FEM simulation of Electrohydraulic Forming · tensile curves with high strain rate around 1000 per...

FEM simulation of Electrohydraulic Forming Author: Daniel Björkström Diploma work for Civilingenjörsexamen (MSc.), KTH Work carried out at Swerea KIMAB KTH Industrial Production, Joining Technology Kungliga Tekniska Högskolan, T-03 Examensarbete 2008-10-01 Stockholm

Abstract In this investigation tensile test data from different strain rates have been used for the fitting of the constitutive material model Johnson-Cook, JC for a selection of different steel grades. This included mild and high strength carbon steels and ferritic and austenitic stainless steels. The strain rates were from 0.0001 up to 1500 per second. The work procedures were to first review and sort the test data. Test data impossible to describe with the JC model or corresponding to dynamic effects or Lüders phenomena have been removed. Then the JC model has been fitted to the selected test data. The fitting has been preformed with a least square technique and also it was decided to perform a manual fitting of the parameters to obtain a good fit of tensile curves with high strain rate around 1000 per second. The reason for the extra manual fitting was that the JC models were intended for a Finite Element Method, FEM simulation with the high velocity forming method Electrohydraulic Forming, EHF. In this forming technique, strain rates go up to approximately 1000 per second. The FEM simulation of EHF has been preformed in ABAQUS, as an explicit dynamic simulation. The FEM model was based on experimental equipment used on an EHF experiment preformed by the University of Oulu in Finland, see Figure 1. The simulations were also verified with the results of that experiment. Due to modest amount of data on the nature of electric discharge or arcs in water, reflection in the experimental tools, the shape of the pulse and efficiency excreta, it was decided to use a reference acceleration in the simulation, instead of energy,

which was the input parameter in the experiment. The simulation results were close to the verification experiment. It was shown that the change of mechanical property for different strain rates can be described with the Johnson-Cook model. It is also possible to use the JC model to perform FEM simulation of Electrohydraulic Forming and obtain close results to the reference experiment with regard to strain distributions and press height.

Figure 1. FEM model of EHF forming

Table of Contents 1. Introduction ................................................................................................................... 5

1.1 Background............................................................................................................ 5 1.2 Objective................................................................................................................ 5 1.3 Procedure............................................................................................................... 6

2. Literature review............................................................................................................ 7 2.1 Electrohydraulic Forming...................................................................................... 7 2.2 Johnson-Cook material model ............................................................................... 9

3. Fitting of the Johnson-Cook constitutive model parameters ....................................... 10 3.1 Materials .............................................................................................................. 10 3.2 Tensile tests at high velocities ............................................................................. 10 3.3 Processing the tensile test data ............................................................................ 12 3.4 Least square fitting of the Johnson-Cook parameters ......................................... 13 3.5 Judging how well the model fit to the test data...................................................16 3.6 Manuel fitting of the Johnson-Cook parameters ................................................. 17 3.7 Results, obtained Johnson-Cook parameters ....................................................... 18

4. Experimental testing, EHF .......................................................................................... 29 4.1 Procedure............................................................................................................. 29 4.2 Material................................................................................................................ 30 4.3 Results, EHF experiment..................................................................................... 30

5. Finite element analysis ................................................................................................ 32 5.1 The model ............................................................................................................ 32 5.2 Properties ............................................................................................................. 33

5.2.1 Material properties, blank............................................................................ 33 5.2.2 Material properties, water............................................................................ 34

5.3 Interaction............................................................................................................ 34 5.4 Constraints........................................................................................................... 34 5.5 Load..................................................................................................................... 35 5.6 Element types, meshes and rigid shell................................................................. 36

5.6.1 Element type and mesh, blank..................................................................... 36 5.6.2 Element type and mesh, water..................................................................... 39 5.6.3 Rigid body, die ............................................................................................ 40

5.7 Results ................................................................................................................. 40 6. Discussion.................................................................................................................... 50

6.1 Fitting of the Johnson-Cook material model ....................................................... 50 6.2 Simulation of EHF free forming.......................................................................... 51

7. Conclusions ................................................................................................................. 53 7.1 Fitting of the Johnson-Cook material model ....................................................... 53 7.2 Simulation of EHF, free forming......................................................................... 53

8. Further work ................................................................................................................ 54 8.1 Further work, fitting of Johnson-Cook model ..................................................... 54 8.2 Further work, simulation of EHF ........................................................................ 54

9. Acknowledgements ..................................................................................................... 55 10. References ............................................................................................................... 56 Appendix A — Plot 1.4016 ................................................................................................. 57 Appendix B — Plot 1.4301 ................................................................................................. 60 Appendix C — Plot 1.4509 ................................................................................................. 63 Appendix D — Plot 1.4512 ................................................................................................. 66 Appendix E — Plot 1400 M................................................................................................ 68

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Appendix F — Plot DPX 800.............................................................................................. 70 Appendix G — Plot HSLA.................................................................................................. 73 Appendix H — Plot Trip 700 .............................................................................................. 75 Appendix I — Plot DP 800 ................................................................................................. 78 Appendix J — Plot IF210.................................................................................................... 81 Appendix K — Results EHF experiment, IF210................................................................. 84 Appendix L — Results EHF experiment, DPX800............................................................. 85 Appendix M — Results EHF experiment, TRIP700........................................................... 86 Appendix N — Results EHF experiment, 1.4016 ............................................................... 87 Appendix O — Results EHF experiment, 1.4509 ............................................................... 88

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1. Introduction

1.1 Background The aim of this study is to increase the utilisation of high strength and stainless steel in the automotive industry. To enable production of safer and lighter car structures with an increased formability of high strength steels with new forming technologies. The use of high strength steel in automotive production has constantly increased resent years to enable cheaper and lighter car structures. This development is demanding new material and manufacturing processes to solve the arising problems which come with these new technologies. One main problem with an increased amount of high strength steel in the car design is the reduction of formability of high strength steels compared with conventional sheet material. One suggestion to overcome some of those problems with a reduction of formability is to use high velocity forming techniques as Impact forming, Electromagnetic forming and Electrohydraulic forming. The specific objective of this project is to:

• establish the possibility of high velocity forming methods of high strength steels and stainless steel sheets for automotive applications

• enumerate the formability of those materials and develop simulation techniques In this part of the investigation the opportunities of the Electrohydraulic Forming method EHF will be established, with a Finite Element Method simulation of selected materials. The investigation also involves to establish the change of mechanical properties during high strain rates, for selected material. This phenomenon will be investigated and described with the constitutional material model Johnson-Cook. The Johnson-Cook material model is being use for the FEM simulation. The present project is a part of the RFCS project HI_VEL focussed on high speed forming methods. The experimental data of this report, like high speed tensile data and Electrohydraulic forming data, are delivered by partners of the HI_VEL project [5].

1.2 Objective The objective of this work is to perform a Finite Element Method, FEM, simulation of the Electrohydraulic Forming method, EHF, and evaluate the process engineering design tool. Educe a material model which describes the material´s mechanical properties during high strain rates, for a selection of grades. The model is to be used for FEM simulation in high strain rate. [5]

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1.3 Procedure The procedure of this work will be to first perform a literature review of the Electrohydraulic Forming method, EHF, and the Johnson-Cook, JC, model. This is to investigate what have been done earlier on these subjects, regarding the fitting of and common usage of the JC model. The history, state of the art and if there has been any earlier FEM simulations of EHF. There have been tensile tests preformed in different strain rates for the selected materials by other partners of the HI_VEL project, Voest Alpine Stahl, and the results have been delivered to Swerea KIMAB. These test results are going to be analysed reviewed and sorted. The Johnson-Cook material model parameters are then going to be fitted to those data. Experiments on Electrohydraulic Forming have been preformed by other partners of the HI_VEL project, Oulu University, and the results have been delivered to Swerea KIMAB. The results are going to bee used in FEM simulations on the Electrohydraulic Forming. A model is going to be built in ABAQUS, based on the experiment equipment used in the experiment. Results of the JC model and the simulations are then going to be evaluated. To survey how the JC model and the simulation work together and how close agreement the simulation results are to the experimental results. Evaluate if the objective of the investigation have been fulfilled.

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2. Literature review A literature review has been preformed on the Electrohydraulic Forming method and on the Johnson-Cook constitutive material model. On the Electrohydraulic Forming method the following has been investigated; the state of the art and applications of this method. On the Johnson-Cook constitutive material model; applications and methods to find the material parameters.

2.1 Electrohydraulic Forming Electrohydraulic Forming, EHF, is a high velocity forming method for sheet materials, this method was extensively studied in between the 50´s and the 70´s [2]. The positive advantages were discovered as early as in the 40´s and was developed and used by the aerospace industry, a few of the larges aerospace manufacturers developed and build machines to meet their own specification. But nowadays this method is moderately used in the commercial industry, even though this method has a lot of advantages over conventional forming methods. [1]

Figure 2. Basic principle of Electrohydraulic Forming [1]

EHF can be compared with the Explosive Forming method and EHF also has much in common with the Electromagnetic Forming, EMF, method. The fundamental principle is the same, the essential different is the source of energy. In Electrohydraulic Forming, is electric energy converted to mechanical energy through a discharge between two electrodes submerged in fluid of water or oil. This arc discharge makes the near fluid to vaporise rapidly and building up a pressure, creating a shock wave. The fluid is in direct contact with the sheet material and pushes it into the die, making it take the shape of the die. The energy needed for this discharge is stored in a large capacitor bank. The size of the capacitor bank is related to the size of the workpiece or the energy needed to form the work piece. If very large pieces are getting worked a large capacitor bank is needed or several discharges are required. The forming process is very fast and last no longer then 200 µs and has a forming speed approximated to 300m/s [1] [6]. The Electromagnetic Forming method is the only high velocity forming method that has been commercially accepted in the metal working industry. It is mostly used to join axisymmetric components, like automotive oil filter canisters. The basic principle of this method is to let an electrical current run through a coil placed adjacent to a workpiece. The

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current causes a high magnetic field around the coil which causes an eddy current in the workpiece and a secondary magnetic field. The magnetic fields are repulsive and cause the workpiece to accelerate towards the die placed next to the workpiece. The force from the magnetic field causes the workpiece to deform into the die. High forming speeds enhance the ductility of the material. High speed also leads to minimum of springback. Reason for this increased formability can be explained by [2];

• Inertial forces act to diffuse deformation; When a sample is deformed in a relatively low strain rate the deformation is spread out in a uniform way, so that the local velocity in the sample is varying linearly through the sample. After passing an instability point the sample starts to neck, the local velocity is changing over a very short distance in the sample, one side will have the same speed as the moving crosshead and the other side will be stuck to the fundament of machine. This leads to a change of speed in the sample and a non-uniformed inertial force in the sample. It is possible through Newton’s law to calculate a critical speed when this inertial force can produce increased formability.

• Change of anisotropy i.e. change of r-value;

Experiments were carried out with ring expansions and the strain to failure was very much dependent on the height of the rings. It seems like this change of formability is due to a change of anisotropy, as the height of the rings increases the major strain and the minor strain increases. The change of deformation anisotropy is referred to as the r-value and is the ratio of the width strain to the thickness strain. A material with a high r-value has in general a high formability.

• Inertial ironing;

Another explanation to the increased formability is the phenomena called inertial ironing. Inertial ironing appears when a relatively ductile materiel hits a harder not so ductile material in a high velocity. The forces of impact makes the more ductile material to deform.

• Change in material constitutive behaviour;

When a material deform under very high strain rate, occur temperature change in the material, which can change the constitutive behaviour of the material.

Figure 3. Increased formability in high strain forming [8]

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2.2 Johnson-Cook material model The tensile stress in a material can differ depending on the strain rate, usually the flow stress increases with a higher strain rate. To be able to achieve as accurate result as possible in a simulation, it is necessary to describe this phenomenon with a constitutive material model. There are several different models to describe this change of mechanical properties. In this project the Johnson-Cook constitutive material model, JC, was chosen. This was decided, because the JC model is a widely used and well recognized model and in the program used for the simulation, ABAQUS, the Johnson-Cook material model is already implemented and the parameters of the model can be given as an input file. The Johnson-Cook model is given in:

( )[ ]

−−

−⋅

+⋅+= •

•

0

0

0

1ln1TT

TTCBA

m

n

ε

εεσ Equation 1

The model expresses the flow stress (σ). The expression is divided in to three brackets, the first part is representing the initial yielding strength and the strength hardening due to stain, where A is representing the initial strength and B and n is represents the hardening due to strain (ε). The second bracket is representing the hardening due to strain rate, where C is

the hardening sensitivity due to strain rate )(•ε and

•

0ε is a normalizing strain rate

reference. The last bracket represents the material softening due to material heating with the parameter T. T0 and Tm are constants and represents the initial temperature and the melting temperature. But in this project the effect of the temperature was neglected and the parameter T, was not evaluated. For some steel grades these parameters have already been evaluated. But for the investigated steel grades in this project the parameters were not yet produced. To obtain these parameters, tensile tests were carried out in different strain rates. The test data were processed and fitted to the Johnson-Cook model with a least square technique [3] [7] [9].

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3. Fitting of the Johnson-Cook constitutive model parameters

To be able to do simulation on EHF of sheet material with FEM technique, it is important to have a material model to describe the changing in the materials mechanical characteristic. The mechanical characteristic will change with degree of strain, strain velocity, and temperature. In this forming method it is especially important to take into account the strain velocity, as the sheet material can experience strain rates around 1000/s.

3.1 Materials The main purpose of this workpackage is to investigate a materials matrix that will have the optimal characteristics in order to perform the assessment on the Electrohydraulic Forming, EHF process window definition [5]. Below, in Table 1 are the selected material and there individual tasks for investigating.

Table 1. The selected material and there investigated range for this work Material

Short name Rm

ASTM [MPa] Thickness

[mm] JC

fitting EHF

exp. & sim.

1.4016 538 0,8 √ √ 1.4512 430 0,8 √ 1.4509 580 0,8 √ √ 1.4301 662 0,8 √

Trip 700 724 1 √ √ DP 800 832 1 √ IF 210 360 0,9 √ √ HSLA 372 0,98 √

DPX 800 800-950* 0,8 √ √ Inve

stig

ated

she

ets

1400 M 1400-1600* 0,5 √ * Provided by producer

• EN-1.4016; Ferritic stainless steel • EN-1.4512; Ti stabilized ferritic stainless steel • EN-1.4509; Ti+Nb stabilized ferritic stainless steel • EN-1.4301; Retained austenitic stainless steel • TRIP 700; Transformation induced plasticity, trip effect steel • DP 800; Dual –Phase steel • IF 210; Interstitial Free galvanised steel • HSLA 260; High Strength Low Alloy galvanised steel • DPX 800; Dual –Phase steel • 1400 M; Martensitic steel

3.2 Tensile tests at high velocities How the mechanical property changes with higher strain rates are of high importance when investigating the EHF techniques for high strength steels and stainless steels. The tests can not be assessed with only one testing technique, so different testes have to be carried out in

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different testing laboratories for different strain rates ranges. The laboratories were; Voestalpine (Austria), RWTH Aachen (Germany), Oulu University (Finland), and Gent University (Belgium). Tests were carried out on the selected grades, with specimen taken parallel to the rolling direction. The reason why different testing techniques have to be carried out are the different deformation mechanisms in the different strain rate ranges. The tests in the strain range from ~0.0001 to ~1/s were performed using a hydraulic driven MTS-810M machine, preformed by Voestalpine. The specimens dimensions were according to the ASTM E517, Alternative, as shown in Figure 4.

Figure 4. ASTM-E517 Specimen A, Alternative [5].

The tests in the strain rates from ~1 to ~100/s were preformed by using a Roell-Amsler HTM2012 machine. The specimens had the dimensions as shown in Figure 5.

Figure 5. Tensile specimen used with the Roller-Amsler HTM2012 machine [5].

To be able to perform the very high strain rate tests, the Split Hopkinson Tensile Bar method, SHTB were preformed by the University of Oulu and the University of Gent. The tested strain rates, which are depending on the tested material, varied from ~600/s up to ~2000/s. The tensile specimens were taken parallel to the rolling direction. The dimensions of the specimen are shown in Figure 6.

Figure 6. Specimen used for the SHTB, Oulu to the left and Gent to the right [5]

When high strain rate tensile testing, with the SHTB are performed the specimen fractures in few milliseconds [5]. Figure 7 shows the increase of the strain rate as during the test. In order to determine the strain rate during SHTB, different methods are commonly used but in this experiment the average true strain rate from yielding of the material to the ultimate tensile strength was used for the definition of the strain rate.

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Figure 7. Instantaneous strain rate during SHBM [5]

3.3 Processing the tensile test data The available test data and there respective strain rate range are stated in Table 2

Table 2. Location of tensile tests, range of strain rate and the used specimen Range of strain rate Location of test place Specimen High velocity ~1000/s Gent, Belgium G3K High velocity ~1000/s Oulu, Finland Geom.

Intermediate velocity ~1-10-100/s Aachen, Germany A20 Low velocity ~1-0,1-0,01-0,001-0,0001/s Voestalpine, Austria ASTM-E517

Data from the high velocity tests were delivered to Swerea KIMAB in engineering strain (εeng) and engineering stress (σeng) the true strain (εtrue) and the true stress (σtrue) were calculated from the equations below [4]:

E

E

engel

eleng

0

0

σσε

εσσ−

=

⇒⋅+= Equation 2

Eeng

totpl

eltotpl

0σσεε

εεε−

−=

⇒−= Equation 3

( )pltrue εε += 1ln Equation 4

( )plengtrue εσσ +⋅= 1. Equation 5

Data from the intermediate velocity range tests were delivered to Swerea KIMAB in true strain and true stress and no further calculations were necessary. Data from the low

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velocity range tests were delivered to KIMAB in force, F and displacement the engineering strain (εeng) and the engineering stress were calculated from the Equations below [4]:

0A

Feng =σ Equation 6

0l

leng

∆=ε Equation 7

3.4 Least square fitting of the Johnson-Cook parameters

All the tensile curves were gathered and reviewed for respective grade. Since all tests were modelled with the JC model editing was performed so that features of the curves which were impossible to describe the JC model were removed. Test data that did not agree with the trend in the curve pattern with increase in strain rate, or had obviously some defect were excluded. If there were some tendency of Lüders phenomena that part was removed from the curve. Some steel grades have a small peak in the beginning of their curve, see Figure 8. This part of the curve was also removed from the curve. There were different amount of available test data from the different laboratories on respective strain rate and also some curves have been excluded. Because of the different amount of available data on each strain rate only one curve was selected from each strain rate, to make the optimizing process to take equal account to the different strain rates. In the review of the curves, tests from the same strain rate were compared with each other. One curve that was in good agreement with the other curves from the same strain rate, were selected to be used for the optimization process. To avoid parts in the curves that are mainly out side the limitation of the Johnson-Cook model, only strains between strain at 0.2 %, Rp0.2, and strain at ultimate tensile strength, Rm, were used, if they had no other limitations such as Lüders phenomena or defects. Below is an exempla of a removed part due to Lüders phenomena or initial peaks.

Available strain ratesHSLA

300

350

400

450

500

550

600

650

700

0 0,02 0,04 0,06 0,08 0,1 0,12 0,14 0,16 0,18

True Strain

Tru

e S

tres

s [M

Pa]

1300/s Tempere 0

0,8153/s Aachen VHA00001

15,5/s Aachen VHB00002

123,2s Aachen VHC00002Removed part

Figure 8. Peaks like this were removed from the test data

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The selected curves were processed in MATLAB to optimize the fitting of the model to the test data. The JC parameters were searched with a least square procedure. The curves from the different strain rates have a big difference in number of points per curve, this would make the optimization procedure take more account to the curves with more points. In general, the curves from the lower velocity range have more points per curve than curves from the higher velocity range, consequently the fit will be better for the curves from lower velocity and poorer for the curves from the higher range of the velocity. To make the optimization procedure take similar account to the whole velocity range, the data were modified to have the same number of points for each curve, to obtain the same weight for each velocity curve. The modifications were done with a linier interpolation in MATLAB, 100 points were chosen for each strain curve. Table 3 contains the selected material, available test data from the four different testing laboratories. The table also contains information on which curves were excluded and the used strain range for each curve.

Table 3 Available test data on the investigated steel grades Strain rate → Steel grade ↓

~0,0001/s Voestalpine

~0,001/s Voestalpine

~0,01/s Voestalpine

~0,1/s Voestalpine

~1/s Voestalpine

~1/s Aachen

~10/s Aachen

~100/s Aachen

~1000/s Oulu

~1000/s Gent

1.4016 0,2-14,3% 0,2-19,1% 0,2-17,9% 0,2-17,7% 0,2-19,7% 0,2-14,3% 0,74-14% 0,2-19,7% Excluded Not available

1.4301 Excluded Excluded Excluded Excluded Excluded 0,2-34,9% 0,3-34,9% 0,2-37,3% 0,2-33,9% Not available

1.4509 0,2-22,6% 0,2-23,9% 0,2-22,3% 0,2-21,7% 0,6-21,6% 0,7-16,6% 0,7-15,2% 0,8-12,7% 0,2-12,1% Excluded

1.4512 Not available Not available Not available Not available Not available 0,2-17,3% 0,7-16,7% 2,1-15,1% Excluded Not available

1400M Not available Not available Not available Not available Not available 0,2-% 0,2-% 0,2-% Not available Not available

DPX 800 0,8-13% 0,8-11,5% 0,8-8,3% 0,8-9% 0,8-9,6% 0,2-9,6% 0,2-10,5% 0,8-10,3% 0,9-11,4% Excluded

HSLA Not available Not available Not available Not available Not available 1,8-13,7% 1,7-11,2% 1,7-9,8% 1,7-16,1% Not available

TRIP 700 0,2-29,9% 0,2-21,6 0,2-20,2% 0,2-18,2% 0,2-19,1% Excluded Excluded Excluded 0,2-21,4% Excluded

DP 800 Not available Not available Not available Not available Not available 0,2-17,2% 0,21-18,1% 0,2-18,1% Excluded Excluded

IF 210 0,2-28% 0,2-25,7% 0,2-30,6% 0,2-24,2% 0,2-28,1% 1-18,6% 2-16,5% 1,8-16,2% 0,2-21,1% Excluded

For material 1.4016, test data from all the strain rates are available except from Gent, but in the first review of the curves, test data from strain rate ~1000/s was rejected. The reason for this was that the curve from strain rate ~1000/s is below the ~100/s curve and close to the ~10/s curve. Data like that was not included in the optimization procedure because of the irrational trend compared to the JC model. See Figure 9 below.

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1.4016

200

300

400

500

600

700

800

0 0,02 0,04 0,06 0,08 0,1 0,12 0,14 0,16 0,18 0,2

True Strain

Tru

e S

tres

s [M

Pa]

1350/s (Oulu, Finland)

103.8/s (Aachen, Germany)

11,6/s (Aachen, Germany)


0,72/s (Voestalpine, Austria)





~1000/s is close to ~10/sand below ~100/s

Figure 9. Visualize the reason way strain rate ~1000/s is excluded

Test data between strain at 0.2 %, Rp0.2 and strain at ultimate tensile strength, Rm was used for the optimization process. In the curve from strain rate ~1/s, it appears to be tendency to Lüders phenomena. The part where Lüders phenomenon is present was removed, for this curve data from 0 to 1 % was removed from the true strain. The strain rate range for this curve and all other curves that have been used for the optimization can be seen in Table 3. In Figure 10, is the selected part from strain rate ~1/s together with the excluded part and the engineering stress and strain.

1.4016, ~1/s, Aachen

200

300

400

500

600

700

800

0 0,02 0,04 0,06 0,08 0,1 0,12 0,14 0,16 0,18 0,2 0,22 0,24 0,26 0,28

True/Engineering Stain

Tru

e/E

ngin

eerin

g S

tres

s [M

Pa]

Dismissed data

Data used for the fitting, ~1/s , Aachen

Engineering stress

1 %Strain

14,3 % Strain

Figure 10. The selected part for evaluating the JC parameters plotted with engineering strain

All the selected and modified tensile test data were collected and put into one input data file. The input file was read by MATLAB and by a linear interpolation function, the data was modified to have 100 points per strain curve. The MATLAB script then carried out a least square procedure to optimize the fitting of the Johnson-Cook model to the selected

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test data. The results from MATLAB are the optimized JC parameters. In Figure 11 are the optimized JC model plotted with the used experimental test data.

Model vs. true stress1.4016

200

300

400

500

600

700

800

0,00 0,02 0,04 0,06 0,08 0,10 0,12 0,14 0,16 0,18 0,20

True Stain

Tru

e S

tress

[MP

a]

Experimental

JC model

excluded data

Figure 11. Plot of the JC model and used test data with excluded test data in red colour.

3.5 Judging how well the model fit to the test data

To estimate how well the generated model is fitting the test data, a standard deviation value was calculated see Equation 8:

( )5.0

1

2)()1(

1

−

−= ∑

=

n

iiitrue JC

ns σ Equation 8

In Equation 8 JCi is the calculated value from the JC model in the ith point. This was calculated for all of the selected data for the fitting in MATLAB. This standard deviation gives an indication of how well the model is fitting to the test data. But because of the large oscillation in the higher strain rate ranges the standard deviation value get large because of the large error in square see Equation 8. This standard deviation value is very much depending on the quality of the selected test data and what strain rates the standard deviation is calculated for. One other way to estimate the accuracy is to plot the two curves in same diagram and do a subjective judgement of the fitting. This is not accurate and it is hard to grade the fitting degree, but it is a good way to build an opinion on where the model is in good agreement with the test data and where the fit do not agree.

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3.6 Manuel fitting of the Johnson-Cook parameters The JC model has a rather good fit to grade 1.4016, see Figure 11, the standard deviation value for the fitting is 19,7 MPa. But for DPX 800 the fitting is of less quality, see Figure 12, with a standard deviation value of 21.5 MPa, as mentioned in the chapter above the standard deviation is not an exact tool to measure how well the fit is. In this case, DPX 800, the model is concentrated around the lower strain rates, due to a concentration of experimental data on that region. The main reason to obtain the JC model is to explore how the grades are deforming under high strain and high strain rates. For this reason it is appropriate to have a good agreement in the high strain and strain rate region. This can be obtained by fitting the model manually and obtaining a good fit on desirable region. The parameters from the least square optimization are a good first approximation for this, with a well fitted curvature to the test data. The parameters were adjusted so the model was changed in height and scattering until desirable fit was obtained.

Model vs. true stressDPX 800

600

700

800

900

1000

1100

1200

0,00 0,02 0,04 0,06 0,08 0,10 0,12 0,14True Strain

Tru

e S

tres

s [M

Pa]

Experimental

JC model

Dismissed data

Figure 12. DPX 800, model fitted with least square method, selected test data and excluded test

data. Above is the least square fitted model of material DPX 800. From the test data parts in the beginning marked in red, are excluded due to the Lüders plateau shape, which is not possible to describe with the JC model. One whole curve is also excluded from the fitting procedure, this curve is from Gent with strain rate ~1000/s, it was decided not to use this curve due to the inconsequent pattern with respect to the others test data which is impossible to describe with the JC model. The fitted model is in poor agreement with the highest and the lowest strain rate, but the fit is of better agreement in the middle region of strain rates.

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Model vs. true stressDPX 800

600

700

800

900

1000

1100

1200

0,00 0,02 0,04 0,06 0,08 0,10 0,12 0,14True Strain

Tru

e S

tres

s [M

Pa]

Experimental

JC model

Dismissed data

Figure 13. DPX 800, manually fitted JC model, selected test data and excluded test data.

Above is the manually fitted model to DPX 800. It was decided, for the FEM simulation, it is desirable to have a model with a good agreement on the higher strain and strain rate regions. The parameters have been adjusted to achieve better fit to the highest and the lowest strain rate. The middle region of strain rates are suffering due to this, with a higher standard deviation value of 31.3 MPa compared to 21.5 MPa in the least square fitted model.

3.7 Results, obtained Johnson-Cook parameters In Table 4 are the obtained Johnson-cook parameters A, B, n and C, the normalizing reference strain rate,

•

0ε , the calculated standard deviation number, s calculated through

Equation 8 and the number of flow stress curves available for predicting of the JC parameters with the least square method for respective grade.

Table 4. The obtained Johnson-Cook parameters for the investigated steel grades with full least square fitting

Steel grade 1.4016 1.4301 1.4509 1.4512 1400 M DPX 800 HSLA TRIP 700 DP 800 IF 210

A [Mpa] 184,5 339,7 335,1 247,2 739 529,2 25,3 419,7 471,9 241,9

B [Mpa] 703,7 1095,6 590,2 440,0 1232,6 967,9 425,5 1110,5 1025,5 419,5

C 0,020 0,025 0,026 0,043 0,0059 0,010 0,060 0,008 0,016 0,027

N 0,261 0,801 0,533 0,446 0,1185 0,337 0,113 0,522 0,581 0,445

ep0 [1/s] 0,010 0,010 0,010 0,010 0,01 0,010 0,010 0,010 0,010 0,010

St. deviation 19,7 23,7 30,8 13,0 26,2 21,5 18,5 12,9 38,4 22,6

No. of strain rates 8 4 9 3 3 9 4 6 3 9

The parameters in the table above are obtained from the MATLAB least square fitting. Grade TRIP 700 has the smallest standard deviation value of 12.9 MPa and DP 800 has the largest value of 38.4 MPa. The main reason for the large standard deviation value is the extreme high oscillation in the strain rate ~100/s, which is making the standard deviation value grow fast. For the other two available strain rates the fit is in good agreement, the fit

19

for the oscillating strain rate ~100/s is probably in good agreement with a mean value of the test data, probably the fitting of DP 800 is not as bad as is first appears. Trip 700 is in good agreement with all the available strain rates and has no curves with excessive oscillation, which leads to a low standard deviation value. C is the parameter which represents the strain rate sensitivity, HSLA has the highest C value of 0.06 and 1400M has the lowest C value. In general, material with lower flow stress obtains higher strain rate sensitivity. Table 5 below contains same parameters as the table above but the JC parameters are obtained by a manual fitting to the selected data. In this case the obtained parameters from the least square fitting in MATLAB, have worked like a first approximation for the manual fitting.

Table 5. The obtained Jonson-Cook parameters for the investigated steel grades with” best” manual fitting

Steel grade 1.4016 1.4301 1.4509 1.4512 1400 M DPX 800 HSLA TRIP 700 DP 800 IF 210

A [Mpa] 365 350 330 250 740 535 125 460 472 200

B [Mpa] 700 1110 580 461 1230 960 325 1100 1026 420

C 0,019 0,025 0,020 0,043 0,006 0,0103 0,060 0,0073 0,016 0,02

n 0,500 0,82 0,440 0,470 0,119 0,32 0,166 0,55 0,582 0,3

ep0 [1/s] 0,010 0,01 0,010 0,010 0,01 0,01 0,010 0,01 0,010 0,01

St. deviation 28,0 24,3 35,0 13,0 26,3 31,3 23,0 15,0 38,4 23,5

No. of strain rates 8 4 9 3 3 9 4 6 3 9

The standard deviation values in Table 5 are calculated on the same test data as the least square fitted models, all the standard deviation values are higher or equal to the values in the table for the least square fitted models. 1.4512 has the lowest value of 13 MPa and DP 800 has the highest value. There are no excessive changes in the standard deviation values for neither of the grades in the table. The largest difference in standard deviation value has DPX 800. Which in the manual fitting has a better agreement on strain rate ~1000/s than the least square fitted parameters has, but in penalty the agreement in the middle-high stain rate range the fit is of lesser agreement.

20


200

300

400

500

600

700

800

0,00 0,02 0,04 0,06 0,08 0,10 0,12 0,14 0,16 0,18 0,20

True Stain

Tru

e S

tres

s [M

Pa]

Experimental

JC model

excluded data

Figure 14. 1.4016, manually fitted JC model, selected test data and excluded test data.

The figure above is the manually fitted model to grade 1.4016, selected test data and excluded test data in red colour. The initially fitting has been performed with 8 different strain rates. Strain rate in ~1000/s has been excluded due to the curve is below strain rate ~100/s. In a subjective judgement the fit is in good agreement with the test data. Test data have a scattering and curvature that can be described well by the model. The standard deviation value is 28 MPa it is rather high compared with the subjective estimation. The high value comes in large portion from the oscillating curve for strain rate ~100/s.

21

1.4301 True vs. model

200

300

400

500

600

700

800

900

1000

1100

1200

0 0,02 0,04 0,06 0,08 0,1 0,12 0,14 0,16 0,18 0,2 0,22 0,24 0,26 0,28 0,3 0,32 0,34 0,36 0,38

True Strain

Tru

e st

ress

[MP

a]

Experimental

JC model

Excluded data


The figure above is the manually fitted model to grade 1.4301, selected test data and excluded test data. The initial fitting has been performed with 4 different strain rates. All test data from Voestalpine have been excluded. This was decided because of the curves are crossing strain rates in higher velocities. In a subjective judgement the fit is in good agreement with the test data, test data have a scattering and curvature that can be described well by the model. The standard deviation value is 24.3 MPa. The only curve that adds a large contribution to the standard deviation value is the test in strain rate ~100/s, due to its large oscillation.

22


200

300

400

500

600

700

0 0,02 0,04 0,06 0,08 0,1 0,12 0,14 0,16 0,18 0,2 0,22 0,24

True Strain

Tru

e S

tres

s [M

Pa]

Experimental

JC model

Excluded data

Figure 16. 1.4509 manually fitted JC model, selected test data and excluded test data.

The figure above is the manually fitted model to grade 1.4501, selected test data and excluded test data. The initially fitting has been preformed with 9 different strain rates. Small parts have been removed in the beginning of the curves they had indications of Lüders phenomena or initial peaks, which could not be described by the model. Strain rate ~1000/s from Gent has been excluded due to that the curve is placed between strain rate ~10/s and ~100/s and using that curve would make it impossible to use tests that are preformed in lower strain rates but are placed above that test in the plot. The JC model capacity is imitated to an increasing stress with an increasing strain rate. In a subjective judgement the fit is not perfect in curvature, the fit is not in good agreement for all strains for any of the curves. The least square fitted curves had a tendency to have to large strain sensitivity, see appendix. The goal of the manual fitting was to obtain a better agreement in the end of the strain, so the model wouldn’t indicate in an excessive strength in high strains. The standard deviation value is 35 MPa, it is one of the investigated grades with the highest value. No excessive oscillation is present. The JC model has problem to describe the test data with a good agreement over the whole strain- strain rate range.

23


200

300

400

500

600

700

800

0,00 0,02 0,04 0,06 0,08 0,10 0,12 0,14 0,16 0,18 0,20

True Stain

Tru

e S

tres

s [M

Pa]

Experimental

JC model

Excluded data


The figure above is the manually fitted model to grade 1.4512, selected test data and excluded test data. The initially fitting has been preformed with 3 different strain rates. Test data were only available from Aachen and Tempere but tests from Tempere were excluded due to the curve were lower in strength than the curve at ~100/ and very close to strain rate curve ~10/s. In a subjective judgement the fit is in good agreement with the test data, it is also one of the investigated grades with the lowest standard deviation value, even with the oscillating strain rate at ~100/s. The fitting of the model is much easier to perform with a smaller number of test data and obviously obtain a low standard deviation value. If the true progress of the tensile strength is the curve from Tempere then it is difficult to describe this progress with a good agreement with the JC model. But this is probably an effect of different testing technique or a defect test. The standard deviation is 13 for both the manually fitted and the least square fitted model, not much could be done to improve the fit manually.

24

Model vs. true stress1400M

1100

1200

1300

1400

1500

1600

1700

0,00 0,01 0,01 0,02 0,02 0,03 0,03

True Stain

Tru

e S

tres

s [M

Pa]

Experimental

JC model

Excluded data

Figure 18. 1400M, manually fitted JC model, selected test data and excluded test data.

The figure above is the manually fitted model to grade 1400M, selected test data and excluded test data. Strain rates were available only from Aachen, and initially fitting has been preformed with all available strain rates. This grade has a very short elongation. The selected region is very short and the curves are constantly crossing each other in the beginning. This makes it hard to investigate the effect of the of strain rate. It is hard to detect any distinct strain rate progress, which was the reason why all curves were selected for the fitting. For the least square fitting one parameter, A had to be estimated and locked to be able to find a reasonable solution in MATLAB. The parameter, A was varied and a new least square solution was obtained this was repeated until the standard deviation value was at minimum. The value of the manually and the least square fitted models are 26.3 respective 26.2 MPa. The model in this case can describe the level of the flow strength but the strain rate sensitivity is not so noticeable. Generally grades with very high tensile strength like this did not have a high strain rate sensitivity.

25

Model vs. true stressHSLA

300

350

400

450

500

550

600

650

700

0,00 0,02 0,04 0,06 0,08 0,10 0,12 0,14 0,16 0,18

True Stain

Tru

e S

tres

s [M

Pa]

Experimental

JC model

Dismissed data

Figure 19. HSLA, manually fitted JC model, selected test data and excluded test data.

The figure above is the manually fitted model to grade HSLA, selected test data and excluded test data. The initially fitting has been preformed with four different strain rates. Test data were only available from Aachen and Tempere. All the available curves contain Lüders phenomena or initial peaks which were removed, the JC model can not describe curves with those phenomena. In a subjective judgement the fit is not in good agreement with the end of the lowest curve and the beginning of the highest curve. In the middle strain range the fit is in fairly good agreement. The standard deviation value is 23 and 18.5 MPa for the manually and the least square fitted model respective.

26

Model vs. true stressTRIP 700

400

500

600

700

800

900

1000

1100

1200

0,00 0,02 0,04 0,06 0,08 0,10 0,12 0,14 0,16 0,18 0,20 0,22 0,24 0,26 0,28

True Strain

Tru

e S

tres

s [M

Pa]

Experimental

JC model

Excluded data

Figure 20. TRIP 700, manually fitted JC model, selected test data and excluded test data.

The figure above is the manually fitted model to grade TRIP 700, selected test data and excluded test data. The initially fitting has been preformed with 6 different strain rates. All test data from Aachen has been excluded, they seems to show a different trend compared to the other data sources. They have almost half the elongation, 200 MPa higher flow strength and another shape in the curvature. The curve from Gent was also excluded, due to it did not agree with the curve from Tempere and it was decided to consequently exclude all test data from Gent due its lack of correlation with the other tensile tests. The standard deviation is 15 MPa and had for the least square fitting the lowest value of 12.9 MPa. In a subjective judgement the fit is of good agreement.

27

Model vs. true stressDP 800

300

400

500

600

700

800

900

1000

1100

1200

0,00 0,02 0,04 0,06 0,08 0,10 0,12 0,14 0,16 0,18 0,20

True Stain

Tru

e S

tres

s [M

Pa]

Experimental

JC Model

Excluded data

Figure 21. DP 800 manually fitted JC model, selected test data and excluded test data.

The figure above is the manually fitted model to grade DP 800, selected test data and excluded test data. The initially fitting has been preformed with three different strain rates. Test data were only available from Aachen, Tempere and Gent but tests from Tempere and Gent were excluded due to the curves, they had a suspiciously large gap between the tests preformed in Aachen at three different strain rates. Tests from Aachen overall have a good agreement with other tests and show rarely any suspected pattern. In subjective judgement the fit is in good agreement with the test data from Aachen in the two lower curves but in the higher strain rate ~100/s it is harder to evaluate the fit due to the oscillation, but it seem to be in good agreement with the mean value of the curve. DP 800 is the grade with the highest standard deviation value of the investigated grades in both the least square and the manually fitted models, this is due to the large oscillation of the ~100/s strain rate. If the true progress of the tensile strength is the curves from Tempere and Gent, then it is hard to describe this progress with a good agreement with the JC model. But in this case it is assumed that this is an effect of different testing technique. The standard deviation value is 38.4 MPa for both the manually fitted and the least square fitted model.

28

Model vs. true stressIF 210

100

200

300

400

500

600

0,00 0,02 0,04 0,06 0,08 0,10 0,12 0,14 0,16 0,18 0,20 0,22 0,24 0,26 0,28 0,30 0,32

True Strain

Tru

e S

tress

[MP

a]

Experimental

JC model

Excluded data

Figure 22. IF 210 manually fitted JC model, selected test data and excluded test data.

The figure above is the manually fitted model to grade IF 210, selected test data and excluded test data. The initially fitting has been preformed with nine different strain rates. Small parts have been removed in the beginning of the curves, they had indications of Lüders phenomena or initial peaks, which could not be described by the model. Strain rate ~1000/s from Gent has been excluded due to the curve is placed between strain rate ~10/s and ~100/s. In a subjective judgement the fit is not perfect in curvature, the fit is not in good agreement on one whole curve for any of the selected curves. This is partly due to the fitting have been a compromise between the low flow strength for the low strain rate curves and the high flow strength for the high strain rate curves in the beginning of the curves. The JC model has problem to describe the test data with a good agreement over the whole strain- strain rate range. No excessive oscillation is present and there are many available strain test curves which lead to a low standard deviation value of 23.5 MPa.

29

4. Experimental testing, EHF

4.1 Procedure Tests on Electrohydraulic Forming were carried of by the University of Oulu at the Stainless Steel Production Studio in Tornio. Tests were preformed on the selected grades, without a die, so called free expansion. Experiments were preformed with two different shaped dies, in this case the die means the shape of the opening in the clamping tool i.e. the base shape of the dome the blank is going to take after the forming process. The shapes of the die were circular with a diameter of 165 millimetres. The clamping force was set to 1200 kN.

Figure 23. Circular die used for the free expansion experiment[5]

The maximum height of the dome was searched by varying the input energy for respective grade. With the maximum energy found, without cracked sheet, tests were repeated with the maximum energy and an etched 5 millimetres circle grid. Measurements on the strain distribution were executed and plots of major and minor strain were preformed. Below are the machine used for the experiment.

Figure 24. The rig used for the Electrohydraulic Forming experiment in Tornio [5]

30

4.2 Material The selected grades for the EHF experiment are the ones marked in grey in the following table;

Table 6. Investigated material for EHF experiment and JC fitting.

Material Short name

Thickness [mm]

JC fitting

EHF experiment

EHF simulation

1.4016 0,8 √ √ √ 1.4512 0,8 √ 1.4509 0,8 √ √ √ 1.4301 0,8 √

Trip 700 1 √ √ √ DP 800 1 √ IF 210 0,9 √ √ √ HSLA 0,98 √

DPX 800 0,8 √ √ √ Inve

stig

ated

she

ets

1400 M 0,5 √

4.3 Results, EHF experiment Below are the free formed sheet of IF210 from the EHF experiments, number 7 in Figure 25, have been marked with an etch grid for a strain distribution measurement.

Figure 25. Formed sheets of grade IF 210 [5]

In Table 7 are the resulting energy and the corresponding dome height from the experiment with IF210. For other grades see appendix. Note, in the experiment, blank number five and six, the input energy is different but they have the same dome height. This indicates that these experiments are not very stringent and more experiments would be appreciated to be able to verify the simulation with an accurate conclusion.

31

Table 7. Input energy and resulting dome height [5]

In Figure 26 are the major and minor strain distribution from the IF210 experiments, also are the results from a traditional bulge test but those experiments are not considered in this report. For the other grades see appendix.

Figure 26. Strain distribution for different experiment with IF210 [5]

32

5. Finite element analysis A dynamic explicit Finite Element, FE analyses were carried out to investigate the possibility to do simulations on the Electrohydraulic Forming method. The simulations were validated through the dome height and the strain distributions from the Electrohydraulic Forming experiment, preformed by the University of Oulu. The program used for the simulation was ABAQUS Explicit.

5.1 The model The model consists of three parts, blank, die and water. The blank is the sheet material that is getting formed, simulation were carried out with five different grades, the same as the one used by the University of Oulu in the experiment. The diameter of hole in the die is 165 millimetres, the blank was made with a diameter of 175 millimetres which represent the diameter of the locking barb in the die with a shaped like a truncated cone, see Figure 27.

Figure 27. Die shaped like a truncated cone with a locking barb and die used for free forming

experiment [5] The die is the tool that shapes the blank, in the simulation the blank is free formed or gets a free expansion, this means that the die only restrict the diameter of the dome and also consists a rounded edge with a radius of 4 millimetres for the blank to get bend over, see Figure 27.

Figure 28. EHF-chamber used in the experiment in Torni [5].

The water is the media which is forming the blank, the water is shaped like the chamber that contains the water. In the EHF experiment the pressure is build up by an arc in the rear

33

end of the tool, which in the simulation is represented by a volume acceleration, placed in the end of the chamber. In Figure 28 is a sketch of the chamber used in the EHF experiment, the water have the same dimensions as the inside the chamber. Below are the three models used in ABAQUS.

Figure 29. Blank, die and water are the modelled parts in the FEM simulation

5.2 Properties The properties of the FE model are based on the properties of the specimen from the EHF experiment that were carried out by the University of Oulu.

5.2.1 Material properties, blank For the blank, the input properties were set to a density of 7800 [kg/m3], Young’s modulus was to 210 GPa and the Poisson’s ratio to 0.3. These properties were kept constant for all the simulated grades. For the plasticity, a Johnson-Cook material model with a strain rate dependent was used. Manually fitted JC material model parameters were used for the simulation. The procedure for obtaining the material parameters for the different grades was earlier described in this report. The blanks are modelled as a shell element and have in the section control, 5 integration points in thickness and the shell thickness is set to the corresponding thickness of sheet materiel from the EHF experiment.

Table 8. Material property for the simulated sheet materials Steel grade IF 210 DPX 800 1.4509 1.4016 Trip 700

Johnson-Cook A [MPa] 200 535 330 365 460

Johnson-Cook B [MPa] 420 960 580 700 1100

Johnson-Cook C 0,02 0,0103 0,020 0,019 0,0073

Johnson-Cook n 0,3 0,32 0,440 0,500 0,55

Johnson-Cook ep0 [1/s] 0,01 0,01 0,01 0,010 0,01

Density [kg/m3] 7800 7800 7800 7800 7800

Poisson’s ratio 0.3 0.3 0.3 0.3 0.3

Young’s modulus [GPa] 210 210 210 210 210

34

5.2.2 Material properties, water The property for the water was set to an acoustic medium with a density of 1000 [kg/m3] and a bulk modulus of 2.3·109 [Pa]. The bulk modulus, K can be defined as:

vV

pVK

∂∂−= Equation 9

In Equation 9 V is the volume and p is the pressure, the speed of sound, c can be described trough the following expression:

ρK

c = Equation 10

5.3 Interaction The Contact interaction between die and blank was set to a surface to surface condition, with contact property tangential behaviour and a friction coefficient of 0.1 in penalty. Between the water and the blank the contact interaction was a tie constraint, with the blank as the master surface and the water as the slave surface. The water had an acoustic impedance condition on the surface that represents the border to the EHF chamber. The condition on the water has been approximated with a non reflecting sphere with a radius of 0.1 meter.

Figure 30. The assembled model, picture from ABAQUS

5.4 Constraints The blank is constrained with an encastre condition i.e. locket on all 6 degree of freedom, on the border that represent the same diameter as the die has the locking barb in the EHF die, see Figure 27. The die is constrained on its reference point with an encastre condition. The water is constrained with an encastre condition, this constrain condition is put on the surface that borders to the EHF chamber.

35

Figure 31. All ingoing parts and there individual constrains in the ABAQUS model

5.5 Load The driving force in the EHF process is the arc in the back of the chamber. In the model it is represented by an acoustic inward volume acceleration placed on the centre of the back surface of the water. The pulse is represented by a Cosine-curve with amplitude of 1 and a length of 100 µs, see Figure 32. Different shapes of pulse have been evaluated but the shape of the pulse has no essential influence of dome height and the strain distribution. It is only the intergraded force under the curve that controls the degree of deflection of the dome.

Inward pulse

0,00

0,25

0,50

0,75

1,00

1,25

0,E+00 2,E-05 4,E-05 6,E-05 8,E-05 1,E-04 1,E-04

Time [s]

Am

plitu

de

Figure 32. The pulse used for the simulation in ABAQUS

Because of the complexity of the connection between the input energy in the experiment and the input volume acceleration in the simulation, a reference magnitude of the pulse is set, for grade IF210 so that the height of the formed blank, the dome, agree with the height of the dome in the EHF experiment. For the other grades, the reference magnitude is recounted with respect to there respective input energy in the experiment. The new magnitude i.e. the acceleration is changed with the square of the change relative to the reference magnitude, see Equation 11

qppq

paK

qEpaKpaKqE

aKEtamtammv

E

=⇒=

⇒=⋅⋅

⇒⋅⋅=⋅=⋅

⋅=⇒⋅⋅=⋅==

2

22

222

22222

)(

22

)(

2

Equation 11

36

In this Equation 11 E is the energy q is the changing fraction of the input energy and p is the changing fraction of the acceleration.

Figure 33. Assembled model and the location of the inward volume acceleration marked in red

5.6 Element types, meshes and rigid shell

5.6.1 Element type and mesh, blank The blank is modelled as a 3D deformable shell. Element type S4R; a 4-node doubly curved thin or thick shell, reduced integration, hourglass control, finite membrane strains. The mesh is a quadratic with a global seeding of 3 millimetres, except on the edge which has a much more refined seeding of 0.5 millimetres in the radius direction. This was necessary to be able to describe the rounded edge on the die, with a smooth strain distribution.

Figure 34. An enlargement of the refined meshed edge of the blank and the blank

37

IF 210 major and minor strain

-0,10

-0,05

0,00

0,05

0,10

0,15

0,20

0 0,02 0,04 0,06 0,08 0,1

Distance [mm]

Str

ain

LE 22

LE 11

Figure 35. Plot of the strain in the minor (LE22) and major (LE 11) direction versus the distance

on the radius In Figure 35 are the strains of the minor and major direction versus distance of the radius. The dip in the beginning of LE11 curve is the strain over the rounded edge of the die. The size of the mesh close to the edge of the blank was chosen with respect of the ability to describe this rounded edge of the die.

38

Strain,different element size of the blank

-0,10

-0,05

0,00

0,05

0,10

0,15

0,20

-0,05 0,00 0,05 0,10 0,15 0,20

LE22

LE11

Blank 1,5mm

Blank 3mm

Blank 6mm

Figure 36. Plot of the strain distribution with the minor versus major direction, with different

element size of the blank In the figure above are the stain distributions of a path in the blank, with different mesh sizes. The path goes from the edge to the centre of the blank. Different sizes of the blank mesh were simulated to verify that the solution had reached convergences. It was decided to use the 3 millimetres mesh on the blank.

Dome height

36

37

38

39

0 2 4 6 8 10 12 14 16

Mesh size [mm]

Dom

e he

ight

[mm

]

Water size, Blank size=3mm

Blank size, Water size=4mm

Figure 37. Plot of the dome height with different mesh sizes on the blank and the water, to

investigate the convergence of the solution Figure 37 contains plot of the dome height with different element sizes of the blank and the water. Different simulations were preformed with element size changed on the blank and

39

element size fixed on water. This was also preformed for the convergence check of the water element size, with water element size changed and blank element size fixed. It was in agreement with the conclusions of the plot of strain distribution, see Figure 36, to use a element size of 3 millimetres on the blank.

5.6.2 Element type and mesh, water The water is modelled as a 3D deformable solid. Element type AC3D8R: an 8-node linear acoustic brick, reduced integration, hourglass control. The element is a hexagonal acoustic type with a seeding of 50 elements on one base diameter (4 millimetres) and element height of 13 millimetres.

Figure 38. Tree different views of the meshed water

Strain,different element size of the water

-0,10

-0,05

0,00

0,05

0,10

0,15

0,20

-0,05 0,00 0,05 0,10 0,15 0,20

LE22

LE11

Water 4mm

Water 7.7mm

Water 2mm

Figure 39. Plot of the strain distribution with the minor versus major direction, with different

element size of the water

In the figure above are the stain distributions of a path in the blank, with different mesh sizes of the water. The path goes from the edge to the centre of the blank. Different sizes of the water were simulated to verify that the solution had converged. It was decide to use the

40

4 millimetres mesh on the water. A convergence check of the dome height was also preformed to verify that the solution had reached convergence, see Figure 37. The 4 millimetre mesh size was in agreement of this check as well.

5.6.3 Rigid body, die The die is modelled as a 3D analytical rigid shell.

Figure 40. Die used in the free expansion simulation from ABAQUS

5.7 Results Below are the different input magnitudes of acceleration from the simulation and the corresponding dome height and maximum strain rate. IF 210 is the reference grade, which all other magnitudes are based on, they are recalculated through Equation 11 and the input energy from the experiment. Table 9. EHF experimental input energy and dome height, the corresponding simulation input acceleration and dome height

Grade Experiment Input energy

[KJ]

Experiment Dome height

[mm]

Simulation Input magnitude of

acceleration

Simulation Dome height [mm]

Simulation Maximum strain

rate [1/s] IF 210 reference 20.2 36 6.9e4 36.1 1345 DPX 800 26.1 37.5 7.87e4 28.4 1307 TRIP 700 27.7 46 8.08e4 30.4 1112 1.4509 20.2 32 6.9e4 31.9 1149 1.4016 18.8 35 6.62e4 31.8 918

Below is a picture of one iso-plot from the simulation of IF 210 in ABAQUS. Magnitude, U in this picture is the height the deformed blank this value has been used as the dome height, which has been used for the searching of the reference magnitude of the acceleration.

41

Figure 41. Iso-plot from the simulation with IF 210 in ABAQUS, showing the dome height as

magnitude Below are the obtained dome heights from the simulations with the corresponding experimental dome height.

Dome height with assumed acceleration

0

5

10

15

20

25

30

35

40

45

50

0 5 10 15 20 25 30 35 40

Simulated Height

Exp

erim

enta

l Hei

ght

DPX 800

Trip 700

1.4509

1.4016

IF210

Figure 42. Obtained dome height of the simulation and there corresponding experimental dome

height with the assumed relation between energy and acceleration, a 45 degree line is drawn to the reference grade, IF210.

42

Material 1.4509 obtained same dome height as in the experiment. Material 1.4016 obtained 3.2 millimetres lower height in the simulation than in the experiment, this can be considered as a good agreement. Material DPX 800 and TRIP 700 are of less agreement with 9.1 and 15.6 millimetres respective lower than in the experiment, this can be considered as of less agreement. Overall, all simulations were lower or equal than the experimental dome heights. Below are plots of the strain rates on one path on the blank through the simulation. On the strain rate axis are the maximum in plane strain rate. On the Node number axis are the nodes on the path, node 1 is on the edge and node 43 on the centre of the blank. On the Time frame axis are 20 time steps from the simulation, one step is 2.5e-6 seconds. Every time step shows the momentary strain rate on the corresponding nodes. On all grades, the maximum strain rate is in the centre or close to the centre of the blank. IF 210 has the highest strain rate, the slowest strain rate has grade 1.4016, see Table 9. The maximum strain rate is not corresponding to the maximum input volume acceleration. IF 210 with the lowest flow stress has the highest strain rate. Grade DPX 800, 1.4016 and TRIP 700 have a local strain rate peak in the end of the simulation on the nodes located on the rounded edge of the die.

1

6

11

16

21

26

31

36

41

S1

S10

S19

0100200300400500600

700800

900

1000

1100

1200

1300

1400

Strain rate[1/s]

Node number

Time frame0 to 5e-5 s

Strain rate IF 210

1300-14001200-1300

1100-12001000-1100900-1000

800-900700-800600-700

500-600400-500

300-400200-300100-200

0-100

Figure 43. The plot is showing the strain rates from the simulation in ABAQUS with IF210,

obtained maximum strain rate 1345/s . On the Node number axis are the nodes from a path which goes from the edge to the centre of the blank, the Time frame axis is showing the time frame from 0

until 5e-5 s when the simulation stops and the Strain rate axis is showing the maximum in plane strain rate.

43

1

6

11

16

21

26

31

36

41

S1

S10

S19

0100200300400500600700800900100011001200

1300

1400

Strain rate[1/s]

Node number


Strain rate DPX 800

1300-1400

1200-1300

1100-1200

1000-1100

900-1000

800-900

700-800

600-700

500-600

400-500

300-400

200-300

100-200

0-100

Figure 44. The plot is showing the strain rates from the simulation in ABAQUS with DPX 800,

obtained maximum strain rate 1307/s. On the Node number axis are the nodes from a path which goes from the edge to the centre of the blank, the Time frame axis is showing the time frame from 0


1

6

11

16

21

26

31

36

41

S1

S10

S19

0

100

200

300

400

500

600

700

800

900

1000

1100

1200

Strain rate[1/s]

Node number


Strain rate TRIP 700

1100-1200

1000-1100

900-1000

800-900

700-800

600-700

500-600

400-500

300-400

200-300

100-200

0-100

Figure 45. The plot is showing the strain rates from the simulation in ABAQUS with TRIP 700,



44

1

6

11

16

21

26

31

36

41

S1

S10

S19

0

100

200

300

400

500

600

700

800

900

1000

1100

1200

Strain rate[1/s]

Node number


Strain rate 1.4509

1100-1200

1000-1100

900-1000

800-900

700-800

600-700

500-600

400-500

300-400

200-300

100-200

0-100

Figure 46. The plot is showing the strain rates from the simulation in ABAQUS with 1.4509,



1

6

11

16

21

26

31

36

41

S1

S10

S19

0

100

200

300

400

500

600

700

800

900

1000

Strain rate[1/s]

Node number


Strain rate 1.4016

900-1000

800-900

700-800

600-700

500-600

400-500

300-400

200-300

100-200

0-100

Figure 47. The plot is showing the strain rates from the simulation in ABAQUS with 1.4016,



45

Below are the major and minor strain distribution plots, from all the simulated grades and with the assumed connection between the energy and the acceleration, see Equation 11, plotted with the measured major and minor strain distribution from the experiment. The plotted strains LE11 and LE22 are the major and minor strains from the experiment on a path which goes from the edge to the centre of the blank.

Major and minor strain IF 210

0,00

0,04

0,08

0,12

0,16

0,20

0,24

0,00 0,04 0,08 0,12 0,16 0,20Strain, LE22

Str

ain,

LE

11

Simulated, Dome height 36,08 mmExperimental EHF, Dome height 36 mm

Figure 48. IF 210, major and minor strain distribution from edge to centre of the blank in the EHF simulation in ABAQUS plotted with corresponding strain distribution from the EHF experiment.

Material IF 210, above was used as the reference material, and has the same dome height in the simulation as in the experiment. The plot has a fairly comparable strain distribution with the measured strain distribution from the experiment and the simulated. The measured experimental major strain, LE11 from the experiment is higher than from the simulation. This can be an effect of that the material is anisotropic and the model used in ABAQUS do not describe this phenomena.

46

Major and minor strain DPX 800

0,00

0,04

0,08

0,12

0,16

0,20

0,00 0,04 0,08 0,12 0,16 0,20Strain, LE22

Stra

in, L

E11

Simulated, Dome height 28,4 mm

Experimental, Dome height 37,5 mm

Figure 49. DPX 800, major and minor strain distribution from edge to centre of the blank in the

EHF simulation in ABAQUS plotted with corresponding strain distribution from the EHF experiment.

Material DPX 800, above has a 9.1 millimetres lower dome height on the simulated sample than the experimental. The strain distribution plot is in good agreement in the lower strain region but the obtained maximum experimental strain are higher than the obtained maximum strain from the simulation, which can be expected with the lower dome height. The experimental strain is not excessive anisotropic and has a similar major and minor strain at maximum.

47

Major and minor strain Trip 700

0,00

0,04

0,08

0,12

0,16

0,20

0,24

0,00 0,04 0,08 0,12 0,16 0,20 0,24Strain, LE22

Stra

in, L

E11


Experimental, Dome height 46

Figure 50. TRIP 700, major and minor strain distribution from edge to centre of the blank in the

EHF simulation in ABAQUS plotted with corresponding strain distribution from the EHF experiment.

Material TRIP 700, above obtained 15 millimetre lower dome height in the simulation than in the experiment. The strain distribution has a good agreement in the lower strain regions but the experimental measurement obtained a much higher strain then the simulated. This can be expected because of the difference in dome height. This material is slightly anisotropic which can not be described with the model.

48

Major and minor strain 1.4509

0,00

0,04

0,08

0,12

0,16

0,00 0,04 0,08 0,12 0,16Strain, LE22

Stra

in, L

E11


Experimental, Dome height 32 mm

Figure 51. 1.4509, major and minor strain distribution from edge to centre of the blank in the EHF simulation in ABAQUS plotted with corresponding strain distribution from the EHF experiment.

Material 1.4509, above has the same dome height in the simulation as in the experiment. The obtained strain distribution from the experiment has a very good agreement with the measured strain distribution. The material is slightly anisotropic and that part can not be described with the model.

49

Major and minor strain 1.4016

0,00

0,04

0,08

0,12

0,16

0,20

0,00 0,04 0,08 0,12 0,16 0,20Strain, LE22

Stra

in, L

E11

Simulated, Dome Height 31,8 mm Experimental, Dome Height 35 mm

Figure 52. 1.4016, major and minor strain distribution from edge to centre of the blank in the EHF simulation in ABAQUS plotted with corresponding strain distribution from the EHF experiment.

Material 1.4016, above has a fairly similar dome height with only 3.2 millimetres lower dome height than in the experiment. The strain distribution plot has a reasonably good agreement between the simulated and the experimental strain distribution. The maximum strain from the simulation is not as high as the measured experimental. The experimental measurement shows no tendency to be anisotropic in the strain distribution plot.

50

6. Discussion The work described in this report can be categorized as the fitting of the Johnson-Cook constitutive material model and the Finite Element Method simulation of the high velocity forming method, Electrohydraulic Forming, EHF.

6.1 Fitting of the Johnson-Cook material model An extensive amount of tensile tests have been carried out in three different strain rate ranges from ~0.0001/s to ~1000/s for ten different materials within the HI_VEL project. The test data were delivered to Swerea KIMAB in true and engineering stress. Test data in true stress were recalculated to engineering stress. The curves of the tensile test data were plotted for respective grade and strain rate range. The plotted curves were reviewed and sorted, so the selected part were following a pattern possible for the JC model to describe, with an increased strength and with an increasing strain rate, no initial peaks or Lüders phenomena present on the curves. The selected test data were gathered for respective grade and modified to obtain same number of points per curve, with a linear interpolation procedure and then with the least square method the parameters were searched to optimise the fit of the model to the test data, all performed in MATLAB. The quality of the fit of the model was estimated by a standard deviation value, a subjective estimation was also carried out by reviewing the model and the test data in the same plot. The model was to be used in the FEM simulation of the high velocity forming method, EHF. It was decided that the model should be manually fitted to obtain a good fit on stress curves with high strain and strain rates. The obtained parameters from the least square fitting were changed until the fit of the model were in good agreement on the high strain and strain rate curves. The investigated materials, obtained model parameters for the least square and manually fitting and the standard deviation value can be seen in Table 4 and Table 5, respectively. The standard deviation values from the manual fitting are spanning from 13 to 38.4 MPa. Some of the factors that are affecting the standard deviation value are;

• number of available strain rate curves, which were used for the calculating of standard deviation value

• oscillation on the test data curves, especially if there were a few number of available test data

• the models ability to describe the shape or curvature of the test data • the models ability to describe the strain rate sensitivity

The strain rate sensitivity, parameter C, is in general lower for material with a high tensile strength and higher for material with lower tensile strength. One exception is grade 1.4301, a stainless steel with retained austenite, the material have fairly high tensile strength of 662 MPa but a rather high C parameter of 0.025. One other exception is material IF 210 an Intestinal Free steel type with a low tensile strength obtained a rather low C value. The lowest strain rate sensitivity has material 1400M which also has the highest tensile strength. The highest strain rate sensitivity has material HSLA of 0.06, which is also one of the materials with the lowest tensile strength.

51

6.2 Simulation of EHF free forming Experiments have been carried out on the forming method Electrohydraulic Forming, EHF within the HI_VEL project. The experiment was preformed with selected material described in Table 1. Results from the experiments were delivered to Swerea KIMAB in input energy, dome height and strain distribution. A model of the experiment equipment was built in ABAQUS. The property of the different material was described with the Johnson-Cook material model. There was decided to use a reference acceleration due to the input force in the model was in acceleration and in the experiment it was energy, and the complexity of the mechanism in experiment, such as pressure, velocity, pulse shape, reflection coefficients, absorption effects, bubble effects and efficiency coefficients. IF 210 was selected to be used for the production of the reference acceleration. Different simulations were preformed with different input acceleration with the reference material, until the dome height was the same as in the experiment. Acceleration used for that simulation was selected to be the reference acceleration. For the other simulations the input energy in the experiment were recalculated to an input acceleration with the relation as described in Equation 11. Dome heights and strain distribution plots were performed and compared with the experimental results, more details can be seen in chapter 5.7 above. Plots on the strain rate were also produced and evaluated with respect of the assumption, that the forming procedure occurs under high strain rates.

• Material IF 210 was used to produce the reference acceleration and consequently the dome height in the simulation is the same as in the experiment.

• Material 1.4509 obtained same dome height as in the experiment, can be considered as of very good agreement.

• Material 1.4016 obtained 3.2 millimetres lower height in the simulation than in the experiment, this can be considered as a good agreement.

• Material DPX 800 is of less agreement with 9.1 millimetres lower than in the experiment.

• Material TRIP 700 obtained a dome height of 15.6 millimetres this can be considered as of less agreement.

Overall all simulations were lower or equal than the experimental dome heights. The dome height is in some case in very good agreement with the experimental dome heights, two of the investigated materials were of less agreement in dome heights. The strain distributions are in reasonably or good agreement of the measured experiment distribution, especially those with good agreement of the dome height. The strain rates during the forming process are high, in agreement with the assumption.

• Material IF 210 was used as the reference material, and has the same dome height in the experiment. The strain distribution is fairly comparable with the strain distribution from the experiment. The measured experimental major strain from the experiment is higher than from the simulation. This can be an effect of an anisotropic material. This phenomenon is not described in ABAQUS and can consequently not be described.

• Material 1.4509 has the same dome height in the simulation as in the experiment. The obtained strain distribution from the experiment has a very good agreement with the measured strain distribution.

52

• Material 1.4016 has a fairly similar dome height with only 3.2 millimetres lower dome height than in the experiment. The strain distribution has a reasonably good agreement between the simulated and the experimental strain distribution. The maximum strain from the simulation is not as high as the measured from the experiment.

• Material DPX 800 has a 9.1 millimetres lower dome height on the simulated sample than the experimental. The strain distribution is in good agreement in the lower strain region but the obtained maximum experimental strain are higher than the obtained maximum strain from the simulation, which can be expected with the lower dome height.

• Material TRIP 700 obtained 15 millimetre lower dome height in the simulation than in the experiment. The strain distribution has a good agreement in the lower strain regions but the experimental measurement obtained a much higher strain then the simulated. This can be expected because of the difference in dome height.

53

7. Conclusions

7.1 Fitting of the Johnson-Cook material model

Fitting of the Johnson-Cook, JC material model has been carried out for flow curves of ten mild, high strength and stainless steels, with strain rates ranging from 0.0001 to 1500 per second. The fitting has been performed with a least square method and a manual fitting method. • The standard deviation for difference between the model and the test data span

from 13 to 38 MPa. Factors that are affecting the standard deviation are oscillation, number of available strain rate curves, ability to describe the shape, curvature and the strain rate sensitivity.

• The strain rate sensitivity, parameter C, is in general lower for material with a higher tensile strength.

• The parameter C is ranging from 0.006 to 0.06.

7.2 Simulation of EHF, free forming

Finite element simulations have been carried out with ABAQUS Explicit on the high velocity forming technique, Electrohydraulic Forming, EHF. In the simulation, the manually fitted JC models are used to describe the mechanical property of the investigated grades. The simulations were verified with EHF experiments preformed within the HI_VEL project. • The simulations gave maximum press heights which were within 34 % of

experimental heights. • The strain distributions are in reasonably good agreement with the measured

experiment distribution, especially those with good agreement of press height. • The peak strain rates during the forming process are high, around 1000/s and

above.

54

8. Further work The work presented in this report involves the fitting of the Johnson-Cook material parameters and the Finite Element Method simulation of the high velocity forming method Electrohydraulic Forming. In the author’s opinion further work could be investigation of:

8.1 Further work, fitting of Johnson-Cook model If more tensile tests were to be carried out for the investigated grades, a much clearer view of the exact progress is strength with higher strain rates, questions about excluded strange test data would be answered For the manually fitted models is seems to be many ways to describe the test data and no correct answer. The model has limitations and the fit must be adjusted to the purpose. This adjustment can with this model and test data be change in infinitely different ways. Further verifications that the model is fitted for the right region of strain rates, for the investigated purpose, the FEM simulation.

8.2 Further work, simulation of EHF According to the literature review there has not been an extensive amount of simulation on EHF. So further verifications on:

• the connection between the used energy and the input acceleration • complexity of the mechanism of experiment, all parameters in the experiment that

effects the result • the acoustic impedance and reflection coefficients, no data were available on this so

the assumed acoustic impedance can be more refined • how the pressure varies during the experiment, what is the maximum pressure and

when does it occur and for how long, what is the shape of pressure pulse • the velocity of the strain rate during the experiment, are the strain rates from the

simulation, close to the experimental • absorption effects, which surfaces are reflecting or absorbing and to what extends • bubble effects, in the experiment there are most likely a bubble formed in the

forming process, how is this bubble effecting the energy needed and the shape of the blank

• efficiency coefficients, it is wanted to connect the needed energy to a specific deflection of the blank

• more experimental data with a finer resolution are needed to do further verification and simulation

55

9. Acknowledgements This work was financed by Swerea KIMAB and RFCS and was a part of the RFCS project HI_VEL. The author would like to express his gratitude to the persons that has been involved in this work, and especially to the following persons:

• Prof. Arne Melander, Swerea KIMAB, for guidance throughout the work

• Tech. Lic. Johannes Gårdstam, Swerea KIMAB, for extensive support on numerical programming and FEM simulations

• Tech. Dr. Olle Skrinjar, Swerea KIMAB, who did the first versions of the FEM

model

• Ludovic Samek, Voest Alpine Stahl, who was responsible for the tensile testing in HI_VEL, for many discussions on the background of the tensile data and the evaluation of the tests. RFSR-CT-2006-00026

56

10. References [1] Opportunities in High-Velocity Forming of Sheet Metal – Metal Forming Magazine – http://archive.metalformingmagazine.com/1997/01/mfjan5.htm, 2007-10-29 [2] Glenn S. Daehn, High Velocity Sheet Metal Forming: State of the Art and Prognosis for Advanced Commercialization, Department of Materials Science and Engineering, the Ohio State University [3] Tuğrul Özel and Yiğit karpat, Identification of constitutive material model parameters for high strain rate metal cutting condition using evolutionary computational algorithms, Department of Industrial and Systems Engineering, Rutgers University [4] ESIS P7-00: Procedure for Dynamic Tensile Tests, ESIS Procedures and Documents, Subcommittee on Dynamic Testing at Intermediate Strain Rates, ISSN 1616-2129, August 2000 [5a] Six-monthly Report no 1, High velocity steel sheets and tubes for applications in the automotive industry, Research Programme of the Research Fund for Coal and Steel, Steel RTD, 01/07/06 – 31/12/06 [5b] Six-monthly Report no 2, High velocity steel sheets and tubes for applications in the automotive industry, Research Programme of the Research Fund for Coal and Steel, Steel RTD, 01/01/07 – 31/06/07 [5c] Mid-Term Report no 3, High velocity steel sheets and tubes for applications in the automotive industry, Research Programme of the Research Fund for Coal and Steel, Steel RTD, 01/07/06 – 31/12/07 [6] J. Varis and H. Martikka, Prototyping of 3D Sheet metal parts using electro hydraulic forming, Lappeeranta University of Technology, Finland, 2005 [7] W. Bleck, P. Larour and A. Bäumer, Dynamic tensile testing and modelling of advanced high strength Steels, Department of Ferrous Metallurgy, RWTH Aachen Universety, Germany, 2006 [8] V. S. Balanethiram, Xiaoyu Hu, Marina Altynova and Glenn S Daehn, Hyperplasticity: Enhanced Formabilety at High Rates, Department of Material Science and Engineering, The Ohio state university, 1994 [9] H. Couque, R. Boulanger and F. Bornet, A modified Johnson-Cook model for strain rates range from 10-3 to 105 s-1, Journal De Physique IV, Eurodymat, 2006 [10] Sergey F. Golovashchenko and Vyachesjav S. Mamutov, Electrohydraulic Forming of Automotive Panels, The minerals and Material Society, 2005

57

Appendix A — Plot 1.4016

Aachen1.4016

200

300

400

500

600

700

800

0,00 0,02 0,04 0,06 0,08 0,10 0,12 0,14 0,16

True strain

Tru

e S

tres

s [M

Pa]

0,81/s Aachen VDA00001



11,65/s Aachen VDB00001



103,9/s Aachen VDC00001


110.0/s Aachen VDC00003

Veostalpine1.4016

200

300

400

500

600

700

0,00 0,02 0,04 0,06 0,08 0,10 0,12 0,14 0,16 0,18 0,20

True strain

Tru

e S

tres

s [M

Pa] 0,00010/s Voestalpine 2/1

0,00010/s Voestalpine 2/2









58

Tempere1.4016

200

300

400

500

600

700

800

0 0,02 0,04 0,06 0,08 0,1 0,12 0,14 0,16 0,18 0,2

True strain

Tru

e S

tres

s [M

Pa]

1350/s Tempere 0

Available strain rates1.4016

200

300

400

500

600

700

800

0 0,02 0,04 0,06 0,08 0,1 0,12 0,14 0,16 0,18 0,2

True Strain

Tru

e S

tres

s [M

Pa]

1350/s Tempere 0









59


200

300

400

500

600

700

800

0,00 0,02 0,04 0,06 0,08 0,10 0,12 0,14 0,16 0,18 0,20

True Stain

Tru

e S

tres

s [M

Pa]

Experimental

JC model

excluded data

Above is the least square fitting of grade 1.4016

60

Appendix B — Plot 1.4301

Aachen1.4301

300

400

500

600

700

800

900

1000

1100

0,00 0,02 0,04 0,06 0,08 0,10 0,12 0,14 0,16 0,18 0,20 0,22 0,24 0,26 0,28 0,30 0,32 0,34 0,36 0,38

True strain

Tru

e S

tres

s [M

Pa]

0,81/s Aachen VCA00001



8,65/s Aachen VCB00001


8,73/s Aachen VB00003

92,50/s Aachen VCC00001



Veostalpine1.4301

200

300

400

500

600

700

800

900

1000

1100

0,00 0,02 0,04 0,06 0,08 0,10 0,12 0,14 0,16 0,18 0,20 0,22 0,24 0,26 0,28 0,30 0,32 0,34 0,36 0,38

True strain

Tru

e S

tres

s [M

Pa] 0,00010/s Voestalpine 1/4









61

Tempere1.4301

200

300

400

500

600

700

800

900

1000

1100

0 0,02 0,04 0,06 0,08 0,1 0,12 0,14 0,16 0,18 0,2 0,22 0,24 0,26 0,28 0,3 0,32 0,34 0,36 0,38

True strain

Tru

e S

tres

s [M

Pa]

1100/s Tempere 0


200

300

400

500

600

700

800

900

1000

1100

0 0,02 0,04 0,06 0,08 0,1 0,12 0,14 0,16 0,18 0,2 0,22 0,24 0,26 0,28 0,3 0,32 0,34 0,36 0,38

True Strain

Tru

e S

tres

s [M

Pa]

1100/s Tempere 0









62

1.4301 True vs. model

200

300

400

500

600

700

800

900

1000

1100

1200

0 0,02 0,04 0,06 0,08 0,1 0,12 0,14 0,16 0,18 0,2 0,22 0,24 0,26 0,28 0,3 0,32 0,34 0,36 0,38

True Strain

Tru

e st

ress

[MP

a]

Experimental

JC model

Excluded data


63

Appendix C — Plot 1.4509

Voestalpine1.4509

200

300

400

500

600

700

0,00 0,05 0,10 0,15 0,20 0,25 0,30

True Strain

Tru

e S

tres

s











Aachen1.4509

300

350

400

450

500

550

600

650

700

0,00 0,02 0,04 0,06 0,08 0,10 0,12 0,14 0,16 0,18

True Strain

Tru

e S

tres

s

0,91/s Aachen VFA00001



14,2/s Aachen VFB00001



120,1/s Aachen VFC00002



64

Gent1.4509

300

400

500

600

700

800

0,00 0,02 0,04 0,06 0,08 0,10 0,12 0,14 0,16 0,18 0,20

True Strain

Tru

e S

tres

s

1130/s Gent P1

1750/s Gent P3

1376/s Gent P4

897/s Gent P5

739/s Gent P6

1270/s Gent P7

1615/s Gent P8

Tempere/Gent1.4509

300

400

500

600

700

0,00 0,02 0,04 0,06 0,08 0,10 0,12 0,14 0,16True Strain

Tru

e S

tres

s

1100/s Tempere 0

1150/s Tempere 1

897/s Gent P5

739/s Gent P6

1270/s Gent P7

65


200

300

400

500

600

700

0 0,02 0,04 0,06 0,08 0,1 0,12 0,14 0,16 0,18 0,2 0,22 0,24

True Strain

Tru

e S

tres

s [M

Pa]

1100/s Tempere 0

1130/s Gent P1










200

300

400

500

600

700

0 0,02 0,04 0,06 0,08 0,1 0,12 0,14 0,16 0,18 0,2 0,22 0,24

True Strain

Tru

e S

tres

s [M

Pa]

Experimental

JC model

Excluded data


66

Appendix D — Plot 1.4512

Aachen1.4512

200

250

300

350

400

450

500

550

600

650

700

0,00 0,02 0,04 0,06 0,08 0,10 0,12 0,14 0,16 0,18 0,20

True strain

Tru

e S

tres

s [M

Pa]

0,92/s Aachen VEA00001



11,65/s Aachen VEB00001



113,96/s Aachen VEC00001

112,64 Aachen VEC00002

110.0/s Aachen VEC00003

Tempere1.4512

200

250

300

350

400

450

500

550

600

650

0 0,02 0,04 0,06 0,08 0,1 0,12 0,14 0,16 0,18 0,2

True strain

Tru

e S

tres

s [M

Pa]

1300/s Tempere 0

67


200

300

400

500

600

700

800

0 0,02 0,04 0,06 0,08 0,1 0,12 0,14 0,16 0,18 0,2

True Strain

Tru

e S

tres

s [M

Pa]

1300/s Tempere 0

113,96/s Aachen VEC00001




200

300

400

500

600

700

800

0,00 0,02 0,04 0,06 0,08 0,10 0,12 0,14 0,16 0,18 0,20

True Stain

Tru

e S

tress

[MP

a]

Experimental

JC model

Excluded data


68

Appendix E — Plot 1400 M

Aachen1400M

1100

1200

1300

1400

1500

1600

1700

0,00 0,00 0,00 0,01 0,01 0,01 0,01 0,01 0,02 0,02 0,02 0,02 0,02 0,03 0,03 0,03

True strain

Tru

e S

tres

s [M

Pa]

0,73/s Aachen VJA00001



11,65/s Aachen VJB00001



103,9/s Aachen VJC00001


110.0/s Aachen VJC00004

Available strain rates1400M

1100

1200

1300

1400

1500

1600

1700

0,00 0,00 0,00 0,01 0,01 0,01 0,01 0,01 0,02 0,02 0,02 0,02 0,02 0,03 0,03 0,03

True Strain

Tru

e S

tres

s [M

Pa]




69

Model vs. true stress1400M

1100

1200

1300

1400

1500

1600

1700

0,00 0,01 0,01 0,02 0,02 0,03 0,03

True Stain

Tru

e S

tress

[MP

a]

Experimental

JC model

Excluded data

Above is the least square fitting of grade 1400M

70

Appendix F — Plot DPX 800

VeostalpineDPX 800

600

700

800

900

1000

0,00 0,02 0,04 0,06 0,08 0,10 0,12 0,14

True Strain

Tru

e S

tres

s[M

Pa]











AachenDPX 800

600

700

800

900

1000

1100

1200

0,00 0,02 0,04 0,06 0,08 0,10 0,12

True Strain

Tru

e S

tres

s [M

Pa]

0,78/s Aachen VIA00001



9,9/s Aachen VIB00001



97,1/s Aachen VIC00001

98,7s Aachen VIC00002

98,8s Aachen VIC00003

71

Tempere/GentDPX 800

600

700

800

900

1000

1100

1200

0,00 0,02 0,04 0,06 0,08 0,10 0,12 0,14 0,16

True Strain

Tru

e S

tres

s[M

Pa]

1450/s Tempere 0

xxxx/s Tempere 1

1669/s Gent P3

1375/s Gent P4

833/s Gent P5

578/s Gent P6

1064/s Gent P7

1317/s Gent P8

GentDPX 800

600

700

800

900

1000

1100

0,00 0,02 0,04 0,06 0,08 0,10 0,12 0,14

True Strain

Tru

e S

tres

s [M

Pa]

914/s Gent P1

1220/s Gent P2

1669/s Gent P3

1375/s Gent P4

833/s Gent P5

578/s Gent P6

1064/s Gent P7

1317/s Gent P8

72

Available strain ratesDPX 800

600

700

800

900

1000

1100

1200

0 0,02 0,04 0,06 0,08 0,1 0,12 0,14

True Strain

Tru

e S

tres

s [M

Pa]

1450/s (Oulu, Finland)









1669/s Gent P3

578/s Gent P6

Above is the least square fitting of grade DPX 800

73

Appendix G — Plot HSLA

AachenHSLA

300

350

400

450

500

550

600

650

700

750

0,00 0,02 0,04 0,06 0,08 0,10 0,12 0,14 0,16 0,18

True Strain

Tru

e S

tres

s







125,6/s Aachen VHC00001

123,2s Aachen VHC00002

124s Aachen VHC00003

TempereHSLA

300

400

500

600

700

0,00 0,02 0,04 0,06 0,08 0,10 0,12 0,14 0,16 0,18

True Strain

Tru

e S

tres

s

1300/s Tempere 0

74

Available strain ratesHSLA

300

350

400

450

500

550

600

650

700

0 0,02 0,04 0,06 0,08 0,1 0,12 0,14 0,16 0,18

True Strain

Tru

e S

tres

s [M

Pa]

1300/s Tempere 0



123,2s Aachen VHC00002

Model vs. true stressHSLA

300

350

400

450

500

550

600

650

700

0,00 0,02 0,04 0,06 0,08 0,10 0,12 0,14 0,16 0,18

True Stain

Tru

e S

tres

s [M

Pa]

Experimental

JC model

Dismissed data

Above is the least square fitting of grade HSLA

75

Appendix H — Plot Trip 700

VoestalpineTRIP 700

300

400

500

600

700

800

900

1000

0,00 0,05 0,10 0,15 0,20 0,25 0,30

True Strain

Tru

e S

tres

s











AachenTRIP 700

300

400

500

600

700

800

900

1000

1100

1200

0,00 0,02 0,04 0,06 0,08 0,10 0,12 0,14

True Strain

Tru

e S

tres

s



0,78 (Aachen, Germany)


9,8 (Aachen, Germany)

8,2(Aachen, Germany)




76

TempereTRIP 700

400

500

600

700

800

900

1000

1100

0 0,05 0,1 0,15 0,2 0,25

True strain

Tru

e st

ress

1350/s Tempere 0

1350/s Tempere 1

1350/s Tempere 2

1480/s Tempere 3

GentTRIP 700

300

400

500

600

700

800

900

1000

1100

0,00 0,05 0,10 0,15 0,20 0,25 0,30

True Strain

Tru

e S

tres

s

1163/s Gent P1

901/s Gent P2

624/s Gent P3

1172/s Gent P4

1471/s Gent P5

1734/s Gent P6

1629/s Gent P7

77

Available strain ratesTRIP 700

200

300

400

500

600

700

800

900

1000

1100

1200

0,00 0,02 0,04 0,06 0,08 0,10 0,12 0,14 0,16 0,18 0,20 0,22 0,24 0,26 0,28

True Strain

Tru

e S

tres

s [M

Pa] 92,7/s (Aachen, Germany)








1350/s Tempere 1

1163/s Gent P1

Model vs. true stressTRIP 700

400

500

600

700

800

900

1000

1100

1200

0,00 0,02 0,04 0,06 0,08 0,10 0,12 0,14 0,16 0,18 0,20 0,22 0,24 0,26 0,28

True Strain

Tru

e S

tres

s [M

Pa]

Experimental

JC model

Excluded data

Above is the least square fitting of grade TRIP 700

78

Appendix I — Plot DP 800

AachenDP 800

200

300

400

500

600

700

800

900

1000

1100

0,00 0,02 0,04 0,06 0,08 0,10 0,12 0,14 0,16 0,18 0,20 0,22 0,24

True strain

Tru

e S

tres

s [M

pa]

0,80/s Aachen VBA00001



11,6/s Aachen VBB00001

11,6/s Aachen VBB00002

11,6/s Aachen VGB00003

99,5/s Aachen VBC00001

97,3/s Aachen VGC00002

97,9/s Aachen VBC00003

TempereDP 800

500

600

700

800

900

1000

1100

1200

0 0,02 0,04 0,06 0,08 0,1 0,12 0,14 0,16 0,18

True strain

Tru

e S

tres

s [M

Pa]

1250/s Tempere 0

1163/s Gent P1

901/s Gent P2

79

GentDP 800

500

600

700

800

900

1000

1100

1200

0 0,02 0,04 0,06 0,08 0,1 0,12 0,14 0,16 0,18

True strain

Tru

e S

tres

s [M

pa]

1163/s Gent P1

901/s Gent P2

624/s Gent P3

1172/s Gent P4

1471/s Gent P5

1734/s Gent P6

1629/s Gent P7

Available strain ratesDP 800

300

400

500

600

700

800

900

1000

1100

1200

0 0,02 0,04 0,06 0,08 0,1 0,12 0,14 0,16 0,18 0,2

True Strain

Tru

e S

tres

s [M

Pa]

1250/s Tempere 099,5/s Aachen VBC0000111,6/s Aachen VBB000010,80/s Aachen VBA000011163/s Gent P1

80

Model vs. true stressDP 800

300

400

500

600

700

800

900

1000

1100

1200

0,00 0,02 0,04 0,06 0,08 0,10 0,12 0,14 0,16 0,18 0,20

True Stain

Tru

e S

tres

s [M

Pa]

Experimental

JC Model

Excluded data

Above is the least square fitting of grade DP 800

81

Appendix J — Plot IF210

AachenIF 210

200

250

300

350

400

450

500

550

600

650

0,00 0,02 0,04 0,06 0,08 0,10 0,12 0,14 0,16 0,18 0,20

True strain

Tru

e S

tres

s [M

pa]

0,76/s Aachen VGA00001










VeostalpineIF 210

100

150

200

250

300

350

400

450

500

550

0,00 0,02 0,04 0,06 0,08 0,10 0,12 0,14 0,16 0,18 0,20 0,22 0,24 0,26 0,28 0,30 0,32

True strain

Tru

e S

tres

s [M

pa]











82

TempereIF 210

300

350

400

450

500

550

600

0 0,02 0,04 0,06 0,08 0,1 0,12 0,14 0,16 0,18 0,2 0,22 0,24 0,26True strain

Tru

e S

tres

s [M

pa]

1340/s Tempere 0

1340/s Tempere 1

1510/s Tempere 2

GentIF 210

300

350

400

450

500

550

600

0 0,02 0,04 0,06 0,08 0,1 0,12 0,14 0,16 0,18 0,2 0,22 0,24 0,26

True strain

Tru

e S

tres

s [M

pa]

792/s Gent P4

1666/s Gent P5

501/s Gent P6

1098/s Gent P7

1331/s Gent P8

1239/s Gent P9

775/s Gent P10

83

Available strain ratesIF 210

100

200

300

400

500

600

0,00 0,02 0,04 0,06 0,08 0,10 0,12 0,14 0,16 0,18 0,20 0,22 0,24 0,26

True Strain

Tru

e S

tres

s [M

Pa]









1340/s Tempere 1

501/s Gent P6

Model vs. true stressIF 210

100

200

300

400

500

600

0,00 0,02 0,04 0,06 0,08 0,10 0,12 0,14 0,16 0,18 0,20 0,22 0,24 0,26 0,28 0,30 0,32

True Strain

Tru

e S

tres

s [M

Pa]

Experimental

JC model

Excluded data

Above is the least square fitting of grade IF 210

84

Appendix K — Results EHF experiment, IF210

85

Appendix L — Results EHF experiment, DPX800

86

Appendix M — Results EHF experiment, TRIP700

87

Appendix N — Results EHF experiment, 1.4016

88

Appendix O — Results EHF experiment, 1.4509

FEM simulation of Electrohydraulic Forming · tensile curves with high strain rate around 1000 per...

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Transcript of FEM simulation of Electrohydraulic Forming · tensile curves with high strain rate around 1000 per...