Study towards invertube
performance during
crash deformation
R.P.J.M.Princen
MT 08.12
TU/e Master Thesis
May 2008
Committee
prof.dr.ir. M.G.D. Geers (Chairman, TU/e)
dr.ir. P.J.G. Schreurs (Coach, TU/e)
dr.ir. V.G. Kouznetsova (Coach, TU/e)
ir. M.P.J. Lambriks (Coach, Corus IJmuiden)
dr.ir. C.H.L.J. ten Horn (Coach, Corus IJmuiden)
Eindhoven University of Technology
Department of Mechanical Engineering
Section Mechanics of Materials
Summary
This thesis presents a study towards invertube performance. A change in the manufacturing
process of the invertube results in failure of the tube during crash deformation. The possible
failure criteria have been discussed in detail. Apart from criteria concerning the deformation
process, e.g. the generation of pre-strains and strain path changes, the geometry of the
invertube, the material and the manufacturing process could also have an influence on the
crash behaviour. Experiments have been done to determine this influence. The results of these
experiments have also been used to validate simulation models in both MSC-Marc/Mentat
and PAM-STAMP. Those models have been developed within this project to reduce the costs
in further research towards invertube performance. The results of the simulations, especially
the force-displacement diagrams and typical deformed shapes, have been compared to the
experimental results for different materials. Because the reduction process could have an
influence on the results, this process has also been implemented in both models. The
simulation results of these extended models matched the experimental results very good. Only
disadvantage of these models is the damage behaviour, which is not yet implemented
accurately. In MSC-Marc/Mentat no suitable damage model is present. The CrachFEM
module within PAM-STAMP gave no unambiguous prediction of failure. The main cause of
this problem is the strain path dependency in the material. Together with the large influence
of the reduction process, these are the main reasons of invertube failure.
In further research it is important to implement an accurate damage model and to focus the
research on the reduction process of the invertube.
2
Contents
Summary .................................................................................................................................... 2
Contents...................................................................................................................................... 3
1: Introduction ............................................................................................................................ 4
2: Invertubes ............................................................................................................................... 6
2.1: Different types................................................................................................................. 6
2.2: Geometry......................................................................................................................... 8
2.3: Working principle ........................................................................................................... 8
3: Possible reasons of failure...................................................................................................... 9
3.1: Manufacturing ................................................................................................................. 9
3.1.1 Tube forming............................................................................................................. 9
3.1.2 Hydroforming............................................................................................................ 9
3.1.3 Spinning .................................................................................................................. 10
3.1.4 Reducing.................................................................................................................. 11
3.2: Strain-path dependency ................................................................................................. 11
3.2.1: Work hardening...................................................................................................... 13
3.2.2: Softening ................................................................................................................ 15
4: Experiments.......................................................................................................................... 16
4.1: Materials........................................................................................................................ 16
4.2: Tube forming................................................................................................................. 17
4.3: Test set up ..................................................................................................................... 19
4.4: Test results .................................................................................................................... 20
4.4.1: Reducing ................................................................................................................ 20
4.4.2: Inversion................................................................................................................. 23
5: Simulation models................................................................................................................ 26
5.1: Model MSC-Marc/Mentat............................................................................................. 26
5.1.1: Material properties ................................................................................................. 26
5.1.2: Yield condition and hardening rule........................................................................ 28
5.2: Model PAM-STAMP .................................................................................................... 29
5.3: Explanation inversion process....................................................................................... 30
5.4: Simulation results.......................................................................................................... 31
5.4.1: MSC-Marc/Mentat ................................................................................................. 32
5.4.2: PAM-STAMP ........................................................................................................ 34
6: The reduction process .......................................................................................................... 36
6.1: Model MSC-Marc/Mentat............................................................................................. 36
6.2: Real reduction process in MSC-Marc/Mentat............................................................... 40
6.3: Model PAM-STAMP .................................................................................................... 42
7: Implementation of damage/fracture ..................................................................................... 45
7.1: Model MSC-Marc/Mentat............................................................................................. 45
7.2: Model PAM-STAMP .................................................................................................... 46
7.2.1: CrachFEM simulation results................................................................................. 47
8: Conclusions .......................................................................................................................... 50
9: Recommendations ................................................................................................................ 51
Appendix A: Other experimental results.................................................................................. 52
Appendix B: PHAST strain measurements .............................................................................. 56
Appendix C: Material PAC-codes............................................................................................ 57
References ................................................................................................................................ 58
3
1: Introduction
Crash safety is becoming more and more an issue within the automotive industry. Official
legislation, insurance requirements and EuroNCap rankings are seriously dictating the design
of a car. The part of a car which has a big influence on the car’s crash behaviour is the socalled crumple zone which is situated in the front and back of the car. The crumple zone in the
front of the car consists mainly of two longitudinals and two crash cans in front of them, as is
shown in figure 1.1. Figure 1.2 gives a schematic representation of the crumple zone.
Figure 1.1: crumple zone in the front of the car
bumper beam
crash cans /
invertubes
engine
longitudinals
Figure 1.2: crumple zone, schematically
During a frontal crash, the bumper beam transfers the load to the crash cans, which absorb an
amount of energy and transfer the load towards the longitudinals. Typical parameters during a
crash are the peak load and the energy absorption. The peak load should be as low as possible,
the energy absorption as high as possible. Another important aspect of implementing a crash
can concerns collisions at very low speeds, approximately 15 [km/h]. In case of such
accidents the crash cans should absorb all the energy, leaving the longitudinals intact. This
energy is the kinetic energy of the car. The energy absorption of the crash cans should be in
the order of 10.000 [J] for a car with mass m = ±1100 [kg] colliding with speed v = 15 [km/h].
In this case only the bumper and crash cans need to be replaced, but not the expensive
longitudinals.
4
A special type of crash can is the so called invertube (inversion-tube). In this master thesis,
research has been done on the working principle of the invertube and the aspects which
influence its performance, because from experiments it is known that for several materials the
invertube will fail during impact and thus will not absorb enough energy. So, the question is:
What is the main reason of failing? And what can be done to prevent this?
In chapter 2 the invertube and its working principle will be explained in detail. Chapter 3
discusses all possible failure criteria of the invertube. The most important experiments are
presented in chapter 4. The results from these experiments will be used to validate simulation
models in MSC-Marc/Mentat and PAM-STAMP, which will be explained in chapter 5. These
models will be extended by a reduction process. The results from these simulations will be
presented in chapter 6. Damage and fracture implementation in both models will be discussed
in chapter 7. At last chapter 8 and 9 will deal with the conclusions and recommendations.
5
2: Invertubes
Crash cans are important components in the whole energy absorbing system. Conventional
crash cans fold, which results in a high first peak in the force-displacement curve, followed by
several lower peaks. The invertube shows a constant deformation process, which results in a
low first peak force and a continuing constant force. This makes the energy absorption per
mass of the invertube much higher than that of the conventional crash can, especially when
the limits are set by the peak loads. In figure 2.1 the conventional crash can and the invertube
are shown together with the typical force-displacement diagrams.
force [N]
force [N]
displacement [mm]
displacement [mm]
Figure 2.1: left: conventional crash can, right: invertube. Below, the corresponding forcedisplacement diagrams.
2.1: Different types
There are different types of invertubes which all have their own advantages and disadvantages
[10]. Different geometries of invertubes for axial impact loading are used. Some of them need
pre-forming and attachments leading to stress concentrations, for example around
attachments. Examples of these invertubes are shown in figure 2.2.
6
Figure 2.2: three invertube geometries
The two geometries in figure 2.3 are the ones which are suitable for use in a car’s crumple
zone because of their crash behaviour and amount of energy absorption. Figure 2.3b, mostly
called the inside-out invertube, works quite well but it cannot be easily implemented in the
car. The bottom part can not be fixed to the bumper or the longitudinal. Besides, extra dies in
the car are needed to control the deformation of the invertube. As a consequence the car
becomes heavier. This is not wanted because of the increasing costs. The one which is finally
used instead of the conventional crash can is the geometry in figure 2.3a.
Figure 2.3: invertube geometries suitable for use in crumple zone
7
2.2: Geometry
Stress-strain response of the invertube material is not only dependent on processes during
deformation of materials, which will be explained later. The geometry of the invertube may
also have an influence on the crash behaviour. Different values of tube diameters and
thicknesses can probably lead to a geometry in which the invertube will no longer fail. Little
research in this field has already been done. This research focussed on the influence of the
amount of reduction on the crash behaviour. Invertubes were made from tubes with two
different diameters (71 and 60 mm) and four different materials (DC04, DP600, TRIP600 and
TRIP700) which will be explained in section 4.1. After reduction, the invertubes have been
tested to investigate their behaviour during a crash. All tubes failed, except for those, which
were made from DC04. Is it possible to stop this failure by watching the geometry of the
invertube? Using different diameter combinations for the invertube could be useful to look at.
Or maybe reduction of the thickness of the tubes could present better performance. A third
option is to look at different combinations of both of these options.
The amount of energy which will be absorbed should also be taken into account. Changing
the geometry of the invertube could have a serious influence on the amount of energy which
can be absorbed by the invertube.
2.3: Working principle
When the selected invertube deforms due to axial loading, the material is consecutively
compressed, bent, stretched and un-bent, and as a consequence deformed along a nonproportional strain path. Several deformed stages during impact are shown and mentioned in
figure 2.4.
First step: compression of the
material and outside bending
of the large diameter
Second step: outside bending
of the small diameter
Last step: small diameter
moves into large diameter due
to stretching of the material
and un-bending around the
corners
(the real inversion process)
Figure 2.4: different strains during impact
8
3: Possible reasons of failure
Besides their geometry, there are several possible causes for the failure of the invertube,
which are all related to the manufacturing process. Manufacturing generates pre-strains in the
material, e.g. during preforming a steel plate into a tube and reducing this tube into an
invertube. Furthermore, the material experiences a lot of strain path changes during forming
and inversion. Every material has its own typical strain-path dependency. In the following
sections these phenomena will be discussed in detail.
3.1: Manufacturing
As mentioned before, in early designs the invertube existed of two tubes of different
diameters which were welded together. Nowadays investigations concentrate on invertubes
made out of one piece of material formed into a tube which gets partly reduced to obtain a
difference in diameters. There are different methods to form an invertube out of one piece of
material. First the forming of a tube out of a steel plate will be described briefly. After that,
three possible methods of forming an invertube out of this tube will be described in detail.
3.1.1 Tube forming
The first stage in the fabrication of an invertube is the tube forming process. In this process a
flat plate is bent into a cylinder form. After that the ends of the plate are welded together. Prestrains will arise in the material due to the tension at the outside diameter, the compression at
the inside diameter of the formed tube and also due to the welding procedure.
3.1.2 Hydroforming
Generally, the hydroforming process can be divided into four phases: filling/preforming, free
forming, calibration and pressure relief. A schematic representation of this process is given in
figure 3.1.
Filling/preforming: During this phase the dies are closed and the tube is filled with liquid. If
the tube is preformed, an internal pressure can be applied to prevent local buckling.
Free forming: The tube expands towards the dies as the pressure increases. In this phase it is
possible to feed material into the expansion zone, and the pressure levels are relatively low.
Calibration: During this phase the pressure is very high and due to frictional forces and tool
geometry no feeding of material into the expansion zone is possible. The axial stroke is only
used to prevent leakage.
Pressure relief: The forming is now completed, and the pressure is decreased. After this phase
the dies are opened.
9
die
water pressure
die
Figure 3.1: schematic representation of the hydroform process
The strain paths during hydroforming depend on the production phase. If feeding of material
is possible, i.e. close to the tube ends during free forming, the strain path will be close to pure
shear. Further away from the feeding zone, the axial material flow will be restrained and
lower flow ability is expected. During calibration, the tube wall will be in contact with the die
and the effect of feeding will be limited due to friction and tool geometry. Thus the extrusion
direction strain will decrease and the strain paths will shift to plane strain. Due to these
processes in hydroforming the thickness of the tube wall varies. The thickness variation along
the circumference of the tube is approximately constant in the tube extrusion direction.
3.1.3 Spinning
Tube spinning is suitable for the manufacturing of a hollow product with an axisymmetric
shape, such as tubular products like the invertube. In the spinning process the tube is rotated
by a motor. A pair of roller tools moves in radial and axial direction. One end of the tube is
locked in the axial direction by a chuck, which is fixed in the axial direction. The other end is
free in the axial direction. Lubrication oil is used to reduce the friction between the roller tool
and tube surface. The roller tools move as follows:
1) Radial indentation: Each of the roller tools indents the tube diametrically by a feed s
at the beginning location.
2) Paraxial travel: The roller tool moves axially towards the free end until over the free
end for a spinning travel.
3) Radial withdrawal: Each of the roller tools withdraws from the tube over a distance s.
4) Axial return: the roller tools return to a new beginning location. The new beginning
location is altered towards the free end in a displacement.
5) New radial indentation: Each of the roller tools indents the tube again in a feed 2s at
the new beginning location.
6) New paraxial travel: The roller tools move axially towards the free end until over the
free end for a new spinning travel.
A schematic representation of the spinning tool is shown in figure 3.2.
10
Figure 3.2: schematic representation of the spinning tool
3.1.4 Reducing
A third possible method to produce invertubes is reducing, which is, compared to
hydroforming and spinning, a relatively cheap method because no expensive tooling is
necessary. For this reason it is for now also the standard production method for invertubes. In
figure 3.3 the working principle of reducing is shown schematically. The reducing tool will be
moved at a speed V towards the tube. During this movement the actual tube radius r1 will be
reduced to radius r2.
invertube
reducing
tool
V
r2
symmetry axis
Figure 3.3: schematic representation of the reducing process
3.2: Strain-path dependency
Compression, bending and stretching of the material during deformation of an invertube leads
to continuous strain path changes, which has a significant effect on the mechanical response
of metals. From experiments it is known that strain path changes can lead to increased
hardening and, on the other hand, softening of the material. In figure 3.4 a so-called forming
limit diagram (FLD) is shown in which different strain-paths are given. The line (1-2-3-4)
shows the strain path of a material which first is exposed to tension, followed by shear and at
last plain strain.
11
Figure 3.4: Forming limit diagram with strain path
Moderate changes of the deformation mode give rise to increased hardening followed by
softening and relatively low hardening, as is illustrated in figure 3.5.
stress
σ2
σ1
σ2
σ1
strain
Figure 3.5: effect of increased reloading yield stress followed by softening and relative low hardening
Deformation histories that include a stress reversal lead to a pronounced so-called
Bauschinger effect, which will be explained later.
All these phenomena can induce necking in the material due to a local drop in stiffness.
The microscopic phenomena associated with strain path changes are commonly understood to
be the occurrence of a dislocation structure in the material and its adaptation to the new
loading [12]. The dislocation cell structure forms under deformation and is observed as a
network of volume elements (e.g. cells) within which the dislocation density is well below
average, mutually separated through boundaries at which dislocations are concentrated. The
morphology of the dislocation structure developed during a particular loading path clearly
depends on the loading characteristics. The dislocation structure is formed to accommodate
the current deformation in a preferential way. After a strain path change, the previously
formed dislocation structure becomes ‘unstable’ under the new loading since its morphology
is not favourable anymore and, moreover; it degenerates by newly activated plastic slip. The
12
resistance and adaptation of the dislocation structure to the loading in a new direction is
typically accompanied by an increased reloading yield stress and a relatively low hardening.
In the following subsections, the work hardening and softening will be described in more
detail.
3.2.1: Work hardening
Work hardening, or strain hardening, is an increase in yield stress due to plastic deformation.
In metallic solids, permanent change of shape originates usually on a microscopic scale by
dislocations which are created by stress. During plastic deformation, many dislocations are
generated within the material. These dislocations influence one another through their stress
fields, which leads to mutual obstruction and therefore to a reduced dislocation mobility.
Generally work hardening is considered to be isotropic or kinematic. During uniaxial loading
the following stress-strain curves are typically observed in case of isotropic hardening (figure
3.6a) and kinematic hardening (figure 3.6b). Kinematic hardening is also known as the
Bauschinger effect. The Bauschinger effect refers to a property of materials where the
material’s stress-strain characteristics change as a result of the microscopic stress distribution
[6]. For example, an increase in tensile yield stress and decrease of compressive yield stress.
While more tensile cold working increases the tensile yield stress, the compressive yield
stress after tensile cold working is actually reduced. The greater the tensile cold working, the
lower the compressive yield stress.
The basic mechanism of the Bauschinger effect is related to the dislocation structure in the
cold worked metal. As deformation occurs, the dislocations will accumulate at barriers and
produce dislocation pile ups and entanglements. Based on the cold worked structure, two
types of mechanisms are generally used to explain the Bauschinger effect. First, local stresses
may be present in the material, which assist the movement of dislocations in the reverse
direction. Thus, the dislocations can move easily in the reverse direction and the yield stress
of the metal is lower. The gathering of dislocations at grain boundaries is the main source of
these so-called back stresses. Second, when the strain direction is reversed, dislocations of the
opposite sign can be produced from the same source that produced the slip-causing
dislocations in the initial direction. Dislocations with opposite signs can attract and annihilate
each other. Since strain hardening is related to an increased dislocation density, reducing the
number of dislocations is less than it would be if the strain had continued in the initial
direction.
stress
stress
σy
σy
d
d
d
strain
strain
d
A
-σy
B
Figure 3.6: A) isotropic hardening, B) kinematic hardening
13
For two- or three-dimensional stress-strain states the difference between isotropic and
kinematic hardening is found in the analysis of the yield surface evolution during this
deformation process [16]. Figure 3.7a shows the change of the yield surface for isotropic
hardening. During loading the surface shape stays the same but it will grow in both stress
directions. In this figure σ1 and σ2 are the principal stresses.
Figure 3.7b shows the kinematic hardening principle during loading. Here again the surface
shape stays the same, but now the yield surface will not grow but will move. This is the
typical behaviour within kinematic hardening.
σ2
σ2
yield surface
yield surface
σ1
σ1
B
A
Figure 3.7: yield surface evolution for, A) isotropic hardening and B) kinematic hardening
In practice, metals show a combination of isotropic and kinematic hardening. So, the yield
surface will simultaneously grow and move in a particular direction. This is also shown in
figure 3.8.
σ2
A
σ1
Figure 3.8: yield surface evolution for combined isotropic and kinematic hardening
14
3.2.2: Softening
Strain softening is, in contrast to strain hardening, a decrease in stress due to plastic
deformation. This principle is shown in figure 3.9.
stress
strain
Figure 3.9: strain softening
15
4: Experiments
The main goal of this research project is to develop a model of the invertube which represents
its behaviour accurately. Test results of experiments are needed to validate such a model. In
this section, these experiments will be explained in detail. First the materials used in this
research will be described together with their behaviour at large deformations. After a short
section on tube forming the test set up will be outlined. At last the most relevant test results
will be shown, including the tests with DC04 from which the forming strains have been
measured. More experimental results can be found in appendix A.
4.1: Materials
There were different steels available for this project at Corus IJmuiden. Each steel has its own
specific characteristics and the question was whether these properties correspond to what is
prompted by the deformation process of the invertube. Later on, these material properties will
also be used in the MSC Marc and PAM-STAMP model.
The materials that have been used in this study are DC04, DP600, DP800dpx, TRIP600,
TRIP700, a stainless steel and two types of HSD. For each steel the composition and the
specific properties in relation to the other steels will be described briefly. The exact values of
the different material properties together with the stress-strain curves will be given later, in
chapter 5, where the models are described.
DC04:
This is cold rolled steel for forming e.g. deepdrawing. This material has the best formability
of all due to the smallest amount of carbon which it contains. (With a large amount of carbon,
the formability of the material decreases.) The composition of the DC04 steels is 100%
ferrite. Furthermore, this material has a low yield strength, which decreases the possibility of
buckling instead of reducing or inverting.
DP600/DP800dpx:
DP materials are steels with a dual phase microstructure consisting of a fine dispersion of hard
martensite particles in a soft pure ferrite matrix. A schematic representation of the material
structure is shown in figure 4.1a. The martensite phase is quite hard and difficult to deform.
DP’s also have a larger amount of carbon then DC04. These two things result in a material
with higher yield strength but a smaller plastic strain before breaking. The numbers 600 and
800 stand for the tensile strength of the materials in [MPa]. The addition ‘dpx’ is added to
indicate that this kind of DP800 has a better deformability than the normal DP800.
16
A
B
Figure 4.1: Schematic representation of the material structure for: A) DP’s, B) TRIP
TRIP600/TRIP700:
This material consists of four phases of which three are most important: ferrite, austenite and
martensite. The fourth one is bainite, which is a little softer than martensite. A schematic
representation is shown in figure 4.1b. During deformation the soft austenite in the TRIP
material transforms into martensite which is much harder than austenite. Because of the
austenite and the amount of carbon, which is a little less present than in DP’s, the TRIP steels
normally have a better deformability. Again the numbers 600 and 700 indicate the tensile
strength in [MPa].
Stainless steel:
This material consists of 100% austenite steel, which has a very good deformability, just like
DC04. However, the 100% austenitic stainless steel has a much higher yield strength than
DC04. A problem which may occur is buckling instead of reducing or inverting. Small
reduction steps during fabrication of the invertubes are therefore very important.
HSD:
HSD is a high strength steel with an excellent formability which also consists of 100%
austenite. The yield stress is about 900 MPa, which is much higher than DC04 and the
stainless steel variant. Because at Corus the welding process of the tube is not yet optimised
the weld remains a weak spot at the moment.
4.2: Tube forming
The tubes that are used in this research were produced at Corus IJmuiden. The production
process is already explained. It is clear that this process has an influence on the performance
of the invertube. Forming the tube out of a piece of steel plate implies straining of the
material. To visualize and quantify these strains a technique developed by Corus IJmuiden
called “Phast” is used. The working principle of this technique is described in more detail in
Appendix B.
From the experimental results it will become clear that DC04 is the only material, used in this
research project, with a good performance during inversion. Therefore, DC04 is used to
determine the strains in the invertube.
17
Tube forming is the first step in producing an invertube. A gridded sheet DC04 has been bent
into a tube-like shape and after that the sheet ends have been welded together. After cutting
the tube through the cross-section as shown in figure 4.2 becomes visible.
Figure 4.2: tube cross-section after forming
With this cross-section it is possible to measure the strains at the material surface after
forming, using the Phast-technique. Figure 4.3 shows the major and minor strains in the
material after tube forming. These are the principal strains. Here, the minor strains are the
strains in radial direction and the major strains are the strains in longitudinal direction.
Figure 4.3a shows that the strains in longitudinal direction, after tube forming, are close to
zero. From figure 4.3b it is clear that most strains in radial direction are negative due to
compression, except for some strains at one edge of the cross section. These are strains due to
the cutting process. The test piece has been cut from a larger tube. This cutting causes strains
which should not be taken into account in determining the strains from tube forming.
A
Figure 4.3: Phast results:
B
A) Major strains: min.=-0,026; max.= 0,048 ,
B) Minor strains: min.=-0.198; max.=-0.013
18
4.3: Test set up
A pressure bench, to perform the experiments, is available at Corus Ijmuiden and is shown in
Figure 4.4a. Figure 4.4b shows a schematic representation of the set up. The pressure bench
consists of a plateau (A) on which the test piece is placed. Also the reducing rings can be
placed within this plateau (a close up of the plateau is shown in Figure 4.5). The top of the
pressure bench (B) stays fixed. In other words, part A moves towards or away from part B
along a vertical line. This movement can be controlled by a computer which is directly
connected to the bench.
B
A
A
B
Figure 4.4: a) pressure bench at Corus Ijmuiden, b) schematic representation
Figure 4.5: close up of the pressure bench plateau
This layout is used both for reducing the uniform tube into an invertube and for the quasi
static performance test in which the invertube will be tested.
The plateau at the bottom will be moved upwards, to make the uniform tube partly reduced or
inverted. Sensors, which are connected to the computer, measure the reaction force on the
plateau during this displacement. By combining the displacement and reaction force into one
graph it is possible to determine the energy absorption during the test. This gives an
impression of the performance of the invertube. If the invertube fails during the test, this is
also visible in this graph because the force then drops to zero very quickly.
19
4.4: Test results
Because of the large amount of test data only the most important results will be presented here
in detail. The chosen results are strongly related to the geometry of the invertube in the
simulation models of MSC-Marc/Mentat and PAM-STAMP. The 71-57 mm diameter
combination is modelled in these simulation programs which will also become clear from
chapter 5. To be able to compare the simulation results with the test results it is important to
have the same geometry in both the model and the test piece. First the forces acting on the
material during reduction will be shown and after that the strains which originate from these
deformations will be presented in more detail. The experimental reduction forces of the other
diameter combinations will be presented in Appendix A.
4.4.1: Reducing
Before the invertubes can be tested for their performance during the quasi-static test on the
pressure bench, the uniform tubes need to be formed by reducing them partially. The tubes all
have a uniform length between 280 and 300mm. The Reduction is done with reduction rings
of various internal diameters. So, it will be possible to create invertubes with different
diameter ratios. The reduction rings have diameters 68mm, 65mm, 60mm, 57mm and 48mm.
Fabrication of the invertube from the uniform tubes will be controlled by a computer. The
reaction force and the total displacement will be measured, from which force-displacement
diagrams can be produced. Some diameter ratios cannot be realised in one single step. In that
case it will be necessary to use subsequent reduction steps to reach the requested diameter
ratio. Applying the first reduction step will always be accomplished by a displacement of
140mm. This means that the invertube will get a smaller diameter over a length of 140mm.
Every next reduction step owns the difficulty to determine exactly the end of this step.
Stopping the reduction too early will result in a transition between the two diameters which is
not fluent, but stopping it too late may extend deformations at places where they are not
considered desirable. To avoid this, the following reduction steps will be accomplished by a
displacement of only 130mm by computer and after that they will still be adjusted manually if
necessary, so that it will be possible to measure the forces during reduction.
The reduction data for the most important experiments are given below in figure 4.6. As
mentioned before, only the test results of the 71-57 mm diameter configuration will be
presented. Every representation will be explained in detail in order to get a good
understanding of the forces acting on the tubes. This information will also be used in chapter
6, in which the implementation of the reduction steps into the MSC-Marc/Mentat model will
be explained.
20
reduction DP600
60
20
50
force (kN)
force (kN)
reduction DC04
25
15
10
71-65
65-60
60-57
5
0
0
50
100
displacement (mm)
40
30
71-65
65-60
60-57
20
10
0
150
0
reduction DP800dpx
50
100
displacement (mm)
150
reduction TRIP600
120
80
100
force (kN)
force (kN)
60
80
60
40
0
0
50
100
displacement (mm)
71-65
65-60
60-57
20
71-60
60-57
20
40
150
0
0
50
100
displacement (mm)
150
Figure 4.6: reduction 71-57 invertube for DC04, DP600, DP800dpx, TRIP600
For DC04 the reduction forces are lowest with respect to the other materials. Reason for that
is the low yield stress. DC04 has a very good formability, but that can also cause some
problems in the reduction process. When the reduction steps are too large there is a chance of
buckling. For that reason three reduction steps are used to produce the 71-57 mm DC04
invertube, i.e. 71-65, 65-60 and finally 60-57.
The DP600 tube has also been reduced in three steps using the same reduction steps. Reason
for this choice is the same as for DC04 reduction. The buckling of the tube for this material is
again a serious problem if the tube gets reduced in only two steps.
The DP800dpx tube is a lot stronger than the DC04 and DP600 tube. For that reason it has
been tried to reduce the tube in only two steps. This worked quite well. It should be clear from
the reduction graphs that the first step generates a much larger force than the second, but the
tube does not buckle during this process.
Because of the phase transformation in TRIP600 during large deformations it was not clear
how this material would react on the reduction process. For this reason these tubes are also
reduced in three steps.
21
When taking a closer look at the graphs some interesting things can be concluded. The
reduction forces for DC04 and DP800dpx decrease for the second and third step and the
forces for DP600 and TRIP600 increase a little. The decrease simply originates from the
smaller diameter reduction of the following steps. The reduction steps of DP600 and TRIP600
are the same as in case of DC04 reduction, but here an increasing trend can be noticed. For
TRIP600 this increase can be ascribed to the phase transformation during deformation.
Austenite transforms in martensite which is much stronger. The increasing trend in DP600
can be ascribed to the hardening of the material. The hardening curve of DP600 is a lot
steeper than the DC04 curve, especially at low plastic strains. The influence of hardening is
much larger for DP600.
Other interesting results are the strains which originate from the deformations in the material
due to the reduction process. The same procedure and material as mentioned in the tube
forming section has been used to determine these strains. First the tube, which got gridded
before its forming, got partly reduced. After that the produced invertube has been cut
overlong and the cross-section, which is used to measure the strains with Phast, is shown in
figure 4.7.
Figure 4.7: invertube cross-section after reducing, at transition point
With this cross-section it is again possible to measure the strains at the material surface after
the reduction process with the Phast-technique. Figure 4.8 shows the major and minor strains
in the material after reduction. The directions of these principal strains are again the
longitudinal respectively the radial direction.
A
Figure 4.8: Phast results:
B
A) Major strains: min.=-0,032; max.= 0,143 ,
B) Minor strains: min.=-0.272; max.=-0.015
22
Figure 4.8a shows positive strains in longitudinal direction in the reduced part of the tube. The
tube becomes longer due to the reduction process. Figure 4.8b shows again the strains in
radial direction, which are all negative due to the compression from the reduction process.
4.4.2: Inversion
After the invertubes are produced from one or more reduction steps the pressure bench is used
to test their performance. The invertubes are placed in the bench and instead of a reducing
ring now a massive plate is placed on the plateau. When the plateau is moving upwards the
invertube will start to invert. This movement of the plateau is again controlled by the
computer. The head of the pressure bench is fixed again. The displacement is prescribed by
the computer and again the reaction force of the invertube on the plateau will be measured.
These measurements together with the displacement result in force-displacement diagrams
which are interesting to use as reference for the performance. These diagrams can be
compared later with diagrams which follow from the inversion simulations in MSCMarc/Mentat and PAM-STAMP.
The data for the most important experiments are shown in figure 4.9. Again the 71-57 mm
diameter combination will be explained in detail. All other experimental results can be found
in Appendix A.
The following force-displacement diagrams give a view in the performance of the different
materials in invertube application. It is clearly visible that a stable force level, which
determines the energy absorption during inversion, is only reached by DC04. The area below
the diagrams indicates the energy which can be dissipated during the inversion process.
The first peaks are interesting to mention during the model validations, but in reality those
peaks will not be visible in a car crash. This first part of the inversion process is still forming
the tube into an invertube.
23
inversion DP600 71-57
120
50
100
40
80
force (kN)
force (kN)
inversion DC04 71-57
60
30
invertube 2
invertube 3
invertube 4
20
10
0
0
50
100
displacement (mm)
invertube 3
invertube 4
invertube 5
invertube 6
60
40
20
0
150
0
inversion DP800dpx 71-57
10
20
displacement (mm)
30
inversion TRIP600 71-57
150
140
invertube 1
invertube 2
invertube 3
120
100
force (kN)
force (kN)
100
50
invertube 2
invertube 3
invertube 4
invertube 5
invertube 6
80
60
40
20
0
0
10
20
displacement (mm)
30
0
0
10
20
30
40
displacement (mm)
50
Figure 4.9: inversion 71-57 for DC04, DP600, DP800dpx, TRIP600
From the force-displacement diagrams of DC04 it is clear that the material has a good
performance during inversion. The invertube does not fail during inversion. But the stable
force level is about 40 [kN], which is too low for application in a car’s crumple zone. The
surface below the force-displacement diagram determines the energy absorption. As
mentioned in the introduction, the kinetic energy of a car at low speeds is about 10.000 [J]. A
force level of 40 [kN] leads to an inversion length of 0.25 [m]. This means that an invertube
length of 0.5 [m] is needed. This is way too long for implementation in the crumple zone of a
car.
From the force-displacement diagrams of the DP-materials it is clear that the invertube fails
during inversion. But the results show good reproducibility. Therefore these results can
indeed be used to validate the simulation models which will be described later.
From the TRIP600 test results can also be concluded that the invertube fails during inversion,
but the results can also be used to validate the simulation models due to good reproducibility,
except of invertubes three and four. Invertube four was already inverting a little during the
reduction process from which follows that the first peak is a lot lower and the second peak
starts a little earlier than it used to start. Invertube three has a different kind of behaviour,
which is more or less a coincidence. This behaviour is probably related to the phase
transformation in TRIP600 which is not equal for every single invertube.
24
A second interesting result of the experiments is the deformed shape after inversion. This
shape can be compared later with those resulting from the simulations. To get a good view of
the deformation it is necessary to cut the invertube overlong as is shown in figure 4.10.
Figure 4.10: invertube cross-section after inversion
With this gridded cross-section it is once again possible to measure the strains at the material
surface after inversion with the Phast-technique. Figure 4.11 shows the major and minor
strains in the material after reducing. Once more these strains are the principal strains in
longitudinal respectively radial direction. Figure 4.11a shows that the strains in longitudinal
direction are much larger now due to the inversion process, especially in the bending area. In
the figure also two white bands are visible. At these bands the strains are unknown. It was not
possible to measure them. In case of the upper band, the strains are too large to measure them
with this grid. The lower band originates from missing grid points. These points are now
below the material surface due to the inversion process. Figure 4.11b shows that the radial
strains do not change very much regarding the reduction process.
A
B
Figure 4.11: Phast results:
A) Major strains: min.=-0,025; max.= 0,271 ,
B) Minor strains: min.=-0.302; max.=-0.020
25
5: Simulation models
One of the goals of this project is to develop validated models of the invertube in MSCMarc/Mentat and PAM-STAMP. To achieve this, the models first need to be generated and all
the material parameters together with yield locus and hardening rule need to be implemented.
Because failure of the invertubes during the tests is one of the research issues, it is also
important to model the damage behaviour of the invertube. After this modelling the
simulation results need to be compared with the results of the experiments which have been
presented before. The most important reason for developing such models is that once a model
is available, it is no longer necessary to do that many tests to find out a good design which is
much more expensive.
5.1: Model MSC-Marc/Mentat
The existing MSC-Marc/Mentat model for the analysis of the invertube was too simple
concerning material properties and damage implementation. The model gave no accurate
information about the damage behaviour and it was not clear what yield criterion and
hardening rule should be implemented. The model consisted of an axisymmetric
representation of the invertube with a wall thickness of 1.5 mm corresponding to the thickness
of most invertubes used during the experiments at Corus. In figure 5.1 the geometry of the
invertube which was modelled and analysed, is shown.
displacement
30mm
90mm
t = 1.5mm
7mm
210mm
Figure 5.1:geometry of the MSC-Marc/Mentat model
Material properties such as yield conditions, hardening rule and specific stress-strain curves
together with the yield stress of different steels are implemented. The way of implementation
will be explained in detail.
5.1.1: Material properties
Every material has its specific material properties. All those material properties also need to
be implemented in the model. For the steels, which are used in this research, all the different
properties are listed in table 5.1. The stress-strain curves which have been implemented in the
model are given in figure 5.2. All these material parameters and stress-strain curves are taken
from so-called Vegter models which are developed by Corus IJmuiden. These models
describe the yield conditions of the materials obtained from experiments. Normally these files
26
are used for implementation in PAM-STAMP models to prescribe the material behaviour.
Later on in this study, these files will also be implemented in the PAM-STAMP models.
Table 5.1: Material parameters
DC04*
DP600*
DP800dpx*
TRIP600*
TRIP700*
E [N/m2]
2.1e11
2.1e11
2.1e11
2.1e11
2.1e11
ν[-]
0.3
0.3
0.3
0.3
0.3
ρ[kg/m3]
7800
7800
7800
7800
7800
R_0[-]
2.1537
0.949
0.763
0.99
0.785
R_45[-]
1.3154
0.8404
1.041
0.908
0.856
R_90[-]
2.1942
1.1658
0.874
1.233
0.895
σy[MPa]
137
380
-------------
K[-]
--------1229
1086
1254
n[-]
--------0.104
0.31177
0.145
ε0[-]
--------0.00235
0.019
0.00049
Where E is the Young’s modulus [N/m2], ν is the Poisson ratio, ρ is the density [kg/m3] of the
material. R_0, R_45 and R_90 are the Lankford coefficients which are used for the Hill ’48
yield criterion. These parameters describe the anisotropy in three different directions within
the material.
R=
ε width
ε thickness
, σy = yield stress [MPa]
(1, 2)
For DC04 and DP600 the stress-strain curve was given by a table of values in strain against
stress. For DP800dpx, TRIP600 and TRIP700 a so-called Krupkowsky law was used for the
n
(3)
stress-strain curve: σ = K (ε + ε 0 )
, of which the parameters K, ε0 and n are listed in the table.
Static tensile curves of the different tested materials
1.4
1.2
True stress
1
0.8
0.6
DC04
DP600
DP800dpx
TRIP600
TRIP700
0.4
0.2
0
0
0.1
0.2
0.3
0.4
0.5
0.6
True strain
0.7
0.8
0.9
1
Figure 5.2: stress-strain curves implemented in simulation models
* The Corus PAC-Codes are listed in Appendix C.
27
5.1.2: Yield condition and hardening rule
The geometry of the invertube is modelled and the first material properties are implemented.
The next step is to find a combination of yield criterion and hardening rule which gives the
best results for this kind of simulations. The two most widely used yield criteria for steels are
the Von Mises criterion, the Hill ’48 criterion and the Barlat criterion. Due to very bad
convergence the Barlat criterion simulations have been cancelled. The two other criteria will
be tested to see if one of them gives results which match with the results of the tests. Together
with this choice it is also important to discuss which hardening rule gives the best results,
isotropic hardening or kinematic hardening. To find out which combination is the best in this
kind of simulations, the experimental results of two materials, DP600 and DC04, were used.
Reason for this choice was that the results of the other experiments were not yet available at
that time. The results of the simulations and the experiments, which have been compared, are
the force-displacement curves and the geometry after deformation. In the force-displacement
curves especially the first peak force and the constant force during the real inversion are
compared with the results from the tests. The total shape of the curves will be discussed in
section 5.3. The upper graph in figure 5.3 shows the different force-displacement curves of
DP600. The lower graph shows the force-displacement curves of DC04. The curves for
Hill’48 with kinematic hardening are missing because this configuration did not converge to a
solution. From the diagram of DP600 it is clear that Von Mises and Hill’48, both with
isotropic hardening, do not differ very much. The reason is that the R-values for DP600 are
very close to one. It is known that Hill’48 with all R-values = 1 represents the Von Mises
criterion. In case of the DC04 steel the differences are much larger. The R-values of DC04
deviate more from R = 1.
DP600 71-57 comparison
120
Von Mises iso
Von Mises kin
hill iso
experiment
100
force (kN)
80
60
40
20
0
0
10
20
30
40
displacement (mm)
50
60
70
DC04 71-57 comparison
60
Von Mises iso
Von Mises kin
hill iso
experiment
50
force (kN)
40
30
20
10
0
0
20
40
60
80
displacement (mm)
100
120
140
Figure 5.3: force displacement diagrams from simulations with different yield locus and hardening
rule.
28
From both graphs of the Von Mises yield criterion combined with kinematic hardening it is
obvious that results from simulation and experiment totally disagree. The forces are much too
low. When all these results are compared with the experiments it is clear that the Hill’48
criterion with isotropic hardening would be the best choice. From now on the model with the
implementation of the Hill’48 yield criterion combined with isotropic hardening will be used.
Experiments will be used to validate this model for all present materials.
5.2: Model PAM-STAMP
The developed MSC-Marc/Mentat model is a 2-dimensional representation of an invertube.
PAM-STAMP will be used to produce a 3-dimensional model. In MSC-Marc/Mentat also 3dimensional models can be created but due to the implicit calculation method the CPU time of
the model will increase exponentially. PAM-STAMP uses an explicit calculation method
which decreases the CPU time a lot.
The axisymmetric geometry of the invertube in MSC-Marc/Mentat is used to develop the 3dimensional geometry in PAM-STAMP. One quarter of the invertube is modelled to decrease
the simulation time. Two symmetry planes are added to achieve this. At last the crash die is
implemented. The final model is shown in figure 5.4.
A
B
Figure 5.4: geometry of the invertube model in PAM-STAMP. A)with symmetry planes and crash die,
B) geometry isolated
After this modelling the Vegter material models, which have already been mentioned, are
implemented. Due to this, the implemented material properties like the density, Poisson’s
ratio and Young’s modulus are exactly the same in both the MSC-Marc/Mentat and PAMSTAMP model. In these files also the yield conditions and hardening rule are implemented.
These differ a little from the ones implemented in the MSC-Marc/Mentat model. In MSCMarc/Mentat the Hill’48 yield locus is used and in PAM-STAMP the Vegter yield locus is
implemented. Some parameters with respect to the yield locus are also used in the MSCMarc/Mentat model, like the R-values.
29
5.3: Explanation inversion process
At this moment, the models are complete and are ready to be compared with the results from
the experiments. But before this comparison will take place, the typical shape of the forcedisplacement curves in combination with the deformed shape of the geometry will be
explained more in detail. The force-displacement curves have a typical shape and they always
show several peaks, both in the simulations and in the tests. This typical shape will be
explained by looking for the corresponding deformed shape at some interesting points within
the curve. The following pictures, figure 5.5 and table 5.2, show for different points on the
curve the typical deformed shape of the invertube, both for the tests and the simulations. In
this way it is possible to get a feeling for what exactly happens during inversion.
Figure 5.5: interesting points on the typical force-displacement curves during inversion. A) first peak,
B) second peak, C) stable inversion
30
Table 5.2: Explanation inversion process with DC04 steel
A
B
C
Experiment
Simulation
MSC Marc
/Mentat
Simulation
PAMSTAMP
The first peak force in the force-displacement diagrams (A) is due to the outward bending of
the tube part with the large diameter to make it easier for the part with the small diameter to
invert into this first part. Until the second peak (B) the small part moves towards the large
part. At the second peak, the two parts of the invertube touch each other. Due to friction the
force rises again and tries to find a stable force level. The behaviour of the invertube at this
stable force level (C) is called the inversion process.
5.4: Simulation results
The MSC-Marc/Mentat and PAM-STAMP simulation results will now be compared with the
experimental test results which are already known from chapter 4. For this comparison the
force-displacement diagrams will be used. Also the geometry of the invertubes after inversion
will be presented to show the behaviour of the invertube for different materials.
31
5.4.1: MSC-Marc/Mentat
In figure 5.6 the results of the MSC-Marc/Mentat inversion simulations are shown together
with the already known results from the experiments. From this comparison it can be
concluded that for the DP-steels the simulations fit the experimental results quite good. The
timing of the peaks is good and the values of the peak forces correspond quite well with the
values from the experiments. For DC04 the timing of the peaks from the simulations also
conforms to the experimental results, but the values of the corresponding peak forces are a
little lower than the values form the tests. Reason for this could be the reduction process,
which has not been taken into account in the simulation model. By implementing this process
the peak forces will rise due to the work hardening which is also working on the model. Due
to this the peak forces probably fit better with the experimental values.
The differences in results for TRIP600 are related to the phase transformations in the material
at large deformations. This phase transformation, in which austenitic steel transforms into
martensitic steel, can not be modelled in MSC-Marc/Mentat.
inversion simulations DP600 71-57
120
50
100
40
80
30
MSC Marc/Mentat
invertube 2
invertube 3
20
10
0
0
50
100
displacement (mm)
force (kN)
force (kN)
inversion simulations DC04 71-57
60
MSC Marc/Mentat
invertube 3
invertube 4
60
40
20
0
150
0
inversion simulations DP800dpx 71-57
80
inversion simulations TRIP600 71-57
150
140
MSC Marc/Mentat
invertube 1
invertube 2
120
50
MSC Marc/Mentat
invertube 2
invertube 5
100
force (kN)
100
force (kN)
20
40
60
displacement (mm)
80
60
40
20
0
0
20
40
60
displacement (mm)
80
0
0
20
40
60
displacement (mm)
80
Figure 5.6: Comparison of MSC-Marc/Mentat inversion simulations with experimental results for:
A) DC04, B) DP600, C) DP800dpx, D)TRIP600
In figure 5.7a to 5.7d the end geometries of the simulation models are given for all four
materials. Because there is no damage included in the models, the simulations do not indicate
32
the failure of the DP- and TRIP600-steels. Figure 5.8 shows the shape of DC04 from the
experiments. The shape of the simulation models match quite well with the shape from the
experiments.
A
B
C
D
Figure 5.7: Different invertube shapes at the end of inversion. A) DC04, B) DP600, C) DP800dpx,
D) TRIP600.
Figure 5.8: Cross-section of the invertube after inversion, for DC04
33
5.4.2: PAM-STAMP
In this section the PAM-STAMP simulation results will be compared with the results from the
experiments. In figure 5.9 not only the experimental results but also the MSC-Marc/Mentat
simulation results are shown together with the results from PAM-STAMP. From the
comparison it can again be concluded that the simulation results for the DP-steels fit the
experimental results quite well. The timing of the peak forces is good. Only difference is the
single peak point in the PAM-STAMP results which is a lot higher as expected. Furthermore,
the differences for DC04 and TRIP600 are also visible. The reasons for these differences are
the same as for the MSC-Marc/Mentat model.
inversion simulations DP600 71-57
120
50
100
40
80
30
MSC Marc/Mentat
PAM STAMP
invertube 2
invertube 3
20
10
0
0
50
100
displacement (mm)
force (kN)
force (kN)
inversion simulations DC04 71-57
60
MSC Marc/Mentat
PAM STAMP
invertube 3
invertube 4
60
40
20
0
150
0
inversion simulations DP800dpx 71-57
80
inversion simulations TRIP600 71-57
200
140
100
MSC Marc/Mentat
PAM STAMP
invertube 2
invertube 5
120
100
force (kN)
MSC Marc/Mentat
PAM STAMP
invertube 1
invertube 2
150
force (kN)
20
40
60
displacement (mm)
80
60
40
50
20
0
0
20
40
60
displacement (mm)
80
0
0
20
40
60
displacement (mm)
80
Figure 5.9: Comparison of PAM-STAMP model results with experiments and MSC-Marc/Mentat
model.
Besides the comparison of the force-displacement diagrams also the deformed shape of the
invertube simulations with PAM-STAMP will be compared with the shape of DC04 after
inversion from the experiments. The shapes of the different materials which are simulated
with PAM-STAMP are shown in figure 5.10a to 5.10d. The shapes of the inversion strongly
relate to the simulations from MSC-Marc/Mentat.
34
A
B
C
D
Figure 5.10: Different invertube shapes at the end of inversion. A) DC04, B) DP600, C) DP800dpx,
D) TRIP600.
35
6: The reduction process
The inversion simulation results in both MSC-Marc/Mentat and PAM-STAMP match the
results of the experiments for DP-steels already pretty good. For DC04 and TRIP600 the
differences are larger. For TRIP600 it is known that there is a phase transformation in the
material during deformation which is not possible to simulate in this model. The differences
in DC04 may be ascribes to the reduction process, which is not yet taken into account. By
adding the reduction process to the simulation models, the existing peaks should rise due to
hardening. The results of these simulations will be outlined in this section, both for the MSCMarc/Mentat and PAM-STAMP model.
6.1: Model MSC-Marc/Mentat
Adding the reduction process should result in an upward shift of the force-displacement
diagram. The peaks and the stable inversion level should both be higher. Due to this the
diagrams for DC04 simulation and experiment should match better. For the DP-steel results
this could have a negative effect, because they already matched quite well with the
experimental results. The modified model is shown in figure 6.1.
crash die
30mm
L = 200mm
t = 1.5mm
reduction tool
displacement
Figure 6.1: Modified MSC Marc model, reduction included
The reduction process implementation is a little simplified, which can be observed from the
figure. During the experiments more reduction steps were needed, but due to the large CPU
time the number of steps has been reduced to one.
First the DP-steels will be simulated to find out what the influence of this implementation is
on the results, because those fitted best in the earlier simulations. After that, the results of
DC04 and TRIP600 will be shown.
The resulting force-displacement diagrams from the simulations including the reduction step,
compared to those from the experiments and earlier simulations are shown in figure 6.2, for
DP600, and figure 6.3, for DP800dpx.
36
DP600 inversion comparison
140
experiment
MSC Marc/Mentat without reduction
MSC Marc/Mentat reduction included
120
force (kN)
100
80
60
40
20
0
0
10
20
30
40
50
60
displacement (mm)
70
80
90
Figure 6.2: DP600 comparison simulations - experiment
DP800dpx inversion comparison
180
experiment
MSC Marc/Mentat without reduction
MSC Marc/Mentat reduction included
160
140
force (kN)
120
100
80
60
40
20
0
0
10
20
30
40
50
60
displacement (mm)
70
80
90
Figure 6.3: DP800dpx comparison simulations – experiment
From these graphs it is clear that for DP600 and DP800dpx with reduction included the peak
forces are indeed higher. The reduction has a positive effect on the DP600 performance. The
forces are higher compared to the experimental results but the difference between simulation
and experiment has become smaller. For DP800dpx, the implementation of the reduction
37
process has a slightly negative effect. The earlier simulation results already matched very well
with the experiments. The peaks are now too high. Possible reasons for this difference will be
explained later on in this section.
The implementation of reduction into the model of DC04 gave some problems. It was not
possible to reduce the material in one step. The model started buckling at the end of the tube.
For that reason one extra reduction step had to be added. The results of this simulation are
shown in figure 6.4. The force-displacement diagram now matches the results of the
experiments much better due to the reduction implementation. The first peak force is similar
to the peak from the experiments, the visibility of the second peak improved and the
simulation seems to move to a stable force level corresponding to the one from the
experiments. Only disadvantage is the fact that the second peak is a little bit too high. Possible
reasons for that will also be explained later on in this section, together with the differences in
the DP600 and DP800dpx comparisons.
DC04 inversion comparison
60
experiment
MSC Marc/Mentat without reduction
MSC Marc/Mentat reduction included
50
force (kN)
40
30
20
10
0
0
20
40
60
80
displacement (mm)
100
120
140
Figure 6.4:DC04 comparison simulations – experiment
The last material which has been modelled in MSC-Marc/Mentat is TRIP600. The forcedisplacement diagrams from the earlier simulations, without reduction, did not match with the
results from the experiments. The simulated forces were much too low regarding the
experiments. Reason for that was the phase transformation in the material from austenite to
martensite. The main difference between those two phases is the strength. Martensite is a lot
stronger than austenite. Adding the reduction process within the simulation provides the same
problems such as described for DC04. Reducing in one step is not possible due to buckling of
the tube during the reduction step. After implementing a second reduction step the model does
not buckle anymore. The force-displacement diagram moves towards the experimental result
which is shown in figure 6.5. But from this graph it is clear that the peak forces are still not
high enough.
38
TRIP600 inversion comparison
140
experiment
MSC Marc/Mentat without reduction
MSC Marc/Mentat reduction included
120
force (kN)
100
80
60
40
20
0
0
10
20
30
40
displacement (mm)
50
60
70
Figure 6.5: TRIP600 comparison simulations – experiment
As said before, the peak forces now are too high both for the DP-steels and DC04, especially
the second peak. This peak could probably be lowered by implementing a second reduction
step. Due to this second reduction step the deformations are not as high as before, which
should lead to a more accurate calculation of the simulations results. Also the stresses in the
material will be less high which could lead to the lower forces. For DC04, this second step
already has been implemented, but for the DP-steels this second step still needs to be
implemented. The results of these simulations should give some insight in the influence of the
number of reduction steps on the behaviour of the invertube during inversion. The upper
graph in figure 6.6 shows the differences of the resulting force-displacement diagrams for
DP600 between one reduction and two reduction steps. The lower graph shows the
differences for DP800dpx.
39
DP600 inversion comparison
force (kN)
150
experiment
MSC Marc/Mentat without reduction
MSC Marc/Mentat reduction included
MSC Marc/Mentat reduction twice
100
50
0
0
10
20
30
40
50
displacement (mm)
60
70
80
90
DP800dpx inversion comparison
200
experiment
MSC Marc/Mentat without reduction
MSC Marc/Mentat reduction included
MSC Marc/Mentat reduction twice
force (kN)
150
100
50
0
0
10
20
30
40
50
displacement (mm)
60
70
80
90
Figure 6.6: comparison results:DP600 and DP800dpx
From these results it is clear that the number of reduction steps has a significant effect on the
behaviour of the invertube during inversion. The second peak force is for both DP-steels
lower after introduction of a second inversion step. From this, it should be useful to simulate
the reduction process with the same number of reduction steps as used in the experiments. In
the next section the results of these simulations will be presented.
6.2: Real reduction process in MSC-Marc/Mentat
It is known now that the number of reduction steps in the MSC-Marc/Mentat model has an
influence on the force-displacement results during inversion. In order to compare the
simulation results and the results of the experiments correctly, it should be useful to simulate
the exact reduction process from the experiments.
Most of the invertubes have been created by three reduction steps, except DP800dpx which
has been reduced by 2 steps. To get a good comparison of the results the model needs to be
extended by the actual number of reduction steps. Together with the number of reduction
steps it is also important to simulate the same reduction diameters of every step. In table 6.1
the experimental reduction steps of all materials are given. These values are also used in the
MSC-Marc/Mentat model.
40
Table 6.1: reduction steps from experiments
Material
DC04
DP600
DP800dpx
TRIP600
Step 1 [mm]
71 – 65
71 – 65
71 – 60
71 – 65
Step 2 [mm]
65 – 60
65 – 60
60 – 57
65 – 60
Step 3 [mm]
60 – 57
60 – 57
****
60 – 57
The results of these simulations, the simulations without reduction, the results from the
simulations with only one reduction step and the experimental results are shown in figure 6.7.
DC04 reality reduction
DP600 reality reduction
60
140
50
120
100
force (kN)
force (kN)
40
30
20
experiment
MSC Marc without reduction
MSC Marc reduction included
MSC Marc reduction reality
10
0
experiment
MSC Marc without reduction
MSC Marc reduction included
MSC Marc reduction reality
0
50
100
displacement (mm)
80
60
40
20
0
150
0
DP800dpx reality reduction
140
experiment
MSC Marc without reduction
MSC Marc reduction included
MSC Marc reduction reality
80
100
100
experiment
MSC Marc without reduction
MSC Marc reduction included
MSC Marc reduction reality
120
100
force (kN)
150
40
60
displacement (mm)
TRIP600 reality reduction
200
force (kN)
20
80
60
40
50
20
0
0
20
40
60
displacement (mm)
80
100
0
0
20
40
60
displacement (mm)
80
Figure 6.7: simulation results real inversion process for DC04, DP600, DP800dpx and TRIP600
From these results it is clear that the forces decrease when the real reduction process is
simulated regarding the results from the earlier reduction simulations. The results of DP600
and DC04 match the experimental results better in comparison with the results from the
simulations with only one reduction step. The results from DP800dpx are still too high and
the results from TRIP600 are, as expected, again lower than the experimental results.
Apart from these results it is also useful to look at the reduction forces working on the
reduction tools during the reduction process. These results can also be compared with the
experimental results. Figure 6.8 shows the reduction forces for all four materials. From this
41
figure it is clear that the resulting graphs are very unstable. This could probably be caused by
the contact of the reduction tool and the material. During the reduction process, the nodes
contacting the reduction tool change continuously. Comparing the results with the
experimental results shows for DP800dpx very good fitting. The simulation results from
DP600 and TRIP600 do not match the experiments correctly. For TRIP600 it is obvious that
the forces are too low. Even during the reduction process the material transforms from soft
austenite to martensite, which is much tougher. For DP600 the simulated forces are slightly
lower.
DC04 reduction forces
DP600 reduction forces
30
60
71-65
65-60
60-57
25
50
40
force (kN)
force (kN)
20
15
30
10
20
5
10
0
71-65
65-60
60-57
0
20
40
60
displacement (mm)
80
0
100
0
DP800dpx reduction forces
20
40
60
displacement (mm)
80
100
TRIP600 reduction forces
120
50
100
71-65
65-60
60-57
40
71-60
60-57
60
force (kN)
force (kN)
80
30
20
40
10
20
0
0
20
40
60
displacement (mm)
80
100
0
0
20
40
60
displacement (mm)
80
100
Figure 6.8: Reduction forces during simulations.
6.3: Model PAM-STAMP
Together with the introduction of the reduction process in MSC-Marc/Mentat, also the PAMSTAMP model has been updated. The reduction tool, which has been developed in PAMSTAMP has the same deformation angle as the MSC-Marc/Mentat reduction tool. An
impression of the modified PAM-STAMP model is shown in figure 6.9.
42
A
B
Figure 6.9: Modified PAM-STAMP model: Reduction implemented
All materials have been simulated again to determine the differences between this simulation
and the earlier simulations without reduction. The results of this comparison are shown in
figure 6.10.
DC04 inversion comparison
DP600 inversion comparison
60
150
experiment
PAM STAMP without reduction
PAM STAMP reduction included
50
100
force (kN)
force (kN)
40
30
20
50
experiment
PAM STAMP without reduction
PAM STAMP reduction included
10
0
0
50
100
displacement (mm)
0
150
0
DP800dpx inversion comparison
80
TRIP600 inversion comparison
250
140
experiment
PAM STAMP without reduction
PAM STAMP reduction included
150
100
experiment
PAM STAMP without reduction
PAM STAMP reduction included
120
100
force (kN)
200
force (kN)
20
40
60
displacement (mm)
80
60
40
50
0
20
0
20
40
60
displacement (mm)
80
0
0
20
40
60
displacement (mm)
80
Figure 6.10: comparison simulations with and without reduction implementation
43
As well as in the MSC-Marc/Mentat simulations, the forces become higher due to adding the
reduction process. Again the implemented hardening rule is the mean reason of this
phenomenon.
44
7: Implementation of damage/fracture
Both the MSC-Marc/Mentat and PAM-STAMP model present a good prediction of the
experimental results. The only important behaviour which is not implemented yet is the
damage or fracture of the material. In this chapter the implementation of a damage or fracture
criterion in both models will be discussed.
7.1: Model MSC-Marc/Mentat
In earlier research it was tried to implement damage in the model of the invertube. With this
implementation it should be possible to predict the moment of failure of the invertube. The
model that was used in that research was the Gurson-Tvergaard-Needleman damage model
(shortly Gurson damage model), which is a continuum description of the mechanical response
of a material containing voids. The amount of damage is given by the volume fraction of the
voids in the material, f. For the increase in the void volume fraction, two contributions were
identified:
- growth of existing voids
- nucleation of new voids
These two contributions can be added to obtain the total increase in the void volume fraction.
f& = f&growth + f&nucleation
(4)
The void growth rate and the void nucleation rate are given by:
f&growth = (1 − f ) ⋅ ε&kkp
f&nucleation =
fN
S ⋅ 2 ⋅π
(5)
1
− ⋅ ε mp −ε n
2
S
(
⋅e
)
2
⋅ ε&mp
(6)
Where ε&kkp is the inelastic volumetric strain rate, fN is the volume fraction of void nucleating
particles, ε mp is the equivalent plastic strain of the material, ε n is the average strain needed
for void nucleation and S is the standard deviation of the strain needed for nucleation.
One of the main shortcomings of the Gurson damage model can be seen directly from the
equations. Shear strains do not lead to damage growth or nucleation. From the strain
measurements on DC04, mentioned in chapter 4, it is clear that shear strains play an important
role in the invertube production processes and performance tests. Figure 7.1 below illustrates
the shear of the deformation process in the forming limit diagram determined from the strain
measurements on DC04.
45
Major
Strains
Minor strains
Figure 7.1: Forming Limit diagram (FLD) = cloud of points representing major and minor strains
situated in an element.
At this moment there is no other suitable damage model present in MSC-Marc/Mentat which
is able to describe the damage in a good way.
7.2: Model PAM-STAMP
At Corus IJmuiden a module within PAM-STAMP is present which can be used to predict
fracture in a material. This module is called CrachFEM [15]. This module is developed by
MATFEM that can be used in a standard forming or crash simulation. The CrachFEM module
determines the risk of failure dependent of the calculated strains which are strongly dependent
on the strain condition and strain history. CrachFEM is taking several different failure
mechanisms into account. Besides instability/necking also ductile fracture and shear fracture
are accounted for. It is an easy to use tool and most of its parameters can be determined using
standard tests.
The CrachFEM module contains the three most common failure modes: Plastic Instability,
Ductile fracture and Shear fracture. The occurrence of these three failure modes depends on
the stress state and the strain rate. The influence of deformation history and strain path
changes is taken into account using a material model that describes the Bauschinger effect.
For each of the failure modes, a failure curve is used. These failure curves are similar to a
forming limit diagram (FLC): failure occurs if the principal strains are above the curve.
Similar to an FLC, the strains in an invertube can be plotted in a graph. The distance between
the strain points and the different failure curves gives the failure risk for that failure mode.
This basically means that the part will fail by the failure mode that it crosses first. Slight
complication is that the Instability curve may move due to strain path and strain rate effects.
Strain path changes can cause a larger or smaller instability risk.
46
Plastic instability
In forming simulations plastic instability (i.e. necking) is predicted by the FE code from the
specified yield locus and the hardening behaviour. Normally, the elements in a crash
simulation are much larger than in a forming simulation, because of increasing CPU-time.
Due to this the necking behaviour of the material cannot be predicted accurately. Therefore,
failure by plastic instability is accounted for in the CrachFEM module. The module uses a
specified model to predict when necking occurs based on the hardening behaviour, strain rate,
yield locus and deformation history.
Next to the risk of Instability, CrachFEM also calculates the Maximum instability risk. The
instability risk is the risk of failure if the current strain path is continued. The Maximum
instability risk is the risk of failure if the strain path changes for the worst.
Ductile fracture
Ductile fracture describes the fracture mechanism where voids nucleate, grow and coalesce in
the material to form a crack. In literature sophisticated models are available that describe this
process in detail, however such models require an element size that is much smaller than that
used for forming or crash simulations. Therefore, a simplified approach is taken by
CrachFEM: a failure curve, just like the FLC, is used.
Shear fracture
Shear fracture occurs when the deformation localises to form shear bands. Shear bands can
occur under all loading types as stress states can always be viewed to have shear components.
These shear stresses can be either in-plane (as in a shear test) or in the thickness direction.
7.2.1: CrachFEM simulation results
In this research the CrachFEM module in PAM-STAMP is used for trying to predict the
critical fracture point in an invertube. From the experiments it is already known that, except
from DC04, every material fails during inversion testing. Only one of the materials is used in
this simulation, DP600. Reason for this is the absence of the parameters, which need to be
implemented, for the other materials. The results of the simulations with the CrachFEM
module are given in figure 7.2, 7.3 and 7.4.
47
Major
strain
Forming limit
curve (FLC)
Minor
strain
Figure 7.2: CrachFEM results DP600: Forming Limit Diagram
Figure 7.3: CrachFEM results DP600: rupture risk
min = -0.585
max = -0.215
The results shown here are related to simulations with the reduction process included. From
these results it can be concluded that the invertube will not fail during inversion. The forming
limit diagram after the reduction and inversion, shown in figure 7.2, does not show strain
points above the forming limit curve. This means that the invertube is not failing during the
simulation. The main reason for this is the strain path dependency, which is not taken into
account by the forming limit diagram. Figure 7.3 shows the rupture risk. The more negative
the value the less the risk. The plastic instability, which determines the instability risk, takes
48
the deformation history into account. Figure 7.4 shows the instability risk (A), followed by
ductile fracture risk (B) and shear fracture risk (C). A risk value of one means failure. From
these pictures it becomes clear that the invertube fails during simulation.
A
B
C
Figure 7.4: A) Instability risk (max = 1.05), B) Ductile fracture risk (max = 0.99), C) Shear fracture
risk (max = 0.56)
49
8: Conclusions
This research focussed on two main questions: Why is the invertube failing during crash? And
what can be done to prevent this?
Research has been done towards invertube failure together with experimental tests and the
development of simulation models in MSC-Marc/Mentat and PAM-STAMP to get an answer
to these questions. From the experiments it became clear that DC04 was the only material,
used in this project, which has a good performance during inversion. All other materials failed
during testing. The results of the experiments, which described good reproducibility, have
been used to validate the simulation models. The simulation results matched the test results
very good but the simulations showed that the reduction process has a large influence on the
inversion process.
The implementation of damage and fracture models has been discussed to be able to predict
the failure in the simulation models. At this moment no suitable damage model is present in
MSC-Marc/Mentat which predicts damage accurately. The CrachFEM module used in the
PAM-STAMP model to predict fracture neither gave an unambiguous prediction. The strain
path dependency in the material is the main cause of this problem. Together with the large
influence of the reduction process, these are the main reasons of invertube failure.
50
9: Recommendations
For using the developed invertube models in both MSC-Marc/Mentat and PAM-STAMP in
further research it is important to develop a damage model which predicts the failure of the
invertube more accurate. The model should take shear and strain path dependency into
account which are both important failure criteria in inversion processes. After the
implementation of this damage model the invertube models can be used for further research in
invertube performance. The geometry of the invertube together with the reduction process can
be simply optimised by changing the simulation models. Both have a large influence on the
performance of the invertube during inversion.
51
Appendix A: Other experimental results
Here, the force-displacement diagrams of all inversion experiments which are not mentioned
in chapter 4 will be presented. All arranged by material and diameter combinations.
DC04:
inversion DC04 71-60
80
invertube 1
invertube 2
force (kN)
60
40
20
0
0
10
20
30
40
50
60
displacement (mm)
inversion DC04 60-58
70
80
90
100
80
force (kN)
60
40
invertube 1
invertube 2
20
0
0
10
20
30
40
displacement (mm)
inversion DC04 60-48
50
60
80
displacement (mm)
100
invertube 1
invertube 2
invertube 3
invertube 4
invertube 5
invertube 6
60
force (kN)
60
40
20
0
0
20
40
120
52
DP600:
inversion DP600 60-48
120
invertube 1
invertube 2
100
80
force (kN)
60
40
20
0
-20
0
5
10
15
20
displacement (mm)
25
30
35
DP800dpx:
inversion DP800dpx 60-48
160
invertube 1
invertube 2
invertube 3
invertube 4
140
120
force (kN)
100
80
60
40
20
0
-20
0
5
10
15
20
displacement (mm)
25
30
35
53
TRIP600:
inversion TRIP600 60-48
120
invertube 1
invertube 2
100
force (kN)
80
60
40
20
0
0
10
20
30
40
displacement (mm)
50
60
70
TRIP700:
inversion TRIP700 60-48
90
invertube 2
invertube 3
80
70
force (kN)
60
50
40
30
20
10
0
0
5
10
15
20
displacement (mm)
25
30
54
HSD:
inversion HSD 60-48
150
invertube 1
force (kN)
100
50
0
0
5
10
15
20
25
displacement (mm)
30
35
40
55
Appendix B: PHAST strain measurements
PHAST [13] is a system for optical strain measurements on pressed sheet metal parts. But it
also can be used in this project to determine the strains in tubes due to deformations. The
system has been developed by Corus Research, Development & Technology and Geodelta
BV. The name of the strain measurement system, based on 3D image processing comes from
PHotogrammetric Automated Strain Tester.
The PHAST system uses a point grid of known dimensions on an undeformed blank. After
applying the grid the part is deformed. Subsequently a beacon is placed next to the area of
interest along with some supplementary markers (figure B1) and using a digital camera, a
series of photos are taken from different positions. In each image features like barcodes and
grid points are detected and their positions are stored. From features that are known, such as
the barcodes on the beacon, the camera positions are reconstructed. Once the camera positions
are known, the 3D position of the unknown features, such as the grid points can be
determined.
Figure B1: A beacon is placed next tot the area of interest along with some markers
The assembly of the grid points into a connected 3D model is integrated with the construction
of 3D coordinates for each grid point. Once the coordinates of the grid points are known, the
strains in the plane of the sheet can be calculated using the known initial grid size. The strain
calculation is based on triangles that can be recognised in the square grid (figure B2).
Figure B2: Strain calculation based on triangles
56
Appendix C: Material PAC-codes
Every material used in this research is property of Corus Ijmuiden. The table below adds the
PAC-codes of each material. PAC stands for Product Application Centre which is part of
Corus IJmuiden.
Table C1:PAC-codes
Material
DC04
DP600
DP800dpx
TRIP600
TRIP700
Stainless steel
HSD
PAC-code
20020141
20050080
20050096
20050094
20040496
Unknown
Unknown
57
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58