiation criteria
of the form of Eq. 共1兲. The right-hand side of this formulation is
meant to be a material constant. With the Characterization of a
ductile fracture model we mean: the determination of the material
parameter C. This is done by experimentally determining the
punch displacement for one clearance at fracture initiation and
simulating this blanking process up to that point of fracture initia-
tion. During this simulation not only the usual state variables are
stored, but also the left-hand side of Eq. 共1兲 is stored as a field
variable. When the experimental punch displacement at fracture is
reached in the simulation, C is determined to be the maximum
value of 兰 f ( ␴ )d␧ p over the entire FEM mesh, and at this point
we declare the criterion to be characterized. The parameter C
should then be valid for any clearance.
If a ductile fracture initiation model is characterized, we can
Fig. 5 Minimum thickness of neck after fracture as a function evaluate the validity of it for the blanking process over the entire
of hydrostatic pressure range of clearances. This evaluation is performed using FEM

478 Õ Vol. 122, AUGUST 2000 Transactions of the ASME

simulations of the blanking process for the other clearances. Dur-
ing the simulations 兰 f ( ␴ )d␧ p is stored as a field variable and as
soon as this field variable reaches the critical C, the punch dis-
placement at fracture is predicted. If the predicted punch displace-
ments for all clearances are within the experimental error, a
proper ductile fracture initiation model for the blanking process is
found 共for this material兲.
3.2 Application of Ductile Fracture Models. A large num-
ber of ductile fracture initiation criteria, taken from literature, are
evaluated according to the explained strategy. A selection of some
good and some special ones are discussed here and mentioned in
Table 2. The plastic work criterion is based on the assumption that
the material can only absorb a certain amount of energy. This
energy criterion was proposed in this form by Freudenthal 关23兴.
The Cockroft & Latham 关24兴 criterion considers the effect of the
maximum principal stress ( ␴ 1 ) over the plastic strain path. Maxi-
mum principal stresses are often used in linear elastic fracture
mechanics to describe brittle fracture. This criterion has already
been used for the blanking process by several authors 关25–27兴.
The b..c notation of Eq. 共3兲 is used here to make sure that the
fracture integral cannot decrease for a growing equivalent plastic Fig. 6 The evaluation of three criteria from literature with one
strain. parameter. The critical values C are determined in the 15

再
percent-experiment; Cockroft & Latham: C Ä1.40"103 †MPa‡;
x, x⬎0 Plastic work: C Ä3.49"103 †MPa‡; Rice & Tracey, C Ä2.32†À‡.
bxc⫽ (3)
0, x⭐0
This assumption is similar to the thermodynamically based theory
in damage mechanics that damage cannot decrease. The Rice &
Tracey criterion is based on a theoretical study of the growth of a
void in an infinite rigid, perfect plastic matrix. The Oyane crite-
rion is derived from a plasticity theory for porous materials, as-
suming that the volumetric strain has a critical level. In this crite-
rion a second parameter A O was inserted, which gives more
freedom to find a valid ductile fracture model. 共This parameter is
proposed as a material constant by Oyane et al., 关28兴兲.
For the evaluation of these criteria, the 15 percent clearance
experiment was taken as the reference experiment in which the C
is determined. For the other clearances the displacement at frac-
ture initiation is predicted and results are shown for the criteria
with only one parameter in Fig. 6. The plastic work or energy
criterion predicts fracture initiation completely wrong. For the
smallest clearance a punch displacement of only 0.39 mm is pre-
dicted. The Cockroft & Latham criterion, that was already used
for the blanking process, does not predict the trend correctly; the
punch displacement at fracture for a small clearance should be
larger than for a wide clearance. The Rice & Tracey 关29兴 criterion
gives comparable results. Fig. 7 Results for the adapted Rice & Tracey and Oyane crite-
To achieve better results the influence of triaxiality on ductile rion
fracture initiation should be changed for the blanking process. For
the Rice & Tracey criterion this is easily realized by varying the
constant A RT ⫽3/2. If this constant becomes a parameter, the cri-
terion starts to resemble the Oyane criterion. The adapted Rice &
Tracey criterion 共A RT ⫽3/2 is changed into A RT ⫽2.9兲 and the Oy-
ane criterion (A O ⫽3.9) yield good results that are presented in
Fig. 7. In Fig. 8 the value of the Oyane integral is drawn as a field
variable in the 15 percent-experiment at the punch displacement,
where experimentally fracture initiation was detected. The maxi-
mum value is located just next to the punch radius and this is in
good agreement with the position that was experimentally found.

Table 2 Four ductile fracture initiation criteria, selected from

literature

Plastic Work 关23兴 兰 ␧ p␴

¯ d␧ p ⫽C
Cockroft and Latham 关24兴 兰 ␧ p b ␴ 1 c d␧ p ⫽C Fig. 8 Field variable plot of the Oyane integral for an axisym-
metric blanking model, at the punch displacement where frac-
Rice and Tracey 关29兴, A RT ⫽3/2 兰␧p exp(ART•␴h /␴ ¯ )d␧p⫽C
ture initiated „15 percent clearance…, with two zoomed plots.
Oyane et al. 关28兴 兰 ␧ p b 1⫹A O • ␴ h / ␴
¯ c d␧ p ⫽C Maximum value is 2.38. The location of the maximum is in
agreement with experimental results.

Journal of Manufacturing Science and Engineering AUGUST 2000, Vol. 122 Õ 479
Table 3 Two ductile fracture initiation criteria, valid for the 4.1 Strategy. The strategy to predict ductile fracture in
blanking process blanking will be the following: firstly, a tensile test is performed,
at room pressure, and the thickness of the neck after fracture is
Rice & Tracey, adapted: A RT ⫽2.9 兰 ␧ p exp(ART•␴h /␴ ¯ )d␧p⫽C
measured. Then, the tensile test has to be simulated up to the point
Oyane et al. 关28兴, A O ⫽3.9 兰 ␧ 关 1⫹A O • ␴ h / ␴
¯ 兴 d␧ p ⫽C where this thickness of the neck is reached. 共This is the point of
p
fracture initiation.兲 This simulation provides the deformation his-
tory of the tensile test, with which the C of a ductile fracture
criterion can be determined. Finally, the characterized ductile
If the C is determined in another blanking experiment 共with an- fracture criterion can be applied to the blanking process for a
other clearance兲 its value will appear to be approximately the specific geometry; during the simulation of this blanking process
same. The two criteria that can predict ductile fracture initiation in 兰 f ( ␴ )d␧ p is stored as a field variable and as soon as this field
the blanking process over a wide range of clearances by perform-
ing only one blanking experiment are summarized in Table 3. The variable reaches the critical C, the punch displacement at fracture
constants C are determined to be 2.76 and 2.38 in the 15 percent is predicted. In this paper this approach will be verified over the
experiment, for the Rice & Tracey and the Oyane criterion, entire range of clearances.
respectively. During the search for a valid ductile fracture initiation criterion,
an extra intermediate verification is performed; the critical param-
4 Characterization of a Ductile Fracture Model in the eter C should also be valid for tensile tests at different hydrostatic
Tensile Test pressures. If a criterion does not fulfill this requirement it is re-
jected, because the influence of hydrostatic pressure on ductile
For industrial applications it would be a great advantage if a fracture should be accounted for correctly.
fracture criterion could be characterized by performing an easy
test, instead of a complicated and difficult, well-conditioned, 4.2 Simulation of Tensile Tests Under Different Hydro-
blanking experiment. In this section the application of the tensile static Pressures. A tensile test is simulated with an FEM com-
test to characterize a ductile fracture criterion is elucidated. putation, using the material data presented in subsection 2.1.1.
Firstly, the strategy to predict ductile fracture in blanking, using The Von Mises yield condition is used, in which the hydrostatic
a tensile test, is explained. Then, the simulation of tensile tests stress component has no influence on the yielding behavior. Thus,
under different hydrostatic pressures along with the results are the calculated force displacement curve for the tensile test is in-
described. Finally, some criteria are evaluated and a new criterion dependent of the hydrostatic pressures. This was already experi-
is proposed because the existing criteria are not valid for both mentally observed in subsection 2.1.3. Therefore, only one FEM-
blanking and tensile tests under different hydrostatic pressures. simulation is required to obtain the stress and strain history for

Fig. 9 Simulation of a tensile test and experimental verification on deformations. In the upper
left corner the undeformed tensile specimen is shown with the modelled part„1Õ8…. Upper right,
the calculated deformations at fracture initiation are shown with five levels of the equivalent
plastic strain. In the center, the three orthogonal views of the deformed specimen are shown with
a zoomed plot of the refined mesh in the neck. At the bottom, the experimental fracture surface
is compared with the calculated cross-sectional area in the neck at fracture initiation. „Mind the
wedge-like shape.…

480 Õ Vol. 122, AUGUST 2000 Transactions of the ASME

 4.3 Application of Ductile Fracture Models, Using a Ten-
sile Test. The idea is to characterize a ductile fracture initiation
model in a tensile test and use this characterized model to predict
punch displacement at fracture initiation in the blanking process.
Of all examined criteria, two were found to be valid for the blank-
ing process in section 3. These criteria of Table 3 are now tested
with this procedure. The first step is to determine the C in the
tensile test with room pressure 共0 MPa兲. Where the C’s were
determined to be 2.76 and 2.38 respectively for the adapted Rice
& Tracey and Oyane criterion in the blanking process, now, in the
tensile tests, the C’s are determined to be 5.76 and 3.64. This
resulted for the adapted Rice & Tracey criterion in an over-
prediction of the punch displacement at fracture of more than 30
percent, and for the Oyane criterion the deviations were within 25
percent. Moreover, both criteria were not able to predict ductile
Fig. 10 The numerical and experimental force displacement fracture initiation for the tensile tests under hydrostatic pressure
curves „left plot…. The crosses are the points where the experi- within satisfying margins as is shown in Fig. 11. From these re-
mental thickness of the neck after fracture is numerically sults it can be concluded that the criteria of Table 3 cannot de-
reached for the three different hydrostatic pressures. In the scribe ductile fracture initiation for both tensile tests under differ-
right plot the deformation history of the overall center of the ent hydrostatic pressures and blanking, for this specific material.
specimen up to the point of fracture initiation „crosses… is Therefore, they are rejected.
presented for the tensile tests under different hydrostatic Because no criterion has been found that satisfies this proce-
pressures.
dure, we propose a new one:

冕 ␧p
B
b 1⫹A G • ␴ h / ¯␴ c ␧ p G d␧ p ⫽C (4)
tensile tests under different hydrostatic pressures. This is because
the stress state can be compensated afterwards for the hydrostatic This criterion incorporates the triaxiality influence of the Oyane
pressure. A three-dimensional calculation is needed to simulate criterion 共Table 3兲 but also the equivalent plastic strain is inserted
the necking process correctly. No imperfection needs to be mod- in the integral. Therefore, the formulation f ( ␴ ) of Eq. 共1兲 is now
elled to initiate the neck due to the chosen boundary conditions. changed to f ( ␴ ,␧ p ), with ␧ p the logarithmic plastic strain tensor.
The modelled tensile specimen, the initial mesh, the deformed Mathematically, this means that the integral will grow faster for
mesh and the fractured specimen are all shown in Fig. 9. It can be larger strains. Physically, this seems reasonable because at larger
seen that the FEM-model predicts the deformation of the tensile strains the dislocation density will be larger. Therefore, the void
specimen well. Also the wedge-like shape of the specimen at frac- initiation is expected to be larger for larger plastic strains. A G is
ture is predicted correctly. The photograph of the fractured surface equal to A O (⫽3.9) and B G is found to be 0.63 to yield a valid
and the FEM-simulation show that the highest plastic deformation criterion that describes ductile fracture initiation for both blanking
is located at the overall center of the specimen. That this center and tensile tests under different hydrostatic pressures. The C is
point is also the point of fracture initiation can be shown by put- determined to be 3.53 in the tensile test at room pressure. The
ting the two fractured halves of the tensile specimen back to- results for the other tensile tests are plotted in Fig. 12. For the 250
gether. They do not fit perfectly because a gap exists in the MPa experiment the deviation is below 10 percent and the predic-
middle; after fracture initiation in the center, there was still some tion falls within the experimental error for the 500 MPa experi-
plastic deformation at the edges.
Besides this verification on deformation behavior, the FEM-
simulation is also checked on the force displacement curve. The
experimental and numerical force displacement curves are de-
picted in the left-hand side of Fig. 10. The only difference be-
tween experiment and FEM-simulation is the point of necking.
This point is completely determined by the shape of the master-
curve for the hardening behavior of Eq. 共2兲. FEM-calculations
demonstrated that if the master-curve was slightly changed, the
numerical point of necking could vary substantially so that the
numerical clamp displacement became even larger as in the ex-
periment. We chose to stick with the master-curve, determined in
subsection 2.1.1. The error made in the description of the defor-
mation history, due to this choice, is very small. This can be
demonstrated at the hand of Fig. 10. In the plot of the triaxiality
versus equivalent plastic strain for the three different hydrostatic
pressures 共plotted in the right-hand side of Fig. 10兲, the homoge-
neous deformation should have lasted a bit longer; the straight
part for the 0 MPa curve at a triaxiality of 1/3, is experimentally a
negligibly tiny part larger. The triaxiality plots for the hydrostatic
pressures of 250 and 500 MPa are deduced from the calculated
one for 0 MPa. 共The wrinkles on the plots are caused by numeri-
cal difficulties to initiate the neck, because no imperfection was
Fig. 11 Validity check in the pressurized tensile tests for the
used to activate the necking process.兲 criteria that performed well with a characterization in the blank-
Now the needed information, to characterize ductile fracture ing process „Table 3…. Rice & Tracey and Oyane et al. deviate
criteria in a tensile test and apply them on the blanking process, is respectively 60 percent and 30 percent from the 500 MPa ex-
present. Also, the validity of criteria for tensile tests over a range periment, when the C is determined in the experiment at room
of superimposed hydrostatic pressures can be checked. pressure.

Journal of Manufacturing Science and Engineering AUGUST 2000, Vol. 122 Õ 481
 The approach that is expected to give the best results, consid-
ering literature, is the characterization of a fracture model in the
blanking process. The two criteria of Table 3 produce good results
if the influence of triaxiality on ductile fracture initiation has been
determined. This means that in an industrial environment the
product shape can be predicted for this material over a large range
of clearances by performing only one blanking experiment, in
which the critical C is determined.
The second approach is the characterization of the fracture
model in an easier tensile test. Because existing criteria do not
provide satisfying results, we have proposed a new criterion in Eq.
共4兲. This criterion is not derived from a physical background but it
incorporates parameters that are known to be important for ductile
fracture initiation. In Fig. 13, it is shown that this criterion can
predict ductile fracture initiation over a wide range of clearances
if the critical C is determined in a tensile test. Furthermore, this
criterion can predict ductile fracture initiation in tensile tests for
different hydrostatic pressures. This is important because it shows
that the criterion can predict fracture for a greatly varying triaxi-
ality, which is known to be an important parameter for ductile
Fig. 12 Validity check of the proposed criterion for the tensile
fracture initiation. This approach yields satisfying results and is of
tests course the more favorable for industry.
The question remains, whether these approaches will also be
valid for other materials. If the formulation of the integral does
not depend on the material 共If A RT and A O in Table 3 and A G and
B G in Eq. 共4兲 are no material parameters兲, both approaches will be
valid for other materials as well. The only material parameter will
then be the critical C. However, this will have to be checked in
future research, where these approaches will be tested for different
materials 关30兴. If, for example, the multiplier in front of the tri-
axiality in the Oyane criterion, A O , will appear to be a material
parameter an extra blanking experiment will be needed in the first
approach to determine this parameter and characterize the ductile
fracture initiation model completely.
The influence of speed on the blanking process is not investi-
gated in the present paper. For this reason, blanking and tensile
speeds are chosen such that similar strain rates are obtained in all
experiments. Preliminary results show a significant but small in-
fluence of blanking speed on the process force, and no effect of
the speed was observed on the product shape of the blanked edge.
A more profound investigation of the effect of punch speed on the
blanking process will be presented in a future publication 关31兴.

Acknowledgments
Fig. 13 Validity check of the proposed criterion for the blank-
ing process This research was funded by the Dutch innovative research
projects 共IOP-C.94.702.TU.WB兲. Jan Post of Philips DAP/LTM
kindly supplied the material and some data for the material model.
Alan Duckett of the IRC in Polymer Science and Technology at
ment. The C, determined in the 0 MPa tensile test, is used to the Leeds University is gratefully acknowledged for his help with
predict fracture initiation in blanking and results are depicted in
Fig. 13. Not all results fall in the experimental range of twice the the pressurized tensile experiments.
standard deviation, but the largest deviation of the predicted
punch displacement at fracture is 6 percent. Nomenclature
It can be concluded that this criterion produces satisfying re-
␴ ⫽ Cauchy stress tensor, MPa
sults in this procedure for this material. Therefore, it is possible to
␴ h ⫽ hydrostatic stress, ␴ h ⫽1/3•( ␴ 1 ⫹ ␴ 2 ⫹ ␴ 3 ) with ␴ 1 ,
predict the punch displacement at fracture initiation over a wide
␴ 2 , ␴ 3 the principal stresses, MPa
range of clearances, by performing one tensile test.
␴ y ⫽ momentary Von Mises yield stress 共history parameter
dependent on ␧ p 兲, MPa
5 Discussion and Conclusion ¯␴ ⫽ equivalent Von Mises stress ¯␴ ⫽(1/2• 关 ( ␴ 1 ⫺ ␴ 2 ) 2
The goal of this research was to predict the product shape of a ⫹( ␴ 2 ⫺ ␴ 3 ) 2 ⫹( ␴ 3 ⫺ ␴ 1 ) 2 兴 ) 0.5, MPa
blanked product. An FEM-model, validated on the deformations ␴ 1 ⫽ maximum principal stress, MPa
in the blanking process, existed but the problem of ductile fracture ␴ h / ¯␴ ⫽ triaxiality
initiation had not been solved yet. The category of local ductile ␧ p ⫽ equivalent logarithmic plastic strain ␧ p ⫽(2/3•(␧ 21
fracture criteria was chosen for this application. For the character- ⫹␧ 22 ⫹␧ 23 )) 0.5 with ␧ 1 ,␧ 2 ,␧ 3 the principal strains
ization of such a model two approaches are discussed in this pa- C ⫽ critical value of fracture model
per. To verify these approaches an experimental setup was built A O ⫽ parameter in Oyane model
and results are presented for the punch displacement at ductile A RT ⫽ parameter in Rice & Tracey model
fracture initiation for five different clearances in the blanking A G ⫽ parameter in newly proposed model
process. B G ⫽ parameter in newly proposed model

482 Õ Vol. 122, AUGUST 2000 Transactions of the ASME

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Journal of Manufacturing Science and Engineering AUGUST 2000, Vol. 122 Õ 483