The influences of the residual forming data on the quasi static axial crash response of a top-hat section

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The influences of the residual forming data on the quasi-static axial crash
response of a top-hat section
Article in International Journal of Mechanical Sciences · May 2009
DOI: 10.1016/j.ijmecsci.2009.03.010
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2. The influences of the residual forming data on the quasi-static axial crash
response of a top-hat section
Recep Gümrük, Sami Karadeniz
Department of Mechanical Engineering, Karadeniz Technical University, Trabzon 61080, Turkey
a r t i c l e i n f o
Article history:
Received 3 September 2008
Received in revised form
5 March 2009
Accepted 12 March 2009
Available online 5 April 2009
Keywords:
Quasi-static crash
Residual-forming data
Top-hat section
LS-DYNA
Blank holder load
a b s t r a c t
In this paper the influences of residual effects of a deep drawing forming process on the axial quasi-
static crash behaviour of straight thin-walled top-hat section were numerically investigated. The
residual forming data on the plastic strains, residual stresses and thickness variations were transferred
to crash models, which include both deformed and nominal meshes. The influence of spring-back or
spring-in on crash performance of the member was also considered. Numerical simulations were
carried out by using the nonlinear finite element code LS-DYNA. As a result of these analyses it appears
that the residual forming data and the effects of spring-back significantly influence the crash response
and they should be considered in computational impact simulations.
2009 Elsevier Ltd. All rights reserved.
1. Introduction
In numerical crash simulations, forming histories of crashed
members are rarely taken into account. This is because of a
general notion that strain hardening due to the plastic strains that
occur during the forming processes compensate any decrease in
the strength of the member due to thickness reduction [1].
However, in some of the recent works it has been shown that
plastic strains and thickness variations that occur during the
forming process are effective parameters that influence the crash
behaviour significantly [2,3]. Therefore, to create reliable and
realistic crash simulation models the forming effects should be
considered. Dutton et al. [2] studied the influence of forming data
of side rails fabricated through tube hydroforming on dynamic
crash performance. They studied the effects of residual-forming
data such as deformed geometry, thickness variations, plastic
strains, residual stresses and stress distributions after spring-back
analysis. Due to these forming data, important differences in both
axial crash modes and rigid-wall displacements were obtained.
With respect to the prediction of the model without forming
effects the largest decrease in rigid-wall displacement was 54%,
which was obtained with the model that contains plastic strain.
One of the other interesting points was that the residual stress
had no noticeable effect. Oliveira et al. [3] studied the effects of
residual tube bending process on the dynamic crash behaviour
of aluminium alloy s-rail structures. The peak dynamic crash force
and absorbed energy capacity predictions of the model with
residual forming effects were 25–30% and 18% higher, respec-
tively, than the predictions of the model without forming effects.
Lee et al. [4] studied the relationships among hardening
models and forming effects. To determine the influence of the
hardening model with residual forming data on impact responses
of S-type tube formed by deep drawing and tube formed by
hydroforming processes were numerically studied for both
isotropic and hardening material models. They found that plastic
strain changes the behaviour significantly and the effects of
kinematic hardening decrease as deformation increases. Cafolla et
al. [5] described the so-called ‘‘forming to crash’’, a three-step
analysis process, to assess the effects of residual-forming proper-
ties on the crash performance of vehicle body structures.
There are two noticeable approaches that have been used in
crash response studies reported in literature. In some of the
studies, the deformed mesh coming from the forming process is
used, whereas in some studies a relatively course mesh created by
meshing the member geometry generated using a solid modelling
program, also called a crash mesh, is employed [5]. So a crash
mesh does not contain the effects of forming and spring-back
analysis, which is generally termed as the geometrical effect. Huh
et al. [6] used the LS-DYNA program to carry out crash analyses of
a front side member of an automobile. The data of plastic strain
and thickness variations related to the deep drawing process of
the member were mapped into the crash model. Although due to
deficiencies in the mapping process some minor discrepancies
existed between the deformed and crash meshes it was pointed
ARTICLE IN PRESS
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journal homepage: www.elsevier.com/locate/ijmecsci
International Journal of Mechanical Sciences
0020-7403/$ - see front matter 2009 Elsevier Ltd. All rights reserved.
doi:10.1016/j.ijmecsci.2009.03.010
Corresponding author. Tel.: +90 462 37729 45; fax: +90 462 325 55 26.
E-mail address: kdeniz@ktu.edu.tr (S. Karadeniz).
International Journal of Mechanical Sciences 51 (2009) 350–362

3. out that the most dominant forming effect on the crash response
of a member is plastic strain. Broene [7] developed an algorithm
to determine the effects of a forming process without actually
carrying out any forming analysis. After bending a flat plate,
Broene conducted a spring-back analysis and then placed the
formed plate between two rigid plates. He used both the
algorithm he developed and the LS-DYNA program in the deter-
mination of the effects of forming on crash performance. The
results obtained using both approaches were in good agreement
with each other. He pointed out that consideration of the forming
data gives rise to higher predictions in the crash force value.
In addition to these studies on crash performance of some
automobile components, influences of forming data of some
components on the crash performance of full- or semi-vehicle
(automobile) models were also investigated. Dutton et al. [8]
modelled the deep-drawing forming of the front rail of a vehicle
and then transferred all the data on the plastic strains and
thickness variations into a full-vehicle model. There were no
substantial differences in the deformation modes predicted by the
models with and without forming effects. However, the model
with the forming effects predicted 18% increase in the peak crash
force. A similar work has been carried out by Chen et al. [1].
In their study, the data coming from manufacturing processes of
some of the components of a vehicle were transferred into a full-
vehicle crash model. They commented on crash responses of the
components and the full model. The full model with the forming
data shows an increase in rigidity and approximately 10% increase
in deceleration. In the case of components, the model without
forming effects predicts much more severe buckling and bending
in the frontal rail. This behaviour may be attributed to the fact
that due to plastic strains, work hardening compensates for the
adverse effects of residual stresses and thickness variations.
Therefore, the overall effect of the forming data was an increase
in stiffness. The main effects of thickness variations and residual
stress were on the fatigue life of components. Similar results were
obtained by Simunovic et al. [9]. It may be concluded here that
although the residual-forming data have some effects on the crash
response of individual components, their effects on the behaviour
of the full model are not very clear [9].
Almost all of the previous works on numerical predictions
of effects of residual-forming properties on the crash behaviour
are focused on the cases of dynamic crash. The main initiative
of the present paper is to better understand the individual and
combined influences of plastic strain, thickness variations and
residual stress on the quasi-static response of a straight thin-
walled top-hat section formed by a deep-drawing process.
A quasi-static response analysis is frequently used for the
assessment of the geometric parameters on crash response of a
component. Such an analysis excludes the associated effects of
inertia and strain rate. Therefore, it may produce useful informa-
tion on the influences of geometric parameters on overall
crashworthiness of a component. Likewise, a quasi-static analysis
of crash models that contain residual-forming effects may
produce information that can be used in the modelling of material
strength, which is a critical component in the success of a realistic
simulation.
The paper consists of three main sections. In the fist section,
to verify the finite-element model, the numerical prediction
of a crash model without forming data was compared with the
experimental result reported in the literature [10]. After having
verified the model, in the second part, three one-step deep-
drawing forming analyses were performed to form three different
top-hat sections by varying the blank holder load. Hence, different
forming data on plastic strain, thickness variations and residual
stress were generated, which are necessary for meaningful
comparisons of the results. In this respect, in the second part, to
allow meaningful comparison of the results, different sets of
residual-forming data of three different top-hat sections were
formed by applying three different blank holder loads. After the
trimming and spring-back analyses three different crash models
were formed. Then, the data on plastic strains, residual stress and
thickness variations were mapped onto the crash models. Finally,
the crash analyses were carried out by using both the deformed
mesh coming from the forming process and the crash mesh. The
results were compared in terms of the peak crash force, absorbed
energy and mean crash force. All analyses were carried out with
the nonlinear finite element analysis code LS-DYNA. The forming
simulations and quasi-static crash analyses were performed
explicitly whereas the spring-back analyses were carried out
implicitly.
2. Finite element model
To establish a static crash model and validate the numerical
results, the mechanical model, geometry and material data
selected were the same as those used in the work of Tarigopula
et al. [10]. A mesh size sensitivity study was carried out by using
the various shell elements available in LS-DYNA. As an outcome,
Belyschko–Tsai four-noded reduced integration shell element
with six degrees of freedom per node was chosen in the meshing
of members. The element dimensions were 2 2 mm2
in the hat
profile whereas the lid (closing plate) was modelled by using
3 3 mm2
elements. Stiffness-type hourglass control was used to
eliminate the zero energy modes. Five integration points through
the element thickness were chosen in order to capture the local
bending accurately. These element formulations and mesh sizes
were similar to the choices made in some of the previous study
reported in the literature [11,12].
2.1. Material data
In the numerical simulations the material data corresponding
to true stress–true strain curves at different strain rates of DP800
ARTICLE IN PRESS
0
Plastic Strain
0
400
800
1200
True
Stress
(MPa)
Strain Rate (1/s)
0.000903
1.029
278
444
0.1 0.2 0.3
Fig. 1. True stress–true plastic strain curves for DP800 high-strength steel.
R. Gümrük, S. Karadeniz / International Journal of Mechanical Sciences 51 (2009) 350–362 351

4. high-strength steel are selected (Fig. 1). These curves were
obtained by conducting a series of static tensile and Split
Hopkinson Pressure Bar compression tests [10]. This material
has a modulus of elasticity of E ¼ 195 GPa, Poisson ratio of
n ¼ 0.33 and density of r ¼ 7850 kg/m3
. In fact, in the present
study, in order to eliminate the effects of strain rate in the quasi-
static crash analyses, the curve corresponding to a strain rate of
0.000903 s1
was used as the stress–strain curve of the material.
2.2. Geometry, boundary conditions and loading
The structural component used in all the crash simulations is
a straight top-hat profile joined by spot welding with a flat lid.
The thicknesses of both the profile and the lid were 1.2 mm and
the length of the component was 410 mm. The corner radii of the
top-hat profile were R2 ¼ 2 mm and R3 ¼ 3 mm. The cross-
sectional dimensions of the component are shown in Fig. 2. In
the numerical simulations, due to symmetry of the top-hat
section, only one half of the members were modelled. In order
to prevent any numerical instability, rotations in y and z directions
of the loading end of the hat profile were constrained.
Although, the boundary conditions in an actual crashing
event are very complicated, depending on many factors such as
constraints of the object to be crashed, it was assumed that the
crashing object is a rigid plate and the non-crashing end of the
component was fully fixed to a supporting rigid wall. The rigid
plate was modelled as an analytical rigid surface and was allowed
to translate horizontally in order to crash axially onto the free
end of the component. In addition, for the nodes placed in a region
beyond a distance of 310 mm from the loading end only the
translations parallel to the axis of members were allowed.
All other degrees of freedoms were constrained to be zero.
The symmetry boundary conditions were satisfied by constraining
the translations in the x direction and rotations in the y and z
directions of the nodes lying on the symmetry plane.
The hat profile and the lid were fixed by spot welding. Starting
from a distance of 5 mm from the loading end of the member,
13 beam spot welds, 25 mm apart from each other, were used
along the centre lines of the flanges of the profile. In the section
between the distances of 310 and 410 mm from the loading end
no spot welds were used. The spot welds were modelled by
beam elements. A frictionless single surface contact algorithm
was selected to prevent nodal penetrations that may occur during
the formation of lobes. The contact between the rigid-wall
and member was maintained by the node to surface contact
algorithm. The coefficient of friction between the rigid plate and
the component was chosen to be 0.3. Neither triggering nor
imperfections were considered.
2.3. Quasi-static crash model and its verification
A quasi-static crash process can be achieved with an artificial
high velocity provided that the inertia effect is minimized, which
can be done by appropriately ramping the velocity. To ensure
a quasi-static loading when using an explicit code, the rigid
plate (body) was given a prescribed velocity field obeying the
function [13]
nðtÞ ¼
p
p 2
dmax
T
1 cos
p
2T
t
h i
(1)
Here T is the total duration of loading and dmax the final
displacement. When integrated from t ¼ 0 to T this expression
yields dmax and if it is differentiated with respect to time it gives
zero acceleration. The variation of the rigid-wall velocity versus
time is shown in Fig. 3. It should be noted here that this
expression gives rise to a crash velocity in the first 0.025 s of the
total crash simulation period that varies sinusoidally with time.
After this period the crash velocity is considered to be constant as
shown in Fig. 3. The crash simulation was terminated at 0.05 s, at
which the total axial displacement of the rigid wall was 229 mm.
Here, in order to eliminate the effects of the axial and transverse
inertia that may occur in the shell elements during the initial
stages of the crash process a gentle contact was maintained by
giving very low initial velocities to the rigid wall.
One of the requirements of a crash event to be accepted as a
quasi-static event is that the amount of kinetic energy developed
in the component during the crash process must not exceed a
certain proportion (usually 5%) of the total internal or strain
energy absorbed by the component [14]. In addition to this, in
quasi-static crash simulations, the effects of strain rate are
ignored, since in a real static crash event, the strain rate effects
are negligible. As far as the present study is concerned there is no
doubt that since the velocity curve was applied in a time span of
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60
R3
60
25
110
Spot Weld
R2
Fig. 2. Cross-section of the component used in the crash simulations (all
dimensions in mm).
0
Time (s)
Velocity
(m/s)
0
2
4
6
8
0.01 0.02 0.03 0.04 0.05
Fig. 3. Prescribed velocity of the rigid wall.
R. Gümrük, S. Karadeniz / International Journal of Mechanical Sciences 51 (2009) 350–362
352

5. 0.05 s the inclusion of effects of strain rate would affect the
results. But this time the problem would be a dynamic crash
problem rather than a quasi-static one. Therefore, the strain rate
effect was excluded in the analyses by choosing the curve
corresponding to a strain rate of 9.03 104
s1
in Fig. 1 to be
the stress–strain curve of the material. Since the above-mentioned
acceptability criteria of a quasi-static crash simulation had been
satisfied the use of the created crash model was justified. This was
achieved by employing different models using various combina-
tions of the data related to the material response, element
dimensions, element formulations, prescribed velocity curves,
boundary conditions of the nodes at the crashing end and ratio of
kinetic energy to internal energy.
Type 24, one of the material models available in LS-DYNA, is a
piecewise linear isotropic elasto-plastic material model. In this
model, strain rate sensitivity is taken into account and the relation
between dynamic stress and the strain rate of a particular metallic
alloy is given by the Cowper–Symonds relation [15]. In the present
study, this material model was adopted. However, as mentioned
before the effects of strain rate were not considered.
Fig. 4 shows some of the crash data obtained at the end of
quasi-static crash simulations together with the experimental
results obtained by Tarigopula et al. [10]. The rigid-wall force
versus axial displacement results corresponding to both the
experimental work and the simulation studies obtained using
the half model of crashing members are shown in Fig. 4(a). A very
good correlation exists between the experimental observation
and the numerical predictions of both the half and full models.
As is seen, the main characteristics of the rigid-wall force–
displacement curves corresponding to the predictions of the full
and the half models are nearly the same. Although there are small
differences between the curves, this result justifies the use of
symmetric models in numerical crash simulations. These small
differences may be attributed to the fact that the full model
contained twice as many elements as the half model. This may
give rise to some numerical errors, such as round-off. It should
also be noted here that the number of peaks and valleys of
the rigid-wall force in both the experimental observation and
numerical prediction are almost the same. However, there are
small shifts among the curves. These shifts may be attributed to
local deformations that may occur at the beginning of the crash
event. The deformation modes of the two approaches are shown
in Fig. 4(b). Comparison of the modes of deformation also shows
that a good agreement between the two studies also exists. Thus,
at this stage we can conclude that our numerical model is
satisfactory in predicting the actual quasi-static crash behaviour
of the top-hat section.
3. Deep-drawing simulations
In order to generate the forming data that can be used in quasi-
static crash simulations, the thin-walled top-hat section was
formed by a one-step deep-drawing process using the implicit
code LS-DYNA. The dimensions of the die used in the simulation of
the forming process are shown in Fig. 5. At the beginning, a blank
having the dimension of 450 260 1.2 mm3
was considered.
Due to the symmetry, only one half of the system was modelled.
The die, punch and blank holder were assumed to be rigid.
The blank was modelled by four-noded shell elements having a
ARTICLE IN PRESS
Fig. 4. Comparison of the experimental observation and the numerical prediction:
(a) variation of the rigid-wall crash force versus rigid-wall displacement and (b)
deformation modes.
100 62.2 R3
R3
Die
R2
Blank Holder
Punch
100
Blank
60
58.8
Fig. 5. Dimensions of the die and the punch used in the deep-drawing process (all
dimensions in mm).
R. Gümrük, S. Karadeniz / International Journal of Mechanical Sciences 51 (2009) 350–362 353

6. dimension of 2 2 mm2
. Five integration points through the blank
thickness were used.
The contact between the parts was maintained as automatic
surface to surface contact and the coefficient of friction was
assumed to be 0.15. In order to include the effects of strain rate on
the forming results, the data representing all true stress–true
strain curves in Fig. 1 were used as the material data.
To generate necessary forming data, the deep-drawing forming
analyses were repeated for the blank holder loads of 50, 400 and
1000 kN. Since, in the forming process no draw beads were
employed on the blank, relatively higher blank holder load values
were considered. The motion of the punch versus displacement
curve and the variation of the blank holder load with time that
were employed in the forming process are shown in Fig. 6.
The plastic strain distribution and the thickness variations
corresponding to a blank holder load of 400 kN are shown in
Fig. 7. As is seen, the largest variations in the thickness and
plastic strains occur at the sidewalls of the top-hat section. The
corresponding variations at the top and bottom surfaces are
relatively small. This is not a surprising result since, besides
the effects of residual stresses and strains introduced into the
material during forming, the frictional forces at the top and
bottom surfaces give rise to an increase in the deformation
resistance of these regions. In addition, relatively small values of
radius of curvature at the corners increase the bending resistance
at these regions. This also results in relatively large deformations
at the sidewalls.
Fig. 8 shows the influence of the blank holder load on the
variations of thickness and plastic strains on a cross-section taken at
the middle section of the member. Due to the symmetry, these
curves represent the data corresponding to only one half of the
cross-section. It is seen from the figure that an increase in the value
of the blank holder load leads to substantial changes in both the
plastic strains and thickness variations for the cases considered.
After the deep-drawing analysis, in order to attain the nominal
dimensions, the hat profile was subjected to a trimming opera-
tion. After the trimming operation, the hat profile and the lid
(closing plate) were fixed along the centrelines of the flanges of
the member by spot welds and then a single spring-back analysis
was carried out using the implicit solver. During the spring-back
analysis, a surface to surface contact was assumed between the
hat profile and the lid. Seventeen spot welds were implemented
by tied nodes to surface contact along the length of each flange.
Fig. 9 shows the nominal geometry and the geometry of a
cross-section after the spring-back analysis of the member. As is
seen, spring-in (negative spring-back) occurs at top and bottom
surfaces of the member. Due to this, the top and bottom surfaces
bend inwards whereas the sidewalls bend outwards. It is apparent
here that as the blank force increases the deviations from the
nominal geometry decrease, indicating that the higher the blank
holder load, the larger the plastic deformations. On the other
hand, a large plastic deformation gradient decreases the effects of
spring-back significantly. For the top-hat geometry considered
here relatively large plastic strains occur on the side walls and
large strain gradients occur in regions that are close to the corners
as shown in Fig. 8. Hence, the cause of the decreasing spring-back
effect may be partly attributed to relatively small values of the
corner radii [16].
4. Quasi-static crash analyses
4.1. Crash models
In this section the analyses were carried out explicitly by using
nine different crash models based on two different meshes. The
first mesh was the deformed mesh (forming mesh) coming from
the deep-drawing analysis. This mesh also contains geometrical
changes due to the spring-back analysis. The geometrical changes
due to the spring-back analysis will be called as the geometrical
effects. The second mesh, which is called as the nominal mesh,
was created by meshing of the CAD drawing of the top-hat
member. Therefore this mesh contains neither the forming nor
any spring-back effects. Table 1 summarizes the crash models and
their contents in terms of the residual forming and the
geometrical effects. As the table reveals, five different analyses
were conducted by using the deformed mesh whereas four
different cases were considered with the nominal mesh. The
extra run was carried out to determine the influences of the
geometrical effects by using the deformed mesh without
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0
Time (s)
0
10
20
30
40
50
60
70
Displacement
(mm)
0
Time (s)
0
100
200
300
400
500
600
Blank
Holder
Load
(kN)
0.005 0.01 0.015 0.02 0.025
0.005 0.01 0.015 0.02 0.025
Fig. 6. Loading curves used in the deep-drawing simulation: (a) motion curve of
the punch and (b) loading curve of blank holder load.
R. Gümrük, S. Karadeniz / International Journal of Mechanical Sciences 51 (2009) 350–362
354

7. the residual-forming effects. It should be noticed here that other
four analyses conducted by using the crash models based on the
deformed mesh contain influences of the geometrical effects
automatically. It is probable that the final effects of the residual-
forming data on the crash performance may themselves be
affected by the geometrical effects. Therefore, the purpose of
conducting some of the crash analyses using the nominal mesh
was to uncover more clearly the individual effects of the spring-
back, thickness variations, plastic strains and residual stresses on
the crash response.
To reveal the influence of the use of deformed mesh containing
neither the residual-forming data nor the spring-back effects on
the crash performance, an additional crash model was created by
using the mesh that was obtained at the end of the deep-drawing
process. A comparison of the results that were obtained using this
mesh and the nominal mesh in terms of the mean crash force is
shown in Fig. 10. As is seen, there are only minor differences
between the curves representing the results of two analyses.
These differences may be attributed to the small geometric
differences between the nominal and deformed meshes and the
local deformations.
In reality, when a workpiece is taken out of the die after the
deep-drawing operation, a spring-back or stress relaxation occurs.
Therefore, before the spot welding operation the side walls of the
profile are pushed out or pulled in to eliminate, to some degree,
the spring-back effects. Then the spot welding operation is carried
out. However, after finishing the spot welding operation and
releasing the side walls a secondary spring-back takes place in the
member. That is to say, in practice, the member is subjected to
spring-back twice. In this study this secondary spring-back
has not been considered. Instead, to uncover the effects of this
consideration, an analysis based on a model that contained only
the geometrical effects that remain after the second spring-back
analysis was carried out. In order to obtain this model the
following procedure was implemented; after taking the top-hat
profile formed by applying a blank holder load of 50 kN out of the
die, it was subjected to the first spring-back analysis. Afterwards,
two rigid walls were placed at the appropriate positions and
the sides of the profile suffering from the spring-in were pushed
outwards to their nominal positions. Then, the hat profile was
joined with the closing plate (lid) by spot welding and afterwards
the second spring-back analysis was carried out. Finally, the mesh
obtained at the end of this full procedure containing no forming
effects was used as the crash model. Fig. 11 shows the rigid-wall
mean crash load predictions of the analyses using the mesh based
on this full procedure and the deformed mesh based on the
procedure used throughout this study. As is seen, there are small
differences between the predicted mean rigid-wall forces
obtained by using the two meshes. The differences diminish as
the axial deformation increases.
4.2. Analyses with the deformed mesh
At the end of the spring-back analysis, the data on the
coordinates of the nodes, the thickness variations, plastic strain
and residual stress distributions were written in a ‘‘dynain’’ result
file [15]. This file was used as an input file in the proceeding crash
analyses. Through this file the forming data were transferred
directly into the crash model by using *INCLUDE command.
ARTICLE IN PRESS
Fig. 7. Residual effects of the deep-drawing process: (a) plastic strain distribution and (b) thickness variations.
R. Gümrük, S. Karadeniz / International Journal of Mechanical Sciences 51 (2009) 350–362 355

8. In addition, depending on the type of analysis being conducted,
the appropriate forming effects were separated by using a code
written in FORTRAN and then transferred into the crash model.
Fig. 12 shows the influences of the individual forming effects
on the quasi-static crash performance, the variations of the crash
force, absorbed energy and mean crash force as functions of rigid-
wall displacement for a member formed by applying a blank
holder load of 400 kN. It should be noticed here that the rigid-wall
force versus displacement curves show substantial deviations
from each others. This behaviour is due to the fact that each of the
forming effects may lead to a different deformation mode as
shown in Fig. 13. In terms of the rigid-wall crash force, the peak
values were obtained if a model contains either the plastic strains
or all residual-forming data. As far as the amount of absorbed
energy is concerned, the model that contains the plastic strains is
the most efficient, i.e. it absorbs the greatest amount of energy for
a given displacement (Fig. 12(b)). Due to the effects of spring-
in, the model considering only the geometrical effects seems
to predict more absorbed energy than the model based on
the nominal mesh. The models considering only the residual
stresses and thickness variations show similar energy-absorbing
behaviours with the model containing only the geometrical
effects. In terms of the mean crash force, a similar behaviour
ARTICLE IN PRESS
Section Distance (mm)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
True
Plastic
Strain
50 kN 400 kN 1000 kN
0 10 30 40 50 60 70 80 90 100 110 120
1 2 3 4
Section Distance
1
1.02
1.04
1.06
1.08
1.1
1.12
1.14
1.16
1.18
1.2
1.22
Thickness
(mm)
50 kN 400 kN 1000 kN
0 10 20 30 40 50 70 80 90 100 110 120
1 2 3 4
20
60
Fig. 8. Variations of residual effects with blank holder load: (a) true plastic strain distribution and (b) thickness variation.
Fig. 9. Effect of the spring-back on the geometry of cross-section.
R. Gümrük, S. Karadeniz / International Journal of Mechanical Sciences 51 (2009) 350–362
356

9. that had been obtained for the absorbed energy was predicted
(Fig. 12(c)). Once more, the biggest mean crash force value was
predicted by the model containing only the plastic strains.
Therefore, it can be stated here that the plastic strains
substantially affect the static crash response.
The residual-forming data cause substantial changes in the
deformation modes as shown in Fig. 13. Although all the
deformation mode predictions are progressive buckling almost
every forming effect leads to a different deformation pattern. In
fact, the deformation modes corresponding to the predictions
of the models covering the residual stresses and geometric effects
are quite similar.
As mentioned above the deep-drawing process of the crash
member was repeated for the blank holder load values of 50, 400
and 1000 kN. Each of these blank holder loads gives rise to
different residual-forming effects on the top-hat profile.
The effects of the blank holder load values on the peak crash
force and the amount of absorbed energy are shown in Fig. 14. For
all the cases considered, the peak values of the rigid-wall crash
force were predicted by the analyses that were based on the
member formed by the blank holder load of 50 kN. The model
covering all the forming effects predicts 18% higher rigid-wall
peak crash force than the model with the nominal mesh. The
predictions of the corresponding force values substantially
decrease when the blank holder load is 400 kN. However, there
are some increases in these values when the blank holder load
is 1000 kN except in the model covering only the thickness
distributions. These increases are partly due to the increases in
the magnitudes of the plastic strains for this value of the blank
holder load. Nevertheless, the major reason of the occurrence
of peak values for a blank holder load of 50 kN is due to the
extent of spring-in, the largest values of which occur for this value
of the blank holder load. As far as the individual forming
effect corresponding to each value of the blank holder load is
concerned, the models covering only the plastic strains give rise to
larger peak crash forces compared with the predictions of the
models with other forming effects. On the other hand relatively
small peak crash force values were predicted by the models that
contain the data on either the thickness variations or residual
stresses.
In terms of the amount of the absorbed energy, the greatest
amount of energy absorption is predicted by the model that uses
the hat profile formed with a 400 kN blank holder load (Fig. 14(b)).
This result may be attributed to the effects of spring-in and the
local deformation that occurs during the forming process of the
top-hat profile. The models containing the plastic strain data
generally predict the greatest amount of energy absorption
whereas the models containing the thickness variations predict
the least amount of energy absorption. In addition, when the
blank holder load is relatively small, the model that covers the
forming effects altogether predicts greater amount of energy
absorption.
ARTICLE IN PRESS
Table 1
Contents of the quasi-static crash models.
Crash model Deformed mesh Nominal mesh
Plastic strain Thickness variation Residual. stress Plastic strain Thickness variation Residual stress
Geometrical effect No No No – – –
All forming effects Yes Yes Yes Yes Yes Yes
Plastic strain Yes No No Yes No No
Thickness variations No Yes No No Yes No
Residual stress No No Yes No No Yes
0
Rigid Wall Displacement (mm)
Rigid
Wall
Mean
Crash
Force
(kN)
Deformed Mesh
Nominal Mesh
0
20
40
60
80
50 100 150 200 250
Fig. 10. Predictions of the rigid-wall mean crash force of two different meshes.
0
Rigid Wall Displacement (mm)
Rigid
Wall
Mean
Crash
Force
(kN)
Full Procedure
Applied Procedure
0
20
40
60
80
50 100 150 200 250
Fig. 11. Effects of the full and applied procedures on crash behaviours without
residual-forming data.
R. Gümrük, S. Karadeniz / International Journal of Mechanical Sciences 51 (2009) 350–362 357

10. Comparison of the results of the crash analyses performed with
the deformed mesh and the results of the analyses that use a
mesh based on the model containing only the geometrical effects
gives a more realistic picture on the effects of residual-forming
data on the quasi-static crash performance. As was mentioned
above, the models containing the forming effects were generated
by transferring the data representing these effects into the models
that contained the geometrical effects. Therefore, the differences
that occur among the predictions of these models represent the
deviations from the model covering only the geometrical effects.
Considering the result of these case studies, it may be
concluded that the models covering only thickness variations of
residual-forming effects predict smaller crash force values and the
least amount of energy absorption among all the other models
considered. The greatest values of these crash performance
indicators are predicted by the models with plastic strains. These
findings are in good agreement with results reported in the
literature for dynamic crash cases [2,3,6].
4.3. Analyses with the nominal mesh
At this stage, it is not clear how the value of the blank holder
load alone influences the crash performance of a model that
contains residual-forming effects. Therefore, this section exam-
ines the influences of these forming effects on quasi-static crash
response by using the nominal mesh having no geometrical
effects. In order to carry out such analyses, using the dynain file
that was created at the end of the spring-back analysis together
with the INCLUDE_STAMPED_PART command, the data on the
forming effects were transferred from the forming mesh into the
nominal mesh. As an example, the plastic strain and thickness
variation data mappings from the deformed mesh at the end of
the spring-back analysis of a member formed with a blank holder
load of 400 kN into a nominal mesh are shown in Fig. 15. The
ARTICLE IN PRESS
Rigid
Wall
Crash
Force
(kN)
All Forming Effects
Plastic Strain
Thickness Distr.
Residual Stress
Geometrical Effect
Nominal Mesh
0
20
40
60
80
100
120
0
Rigid Wall Displacement (mm)
Absorbed
Energy
(kJ)
All Forming Effects
Plastic Strain
Thickness Distr.
Residual Stress
Geometrical Effect
Nominal Geometry
0
2
4
6
8
10
12
Rigid
Wall
Mean
Crash
Force
(kN)
All Forming Effects
Plastic Strain
Thickness Distr.
Residual Stress
Geometrical Effect
Nominal Geometry
0
20
40
60
80
50 100 150 200 250
0
Rigid Wall Displacement (mm)
50 100 150 200 250
0
Rigid Wall Displacement (mm)
50 100 150 200 250
Fig. 12. Residual-forming effects on the crash performance of members: (a) rigid-wall crash force, (b) absorbed energy and (c) mean crash force.
Fig. 13. Effects of the residual-forming data on deformation modes of a member
formed by applying a blank holder load of 400 kN.
R. Gümrük, S. Karadeniz / International Journal of Mechanical Sciences 51 (2009) 350–362
358

11. minor differences between the meshes after the mapping are
due to the differences in two geometries caused by the effects of
the spring-back.
Using the nominal mesh, the quasi-static crash performance of
a member formed with a blank holder load of 400 kN is given in
Fig. 16. Unlike the results obtained from the analyses based on the
deformed mesh, here the curves representing the peak crash force
versus rigid-wall displacement responses of the models with the
forming effects show similar characteristics (Fig. 16(a)). Once
again, the peak and mean crash force values and the greatest
amount of energy absorption were predicted by the model that
contained only plastic strains. On the other hand, the analysis
with thickness variations predicts the least values of these
quantities for a given displacement. In addition to this it is quite
noticeable here that the prediction of the crash model that
contains residual stress data and the prediction of the analysis
with the nominal mesh was virtually identical. This result
indicates that the residual stress has a very limited effect on the
static crash performance.
The deformation modes corresponding to progressive buckling
modes that occurred at the crashing end of the member are shown
in Fig. 17. As is seen from the figure, the transferring of the data
related to the residual-forming variable to the nominal mesh did
not result in substantial differences in the deformation modes
compared with the results of the analyses based on the deformed
mesh. It should be notice here that even the numbers of lobs are
the same for the cases considered.
Fig. 18 shows the influence of blank holder load values on
the peak crash force value and energy absorption capacity of the
member. This figure reveals that the models containing all the
forming effects and the plastic strain predict much greater values
of the peak crash force and energy absorbed than the
corresponding predictions of models containing residual stresses
and the thickness distributions. On the other hand, the model that
contains thickness variations predicts some decreases in the peak
crash force values as the blank holder load increases. The reason
for this is that an increase in the blank holder load value results in
appreciable increases in the magnitudes of plastic strains and
thickness reductions. When the combined forming effects are
taken into account it may be concluded that the crash load level
may be considered as constant and its value is approximately
equal to the value predicted by the model that uses the nominal
mesh. In terms of the energy absorption capacity, there is no
appreciable change in this capacity for the model that contains
only the residual stress data (Fig. 18(b)). The model with all the
forming effects predicts a nearly constant energy absorption
capacity, which may be considered as independent from the value
of the blank holder load. This behaviour may be attributed to the
fact that the negative effects of the thinning of the member on its
energy absorption capacity are compensated by the increased
plastic strains as the blank holder load is increased. The model
that contains the plastic strains predicts an ever increasing energy
absorption capacity as the blank holder load increases. The
opposite of this behaviour occurs if the model that contains only
thickness variations is used.
As a conclusion it may be stated that if the nominal mesh is
used, the effects of the residual-forming data on the overall quasi-
static crash behaviour of a top-hat section are more apparently
displayed.
5. Conclusions
In this paper, the influences of the residual-forming data on the
quasi-static crash performance of a thin-walled top-hat section
are examined by mapping the forming data into the crash
simulation models. The forming data on the thickness variations,
plastic strains and residual stresses predicted by the deep-
drawing simulation analyses of the section and the effects
of spring-back are considered. The specific conclusions reached
in this numerical study are stated below.
Irrespective of which crash model is used the most influencing
forming parameters on the quasi-static crash behaviour are
plastic strains and thickness variations, the same parameters
that were identified in the studies on the dynamic crash
simulations reported in the literature. The plastic strain
increases rigidity and hence increases collapse resistance of
crash members, whereas the thinning of members adversely
affects these properties. The residual stress has limited effects
on crash performance.
ARTICLE IN PRESS
0
Blank Holder Load (kN)
70
80
90
100
110
120
130
140
150
Peak
Cash
Force
(kN)
All Forming Effects
Plastic Strain
Thickness Distr.
Residual Stress
Geometrical Effect
Nominal Mesh
0
Blank Holder Load (kN)
6
7
8
9
10
11
12
13
Absorbed
Energy
(kJ)
All Forming Effects
Plastic Strain
Thickness Distr.
Residual Stress
Geometrical Effect
Nominal Mesh
400 800 1200
400 800 1200
Fig. 14. Effects of blank holder load on crash performance: (a) variation of the peak
crash force and (b) variation of absorbed energy.
R. Gümrük, S. Karadeniz / International Journal of Mechanical Sciences 51 (2009) 350–362 359

12. ARTICLE IN PRESS
Fig. 15. Mapping of the residual-forming data onto the nominal mesh: (a) thickness mapping and (b) plastic strain mapping.
0
Rigid Wall Displacement (mm)
Rigid
Wall
Crash
Force
(kN)
All Forming Effects
Plastic Strain
Thickness Distr.
Residual Stress
Nominal Geometry
0
20
40
60
80
100
120
Absorbed
Energy
(kJ)
All Forming Effects
Plastic Strain
Thickness Distr.
Residual Stress
Nominal Geometry
0
2
4
6
8
10
Mean
Crash
Force
(kN)
All Forming Effects
Plastic Strain
Thickness Distr.
Residual Stress
Nominal Geometry
0
20
40
60
80
50 100 150 200 250 0
Rigid Wall Displacement (mm)
50 100 150 200 250
0
Rigid Wall Displacement (mm)
50 100 150 200 250
Fig. 16. Predictions of the analyses with the nominal mesh of a member formed by applying a blank holder load of 400 kN: (a) rigid-wall crash force, (b) absorbed energy
and (c) mean crash force.
R. Gümrük, S. Karadeniz / International Journal of Mechanical Sciences 51 (2009) 350–362
360

13. If the nominal mesh is used in the crash model, the effects of
residual-forming data on the overall quasi-static crash beha-
viour are more apparently displayed.
The crash analyses of the model based on the nominal mesh
covering all the residual-forming data considered in this study
predict almost a constant peak crash force and absorbed
energy value even if the residual-forming data change with the
blank holder load. A model that uses the nominal mesh
without the forming data predicts approximately 10% less
amount of absorbed energy than the model with forming data.
In terms of the peak crash force the difference between the two
predictions is less than 5%.
The spring-back effects, which are called as the geometrical
effects, may lead to substantial changes in the crash behaviour.
Due to the spring-back effects the crash models that employ
the deformed mesh in studying the forming effects may not
represent the behaviour as clearly as those with the nominal
mesh.
There are substantial differences among the predictions of the
crash models considering data on a single effect of pre-crash
processes. Therefore, these models can be useful only in the
evaluation of influences of these individual effects.
Although, the analyses carried out in the present study indicate
that the considered residual-forming data do not have very
substantial influence on the quasi-static crash response, a
realistic crash model should contain combined effects of all the
pre-crash processes, i.e. forming data together with the true
geometry of the crash member after the forming and spring-
back processes for achieving reliable simulation results.
It should also be mentioned here that the conclusions drawn
from the current numerical study were based on a particular
material, geometric shape, loading conditions and forming
process. Especially, the results are influenced by the sensitivity
of the strength of the applied materials to plastic deformations
that take place during the forming process. Therefore these
findings might not be true for other materials, geometries and
loading conditions. Experimental works are also needed to verify
these numerical predictions.
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ARTICLE IN PRESS
Fig. 17. Predictions of deformation modes by analyses with the nominal mesh of a
member formed by applying a blank holder load of 400 kN.
0
Blank Holder Load (kN)
80
90
100
110
120
130
Peak
Crash
Force
(kN)
All Forming Effects
Plastic Strain
Thickness Distr.
Residual Stress
Nominal Mesh
6
7
8
9
10
11
Absorbed
Energy
(kJ)
All Forming Effects
Plastic Strain
Thickness Distr.
Residual Stress
Nominal Mesh
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Blank Holder Load (kN)
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Fig. 18. Influences of the blank holder load on crash performance predicted by
analyses with the nominal mesh: (a) peak crash force versus blank holder load and
(b) absorbed energy.
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ARTICLE IN PRESS
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