CHARACTERIZATION OF SHEET MATERIALS FOR STAMPING AND
FINITE ELEMENT SIMULATION OF SHEET HYDROFORMING
THESIS
Presented in Partial Fulfillment of the Requirements for
the Degree Masters in the Graduate
School of the Ohio State University
By
Amin E. Al-Nasser, B.E
*****
The Ohio State University
2009
Thesis Committee:
Approved by
Professor Taylan Altan, Advisor
Associate Professor Jerald Brevick
……………………………………………………..
Advisor
Industrial and Systems Engineering
Graduate Program
Copyright by
Amin Al-Nasser
2009
ABSTRACT
The increase in using Advanced High Strength Steel (AHSS) and aluminum sheet
materials is accompanied by many challenges in forming these alloys due to their
unique mechanical properties and/or low formability. Therefore, developing a
fundamental understanding of the mechanical properties of AHSS as compared
to conventional Draw Quality Steel (DQS) is critical to successful process/ tools
design. Also, alternative forming operations, such as warm forming or sheet
hydroforming, are potential solutions for the low formability problem of
aluminum alloys. Identifying potential difficulties in forming these materials
early in the product realization process is important to avoid expensive late
changes. Finite Element (FE) simulation is a powerful tool for this purpose
provided that the inputs to the FE model, including the flow stress data, are
reliable. However, obtaining the flow stress under near production condition
(state of stress, strain rate, temperature) may be challenging especially if the flow
stress is required at elevated temperature for warm forming applications.
In this study, room temperature uniaxial tensile and biaxial Viscous Pressure
Bulge (VPB) tests were conducted for five AHSS sheet materials; DP 600, DP 780,
DP 780-CR, DP 780-HY, and TRIP 780, and the resulting flow stress curves were
compared. Strain ratios (R-values) were also determined in the tensile test and
used to correct the biaxial flow stress curves for anisotropy. The pressure vs.
dome height raw data in the VPB test was extrapolated to the burst pressure to
obtain the flow stress curve up to fracture. Results of this work show that flow
stress data can be obtained to higher strain values under biaxial state of stress.
ii
Moreover, it was observed that some materials behave differently if subjected to
different state of stress. These two conclusions, and the fact that the state of stress
in actual stamping processes is almost always biaxial, suggest that the bulge test
is a more suitable test for obtaining the flow stress of AHSS sheet materials to be
used as an input to FE models. An alternative methodology for obtaining the
flow stress from the bulge test data, based on FE-optimization, was also applied
and shown to work well for the AHSS sheet materials tested.
Elevated temperature bulge tests were made for three aluminum alloys; AA5754O, AA5182-O, and AA3003-O, using a special machine where the tools and
specimen are submerged in a fluid heated to the required temperature. Several
challenges were faced in the experiments such as leakage of the bulging fluid
and sample pre-bulging in the clamping stage prior to the test. Moreover, it was
originally planned to measure the dome curvature by using three LVDTs; one at
the dome apex, and the others at different off-center locations. However, the
probes slightly penetrated the soft sheet. Consequently, the off-center probes
deflected and gave incorrect data. As a result of these challenges, the pressure
and dome height data was not considered reliable to be used in determining the
flow stress curves. Only the experimental data is included in this report for
documentation purposes, while the calculated flow stress curves are not
included.
A Sheet Hydroforming with a Punch (SHF-P) process was successfully simulated
using the FE software Pamstamp 2G 2007. The objective was to develop a
fundamental understanding of the process to reduce the expensive experimental
trial and error. A systematic methodology to design the process was suggested
and applied using FE simulation. A considerable improvement in the thinning
distribution in the part was achieved by properly selecting the blankholding and
pot pressure curves. It was also found that SHF-P with a clamped flange (stretch
iii
forming) is detrimental to the sheet thinning and that flange draw-in is required
to benefit from this process.
iv
Dedicated to my mother (Wafa’ Al-Khasawneh), father (Eyad Al-Nasser),
and brothers (Said Al-Nasser, Ahmad Al-Nasser, Kamal Al-Nasser)
v
ACKNOWLEDGEMENT
I am sincerely grateful to my advisor, Prof. Taylan Altan for his supervision
during my Masters studies at the Engineering Research Center for Net Shape
Manufacturing (ERC/NSM). His intellectual support, encouragement, and
guidance are the main factors for making this research work possible. I also
thank my committee member Dr. Jerald Brevick for his continuous support and
valuable feedback.
Special thanks to the sponsors of this research; the Auto-Steel Partnership (A/S
P), Dr. Mike Bzdok, and the United States Steel (USS), Dr. Ming Chen, for
supporting the AHSS sheet characterization project. Special thanks to Interlaken
Technology Corporation (ITC), Dr. Patrick Cain, and the Applied Engineering
Solutions, LLC (AES), Dr. David Guza, for working with the ERC/NSM and
providing technical support for the elevated temperature bulge testing. I also
gratefully thank General Motors R&D, Dr. John Carsley, for supporting the sheet
hydroforming project.
I thank my colleagues and the visiting scholars of the ERC/NSM, Dr. Ajay
Yadav, Dr. Partchapol Sartkulvanich, Dr. Hyunok Kim, Dr. Serhat Kaya, Dr.
Yeon Sik Kang (Posco), Lars Penter (Dresden Germany), Gaetano Pittala (Prato
Italy), Parth Pathak, Thomas Yelich, Nimet Kardes, Dario Braga (Brescia Italy),
Yurdaer Demiralp, Adam Groseclose, and Soumya Subramonian for their
assistance and encouragement.
vi
VITA
August 11, 1981 …………………………... Born, Amman-Jordan
2004 ………………………………………... B.E, Industrial Engineering
The University of Jordan, Amman –
Jordan
2007-2009 ………………………………… Graduate Research Associate
Engineering Research Center for Net
Shape Manufacturing (ERC/ NSM),
Columbus- Ohio- USA
2004-2007 ………………………………… Junior Industrial Consultant
Abu-Ghazaleh and Co. Consulting
(AGCON), Member of Talal AbuGhazaleh and Co. International (TAGI)
Amman- Jordan
vii
PUBLICATIONS
Nasser A., Yadav A., Pathak P., Altan T., (2009), “Determination of the Flow
Stress of Five AHSS Sheet Materials (DP 600, DP 780, DP 780-CR, DP 780-HY and
TRIP 780) using the Uniaxial Tensile and the Biaxial Viscous Pressure Bulge
(VPB) Tests”, Journal of Material Processing Technology, (In the progress of
publication)
Nasser A., Sung J., Kim H., Yadav A., Palaniswany H., (2009), “Forming of
Advanced High Strength Steels (AHSS)” Chapter for ASM Sheet Metal Forming
Handbook, Editor: Prof. Taylan Altan (In Progress)
Nasser A., (2007), “Supplier Evaluation and Selection” Module for “Arab
Certified Quality Manager (ACQM)”, Arab Knowledge and Management Society
(AKMS), 1st Edition, Department of National Library, Amman, Jordan
FIELD OF STUDY
Major Field: Industrial and Systems Engineering (Manufacturing)
viii
NOMENCLATURE
Latin Letters
dc
hd
hm,F and hm,S
hs,F and hs,S
M
p
ΔR
Rc
Instantaneous cross sectional area (Tensile test)
Original cross sectional area (Tensile test)
Diameter of die cavity (Bulge test)
Engineering strain in axial direction (Tensile test)
The objective function to be minimized (Optimization
Methodology)
Instantaneous load (Tensile test)
Clamping force (Bulge test)
Dome height (Bulge test)
The measured dome height at time t (Optimization
Methodology)
The simulation dome height at time t (Optimization
Methodology)
The measured dome heights at time t in the fast and slow
tests, respectively (Optimization Methodology)
The simulation dome heights at time t in the fast and slow
simulations, respectively (Optimization Methodology)
Strength Coefficient
Instantaneous gauge length (Tensile test)
Initial gauge length (Tensile test)
Strain rate sensitivity exponent
Number of datapoints used to apply the FE optimization
methodology for the fast test at elevated temperature
Strain hardening exponent
Number of datapoints used to apply the FE optimization
methodology at room temperature (or for the slow test at
elevated temperature)
Bulging pressure (Bulge test)
Strain ratio (Plastic Anisotropy or Normal Anisotropy)
Average strain ratio
Planer anisotropy
Strain ratio in the rolling direction
Strain ratio 45o to the rolling direction
Strain ratio in the transverse direction
Radii of curvature in the principle directions at the dome
apex (Bulge test/non-axisymmetric)
Die corner radius (Bulge test)
ix
Rd
S
Radius of curvature at dome apex (Bulge test)
Engineering stress (Tensile test)
Time point at which simulation and experiment were
compared (Optimization Methodology)
Initial sheet thickness (Bulge test)
Instantaneous thickness at dome apex (Bulge test)
td
Greek Letters
and
and
Effective strain
True (effective) strain rates before and after the jump in the
Jump Rate Method (Tensile Test)
True strain in axial direction (Tensile test)
True strain in thickness direction (Tensile test, Bulge test)
True strain in width direction (Tensile test)
Principle strains in the sheet surface (Bulge test)
Principle strain in the sheet thickness direction (Bulge test)
True stress in axial direction (Tensile test)
Effective stress
Principal stresses in the sheet surface (Bulge test)
Principal stress in the sheet thickness direction (Bulge test)
True (effective) stress before and after the strain rate jump
in the Jump Rate Method (Tensile Test)
Effective stress corrected for anisotropy (Bulge test)
Effective stress not corrected for anisotropy (Bulge test)
x
TABLE OF CONTENTS
ABSTRACT ....................................................................................................................... ii
ACKNOWLEDGEMENT ............................................................................................... vi
VITA ................................................................................................................................. vii
NOMENCLATURE ........................................................................................................ ix
LIST OF FIGURES .......................................................................................................... xv
LIST OF TABLES ........................................................................................................... xxi
CHAPTER 1 INTRODUCTION AND MOTIVATION ............................................... 1
1.1
Sheet Metal Forming ......................................................................................... 1
1.2
Deep Drawing .................................................................................................... 4
1.3
Sheet Hydroforming ......................................................................................... 6
1.4
High Strength and Light Weight Sheet Materials ........................................ 7
1.4.1
Advanced High Strength Steels (AHSS) ................................................. 7
1.4.2
Aluminum Alloys .................................................................................... 11
CHAPTER 2 OBJECTIVES AND APPROACH .......................................................... 13
2.1
Objectives.......................................................................................................... 13
2.2
Rational of the Study ...................................................................................... 15
2.3
Approach .......................................................................................................... 16
CHAPTER 3 BACKGROUND AND LITERATURE REVIEW ................................. 17
3.1
Determination of the Flow Stress of Sheet Metals ...................................... 17
3.1.1
Uniaxial Tension ...................................................................................... 17
3.1.2
Biaxial Tension/ Bulge test ..................................................................... 20
xi
3.2
Mechanical Properties of AHSS as related to Sheet Metal Forming ........ 24
3.3
Mechanical Properties of Aluminum Alloys as related to Sheet Metal
Forming........................................................................................................................ 29
3.4
Strain Localization (Necking) in Sheet Metal Forming.............................. 33
3.5
Principles of Sheet Hydroforming with a Punch (SHF-P)......................... 36
3.5.1
Overview of Deep Drawing ................................................................... 36
3.5.2
Description, Advantages, and Disadvantages of SHF-P Process...... 41
3.5.3
Process Window in SHF-P Process ........................................................ 43
CHAPTER 4 DETERMINATION OF THE FLOW STRESS OF FIVE AHSS SHEET
MATERIALS AT ROOM TEMPERATURE ................................................................ 46
4.1
Experimental Setup-Uniaxial Tensile Test................................................... 46
4.2
Experimental Setup-VPB Test ....................................................................... 47
4.3
Testing Matrix .................................................................................................. 48
4.4
VPB Test (Combined FE - Membrane Theory Inverse Analysis) ............. 49
4.4.1
Isotropic Materials ................................................................................... 49
4.4.2
Anisotropic Materials .............................................................................. 51
4.5
VPB test (Combined FE - Optimization Inverse Analysis) ....................... 51
4.6
Results ............................................................................................................... 56
4.6.1
Tensile Test................................................................................................ 56
4.6.2
VPB Test (Combined FE - Membrane Theory Inverse Analysis) ...... 60
4.6.3
VPB Test (Combined FE - Optimization Inverse Analysis) ............... 64
4.6.4
Comparison of Different Techniques .................................................... 66
4.6.5
Fit
Variation of Strain Hardening and the Suitability of the Power Law
..................................................................................................................... 69
CHAPTER 5 DETERMINATION OF THE FLOW STRESS OF ALLUMINUM
SHEET MATERIALS AT ELEVATED TEMPERATURE ......................................... 73
5.1
Experimental Setup (Machine and Tool Design) ........................................ 73
5.2
Testing Matrix .................................................................................................. 78
xii
5.3
Combined FE - Optimization Inverse Analysis at Elevated Temperature
............................................................................................................................ 78
5.4
Results ............................................................................................................... 81
5.4.1
Problems Encountered and Solved ....................................................... 81
5.4.2
Problems Encountered and not Solved................................................. 83
5.4.3
Experimental data .................................................................................... 84
CHAPTER 6 A SYSTEMATIC METHODOLOGY FOR DESIGNING A SHF-P
PROCESS USING FE SIMULATIONS ........................................................................ 88
6.1
Model Part and Tools Geometry ................................................................... 88
6.2
Approach and Methodology for Designing SHF-P Process using FE
Simulations .................................................................................................................. 91
6.2.1
General Approach .................................................................................... 91
6.2.2
Detailed Methodology............................................................................. 92
6.3
FE Model using Pamstamp 2G 2007 ............................................................. 94
6.4
Simulation Matrix............................................................................................ 98
6.4.1
Stretch Forming and hydroforming without Draw-In ....................... 98
6.4.2
Preliminary Simulation of Deep Drawing and Hydroforming with
Draw-In .................................................................................................................... 99
6.4.3
Deep Drawing and Hydroforming with Draw-In (According to the
Proposed Methodology) ...................................................................................... 100
6.5
Results ............................................................................................................. 102
6.5.1
Stretch Forming and hydroforming without Draw-In ..................... 102
6.5.2
Preliminary Simulation of Deep Drawing and Hydroforming with
Draw-In .................................................................................................................. 103
6.5.3
Deep Drawing and Hydroforming with Draw-In (According to the
Proposed Methodology) ...................................................................................... 106
CHAPTER 7 DISCUSSION, CONCLUSIONS AND FUTURE WORK ................. 109
7.1
Discussion and Conclusions ........................................................................ 109
7.1.1
Characterization of AHSS at Room Temperature ............................. 109
xiii
7.1.2
Characterization of Aluminum Alloys at Elevated Temperature ... 116
7.1.3
Design of SHF-P Process ....................................................................... 117
7.2
Future Work ................................................................................................... 120
REFERENCES ............................................................................................................... 122
APPENDIX A AQUADRAW MODULE IN PAMSTAMP 2G 2007 ..................... 128
xiv
LIST OF FIGURES
Figure 1.1 Classification of metals manufacturing processes as related to this
study .................................................................................................................................. 2
Figure 1.2 Schematic showing the basic deep drawing operation [Marciniak et al,
2002] ................................................................................................................................... 5
Figure 1.3 A non-axisymmetric part made by deep drawing [Palaniswany, 2007] 5
Figure 1.4 Schematic illustration of (a) the SHF-P process [Aust, 2001] (b) SHF-D
process [Palaniswany, 2007] ........................................................................................... 6
Figure 1.5 Example parts produced by (a) the SHF-P process [Maki, 2003] (b) the
SHF-D process [Yadav, 2008] ......................................................................................... 7
Figure 1.6 Example part (B-Pillar) usually made from higher strength AHSS
grades [Fekete, 2006] ....................................................................................................... 8
Figure 1.7 Total Elongation vs. Ultimate Tensile Strength “Banana Curve” of
automotive steels [World, 2009]..................................................................................... 9
Figure 1.8 Microstructure of DP steels [Sung et al, 2007] ........................................... 9
Figure 1.9 Microstructure of TRIP steels [Sung et al, 2007] ..................................... 10
Figure 3.1 Viscous Pressure Bulge (VPB) test tooling [Nasser et al, 2009] ............ 22
Figure 3.2 Geometrical features of the VPB test [Nasser et al, 2009] (nomenclature
is before chapter 1) ......................................................................................................... 22
Figure 3.3 Variation of the instantaneous n-value with engineering strain for
HSLA 350/450, DP 350/600, and TRIP 350/600 [World, 2009] .............................. 25
Figure 3.4 Relationship between the r-value and the UTS of various steel
Materials [Sadakopan et al, 2003] ................................................................................ 27
Figure 3.5 Variation of instantaneous strain hardening of DP 600 and TRIP 600
with sheet thickness [Sadakopan et al, 2003] ............................................................. 28
Figure 3.6 Flow stress curves of TRIP 800 coming from different suppliers
[Khaleel et al, 2005] ........................................................................................................ 28
Figure 3.7 Engineering Stress-strain curves of AA3003-H111 at different
temperatures and a strain rate of 0.0083 sec-1 [Abbedrabbo et al, 2006-b] ............ 29
Figure 3.8 True stress-true strain curves of AA5754-O at different temperatures
and a strain rate of 0.0083 sec-1 [Abbedrabbo et al, 2006-a] ..................................... 30
xv
Figure 3.9 Effect of strain rate on the flow stress of AA3003-H111 obtained by the
tensile test at four temperatures; 25 oC, 93.3 oC, 204.4 oC, and 260 oC. “Jump-rate
test” was used (note that at 150 oC, the sample failed at 150 min-1. Thus, data is
not available after that). [Abbedrabbo et al, 2006-b] ................................................. 31
Figure 3.10 Schematic illustration of the deep drawing process of a round cup
[Kalpakjian et al, 2009] .................................................................................................. 37
Figure 3.11 Schematic illustration of the variation of sheet thickness in deep
drawing using flat-headed punch (left) and hemispherical-headed punch (right).
(Thickness variation is exaggerated) [Johnson et al, 1973] ...................................... 38
Figure 3.12 State of stress (a) in the flange and (b) in the side wall during deep
drawing of a cylindrical cup [Kalpakjian et al, 2003] ............................................... 38
Figure 3.13 Process window in the SHF-P Process [Palaniswany, 2007] ............... 43
Figure 4.1 A flow chart describing the FE-based inverse analysis methodology
used to determine the flow stress curve of sheet materials [Gutscher et al, 2004] 50
Figure 4.2 (left) Schematic of the dome height evolution with time (or pressure).
(right) Schematic showing how the calculated (simulation) dome height may
deviate from the measured dome height if the simulation flow stress input is not
correct [Penter et al, 2008] ............................................................................................. 52
Figure 4.3 3D view of design space, showing objective function (response)
obtained for each combination of K and n (design variables) [Penter et al, 2008] 54
Figure 4.4 A schematic showing the selected design points (red, big) and the
computationally expensive full factorial points (black, small) [Penter et al, 2008]
........................................................................................................................................... 55
Figure 4.5 Minimization of objective function 'E' using RSM as applied to room
temperature bulge test. In each iteration (set of 10 FE simulations), the margins
for 'K' and 'n-value' keep shrinking to a smaller design space, until the objective
function is minimized (the convergence criterion is met). (left) the result of the
second iteration. (right) the result of the final iteration [Penter et al, 2008] .......... 55
Figure 4.6 Comparison of Engineering Stress - Engineering Strain curves of
various AHSS grades obtained by the tensile test .................................................... 57
Figure 4.7 Comparison of True Stress - True Strain curves of various AHSS
grades obtained by tensile test ..................................................................................... 57
Figure 4.8 True Stress - True Strain curves of DP 780-HY at 0, 45, and 90 degrees
with respect to rolling direction obtained by tensile test ......................................... 58
Figure 4.9 Uniform and Total Elongation of various AHSS grades (Gauge Length:
2 in) (Average values are shown) ................................................................................ 59
xvi
Figure 4.10 UTS and 0.2% Offset Yield Strength of various AHSS grades
(Average UTS values are shown) ................................................................................ 59
Figure 4.11Experimental Pressure versus time curve for sample 1 of TRIP 780
steel sheet material ......................................................................................................... 61
Figure 4.12 Example tested specimens for TRIP 780 sheet material (a) sample
burst (b) sample not burst ............................................................................................. 61
Figure 4.13 Burst pressures of the five AHSS materials tested ............................... 62
Figure 4.14 Experimental pressure versus dome height curves obtained from the
VPB test for the five AHSS sheets materials tested (These curves are the
measured curves without any extrapolation). ........................................................... 62
Figure 4.15 Comparison of the flow stress curves of the five AHSS materials
tested using the VPB test (these curves are neither corrected for anisotropy, nor
extrapolated) ................................................................................................................... 63
Figure 4.16 Pressure versus dome height curve (for TRIP780, sample 6)
extrapolated from last measured datapoint (212 bars) up to burst pressure (226
bars) using second order polynomial approximation .............................................. 63
Figure 4.17 The flow stress curve of TRIP 780 (sample 6) obtained from both
experimentally measured and extrapolated pressure vs. dome height curves .... 64
Figure 4.18 Optimization history of the design variables K and n for DP 600.
Number of iterations to converge is 12 ....................................................................... 65
Figure 4.19 Flow Stress curves of the five AHSS materials tested obtained using
the combined FE-optimization methodology. Curves are plotted up to the last
datapoint obtained from the combined FE-membrane theory methodology (also
shown in the figure, the K-value in MPa and the n–value) ..................................... 65
Figure 4.20 Comparison of True Stress- strain curves of DP 600 determined by
the Tensile test and VPB test (different methodologies) (Curves are not
extrapolated) ................................................................................................................... 66
Figure 4.21 Comparison of True Stress- strain curves of DP 780 determined by
the Tensile test and VPB test (different methodologies) (Curves are not
extrapolated) ................................................................................................................... 67
Figure 4.22 Comparison of True Stress- strain curves of DP 780-CR determined
by the Tensile test and VPB test (different methodologies) (Curves are not
extrapolated) ................................................................................................................... 67
Figure 4.23 Comparison of True Stress- strain curves of DP 780-HY determined
by the Tensile test and VPB test (different methodologies) (Curves are not
extrapolated) ................................................................................................................... 68
xvii
Figure 4.24 Comparison of True Stress- strain curves of TRIP 780 determined by
the Tensile test and VPB test (different methodologies) (Curves are not
extrapolated) ................................................................................................................... 68
Figure 4.25 Normalized Strain Hardening (NSH) vs. Strain for DP 600 obtained
from both VPB flow stress data (combined FE-membrane theory methodology)
and from the Power Law Fit Curve (Note that data for DP 600 was collected up to
bursting since a sample accidentally burst during the test) ............................................. 70
Figure 4.26 Normalized Strain Hardening (NSH) vs. Strain for DP 780 obtained
from both VPB flow stress data (combined FE-membrane theory methodology)
and from the Power Law Fit Curve ............................................................................. 70
Figure 4.27 Normalized Strain Hardening (NSH) vs. Strain for DP 780-CR
obtained from both VPB flow stress data (combined FE-membrane theory
methodology) and from the Power Law Fit Curve ................................................... 71
Figure 4.28 Normalized Strain Hardening (NSH) vs. Strain for DP 780-HY
obtained from both VPB flow stress data (combined FE-membrane theory
methodology) and from the Power Law Fit Curve (Note that data for DP 780-HY
was collected up to bursting since a sample accidentally burst during the test).............. 71
Figure 4.29 Normalized Strain Hardening (NSH) vs. Strain for TRIP 780 obtained
from both VPB flow stress data (combined FE-membrane theory methodology)
and from the Power Law Fit Curve ............................................................................. 72
Figure 5.1 A schematic of the Fluid-based Elevated Temperature Biaxial Bulge
Test Apparatus [Designed by the Applied Engineering Solutions (AES), LLC] .......... 74
Figure 5.2 Schematics showing the design and dimensions of (a) the tools, (b)
lockbead (within the tools), designed to be suitable for the ET bulge test [Yadav,
2008] ................................................................................................................................. 76
Figure 5.3 A schematic showing the clamped sheet during the bulging process
and the LVDTs which were planned to be used to measure the dome height and
sample curvature profile [Designed by the Applied Engineering Solutions (AES),
LLC] ................................................................................................................................. 76
Figure 5.4 A picture showing the arrangement designed to measure the sample
bulge curvature profile without the need to submerge the LVDTs in the heated
fluid [Designed by the Applied Engineering Solutions (AES), LLC] ..................... 77
Figure 5.5 The fluid-based elevated temperature biaxial bulge test apparatus
[Designed by the Applied Engineering Solutions (AES), LLC] .............................. 77
Figure 5.6 (left) A schematic showing the fast (high pressurization rate) and slow
(low pressurization rate) pressure curves. (right) a schematic showing the
xviii
difference in dome height between two samples, one pressurized fast and the
other pressurized slow .................................................................................................. 80
Figure 5.7 Experimental Pressure vs. Dome height curves of AA3003-O at three
temperatures; 200 oC, 230 oC, 260 oC, and two speeds; fast (2 in3/sec) and slow
(0.2 in3/sec). Note that for the fast test, increasing the temperature from 200 oC to
230 oC, resulted in an increase in the pressure .......................................................... 85
Figure 5.8 Experimental Pressure vs. Dome height curves of AA5182-O at three
temperatures; 200 oC, 230 oC, 260 oC, and two speeds; fast (2 in3/sec) and slow
(0.2 in3/sec). .................................................................................................................... 86
Figure 5.9 Experimental Pressure vs. Dome height curves of AA5754-O at three
temperatures; 200 oC, 230 oC, 260 oC, and two speeds; fast (2 in3/sec) and slow
(0.2 in3/sec). .................................................................................................................... 87
Figure 6.1 One quarter of the model part to be made by the SHF-P process ........ 89
Figure 6.2 2D sketch of the tools geometry and dimensions. The sketch shows the
blank holder and the die with a lockbead. Another set of tooling similar to this,
but without a lockbead, will also be used .................................................................. 90
Figure 6.3 FE model of the SHF-P (a) without a lockbead (b) with a lockbead.
Prepared using Pamstamp 2G 2007 (reverse punch and die corner radius are
parts of the pressure pot) .............................................................................................. 95
Figure 6.4 Schematics showing (a) the punch full stroke and (b) the locking stroke
(if a lockbead is used) .................................................................................................... 97
Figure 6.5 Flow Stress curve of AA5754-O (1 mm) obtained using the VPB test
(data is not extrapolated) [Penter et al, 2008] ............................................................. 98
Figure 6.6 Simulation matrix of stretch forming with and without pot pressure 98
Figure 6.7 Preliminary simulation matrix of deep drawing and SHF-P with drawin ....................................................................................................................................... 99
Figure 6.8 Simulation matrix of deep drawing and SHF-P with draw-in
(according to the proposed methodology) ............................................................... 100
Figure 6.9 BHF curves used in simulating the deep drawing process with 240 mm
blank radius. Also shown (with a circle) the punch stroke at which the flange
started to wrinkle in the simulation (details can be found in the Results section)
......................................................................................................................................... 101
Figure 6.10 Pot pressure curves used in simulating the SHF-P process with 240
mm blank radius and BHF curve 4 selected from deep drawing simulations plus
an addition force to prevent blankholder lifting because of the pot pressure. The
extra force applied is also shown for each curve..................................................... 101
xix
Figure 6.11 Comparison of the thinning distribution in stretch forming
simulations with zero and 100 bars pot pressure, at a punch stroke of 13 mm. It
can be seen that thinning at punch corner radius (point D) increases with
pressure increase, indicating that SHF-P is detrimental if the sheet is totally
clamped (stretch forming). Other pressure values were tried and shown to give
similar results ............................................................................................................... 102
Figure 6.12 Effect of BHF on the thinning distribution in deep drawing
simulation of 176.3 mm radius sheet (Material: AA5754-O). Two BHF were used;
60, and 140 KN. Thinning was recorded at 20 mm stroke. Only thinning in the
punch-die clearance is shown .................................................................................... 104
Figure 6.13 Effect of pot pressure on the thinning distribution in SHF-P
simulation of 176.3 mm radius sheet (Material: AA5754-O). Two pot pressure
were used; 40, and 60 bars. 140 KN BHF was used in both simulations. Thinning
was recorded at 20 mm stroke. Only thinning in the punch-die clearance is
shown ............................................................................................................................. 104
Figure 6.14 Sheet bulging (in the punch-die clearance) against the drawing
direction in SHF-P simulations with two different pot pressures; 40 and 60 bars
(Material: AA5754-O). Excessive pot pressure stretch forms (and thins) the sheet
......................................................................................................................................... 105
Figure 6.15 Comparison of thinning distribution at 20 mm stroke in deep
drawing and SHF-P (40 bars pot pressure) obtained by FE simulations (Material:
AA5754-O). The BHF in the two simulations is 140 KN. Thinning in SHF-P is
lower than deep drawing. Two necks form in deep drawing, while only one
forms in SHF-P ............................................................................................................. 105
Figure 6.16 Comparison of the thinning distribution at the end of the stroke
between deep drawing (with selected BHF curve 4) and SHF-P with two different
pressure curves (see simulation matrix). Note the considerable improvement in
thinning distribution when using SHF-P ................................................................. 108
xx
LIST OF TABLES
Table 1.1 Sheet Metal Forming Process as a System [Sung et al, 2007] .................... 3
Table 1.2 Designation and general properties of Wrought Aluminum Alloys
[based on Kalpakjian et al, 2009].................................................................................. 12
Table 1.3 Temper designation of wrought and cast aluminum alloys [Stamping,
Nov 2008] ........................................................................................................................ 12
Table 3.1 Hardening parameters of three aluminum alloys as a function of
temperature obtained by fitting the flow stress data obtained from the uniaxial
tensile test. Materials are assumed to follow the Field and Backofen constitutive
model [based on Abbedrabbo et al, 2006-a and Abbedrabbo et al, 2006-b] .......... 32
Table 3.2 Summary of possible defects in the SHF-P process, and corresponding
causes and solutions. Reference is made to Figure 3.13. Prepared based on [Kaya
2008, Palaniswany 2007, Yadav 2008] ......................................................................... 45
Table 4.1 The test matrix used for the tensile and VPB tests of the five AHSS sheet
materials .......................................................................................................................... 49
Table 4.2 Comparison of Anisotropy Ratios of various AHSS grades ................... 58
Table 4.3 Comparison of the K and n-values obtained using both the tensile and
VPB tests (two methodologies) for the five AHSS materials ................................... 69
Table 5.1 Testing matrix of AA5754-O, AA5182-O, and AA3003-O at elevated
temperature..................................................................................................................... 78
Table 6.1 Summary of the parameters used in the deep drawing and SHF-P FE
simulations ...................................................................................................................... 96
Table 6.2 Simulation results of applying step 1 of the proposed methodology;
Initial estimation of the blank radius. A preliminary BHF of 60 KN was used. . 106
Table 6.3 Simulation results of applying step 2 of the proposed methodology;
Initial estimation of the BHF curve. .......................................................................... 107
Table 7.1 Comparison between the stress levels in the tensile and VPB tests
(calculated using the combined FE-Membrane theory methodology) at a strain
values equal to the true strain at the onset of necking in the tensile test ............ 112
xxi
Table 7.2 Comparison between the maximum true strain that can be obtained in
the tensile test and that obtained in the VPB test (calculated using the combined
FE-Membrane theory methodology) ......................................................................... 113
xxii
CHAPTER 1
INTRODUCTION AND MOTIVATION
1.1
Sheet Metal Forming
Of the four families of metals manufacturing processes (see
Figure 1.1), metal forming is a major family where the plasticity property of
metallic materials is utilized to form them into useful shapes. Metal forming is
classified into sheet forming and bulk forming. Sheet forming is a type of metal
forming by which bends, shallow and deep recessed shapes are made from a
sheet metal. The initial workpiece (sheet) has a large surface area to volume ratio,
as opposed to the “billet” in bulk forming which has a low ratio. Another
difference is that stretching (tensile stresses) is predominant in sheet forming
processes, while compression is predominant in bulk forming.
To successfully design or improve a sheet metal forming process, it should be
considered as a system of components/ elements. A fundamental understanding
of the relationships between process inputs (such as the sheet, the tools,
sheet/tools interfaces, equipment) and process output (product) is extremely
important. Typical components of the sheet metal forming process are shown in
Table 1.1.
1
In this study, we focus on three sheet metal forming processes; Drawing, Stretch
forming, and Hydroforming. The first two are widely used, where the third is a
non-conventional process used for special applications. The following sections
describe these processes briefly. More details are given in the Background and
Literature Review chapter.
Figure 1.1 Classification of metals manufacturing processes as related to this
study
2
Sheet
material
Tooling
Condition at
tool/material
interface
Deformation
Zone
Equipment
used
Product
Flow stress (as a function of strain, strain rate,
temperature and microstructure).
Formability (forming limit diagrams, Stretch bend
limits).
Surface Texture.
Initial conditions (composition, history/ prestrain).
Plastic anisotropy.
Blank size, location, and thickness.
Tool geometry and forces.
Surface conditions.
Material / heat treatment / hardness.
Temperature.
Lubricant type and temperature.
Insulation and cooling characteristics of the
interface layer.
Lubricity and frictional shear stress.
Characteristic related to lubricant application and
removal.
Strain (kinematics), strain rate.
Stresses (variation during deformation).
Temperatures (heat generation and transfer).
Speed / production rate.
Cushion capabilities.
Force / energy capabilities of press ram.
Rigidity and accuracy.
Geometry and failure.
Dimensional accuracy/tolerances.
Surface finish.
Microstructure, metallurgical and mechanical
properties.
Table 1.1 Sheet Metal Forming Process as a System [Sung et al, 2007]
3
1.2
Deep Drawing
Deep Drawing is a sheet metal forming process by which cylindrical or
cylindrical-like shapes are made from a sheet metal blank. Figure 1.2 shows the
basic deep drawing operation. Initially the sheet is held between the die and
blank holder. After that, the punch moves down and draws the sheet into the die
cavity. If the punch stroke is small with respect to the punch diameter, then the
process is called “Shallow Drawing”. If the sheet is totally clamped in the flange
region and not allowed to flow into the die cavity, then the process is called
“Stretch Forming”. The most important defects observed in the deep drawing
process are tearing in the side wall or wrinkling in the flange. Process parameters
should be properly selected to eliminate defects. Usually deep drawing is
performed at room temperature. However, for some materials, the sheet material
may be heated in the flange region to improve the formability.
Deep drawing is used to produce high variety of products, such as beverage
cans, pans, sinks, containers, and automotive panels [Kalpakjian et al, 2009].
Figure 1.3 shows an example of a non-axisymmetric part produced by deep
drawing.
4
Figure 1.2 Schematic showing the basic deep drawing operation [Marciniak et al,
2002]
Figure 1.3 A non-axisymmetric part made by deep drawing [Palaniswany, 2007]
5
1.3
Sheet Hydroforming
Sheet hydroforming (SHF) is similar to deep drawing except that either the
punch or the die is replaced by a pressurized hydraulic medium. If the die is
eliminated, then the process is called sheet hydroforming with a Punch (SHF-P)
and the pressurized fluid forms the sheet around the punch (see Figure 1.4-a). If
the punch is eliminated, then the process is called Sheet Hydroforming with a
Die (SHF-P) or Hydro-Mechanical Deep Drawing (HMD) and the pressurized
fluid forms the sheet in the die cavity (see Figure 1.4-b). Example parts produced
by sheet hydroforming are shown in Figure 1.5. The improved drawability and
the elimination of one piece of tooling are the main advantages of SHF. On the
other hand, it is a slow process and only feasible for low production quantities of
difficult-to-draw parts. Part of this study is concerned about simulating the SHFP process. Therefore, a detailed description of this process, its mechanics,
advantages and disadvantages, as compared to conventional deep drawing will
be given in the Background and Literature Review Chapter.
(a)
(b)
Figure 1.4 Schematic illustration of (a) the SHF-P process [Aust, 2001] (b) SHF-D
process [Palaniswany, 2007]
6
(a)
(b)
Figure 1.5 Example parts produced by (a) the SHF-P process [Maki, 2003] (b) the
SHF-D process [Yadav, 2008]
1.4
High Strength and Light Weight Sheet Materials
1.4.1
Advanced High Strength Steels (AHSS)
Fuel economy, environmental concerns, and crashworthiness are the main
reasons for replacing conventional steels by the Advanced High Strength Steels
(AHSS) in the automotive industry. It was reported that replacing mild steel with
High Strength Steels (HSS) may result in 10-25% reduction in mass [Powers,
2000]. Figure 1.6 shows an example part (B-Pillar), critical for crash resistance of
the car, usually made of higher strength AHSS grades.
“AHSS are multi-phase steels which contain martensite, bainite, and/or retained
austenite in quantities sufficient to produce unique mechanical properties”
[Shaw et al, 2001-a]. This study is concerned about two types of AHSS; Dual
Phase (DP) steels and Transformation-Induced Plasticity (TRIP) steels. Other
types include Martensitic Steels (MS), Complex Phase (CP) steels, Hot Forming
(HF) steels, and Twinning-Induced Plasticity (TWIP) steels. Some of these types
7
are shown in Figure 1.7. The microstructure of DP steels is composed of ferrite
and martensite (see Figure 1.8), while the microstructure of TRIP steels is a
matrix of ferrite, in which martensite and/or bainite, and more than 5% retained
austenite exist (see Figure 1.9).
Figure 1.6 Example part (B-Pillar) usually made from higher strength AHSS
grades [Fekete, 2006]
8
Mild Steels
AHSS
HSS
Figure 1.7 Total Elongation vs. Ultimate Tensile Strength “Banana Curve” of
automotive steels [World, 2009]
(a) SEM image of DP Steel
(b) Schematic of the DP
steel microstructure
Figure 1.8 Microstructure of DP steels [Sung et al, 2007]
9
(a) SEM image of TRIP Steel
(b) Schematic of the TRIP
steel microstructure
Figure 1.9 Microstructure of TRIP steels [Sung et al, 2007]
The increased formability of AHSS is the main advantage over conventional HSS.
Nevertheless, compared to Draw Quality Steels (DQS), AHSS steels have
relatively low ductility [Nasser et al, 2009]. Figure 1.7 shows the relation between
the total elongation (EL) and Ultimate Tensile Strength (UTS) for different
automotive steels. This curve is usually referred to as the “Banana Curve”. This
chart shows a dramatic drop in the EL with increased strength of the material.
Moreover, it shows an overlap between different grades families, which suggests
that classification based on this chart only is not sufficient [Sung et al, 2007].
In this study, the flow stress and strain ratios of five AHSS grades, of interest to
the automotive industry, are determined using both the tensile and bulge test, to
develop a fundamental understanding of the mechanical behavior of these
materials as related to sheet metal forming.
10
1.4.2
Aluminum Alloys
Similar to AHSS, fuel economy and environmental concerns are the two main
reasons for the trend to replace conventional steels with light weight metals such
as aluminum and magnesium alloys. However, the manufacturing of these alloys
by conventional stamping is difficult, due to their limited formability at room
temperature. To overcome this problem, non-conventional operations such as
warm forming or SHF can be used.
Table 1.2 shows the designation and general properties of Wrought Aluminum
Alloys. Table 1.3 shows the temper designation of both wrought and cast
aluminum alloys. Two series are related to this study; 3xxx and 5xxx. The former
is softer and more formable. Three sheet alloys; AA5754-O, AA5182-O, and
AA3003-O are tested at elevated temperature (200 oC to 300 oC) using the Viscous
Pressure Bulge (VPB) test to obtain their flow stress curves. In addition, room
temperature SHF-P of AA5754-O was simulated using the FE software
Pamstamp 2G 2007 to understand the fundamentals of this relatively new
process.
11
1xxx
Major
alloying
elements
Pure Al
2xxx
Al, Cu
Designation
3xxx
4xxx
5xxx
6xxx
7xxx
8xxx
General properties
Excellent corrosion resistance, high electrical
and thermal conductivity, good workability,
low strength, not heat treatable
High strength-to-weight ratio, low corrosion
resistance, heat treatable
Al, Mn
Good workability, moderate strength, generally
not-heat treatable
Al, Si
Lower melting point, forms an oxide film of
dark grey to charcoal in color, generally nonheat treatable
Al, Mg
Good corrosion resistance and weldability,
moderate to high strength, non-heat treatable
Al, Mg, Si Medium strength, good formability,
machinability, weldability, and corrosion
resistance, heat treatable
Al, Zn
Moderate to very high strength, heat treatable
others
-
Table 1.2 Designation and general properties of Wrought Aluminum Alloys
[based on Kalpakjian et al, 2009]
Temper
Designation
F
O
H
W
T
Description
As fabricated
Annealed
Strain hardened (wrought product only)
Solution heat treatment
Heat treated to produce stable tempers other than F,
O, or H
Table 1.3 Temper designation of wrought and cast aluminum alloys [Stamping,
Nov 2008]
12
CHAPTER 2
OBJECTIVES AND APPROACH
2.1
Objectives
The overall objective of this study is to determine the flow stress of AHSS and
aluminum sheet materials, of interest to the automotive industry, at room and
elevated temperatures, respectively. In addition, to optimize critical process
parameters in the SHF-P process by using FE simulation.
The detailed objectives of this study are to:
1) Determine the flow stress curves of five AHSS sheet materials; DP 600, DP
780, DP 780-CR, DP 780-HY, and TRIP 780, at room temperature.
2) Compare the flow stress curves obtained under balanced biaxial state of
stress with those obtained under uniaxial condition for the AHSS
materials tested.
3) Investigate the suitability, advantages and disadvantages of different
inverse analysis methodologies for obtaining the flow stress curves of
sheet materials tested using the VPB test.
4) Study the effect of anisotropy correction on the flow stress curves of the
AHSS materials tested using the VPB test.
13
5) Investigate the strain hardening characteristics and formability of the
AHSS materials tested, as related to sheet metal forming.
6) Extend the FE-based optimization methodology for determining the flow
stress of sheet materials from the room temperature domain to elevated
temperature.
7) Investigate the difficulties associated with testing sheet materials at
elevated temperature using the hydraulic bulge test, as well as the
challenges in analyzing the experimental data for obtaining the material
properties.
8) Develop a fundamental understanding of the effect of various process
parameters involved in the SHF-P process.
9) Investigate the capabilities of FE simulation in modeling the SHF-P
process.
10) Develop a simple and systematic methodology for designing/ optimizing
the SHF-P process using FE simulation.
11) Develop simple and applicable guidelines for designing/ optimizing the
SHF-P process.
12) Quantify the improvement in the thinning distribution attained by
replacing the deep drawing process by the SHF-P process.
14
2.2
Rational of the Study
The following points emphasize the importance of this research work:
1) Crash worthiness, fuel economy, and environmental concerns are driving
forces for the increased use of AHSS and aluminum sheet materials,
especially in the automotive industry.
2) Determining the flow stress of AHSS and understanding the its unique
mechanical properties as compared to conventional DDS are necessary for
material selection and process/ tools design.
3) The low formability of aluminum alloys is a driving force for nonconventional
processes
such
as
warm
forming
and/or
sheet
hydroforming.
4) Determining the flow stress of sheet materials in the warm forming range
under near-production state of stress is necessary for running reliable FE
simulations.
5) Sheet hydroforming is a relatively new process. Thus, it is important to
understand the process parameters and to develop guidelines for process
design, in order to avoid expensive experimental trials.
15
2.3
Approach
The following tasks were performed to achieve the objectives of the study:
1) Determination of the mechanical properties of the five AHSS materials
using both the uniaxial tensile and biaxial VPB tests (Chapter 4).
2) Testing a promising methodology for determining the flow stress of sheet
materials at elevated temperature by applying it initially to the AHSS
room temperature VPB test (point 1) (Chapter 4).
3) Extending the methodology (point 2) to consider the strain rate effect in
order to be applicable for the elevated temperature bulge test (Chapter 5).
4) Testing different aluminum alloys at elevated temperature using the bulge
test and applying the elevated temperature methodology (point 3) to
obtain the flow stress (Chapter 5).
5) Suggesting a methodology for designing process parameters (blank
radius, pot pressure, blankholding force) in SHF-P of AA5754-O and using
FE simulation to validate the methodology (Chapter 6).
16
CHAPTER 3
BACKGROUND AND LITERATURE REVIEW
3.1
Determination of the Flow Stress of Sheet Metals
3.1.1
Uniaxial Tension
Note: This section is prepared based on [Hosford et al 1993, Kalpakjian et al 2009,
ASTM E646-07 2007, and ASTM E517-00 2006].
In the sheet tensile test, the testing specimen (coupon) is usually prepared
according to the dimensions specified in the ASTM standard; ASTM E614 [ASTM
E646-07, 2007]. The method of preparing the specimen (blanking, wire EDM, …)
should be reported since the edge quality may affect the testing results. The
specimen is gripped from the two ends and loaded in the axial direction. It is
common to use universal testing machines for the tensile test. The load is
continuously increased until the specimen fails. Both the load and extension are
measured. The specimen gauge length is the length of which the extension is
measured. Usually, it is two inches and is measured using a device called the
“Extensometer”. Sometimes, the extensometer is calibrated to directly give the
engineering strain.
The Engineering Strain (e) is defined as the change in the gauge length divided
by the original gauge length:
Equation 1
17
Note: All nomenclatures are summarized before the beginning of chapter 1.
The Engineering Stress (S) is defined as the instantaneous load divided by the
original cross sectional area:
Equation 2
The incremental true strain (
is defined at any moment during the test as the
incremental change in gauge length divided by the instantaneous gauge length.
Based on this definition, the total true strain ( can be calculated using:
Equation 3
The true stress is defined at any moment during the test as the instantaneous
load divided by the instantaneous cross sectional area:
Equation 4
The relations between the true and engineering stress and strain are:
Equation 5
Equation 6
The true stress-true strain curve of the material is commonly referred to as the
“Flow Stress” curve. A material model may be fit into the flow stress curve of the
material. The most common material model at room temperature is the
Hollomon Power Law:
Equation 7
At elevated temperatures where the strain rate sensitivity becomes more
important, the Field and Backofen material model can be used:
Equation 8
18
More than one method can be used to obtain the m-value in the tensile test. Only
one method, called the “Jump rate Method” will be briefly described, since it will
be referred to later in this chapter. In this method, the strain rate is suddenly
increased during the test and the flow stress is recorded instantaneously before
and after the jump. Using Equation 8, the following formula can be easily
derived to calculate the m-value:
Equation 9
An important mechanical property in sheet metal forming is the plastic
anisotropy. Plastic anisotropy (also called normal anisotropy or strain ratio) is
usually determined from the tensile test. It is defined as the ratio of the width
true strain to the thickness true strain:
Equation 10
The
-value may change from time to time during the tensile test. Therefore, to
compare different materials, the - value should be determined at the same axial
strain.
For convenience, the thickness strain is not measured. Instead, the axial and
width strains are measured and the thickness strain is calculated from the
principle of volume constancy:
Equation 11
Note: the ASTM standard E517-00 [ASTM E517-00, 2006] states that the plastic
component of the total strain should be used in calculating the strain ratio.
19
Subtracting the elastic strain from the total strain will not have a considerable
effect on the R-values and therefore in this study, the total strain values were
used in all calculations.
The
-value may also change from a direction to another in the plane of the
sheet. Therefore, it is common to obtain the -value in the rolling direction (0o),
transverse direction (90o), and 45 degrees to the rolling direction (45o) and report
the average value:
Equation 12
Materials having high
deforms easier in the width direction compared to the
thickness direction. This thickness change resistance is desirable when the sheet
is used in deep drawing applications. More details will be given later.
The variation of the - value from a direction to another in the plane of the sheet
is not desirable in deep drawing since it will cause variation in the flow of the
flange from a direction to another, resulting in what is called “Earing”. The
tendency of the sheet material to ear when deep drawn is characterized by a
parameter called the “Planer Anisotropy (
”:
Equation 13
3.1.2
Biaxial Tension/ Bulge test
To determine the Flow Stress of sheet materials under biaxial state of stress, the
bulge test can be used. At the ERC/NSM, a viscous material is used instead of
the commonly used hydraulic fluid. Therefore, the name “Viscous Pressure
Bulge (VPB)” test is used. This name will be used throughout this report.
20
Figure 3.1 is a schematic of the tooling used in the VPB test. The upper die is
connected to the slide and the cushion pins support the lower die (the blank
holder) to provide the required clamping force. The punch in the lower die is
fixed to the press table and therefore stationary.
At the beginning, the tooling is open and the viscous material is filled into the
area on the top of the punch. When the tooling closes, the sheet is totally
clamped [Figure 3.1-a] between the upper and lower dies using a lockbead to
prevent any material draw-in, in order to maintain the sheet in a pure stretching
condition throughout the test. The clamping force (the selected press cushion
force) depends on the material and thickness tested. The slide then moves down
together with the upper die and blank holder. Consequently, the viscous
medium is pressurized by the stationary punch and the sheet is bulged into the
upper die. Since the tools are axisymmetric, the sheet is bulged under balanced
biaxial stress. Figure 3.2 shows the details of the geometrical features of the VPB
test tooling.
21
Potentiometer
Test Sample
Upper die
Lower die
Viscous Medium
Pressure Transducer
(a) Before Forming
Stationary Punch
(b) After Forming
Figure 3.1 Viscous Pressure Bulge (VPB) test tooling [Nasser et al, 2009]
Figure 3.2 Geometrical features of the VPB test [Nasser et al, 2009] (nomenclature
is before chapter 1)
22
The membrane theory is usually used to calculate the flow stress from the
experimental data [Gutscher et al, 2000]. This theory assumes that the dome is
spherical in shape and neglects bending stresses in the sheet. The relationship
between membrane stresses and process parameters is:
Equation 14
Under balanced biaxial tension, which is the case in the bulge test, the formula
reduces to:
Equation 15
The average compressive stress in the thickness direction is -p/2. Using VonMises yield criterion, the effective stress and effective strain can be calculated:
Equation 16
Equation 17
Equation 18
Equation 19
It can be noticed from Equations 17 and 19 that the pressure, radius of curvature
and thickness at the dome apex should be measured to be able to calculate the
effective stress and strain. To reduce the number of measured parameters,
different FE-based inverse analysis methodologies are used at the ERC/NSM
where only two relatively easy-to-measure parameters are required. These are
the bulging pressure, measured using a pressure transducer, and the dome
23
height, measured using a potentiometer. More details about these methodologies
are given in the Chapter 4.
[Hecht et al, 2005] conducted elevated temperature bulge test on magnesium
AZ31-O and reported that at high dome heights (dome height/ die cavity
diameter > 0.4), the shape of the dome near the apex is no longer spherical and
that the best fit to the dome shape is a parabola. CCD cameras were used to
instantaneously measure the radius of the dome. [Kaya, 2008] reported a similar
result for the same alloy except that the spherical assumption was found to be
valid up to a dome height/ die cavity diameter ratio of 0.2. [Koc et al, 2007]
tested AA5754-O at elevated temperatures and was able, through controlling the
flow rate of the pressurizing fluid, to maintain a nearly constant strain rate at the
dome apex. Moreover, the strain at the dome apex was measured by using a
noncontact sensor (ARAMIS). However, it was assumed that the dome is
spherical in shape and the membrane theory equations were used. In this study,
elevated temperature bulge test experiments were made on AA5754-O, AA5182O, and AA3003-O.
3.2
Mechanical Properties of AHSS as related to Sheet Metal Forming
This study is concerned about two types of AHSS, DP and TRIP steels. DP steels,
have high initial strain hardening and a high Tensile-to-Yield Strength ratio,
which accounts for the relatively high ductility, compared to conventional HSS
[Chen et al, 2005 and Shaw et al, 2001-b]. The soft ferrite plastically flows before
the hard martensite. The ferrite at the phase boundary encounters high stress
concentration resulting in more plastic deformation. This explains the high initial
24
strain hardening of DP steels. When the martensite phase starts to deform
plastically, the strain hardening rate decreases.
TRIP steels retains its strain hardening to high strain values. This is due to the
retained austenite-to-martensite phase transformation which takes place during
plastic deformation. The formation of the hard martensite, and the stress
concentration resulting from the volume expansion during phase transformation,
increases the strain hardening of the material and thus both the uniform and
total elongation [Sung et al, 2007].
Figure 3.3 Variation of the instantaneous n-value with engineering strain for
HSLA 350/450, DP 350/600, and TRIP 350/600 [World, 2009]
The variation of the strain hardening characteristic of a material with strain can
be illustrated by plotting the instantaneous n-value (d ln /d ln ) vs. strain.
Figure 3.3 shows how the instantaneous n-value changes for DP 600 and TRIP
600 as compared to a conventional HSS grade, High Strength-Low Alloy (HSLA)
25
steel. It can be seen that the n-value for HSLA steel decreases slightly with strain.
The decrease for DP steels is more pronounced. For TRIP steel, the n-value at the
beginning is low compared to DP steel. However, it is maintained at a relatively
high value to a larger strain, and then drops at the end. The decrease in the nvalue for DP 350/600 is explained by the martensite starting to deform
plastically. The constant n-value of TRIP 350/600 is explained by the straininduced phase transformation. The following conclusions can be drawn from the
discussion above. First, the power law (
which was used extensively to
describe the behavior of many materials may not be valid for AHSS because of
the variation of the n-value. Second, the fact that the hardening behavior of
AHSS changes with time and is highly dependent on the microstructure
evolution raises questions on the suitability of using extrapolated flow stress
data to run FE simulations.
Figure 3.4 shows a clear relationship between the average strain ratio (
)
and the UTS of the material. The stronger the material, the lower the
and therefore the formability. A value, slightly below one, is asymptotically
reached. The
of DP and TRIP steels is close to or slightly less than one.
26
Figure 3.4 Relationship between the r-value and the UTS of various steel
Materials [Sadakopan et al, 2003]
It was reported [Sadakopan et al, 2003] that the mechanical properties of AHSS
sheets, coming from the same supplier, may not be consistent. Variation in
thickness, heat treatment, coil, and batch may result in different properties.
Figure 3.5 shows the variation of instantaneous strain hardening of both DP 600
and TRIP 600 with sheet thickness. Variation in strain hardening behavior will
affect the material formability.
Figure 3.6 shows the flow stress curves of TRIP 800 sheets coming from different
suppliers. It can be seen that strain hardening, uniform elongation and total
elongation all are different for the three curves.
27
Figure 3.5 Variation of instantaneous strain hardening of DP 600 and TRIP 600
with sheet thickness [Sadakopan et al, 2003]
Figure 3.6 Flow stress curves of TRIP 800 coming from different suppliers
[Khaleel et al, 2005]
28
3.3
Mechanical Properties of Aluminum Alloys as related to Sheet Metal
Forming
Figure 3.7 shows the flow stress curve of AA 3003-H111 sheets tested by the
tensile test in the temperature range from 25 oC to 232 oC. Convection heating
was used. The strain rate in the test was 0.0083 sec-1. It can be seen that the UTS
decreases from about 115 MPa to 55 MPa when increasing the testing
temperature from room temperature to 232
oC.
Also, the total elongation
increases from about 33% to 50%. This increase in ductility when increasing the
temperature is the main reason for the trend toward warm forming of aluminum
magnesium alloys. [Abbedrabbo et al, 2006-a] showed similar behavior of
AA5754-O and AA5182-O (see Figure 3.8).
Figure 3.7 Engineering Stress-strain curves of AA3003-H111 at different
temperatures and a strain rate of 0.0083 sec-1 [Abbedrabbo et al, 2006-b]
29
Figure 3.8 True stress-true strain curves of AA5754-O at different temperatures
and a strain rate of 0.0083 sec-1 [Abbedrabbo et al, 2006-a]
[Abbedrabbo et al, 2006-b] used the “Jump-rate test” to study the strain rate
sensitivity of AA3003-H111 at several elevated temperature. Three strain rates;
10, 50, and 150 min-1, were used. Results are shown in Figure 3.9. It is clear that
the strain rate effect is more important at elevated temperature. Strain rate
sensitivity of AA5754-O and AA5182-O can be found in [Abbedrabbo et al, 2006a].
30
Figure 3.9 Effect of strain rate on the flow stress of AA3003-H111 obtained by the
tensile test at four temperatures; 25 oC, 93.3 oC, 204.4 oC, and 260 oC. “Jump-rate
test” was used (note that at 150 oC, the sample failed at 150 min-1. Thus, data is
not available after that). [Abbedrabbo et al, 2006-b]
The equations in Table 3.1 [based on Abbedrabbo et al, 2006-a and Abbedrabbo
et al, 2006-b] show how the three hardening parameters K, n and m change with
temperatures for AA3003-H111, AA5754-O, and AA5182-O. The materials were
assumed to follow the Field and Backofen constitutive model (
) and
the parameters were obtained by fitting the experimental data obtained in the
uniaxial tensile test. It can be seen that K and n decrease linearly with
temperature, while m increases exponentially with temperature. [Li et al, 2003]
reported curves relating the n-value of AA5754+Mn and AA5182 with
temperature. Trends and curves shapes are similar.
31
Hardening
parameter
K (Ta) in
MPa
AA3003-H111
AA5754-O
AA5182-O
-0.5058*T+210.40
(for T = 25-260 oC)
503.7-0.592*T
(for T = 25-93 oC)
641.3-1.829*T
(for T = 93-260 oC)
0.3304 -0.000529*T
(for T = 25-93 oC)
0.4048-0.001192*T
(for T = 93-260 oC)
0.00118*exp(0.0161*T)
(for T = 25-260 oC)
551.2-0.4623*T
(for T = 25-93 oC)
672.3-1.8926*T
(for T = 93-260 oC)
0.3135-0.000363*T
(for T = 25-93 oC)
0.3687-0.001065*T
(for T = 93-260 oC)
0.00106*exp(0.01743*T)
(for T = 25-260 oC)
n(Ta)
-0.0004*T+0.2185
(for T = 25-260 oC)
m(Ta)
0.0018*exp(0.0147*T)
(for T = 25-260 oC)
Table 3.1 Hardening parameters of three aluminum alloys as a function of
temperature obtained by fitting the flow stress data obtained from the uniaxial
tensile test. Materials are assumed to follow the Field and Backofen constitutive
model [based on Abbedrabbo et al, 2006-a and Abbedrabbo et al, 2006-b]
a
The temperature T is in oC
[Li et al, 2003] attributed the increase in the total elongation of AA5754+Mn and
AA5182 to the increase in post-uniform elongation. This is related to the higher
m-value at elevated temperature which results in more resistance of the material
to strain localization in the neck region (where strain rate is high) after
instability. Moreover, it was shown that one order of magnitude increase in the
strain rate, at elevated temperature, will dramatically reduce the total elongation
of these two alloys.
Another reason for forming 5xxx series aluminum at elevated temperature is the
dynamic strain aging behavior at room behavior which results in Stretcher Strain
marks/ Lueder‟s bands (serrated flow stress curve) [Abbedrabbo et al, 2006-a,
Bolt et al, 2001, Sivakumar, 2006]. Lueder‟s Bands deteriorate the surface quality
(results in coarse surface appearance) of the product and may cause difficulties in
subsequent coating/ painting operations [Kalpakjian et al, 2009]. The migration
32
of the Magnesium solute atoms in 5xxx aluminum to dislocations explains this
behavior [Abbedrabbo et al, 2006-a]. Another way of interpreting this
phenomenon from the macroscopic perspective is the negative m-value of these
alloys at room temperature. [Hosford et al, 1993] reported m-value of -0.008 for 1
mm-thick AA5182-O sheets. [Abbedrabbo et al, 2006-a] reported that the serrated
behavior disappears at temperatures above 93 oC for AA5182-O and above 121
oC
3.4
for AA5754-O.
Strain Localization (Necking) in Sheet Metal Forming
The formability in sheet metal forming processes highly depends on the
resistance of the sheet material to strain localization (necking). In the simple
uniaxial tensile test, two main types of necks form; The diffuse type, where the
neck forms in the width direction, and the localized type, where it forms in the
thickness direction (within the diffuse neck region). Among others, the strain and
strain rate hardening of the sheet play an important role in postponing necking,
thus increasing the sheet ductility. Strain rate effect will be discussed briefly at
the end of this section and the strain hardening effect will be discussed in more
details. The diffuse neck in the tensile test forms when the maximum force is
reached, while the localized neck forms, in the post-uniform region, close to the
fracture point. The criterion for plastic instability (diffuse necking) is [Hosford et
al, 1993]:
which is from the volume constancy
33
Thus the condition for instability in the tensile test is:
Equation 20
This value which has to be equal to one in order for the diffuse neck to form is
called the “Normalized Strain Hardening (NSH)” [Bird et al, 1981]. It is the
instantaneous slope (strain hardening) of the flow stress curve divided
(normalized) by the instantaneous stress. Before necking, the NSH is higher than
one and it continuously decreases, even after diffuse necking, up to the fracture
point. The localized neck forms when the NSH is about 0.5. The values at which
necks form may vary depending on the strain rate sensitivity, the angle of the
localized neck with respect to the loading direction, etc. [Bird et al, 1981]. Initial
instability under balanced biaxial tension takes place when NSH equals to 0.5,
while in plane strain (ex: side cup wall in deep drawing), instability starts at
NSH equals to 0.866.
Throughout the tensile test, the cross sectional area continuously decreases,
while the strength increases due to strain hardening. Before initial necking, the
rate of increase in strength due to strain hardening is higher than the rate of area
reduction, thus the load-carrying capacity of the sheet increases. This is why the
engineering stress-strain curve increases up to the UTS. Since the slope of the
flow stress curve decreases with strain (the material looses from its strain
hardening characteristic), a point (instability point) is reached in the test where
the rate of area reduction becomes equal to the rate of increase in strength due to
strain hardening. At this point, the UTS is reached and the instability condition is
started (the specimen will deform under a decreasing load).
If the material follows the Hollomon Power Law,
shown using Equation 20 that the condition for necking is
34
, then it can be easily
[Hosford et al,
1993]. This is not unexpected since the n-value is a measure of the slope of the
flow stress curve (strain hardening behavior) and the necking phenomenon is
closely related to strain hardening as described above.
In the bulge test (balanced biaxial state of stress), the condition for instability
(drop in the membrane force) is
[Hosford et al, 1993]. Even at strain value
higher than this value, localized neck will not form easily. The reason is that the
formation of a localized neck should be accompanied by a local increase in the
surface area, which will appear in the form of a local bulge on the dome. The
radius of curvature in this local bulge is smaller than elsewhere in the test
specimen. Therefore, according to Equation 17, the membrane stress will
decrease locally and localized necking will be postponed. Many materials were
tested in the Center for Precision Forming (CPF), formerly called the Engineering
Research Center for Net Shape Manufacturing (ERC/NSM) using the biaxial
bulge test. Experimental results validate the theoretical conclusion that flow
stress data can be collected in the bulge test to much higher strain values than
can be reached in the uniaxial tensile test. Flow stress data obtained using the
bulge test can be found in [Nasser et al 2009, Nasser et al 2008, Nasser et al 2007,
Sartkulvanich et al 2008, Penter et al 2008, Pathak et al 2008, Kim et al 2008, Kim
et al 2007-a, Kim et al 2007-b, Palaniswamy et al 2007, Yadav et al 2007,
Spampinato et al 2006, Bortot et al 2005, Kaya et al 2005, Braedel et al 2005, and
Gutscher et al 2000].
Strain localization is more difficult in materials with positive strain rate
sensitivity exponent (m). Once the neck forms, the strain rate (and thus the flow
stress) in the neck region increases. This will result in more resistance for
deformation in the neck region and will allow more deformation to take place in
the rest of the specimen/ part. The resulting effect is more post-uniform
elongation [Hosford et al, 1993 and Wagoner et al, 1996]. [Hosford et al, 1993]
35
argued that since a homogeneous material does not exist, higher m-value will
resist early necking and thus increase the uniform elongation as well.
3.5
Principles of Sheet Hydroforming with a Punch (SHF-P)
3.5.1
Overview of Deep Drawing
Since Deep Drawing is a special case of Sheet Hydroforming with a punch (SHFP), where the pot pressure is equal to zero (as will be described later), deep
drawing principles and mechanics are described here.
In the simplest Deep Drawing (DR) of a cylindrical flat-bottom cup, a round
blank of initial thickness (T) and diameter (Do) is placed on a die with a round
opening (cavity) and a die corner radius, Rd. An annular Blankholder (sometimes
called a binder or hold-down ring) is used to hold the blank in place. A
cylindrical punch, with a diameter Dp and corner radius Rp moves down to draw
the sheet into die opening. The punch-die clearance (c) should be larger than the
sheet thickness. Figure 3.10 is a schematic illustration of the deep drawing
process.
36
Figure 3.10 Schematic illustration of the deep drawing process of a round cup
[Kalpakjian et al, 2009]
When the punch starts to move down, the sheet in the clearance region stretch
bends around the punch and die corner radii. The sharper the radii, the higher
the thinning the sheet will undergo. This initial stretching will strain harden the
sheet in the clearance and increase it load-carrying capacity, but will also form
two necks near the punch corner radius (see Figure 3.11). [Kaya 2008] called this
part of the stroke the “Critical Stroke” and estimated it by R p + Rd + T. As the
punch travels more, the material in the flange (between die and blankholder) will
be drawn in the radial direction and subjected to circumferential (hoop)
compressive stresses (see Figure 3.12-a). If not held-down with enough
Blankholder Force (BHF), compressive stresses in the flange will cause plastic
buckling (wrinkling). The induced hoop stresses on elements moving toward the
center and the friction forces at the tools-blank interface will resist material flow,
thus subjecting the elements in the flange to tensile stresses in the radial direction
37
(see Figure 3.12-a). The hoop compressive stress is higher than the radial tensile
stress. As a result, the sheet thickens as it flows in the flange region.
Figure 3.11 Schematic illustration of the variation of sheet thickness in deep
drawing using flat-headed punch (left) and hemispherical-headed punch (right).
(Thickness variation is exaggerated) [Johnson et al, 1973]
Figure 3.12 State of stress (a) in the flange and (b) in the side wall during deep
drawing of a cylindrical cup [Kalpakjian et al, 2003]
38
The force required to draw the material in the die opening is transmitted to the
flange through the cup side wall. Therefore, the wall is subjected to tensile
stresses in the axial direction (see Figure 3.12-b). Since the sheet is stretched in
the axial direction, it should contract in both the thickness and hoop direction.
However, for cylindrical geometries with small clearances, the sheet will stick to
the punch, which will prevent further hoop contraction, putting the sheet in this
region in a plane strain condition with tensile hoop stresses (see Figure 3.12-b).
Most of the energy requirement (deformation and friction) of the process is
consumed in the flange. Therefore, the larger the flange region, the higher the
punch force required (and the higher the axial stress in the side wall). If the axial
stress in the side wall exceeds a critical value, tearing will occur. The ratio of the
blank diameter and punch diameter is called the drawing ratio (DR). If the DR
exceeds a critical value, called the Limiting Drawing Ratio (LDR), tearing will
occur. The most important factor which affects the LDR is the Average Strain
Ratio (
of the material. The higher the
, the higher the LDR
because of two main reasons:
1) Materials with high
are easy to deform in the hoop direction in
the flange. Thus, the required punch force is lower.
2) Materials with high
are not easy to thin in the side wall.
Thinning resistance will increase the load–carrying capacity and enable
more force to be transmitted to the flange without excessive thinning or
tearing.
Other factors which affect the LDR include:
1) Friction at the blank-blankholder and blank-die interface. The lower the
friction, the higher the LDR.
39
2) Friction at the blank-punch interface. The higher the friction, the higher
the LDR. As mentioned previously, the sheet usually necks around the
punch corner radius. This neck makes strain localization (and tearing) in
this region easier, especially if all the punch force is transmitted to the
flange through this lower part of the cup. If the friction force between
punch and the sheet is high, then part of the punch force will reach the
flange through the upper portion of the cup side wall. As a result, the LDR
increases.
3) Punch and die corner radii. The higher the radii, the higher the LDR.
4) Material strain hardening. Highly strain hardening materials have higher
LDRs.
The BHF is an important process design variable. Applying insufficient BHF will
result in flange wrinkling, while BHF higher than required may result in side
wall tearing. The punch-die clearance is usually 7 to 14% higher than the sheet
thickness [Kalpakjian et al, 2009]. Too small a clearance will result in sheet
ironing (in the clearance) and probable shearing (since the sheet thickens in the
flange). Too high a clearance may cause side wall wrinkling.
Warm forming (deep drawing) of aluminum alloys is usually done between 200
oC
and 300 oC, in order to benefit from the increase in formability. The die and
blankholder are usually heated, especially at the corners (for box-shaped parts)
to reduce the flow stress and improve the formability. [Bolt et al, 2001] reported
20-25 % increase in drawing depth of a box-shaped part of AA5754-O when the
temperature was increased from 20 oC to 175 oC. They also reported about 70%
increase in the drawing depth of a conical rectangular part when the temperature
is increased from 20 oC to 250 oC. Moreover, the tendency for flange wrinkling
was reduced. Straight parts of the flange may be cooled by circulating oil/ water
to reduce metal flow in these regions, resulting in an effect similar to the draw
40
bead effect. Another interesting result is the very small reduction in the hardness
of finished parts formed at 250
oC
compared to parts formed at room
temperature.
3.5.2
Description, Advantages, and Disadvantages of SHF-P Process
Sheet Hydroforming with a Punch (SHF-P) process is similar to regular deep
drawing (stamping) operation except that the sheet is drawn into the die cavity
against a counter hydraulic pressure in a chamber usually called the pressure pot
(see Figure 1.4-a). As mentioned previously, increasing the friction force between
the sheet and the punch reduces side wall thinning by reducing the portion of
the punch force transmitted to the flange region through the lower, critical, and
highly thinned portion of the side cup wall. In SHF-P process, the pot pressure
will push the sheet against the punch. The high contact pressure at the sheetpunch interface will increase the friction force, which will reduce the thinning
and increase the LDR.
Two main types of SHF-P exist. In the first, called the “Passive” SHF-P, the
pressure is generated by the punch moving toward the pot which is full with a
relatively incompressible fluid (usually water). The pot pressure profile (pressure
vs. time) is controlled by a valve which regulates the fluid flow out of the pot to
maintain the required pot pressure curve. In the second type, called the “Active”
SHF-P, an external pump is used to generate the pot pressure.
Following are the benefits of the SHF-P Process:
1) Higher LDR than conventional stamping, because:
41
a) The pot pressure separates the sheet from the die corner radius.
Therefore, no friction energy is consumed at this location, which
lowers the punch force and increases the LDR.
b) Higher contact pressure between the sheet and punch reduces thinning
and increases the LDR.
2) Pot pressure reduces/eliminates side wall wrinkling.
3) Better surface finish since there is no rubbing between the sheet and the
die corner.
4) Although not convenient, small leakage of the pressurizing medium from
the pot will reduce the friction coefficient between the sheet and die, and
may increase the LRD.
5) Female die is not required since the pot pressure can form the sheet
against impressions made in the punch. Thus, the cost of tools material,
machining, and maintenance, as well as tools manufacturing lead time are
all reduced.
The disadvantages of SHF-P compared to conventional stamping are:
1) Higher cycle time/ lower production rate.
2) Pot pressure increases both the required ram and blankholder force
(larger presses required)
3) Dimensional tolerances may not be attainable without a solid die.
42
3.5.3
Process Window in SHF-P Process
In the SHF-P process, two main process parameters, the pot pressure and BHF,
should be optimized to successfully form a part. The two parameters should be
controlled together and can be varied with the punch stroke to produce defect
free parts. The limits of the two parameters in which the process operates
successfully are called the “Process Limits” and the region within the limit is
called the “Process Window” (see Figure 3.13).
Figure 3.13 Process window in the SHF-P Process [Palaniswany, 2007]
Table 3.2 summarizes the possible defects in the SHF-P process, and explains
corresponding reasons and solutions. This table can be used as a guideline for
43
trial and error experiments and/or FE simulation and will refer to hereinafter.
Defects include tearing at upper and lower portions of the cup, bursting in the
punch-die clearance, flange wrinkling, side wall wrinkling. [Meinhard et al,
2005] stated that small BHF should be applied at the beginning of the process
and then increased toward the end of the process. The reason is that the sheet
thickens as it flows in the flange and therefore parts of the flange loose contact
with the tools at the end of the stroke and becomes easier to wrinkle. Moreover,
higher BHF is required to generate the same moment about the die corner (in
order to prevent lifting) at the end of the stroke where the flange width becomes
smaller. [Yadav 2008, Kaya 2008, and Palaniswany 2007] used variable
(increasing) BHF and pot pressure and showed an increase in the LDR.
[Palaniswany, 2007] developed a sequential optimization technique combined
with FE simulation to optimize the BHF and pot pressure curves in the SHF-P
process. The stroke was divided into small increments. In each increment, the pot
pressure and BHF were optimized by running FE simulations. Thinning at the
end of the increment was the objective function to be minimized subjected to the
constraint that no defects should be observed. After optimizing each increment,
the output of the increment was used as an input to the next in a sequential
manner, thus the name “Sequential Optimization, until the end of the stroke.
Although, highly automated, the complexity associated with the optimization
makes this methodology difficult to apply in the industry. It was noticed from
the work by [Yadav 2008, Palaniswany 2007] that the optimum pot pressure and
BHF curves can be divided into three distinct regions where the curves are either
constant or increasing (almost) linearly with the stroke. This idea will be utilized
in this study to develop a simple FE-based methodology to optimize the process
parameters in the SHF-P process. Details are explained in the methodology
section.
44
#
1
Defect
(references to
Figure 3.13)
Reasons
Tearing in lower
portion of the cup
side wall (2)
BHF higher than required to
prevent wrinkling/ leakage, or
Reduce BHF (AA‟)
Pot pressure low (not fullybenefiting from SHF-P process)
Note: pressure drop may be
due to leakage (see point 3
below)
Increase pot pressure (AA‟‟)
Note: BHF should be slightly
increased to avoid lifting and
therefore
wrinkling
and
leakage
Sheet bulges against the
drawing
direction
(subsequently bursts) if high
pot pressure is applied and the
sheet is (almost) clamped due
to high BHF (usually observed
if the clearance is large/ at the
beginning of the stroke for
conical punches)
Low BHF or high pot pressure
Reduce pot pressure (CC‟)
Note: BHF should also be
reduced as well since (after
reducing the pot pressure) it is
higher than required
2
Bulging against
drawing direction
followed by
Bursting in the
clearance (4, 5)
3
Leakage,
and
subsequently
flange wrinkling
(6)
First, Increase the BHF until
leakage is eliminated.
If the sheet excessively bulges
against the drawing direction
or burst in clearance, this
means that both BHF and pot
pressure are large  go to
point 2 above
4
Bursting in the
upper portion of
the cup side wall
(8)
High BHF
Note: since no bulging against
the drawing direction is
observed, pot pressure is most
probably suitable
5
Side
wrinkling
Clearance is large and pot
pressure is low, or
wall
Solutions
Low BHF  flange wrinkling
 side wall wrinkling
Note: proper sealing may
eliminate/ reduce leakage
Reduce the BHF (DD‟)
Note: The pot pressure may
need to slightly reduced if
lifting/wrinkling/
leakage
was observed after reducing
the BHF
Increase pot pressure
Increase BHF
Table 3.2 Summary of possible defects in the SHF-P process, and corresponding
causes and solutions. Reference is made to Figure 3.13. Prepared based on [Kaya
2008, Palaniswany 2007, Yadav 2008]
45
CHAPTER 4
DETERMINATION OF THE FLOW STRESS OF FIVE AHSS
SHEET MATERIALS AT ROOM TEMPERATURE
4.1
Experimental Setup-Uniaxial Tensile Test
To eliminate edge effect problems associated with shearing operations, tensile
test specimens were prepared by wire EDM process. For each of the five AHSS
materials (DP 600, DP 780, DP 780-CR, TRIP 780, and DP 780-HY), at least three
samples were prepared at each of the three orientations (0, 45o, and 90o) with
respect to the rolling direction. Specimen dimensions specified in the
International Standard ASTM E 646 – 07 [ASTM E646-07, 2007] were used. MTS
810 FlexTest Material Testing Machine, 100 KN in capacity, was used for testing.
A hydraulic wedge grips and a 2-inch Epsilon extensometer were used in all the
tests. Samples were loaded at a strain rate of 0.1 min-1 (1.67 Χ 10-3 sec-1) which is
also according to the previously mentioned standard.
Before starting the test, the specimen was properly aligned with the loading axis
and gripped carefully to avoid twisting. Samples were loaded to an engineering
strain of 8% (+ 0.5 %) where the test was stopped and the sample width was
measured for the purpose of determining the Strain Ratio (only for DP 780-HY at
90o, the test was stopped at about 7% since this grade at this direction has less
uniform elongation). A micrometer with a minimum division of 0.01 mm (+0.005
46
mm) was used to measure the width at three locations within the gauge length
(as recommended by the standard ASTM E 517 [ASTM E517-00, 2006]) and the
average width was calculated. After measuring and recording the width, the
sample is loaded again until failure. Throughout the test, both the load and the
measured engineering strain were recorded to be used in calculating the true
stress and strain. The test matrix is summarized in Table 4.1.
4.2
Experimental Setup-VPB Test
For each of the five AHSS materials, at least six-10 in X 10 in square samples
were sheared. All samples are 1 mm-thick and were prepared from the same
sheets from which tensile testing coupons were prepared. Minster Tranemo
DPA-160-10 hydraulic press, 160 metric tons in capacity, was used for the test.
Honeywell (S-model) pressure transducer and ETI (LCP 12 S-100 mm)
potentiometer were used to measure the bulging pressure and dome height,
respectively. National Instrument (SCXI) Data Acquisition System (Hardware:
SCXI-1000 and software SCXI-1520) was used to collect the data. Measuring
devices were calibrated before the test to ensure accurate measurements. The
clamping force was set to 100 metric tons to ensure no draw-in of the sheet
material in the die cavity. The die cavity diameter of bulge test tools available at
the ERC/NSM is 4.161 in (105.7 mm) and the die corner radius is 0.25 in (6.35
mm).
The potentiometer used is a delicate device and cannot withstand impact loading
at the burst of the specimen. Thus, for each material, at least one sample was
burst without a potentiometer to know the bursting pressure. To avoid bursting
47
the other samples, they were pressurized to 90 to 95% of the burst pressure while
the potentiometer was used to measure the bulge height.
Pressure vs. dome height raw data, sheet thickness, and strain ratios at 0 o and 90o
were used as inputs to the excel macro to calculate the flow stress curve. To
obtain the flow stress curve assuming the material is isotropic, value of one was
used for both R0 and R90. Since it is not possible to obtain experimental data up to
the burst pressure, and in order to get a rough estimate of the material
formability under balanced biaxial condition, the data was extrapolated to the
burst pressure using a higher order polynomial approximation. The extrapolated
curve was then used in the excel macro to obtain the flow stress curve. The dome
height of the burst samples can be used as a measure of material formability
under balanced biaxial condition. However, since the main objective of the study
was not to evaluate the formability, the number of samples burst and measured
was not sufficient from the repeatability point of view. Thus, these results are not
presented in this paper. Table 4.1 summarizes the test matrix for both the tensile
and the VPB tests.
4.3
Testing Matrix
Table 4.1 summarizes the tests performed to obtain the experimental data to be
used in determining the flow stress of the five AHSS materials using the different
techniques described above.
48
#
1
2
3
4
5
Material
DP 600
DP 780
DP 780-CR
DP 780-HY
TRIP 780
Thickness
1 mm
1 mm
1 mm
1 mm
1 mm
0o
3
3
4
3
3
Number of samples tested
Tensile Testa
VPB test
45o
90o
Total
Burst
3
4
6
1
2
4
10
4
3
4
7
1
3
2
7
2
3
3
7
2
Table 4.1 The test matrix used for the tensile and VPB tests of the five AHSS sheet
materials
It was originally planned to test at least 3 samples for each condition. However, some
samples were lost during the initial trials and therefore not included in this table
a
4.4
VPB Test (Combined FE - Membrane Theory Inverse Analysis)
4.4.1
Isotropic Materials
The methodology used for determining the flow stress of the sheet from the
bulge test data assumes that the material follows the Hollomon power law
(Equation 7). The effective stress and strain equations from the classical
membrane plasticity theory are used (Equations 17 and 19).
In addition to the bulging pressure which can be easily measured in the test,
Equations 17 and 19 contain two other unknowns; the thickness and radius of
curvature at the dome apex. To determine these unknowns, a series of FE
simulations with different material properties (different n-value) were
previously conducted at the ERC/NSM using the commercial FE software
PAMSTAMP to generate a database. (Refer to [Nasser et al 2007, Gutscher et al
2004, Gutscher et al 2000]) This database shows how the thickness and radius of
49
curvature at the dome apex change with the dome height for different n-values.
The Von-Mises yield criterion was used in the simulations.
An excel macro was then developed to iteratively determine the flow stress curve
of the material using both the database and the experimental pressure vs. dome
height curve. A flow chart describing this FE-based inverse analysis
methodology is shown in Figure 4.1. An initial guess of the n-value is made.
Using the measured dome height and the database, the radius of curvature and
thickness at the dome apex are calculated. Now that all the information needed
are available, the membrane theory equations can be used to calculate the
effective stress and strain. The power law is then used to represent the resulting
curve. Another iteration is performed with a different n-value, and the process
continues until the difference in the n-value between two subsequent iterations
becomes less than or equal to 0.001. At this moment, the iterations are stopped,
and the flow stress curve is extracted and reported.
Figure 4.1 A flow chart describing the FE-based inverse analysis methodology
used to determine the flow stress curve of sheet materials [Gutscher et al, 2004]
50
4.4.2
Anisotropic Materials
Since sheet materials are usually anisotropic (i.e. mechanical properties vary
from one direction to another), the flow stress curve obtained in the bulge test
may not be accurate if the material is assumed to be isotropic. Therefore in this
study, the calculated flow stress curve using the methodology described in the
previous section was corrected for anisotropy. While Von-Mises yield criterion is
used in the methodology described above, Hill‟s anisotropic yield criteria is used
in this section [Hill, 1990]. Following is the correction factor used to correct for
anisotropy: (for more details, refer to [Bortot et al, 2005])
Equation 21
If the material does not have any planar anisotropy (i.e. R-value is the same in all
directions), then Equation 21 simplifies to Equation 22:
Equation 22
4.5
VPB test (Combined FE - Optimization Inverse Analysis)
This new optimization methodology is still based on the inverse analysis
technique that was described above. The idea is that minimizing, thus the name
optimization, the difference in dome height between the simulation and the
experiment can be achieved only if the simulation flow stress input is very close,
or equal, to the flow stress of the material tested. Therefore, the objective function
to be minimized in this optimization is the difference between the experimental
and measured dome heights, at selected pressure (or time) values, formulated in
a least square sense. (see Figure 4.2 and Equation 23)
51
Figure 4.2 (left) Schematic of the dome height evolution with time (or pressure).
(right) Schematic showing how the calculated (simulation) dome height may
deviate from the measured dome height if the simulation flow stress input is not
correct [Penter et al, 2008]
The AHSS sheet materials were assumed to follow the Hollomon power law
(Equation 7). The objective function used for the room temperature bulge test is:
Equation 23
: the objective function to be minimized
: time point at which simulation and experiment were compared
: number of datapoints selected for the optimization
: the measured dome height at time t
: the simulation dome height at time t
To apply the optimization methodology, the optimization software LS-OPT was
used to generate FE simulation files with different combinations of the
rheological parameters „K‟ and „n‟. The FE software LS-DYNA was used to run
the simulations. In each simulation, the sheet is pressurized with the same
experimental pressure vs. time curve and the simulated dome height evolution
52
with time could be determined. As described above in the formulation of the
objective function, the simulated and experimental dome heights at the selected
points of time were compared. The inputs to the LS-OPT file are:
1. The experimental dome heights at the selected points of time.
2. The simulation times at which the simulated dome height should be
extracted.
3. The formulation of the objective function based on (1) and (2).
The Response Surface Methodology (RSM) was used in the optimization. The
objective of applying the RSM is to find the combination of the two rheological
parameters, called the “Design Variables”, which will minimize the objective
function, called the “Response”. As applied in this study, the RSM can be
described briefly as follows:
1. An initial guess of the ranges of K and n, is made (based on data in the
literature) and used as an input to LS-OPT. These ranges define the
“Design Space”. Within each range, a starting value is selected. The
starting values define the “Baseline Design”. See
2. Figure 4.3.
3. Within the design space, LS-OPT will select certain combinations of the
rheological parameters (each combination called a “Design Point”), for
which LS-DYNA files will be generated and run. The number of design
points selected for room temperature bulge test was ten. See Figure 4.4.
4. From each LS-DYNA simulation file, the dome height will be extracted at
the selected points of time. Using the simulated dome height and
corresponding experimental dome heights, the objective function
(response), hereinafter referred to with “E”, is calculated (See
5. Figure 4.3).
53
6. Having the value of E for each combination, a second order polynomial
curve can be fit and the minimum value can be obtained. The minimum
point is the closest to the correct (optimal) point. See
7. Figure 4.5 (left). If the K and n values used in the simulation are the
correct values, then the calculated E value should ideally be equal to zero
(i.e the simulation exactly matches the experiment).
8. A “Sub-region” within the initial design space is selected by LS-OPT.
Within this new region, steps (2) to (4) above are repeated iteratively until
the convergence criterion is met. The final K and n values are considered
to be the optimal values. In this study, the optimization converges when
the difference in the objective function and design variables between two
subsequent iterations become less than 0.003 and 0.01, respectively. See
9. Figure 4.5.
Figure 4.3 3D view of design space, showing objective function (response)
obtained for each combination of K and n (design variables) [Penter et al, 2008]
54
Figure 4.4 A schematic showing the selected design points (red, big) and the
computationally expensive full factorial points (black, small) [Penter et al, 2008]
Results for second iteration
(FE simulations 11 through 20)
Results for eighth (final) iteration
(FE simulations 71 through 80)
Figure 4.5 Minimization of objective function 'E' using RSM as applied to room
temperature bulge test. In each iteration (set of 10 FE simulations), the margins
for 'K' and 'n-value' keep shrinking to a smaller design space, until the objective
function is minimized (the convergence criterion is met). (left) the result of the
second iteration. (right) the result of the final iteration [Penter et al, 2008]
55
4.6
Results
4.6.1
Tensile Test
Figure 4.6 and Figure 4.7 show a comparison of the engineering and true stressstrain curves obtained by the tensile test, respectively. No considerable variation
of the flow stress curves between different samples orientations was observed.
Thus the flow stress curves for all materials and orientations are not presented.
As an example, the true stress – true strain curves of DP 780-HY for the three
orientations are shown in Figure 4.8.
Table 4.2 summarizes the strain ratios of the five AHSS materials in the three
orientations, as well as, the average strain ratio and planar anisotropy. Figure 4.9
and Figure 4.10 compare the average values (0o, 45o, 90o) for the uniform
elongation, total elongation, UTS, and 0.2% offset yield strength of the five AHSS
tested by the tensile test.
56
Engineering Stress (Mpa)
1000
TRIP 780
900
800
DP 780-CR
700
600
500
400
300
200
DP 780-HY
100
DP 600
DP 780
0
0
5
10
15
20
25
30
Engineering Strain (%)
Figure 4.6 Comparison of Engineering Stress - Engineering Strain curves of
various AHSS grades obtained by the tensile test
1000
DP 780-HY
True Stress (MPa)
900
800
700
600
500
400
DP 780
300
200
TRIP 780
DP 780-CR
100
DP 600
0
0
0.05
0.1
0.15
0.2
True Strain
Figure 4.7 Comparison of True Stress - True Strain curves of various AHSS
grades obtained by tensile test
57
1000
True Stress (MPa)
900
800
700
0 degrees
600
500
45 degrees
400
300
90 degrees
200
100
0
0
0.02
0.04
0.06
0.08
0.1
True Strain
Figure 4.8 True Stress - True Strain curves of DP 780-HY at 0, 45, and 90 degrees
with respect to rolling direction obtained by tensile test
0o
45o
90o
ΔR
DP 600
0.942
1.01
1.08
1.01
0.001
DP 780
0.802
0.9
0.874
0.87
-0.062
DP 780CR
0.925
0.811
1.064
0.90
0.184
TRIP 780
0.498
0.872
0.583
0.71
-0.332
DP 780HY
0.843
1.108
0.931
1.00
-0.221
Table 4.2 Comparison of Anisotropy Ratios of various AHSS grades
58
Uniform/Total Elongation (%)
30
26
Uniform Elongation (%)
Total Elongation (%)
25
19
18
17
20
16
17.5
14.5
15
10.5
9
8
10
5
0
DP 600
DP 780
DP 780-CR
TRIP 780
DP 780-HY
UTS/ 0.2% Offset Yield Strength
(MPa)
Figure 4.9 Uniform and Total Elongation of various AHSS grades (Gauge Length:
2 in) (Average values are shown)
0.2% offset yield strength
1000
866.5
800
837.5
601
600
600
400
819
831
UTS
523
502
482
379
200
0
DP 600
DP 780
DP 780-CR
TRIP 780
DP 780-HY
Figure 4.10 UTS and 0.2% Offset Yield Strength of various AHSS grades
(Average UTS values are shown)
59
4.6.2
VPB Test (Combined FE - Membrane Theory Inverse Analysis)
Figure 4.11 shows a sample pressure vs. time curve for TRIP 780 from which the
burst pressure was obtained. The burst pressure was about 225 bars for sample 1
and 226 bars for sample 2. Figure 4.12 shows a picture of a burst sample (a) and a
sample bulged but not burst (b) for TRIP 780. Since a large clamping force (100
metric tons) was used, no material draw-in was observed in all tests. Figure 4.13
compares the burst pressures, while Figure 4.14 compares the experimental
pressure vs. dome height curves of the five AHSS materials obtained by the VPB
test. The corresponding flow stress curves are compared in Figure 4.15. The
curves of both DP 600 and DP 780-HY were obtained up to bursting since a
sample accidently burst during the test. As an example of experimental data
extrapolation to the burst pressure,
Figure 4.16 shows the pressure vs. dome height curve of TRIP 780 (sample 6)
with and without extrapolation. Figure 4.17 shows the flow stress curve of TRIP
780 (sample 6) obtained from both experimentally measured and extrapolated
pressure vs. dome height curves.
60
250
Pressure (bars)
200
Burst pressure ~ 225 bar
150
100
50
0
0
0.5
1
1.5
2
2.5
3
Time (seconds)
Figure 4.11Experimental Pressure versus time curve for sample 1 of TRIP 780
steel sheet material
(a) TRIP 780 (Sample 2)–
Burst
(b) Sample 7
Figure 4.12 Example tested specimens for TRIP 780 sheet material (a) sample
burst (b) sample not burst
61
Burst Pressure (bars)
250
200
236
228
220
226
DP 780
DP 780-CR
DP 780-HY
TRIP 780
178
150
100
50
0
DP 600
Figure 4.13 Burst pressures of the five AHSS materials tested
250
DP 780-CR
Pressure (bars)
200
DP 780
150
100
DP 780-HY
50
TRIP 780
0
0
5
10
15
DP 600
20
25
30
35
Dome Height (mm)
Figure 4.14 Experimental pressure versus dome height curves obtained from the
VPB test for the five AHSS sheets materials tested (These curves are the
measured curves without any extrapolation).
62
1400
DP 780-CR
TRIP 780
True Stress (MPa)
1200
1000
800
600
400
DP 600
200
DP 780-HY
DP 780
0
0
0.1
0.2
0.3
0.4
0.5
0.6
True Strain
Figure 4.15 Comparison of the flow stress curves of the five AHSS materials
tested using the VPB test (these curves are neither corrected for anisotropy, nor
extrapolated)
250
Burst pressure = 226 bars
Pressure (bars)
200
Extrapolated
150
100
50
0
0
5
10
15
20
25
30
35
Dome Height (mm)
Figure 4.16 Pressure versus dome height curve (for TRIP780, sample 6)
extrapolated from last measured datapoint (212 bars) up to burst pressure (226
bars) using second order polynomial approximation
63
1400
True Stress (MPa)
1200
1000
From Extrapolated data
800
600
From Measured data
400
200
From extrapolated data
0
0
0.1
0.2
0.3
0.4
0.5
0.6
True Strain
Figure 4.17 The flow stress curve of TRIP 780 (sample 6) obtained from both
experimentally measured and extrapolated pressure vs. dome height curves
4.6.3
VPB Test (Combined FE - Optimization Inverse Analysis)
Figure 4.18 shows how the values of K and n converge to the optimal values for
DP 600. The initial range for each material was selected based on the results
obtained from the combined FE-membrane theory methodology. The number of
simulation points in each iteration was selected to be 10 point. The average
number of iterations until convergence was 8 iteration, with an average of 17
minutes per iteration.
Figure 4.19 compares the flow stress curves of the five AHSS materials tested
obtained from the optimization methodology. The curves are plotted from the
optimal K and n values. Last datapoint on the curves is selected to be the same as
the values reported for the combined FE-membrane theory methodology.
64
(a) K-value
(b)
n-value
Figure 4.18 Optimization history of the design variables K and n for DP 600.
Number of iterations to converge is 12
1400
DP 780-CR
(1346,0.14)
1200
True Stress (MPa)
1000
800
600
400
TRIP 780
(1378, 0.174)
200
DP 600
(980, 0.143)
DP 780
DP 780-HY
(1284,0.093) (1171,0.094)
0
0
0.1
0.2
0.3
True Strain
0.4
0.5
Figure 4.19 Flow Stress curves of the five AHSS materials tested obtained using
the combined FE-optimization methodology. Curves are plotted up to the last
datapoint obtained from the combined FE-membrane theory methodology (also
shown in the figure, the K-value in MPa and the n–value)
65
4.6.4
Comparison of Different Techniques
Figure 4.20 through Figure 4.24 compare the flow stress curves determined by
the tensile and VPB tests (two methodologies) for the five AHSS materials tested.
Table 4.3 shows the K and n-values obtained from the different tests and
True Stress (MPa)
methodologies.
1000
900
800
700
600
500
400
300
200
100
0
Tensile Test
VPB-Membrane (with
anisotropy correction)
VBP-Membrane (without
anisotorpy correction)
VPB-Optimization
0
0.1
0.2
0.3
0.4
0.5
0.6
True Strain
Figure 4.20 Comparison of True Stress- strain curves of DP 600 determined by
the Tensile test and VPB test (different methodologies) (Curves are not
extrapolated)
66
1400
True Stress (MPa)
1200
1000
Tensile Test
800
VPB-Membrane (with
anisotropy correction)
600
400
VBP-Membrane (without
anisotropy correction)
200
VPB-Optimization
0
0
0.05
0.1
0.15
0.2
0.25
True Strain
0.3
0.35
0.4
Figure 4.21 Comparison of True Stress- strain curves of DP 780 determined by
the Tensile test and VPB test (different methodologies) (Curves are not
extrapolated)
1200
True Stress (MPa)
1000
Tensile Test
800
600
VPB-Membrane (with
anisotropy correction)
400
VBP-Membrane (without
anisotropy correction)
200
VPB-Optimization
0
0
0.05
0.1
0.15
0.2
0.25
True Strain
Figure 4.22 Comparison of True Stress- strain curves of DP 780-CR determined
by the Tensile test and VPB test (different methodologies) (Curves are not
extrapolated)
67
1200
True Stress (MPa)
1000
Tensile Test
800
600
VBP-Membrane (with
anisotropy correction)
400
VBP-Membrane (without
anisotropy correction)
200
VPB-Optimization
0
0
0.1
0.2
0.3
0.4
0.5
0.6
True Strain
Figure 4.23 Comparison of True Stress- strain curves of DP 780-HY determined
by the Tensile test and VPB test (different methodologies) (Curves are not
extrapolated)
1400
True Stress (MPa)
1200
1000
800
Tensile Test
600
VBP-Membrane (with
anisotropy correction)
400
VBP-Membrane (without
anisotropy correction)
200
VPB-Optimization
0
0
0.05
0.1
0.15
0.2
0.25
0.3
True Strain
Figure 4.24 Comparison of True Stress- strain curves of TRIP 780 determined by
the Tensile test and VPB test (different methodologies) (Curves are not
extrapolated)
68
K
(MPa)
952
1541
1436
na
R2b
0.175
0.188
0.187
0.9975
0.9877
0.9736
VPB-Membrane (w/o
correcting for
anisotropy)
K
nc
R2b
(MPa)
1056
0.167 0.9816
1382
0.116 0.9613
1437
0.155 0.9701
1332
0.142
0.9882
1220
0.097
0.9544
1171
0.094
1444
0.208
0.9934
1454
0.183
0.9755
1378
0.174
Tensile test
Material
DP 600
DP 780
DP 780CR
DP 780HY
TRIP
780
VPBOptimization
K
(MPa)
980
1284
1346
n
0.143
0.093
0.14
Table 4.3 Comparison of the K and n-values obtained using both the tensile and
VPB tests (two methodologies) for the five AHSS materials
a The n-value in the tensile test was obtained by fitting the power law in the range from the 0.2% offset yield
point to the instability point
b
R2 is the square of the Correlation Coefficient
c The
n-value in the VPB test was obtained by fitting the power law in the strain range from about 0.04 to
the last datapoint available without extrapolation (note that the range in which the curve is fit affects the fit
parameters)
4.6.5
Variation of Strain Hardening and the Suitability of the Power Law Fit
Figure 4.25 through Figure 4.29 show how the value of the Normalized Strain
Hardening (NSH), calculated from bulge test flow stress data (without
anisotropy correction), change with strain. In these charts, curves are calculated
using both the original flow stress datapoints (as taken from the excel macro),
and from the Hollomon Power law fit curves shown in Table 4.3. Comments on
these charts can be found in the conclusions chapter.
69
NSH
5
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
From power law fit curve
From experimental datapoints
0
0.1
0.2
0.3
0.4
0.5
0.6
True Strain
NSH
Figure 4.25 Normalized Strain Hardening (NSH) vs. Strain for DP 600 obtained
from both VPB flow stress data (combined FE-membrane theory methodology)
and from the Power Law Fit Curve (Note that data for DP 600 was collected up to
bursting since a sample accidentally burst during the test)
5
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
From power law fit curve
From experimental datapoints
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
True Strain
Figure 4.26 Normalized Strain Hardening (NSH) vs. Strain for DP 780 obtained
from both VPB flow stress data (combined FE-membrane theory methodology)
and from the Power Law Fit Curve
70
NSH
5
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
From power law fit curve
From experimental datapoints
0
0.05
0.1
0.15
0.2
0.25
True Strain
Figure 4.27 Normalized Strain Hardening (NSH) vs. Strain for DP 780-CR
obtained from both VPB flow stress data (combined FE-membrane theory
methodology) and from the Power Law Fit Curve
4
3.5
3
NSH
2.5
From power law fit curve
2
1.5
From experimental datapoints
1
0.5
0
0
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
True Strain
Figure 4.28 Normalized Strain Hardening (NSH) vs. Strain for DP 780-HY
obtained from both VPB flow stress data (combined FE-membrane theory
methodology) and from the Power Law Fit Curve (Note that data for DP 780-HY
was collected up to bursting since a sample accidentally burst during the test)
71
5
4.5
4
3.5
From power law fit curve
NSH
3
2.5
From experimental datapoints
2
1.5
1
0.5
0
0
0.05
0.1
0.15
0.2
0.25
0.3
True Strain
Figure 4.29 Normalized Strain Hardening (NSH) vs. Strain for TRIP 780 obtained
from both VPB flow stress data (combined FE-membrane theory methodology)
and from the Power Law Fit Curve
72
CHAPTER 5
DETERMINATION OF THE FLOW STRESS OF ALLUMINUM
SHEET MATERIALS AT ELEVATED TEMPERATURE
5.1
Experimental Setup (Machine and Tool Design)
A fluid-based elevated temperature biaxial bulge system was designed and
developed by Applied Engineering Solutions, LLC (AES) wherein the tested
samples were submerged within a heated fluid. Die design was collaboratively
accomplished with the CPF. Figure 5.1 shows a schematic of the machine design,
which consists essentially of the tools (the forming die and seal plate/blankholder), heat transfer fluid, a heating system, fluid tank, fluid pressurization
(fluid intensifier) system, and sensors to measure sample bulge deformation,
bulging pressure, temperature, and the pressurizing fluid volume flow rate. All
machine components were selected for elevated temperature applications.
73
LVDT
Sensors
Computer
Controller
Die
Seal
Plate
Bulge Test
Specimen
Hydraulic
Power
Supply
Hydraulic
Ram
Hydraulic
Ram
Heat Exchanger
Fluid
Preheater
Fluid Tank
Fluid
Heater
Fluid
Pressure
Intensifier
@ 2008 Applied Engineering Solutions, LLC
Figure 5.1 A schematic of the Fluid-based Elevated Temperature Biaxial Bulge
Test Apparatus [Designed by the Applied Engineering Solutions (AES), LLC]
The test is divided into two main stages; clamping and bulging. The sample is
first clamped between the die and blank holder to prevent the material from
flowing into the die cavity during the test, thus maintaining a stretch forming
condition. Critical to the clamping process is the lockbead design. A series of FE
simulations of the clamping and bulging stages of the test, with various possible
lockbead designs, were made with flow stress data from the literature, in order
to select the design which prevents sheet draw-in [Yadav, 2008]. The design
which properly clamps the sheets without excessive thinning or cracking in the
clamping stage, and maintains the sheet clamped throughout the test was
selected, taking into consideration the hold-down capacity of machine (25 tons).
Figure 5.2 shows a schematic of the designed ET tools. While clamped, the
intensifier pressurizes the sheet with the required volume flow rate of the
74
bulging fluid. Figure 5.3 shows schematically the clamped sheet during the
bulging process. Two flow rates; 2 in3/second and 0.2 in3/second, were selected
to result in a wide range of strain rates. Corresponding pressure vs. time can be
measured using the pressure sensor and the resulting range of strain rates in the
sheet can be estimated from the FE simulation.
The criteria for the test machine design were: a) to provide a near-isothermal
bulge condition at elevated temperatures, b) to control and measure the
pressurizing fluid volume flow rate, and c) to measure the resulting pressure and
sample deformation which are the key inputs to the optimization. In order to
ensure the near-isothermal conditions of the test blank, the die, seal plate, and
sample were submerged in a hot heat transfer liquid. To avoid heat transfer
fluid oxidation, the heating system was divided into two components: 1) a fluidfilled tank used to submerge the sample and tools, and 2) a closed-loop external
fluid heating unit and circuit. The heat transfer liquid inside the tank was heated
via a heat exchanger located within the tank wherein heated heat transfer fluid
was circulated via the external (closed loop) fluid heating unit located near the
machine. The system was designed to reach controlled temperatures up to 300
oC.
Three Linear Variable Differential Transducers (LVDTs) were used to
capture real-time sample dome height (and shape) during the test. Due to the
high temperatures required, no LVDTs capable of being submerged in a hot fluid
were commercially available to allow their arrangement as originally proposed
and depicted in Figure 5.3. Therefore, AES designed a remote method to sense
dome height deformation using three sample contact probes which were
connected to each of the three LVDTs via individual coaxial cables.
This
arrangement, as shown in Figure 5.4, allowed the measurement of the sample
bulge curvature profile as a function of time. The applied fluid pressure was
75
measured using a pressure transducer within the intensifier unit, and the sample
temperature was determined via a thermocouple located within the fluid tank.
Figure 5.5 illustrates the constructed elevated temperature bulge test equipment
and includes a photograph of a produced bulged sample.
Maximum available
tonnage = 25 tons
Center line
UPPER PLATE / DIE
Ø 101.8 (~ 4”)
Die entry corner
radius (R)
Sheet
Lockbead
required
LOWER PLATE
(b)
(a)
Figure 5.2 Schematics showing the design and dimensions of (a) the tools, (b)
lockbead (within the tools), designed to be suitable for the ET bulge test [Yadav,
2008]
Figure 5.3 A schematic showing the clamped sheet during the bulging process
and the LVDTs which were planned to be used to measure the dome height and
sample curvature profile [Designed by the Applied Engineering Solutions (AES),
LLC]
76
Figure 5.4 A picture showing the arrangement designed to measure the sample
bulge curvature profile without the need to submerge the LVDTs in the heated
fluid [Designed by the Applied Engineering Solutions (AES), LLC]
@ 2008 Applied Engineering Solutions,
LLC
@ 2008 Applied Engineering Solutions, LLC
@ 2008 Applied Engineering Solutions,
LLC ©2008 Applied
Engineering
Solutions, LLC
Figure 5.5 The fluid-based elevated temperature biaxial bulge test apparatus
[Designed by the Applied Engineering Solutions (AES), LLC]
77
5.2
Testing Matrix
Table 5.1 is a summary of the tests performed at elevated temperature:
Material
Thickness
(mm)
AA5754-O
AA5182-O
AA3003-O
1
1
1
Temperature
(oC)
200 230 260
√
√
√
√
√
√
√
√
√
Pressurization
rate (in3/sec)
0.2 and 2
0.2 and 2
0.2 and 2
# of
samples/
condition
3
3
3
Table 5.1 Testing matrix of AA5754-O, AA5182-O, and AA3003-O at elevated
temperature
5.3
Combined FE - Optimization Inverse Analysis at Elevated Temperature
Note: This section describes the difference between applying the optimization
methodology to the elevated temperature and room temperature bulge test.
At elevated temperatures, the material is strain rate sensitive. Thus, the material
model to be used should be a function of the strain rate. [Abbedrabbo et al, 2006a and b] showed that the Field and Backofen material model (Equation 8) is
suitable to describe the behavior of AA5754-O, AA5182-O, and AA3003-H111.
Since these are the materials of interest in this study (except the temper of
AA3003), this material model will be used.
Since the material at elevated temperature is strain rate sensitive, the
deformation speed (pressurization rate) should be changed in the experiment to
result in a wide range of strain rates in order to determine the m value. Thus, two
samples, one pressurized fast (2 in3/second), and the other pressurized slow (0.2
78
in3/second) were tested and the resulting dome height evolutions were
compared with FE simulations run with the corresponding pressure vs. time
curves. Figure 5.6 shows schematically the fast and slow pressure curves and
how the pressurization rate affects the dome height. The new objective function
to be minimized should have two terms; one associated with the high
pressurization rate test and the other associated with the low pressurization rate
test and is formulated as follows:
Equation 24
where;
E: is the objective function to be minimized
t: time point at which simulation and experiment were compared
N and M: are the numbers of datapoints selected for the fast and slow tests,
respectively
hm,F and hm,S: are the measured dome heights at time t in the fast and slow tests,
respectively
hs,F and hs,S: are the simulation dome heights at time t in the fast and slow
simulations, respectively
79
Figure 5.6 (left) A schematic showing the fast (high pressurization rate) and slow
(low pressurization rate) pressure curves. (right) a schematic showing the
difference in dome height between two samples, one pressurized fast and the
other pressurized slow
Instead of running FE simulations with two parameters; K and n, as was the case
for room temperature, LS-OPT generates LS-DYNA FE simulations files for
selected combinations of the three parameters; K, n, and m. In Each LS-DYNA
file, two bulging processes (Fast and Slow) are simulated simultaneously and the
dome height in each can be extracted. 16 design points were used for the
elevated temperature bulge tests.
In order to reduce the simulation time, time scaling was used where the time in
the experimental pressure vs. time curve was divided by 100. Since the material
is strain rate sensitive at elevated temperature, this will result in the strain rate
approximately 100 times higher. Therefore, the Field and Backofen material
model (Equation 8) should be modified as follows:
Equation 25
80
5.4
Results
5.4.1
Problems Encountered and Solved
Following are the major problems encountered and solved in the elevated
temperature bulge test experiments and simulations:
Samples Pre-bulging in the Clamping Stage (AA5754-O and AA5182-O):
The sheet specimen and the tools are totally submerged in warm oil. During
the clamping stage, oil was entrapped between the specimen and male die,
resulting in the sample pre-bulging prior to the test. This pre-bulging
problem was solved by using a check valve to relieve the entrapped oil in the
clamping stage. This problem was encountered while testing AA5754-O and
AA5182-O.
Pressure drop in the testing of AA-3003-O:
After solving the problem described in section above, another problem
resulted from using the check valve. The program controlling the machine
was set to have a time delay between the clamping and bulging stages. Once
the bulging stage starts, it was noticed that the pressure curve does not
increase instantaneously and that the pressure may even drop at the
beginning of the process. It was found later that the check valve required
81
some time to close after relieving the oil in the clamping stage. As a result,
some leakage took place and was responsible for the pressure drop. To solve
this problem, the time delay between the clamping and bulging stages was
increased to give the check valve enough time to close; thus, prevent leakage.
This problem was encountered while testing AA3003-O.
It should be noted that enough testing materials and time were not available to
repeat the experiment after solving the problems described above.
Termination Errors in FE Simulations
Some combinations of the three design variables (rheological parameters); K,
n, and m may result in invalid simulation results (very large dome height);
thus resulting in a termination error. To reduce the likelihood of termination
errors, constraints were set on the dome height extracted from the
simulation. The constraint is basically an upper-bound equal to 120% of the
measured dome height. Thus, “when selecting the design points
(combinations K, n, and m), the optimization should select the combinations
which do not cause the simulated dome height to deviate more than 20%
from the measured dome”.
At least 7 design point (at room temperature), and 10 design points (at
elevated temperature) are required to fit the second order polynomial curve.
Therefore, loosing design points because of the reason described above may
result in the number of point to become less than the minimum required. As
a result, the optimization stops before the convergence criterion is met.
82
5.4.2
Problems Encountered and not Solved
Uniqueness of Optimization Results
It was noticed that the initial guess of the range of the design variable (K, n,
and m) may affect the optimization results at elevated temperature. A slight
shift of the initial range up or down, widening, or narrowing the range
resulted in small difference in the optimal results. If the optimal value is
relatively small (such as in the case of the m-value), the percentage variation
in the optimal value due to selecting different initial range may be high.
Measurement of sheet radius of curvature
In room temperature bulge test, the shape of the dome may be assumed to be
spherical and thus, the dome height is sufficient to characterize the dome
evolution. However, this may not be the case at ET. The variation of the
strain from one location to another in the sample and the effect of strain rate
on the material flow stress will affect the strain distribution in the sample.
This will change the deformation behavior of the sheet and may not result in
a spherical bulge. To take this into consideration in the analysis, it was
originally planned (as previously described) to measure the dome height at
the center, and two different off-center locations to estimate the radius of
curvature beside the dome apex height. This will provide additional
83
information to the analysis, resulting in more robust method for determining
material properties.
The three LVDTs were fixed on the machine, but a technical problem
prevented the use of the off-center LVDTs. At ET, the material is relatively
soft and the tip of the probes may slightly penetrate in the sheet. This caused
a lateral deflection in the probes. As a result, only the center LVDT was used.
5.4.3
Experimental data
Although not reliable, it was decided to include the experimental data for
documentation purposes. Several trials were made to apply the optimization
methodology. Results did not match the data in the literature and therefore are
not included in this report. Figure 5.7 through Figure 5.9 shows the experimental
pressure vs. dome height curves obtained at three temperatures; 200 oC, 230 oC,
and 260 oC, and two pressurization rates; fast (2 in3/sec) and slow (0.2 in3/sec)
for the three materials tested; AA5754-O, AA5182-O, and AA3003-O.
84
Pressure (MPa)
230 oC
200 oC
4
3.5
3
2.5
2
1.5
1
0.5
0
Fast
260 oC
200 oC
230 oC Slow
260 oC
0
5
10
15
Dome Height (mm)
20
25
Figure 5.7 Experimental Pressure vs. Dome height curves of AA3003-O at three
temperatures; 200 oC, 230 oC, 260 oC, and two speeds; fast (2 in3/sec) and slow
(0.2 in3/sec). Note that for the fast test, increasing the temperature from 200 oC to
230 oC, resulted in an increase in the pressure
85
AA5182-O at 260oC
6
Pressure (MPa)
Pressure (MPa)
7
5
4
3
2
1
0
0
10
20
AA5181-O at 230oC
8
7
6
5
4
3
2
1
0
30
0
Slow
Figure
5.8
Experimental
Pressure vs. Dome height
curves of AA5182-O at three
temperatures; 200 oC, 230 oC,
260 oC, and two speeds; fast (2
in3/sec) and slow (0.2 in3/sec).
Pressure (MPa)
Fast
10
20
30
Dome height (mm)
Dome height (mm)
AA5182-O at 200oC
8
7
6
5
4
3
2
1
0
0
10
20
Dome height (mm)
86
30
AA5754-O at 260 oC
6
Pressure (MPa)
Pressure (MPa)
7
5
4
3
2
1
0
0
10
20
AA5754-O at 230 oC
8
7
6
5
4
3
2
1
0
0
30
30
AA5754-O at 200 oC
Pressure (MPa)
Slow
Figure 5.9 Experimental Pressure vs.
Dome height curves of AA5754-O at
three temperatures; 200 oC, 230 oC, 260
oC, and two speeds; fast (2 in3/sec)
and slow (0.2 in3/sec).
20
Dome Height (mm)
Dome Height (mm)
Fast
10
8
7
6
5
4
3
2
1
0
0
10
20
Dome Height (mm)
87
30
CHAPTER 6
A SYSTEMATIC METHODOLOGY FOR DESIGNING A SHF-P
PROCESS USING FE SIMULATIONS
6.1
Model Part and Tools Geometry
The model part used in this study to develop guidelines for designing SHF-P
process is a flat-headed conical part with a round pocket in its base. This part
was initial designed at General Motors R&D (the sponsor of this study). Sheet
material to be formed is aluminum AA5754-O, 1 mm in thickness. For conical
parts, the punch-die clearance is large at the beginning of the stroke and
decreases with stroke. Thus, it is easier for the sheet to bulge against the drawing
direction in such a geometry compared to a cylindrical part. This adds to the
difficulty in designing the process, and usually makes it necessary to start with a
small pot pressure and then increase it with the stroke. Moreover, thinning and
side wall wrinkling observed in conventional deep drawing of conical parts is
higher than cylindrical parts because of the suspended (unsupported) region in
punch-die clearance. Therefore, one may appreciate using SHF-P process for
conical parts more than for cylindrical parts. The initial clearance between the
punch and blankholder (considering punch and blankholder corner radii) is
15.23 mm and the conical angle is 84o. Figure 6.1 shows the model part to be used
in this study.
88
Flat base
Die
corner
Tapered
wall
Punch
corner
Pocket
Figure 6.1 One quarter of the model part to be made by the SHF-P process
One objective of SHF-P is to eliminate the die in order to reduce tools cost.
Alternatively, the punch should have the topographies required in the final part
after. To study this, the punch was designed to have a round pocket in which the
sheet will be formed. Stretch forming sheet in the pocket can be considered a
Sheet Hydroforming with a Die (SHF-D) process. Since it may not possible to
completely fill the pocket using the pot pressure, a reverse punch was designed
to completely fill the pocket at the end of the stroke.
Originally, tools were designed to have drawbeads in them. However, the
clearance between the bead and the groove was very small (about 1.09 mm)
which is very tight for a 1 mm thick sheet. Moreover, bead and groove corner
radii were extremely small (about 3 mm and 2 mm, respectively). Simulations
with the lockbead (see Results section) showed that it is impossible to draw the
89
sheet from the flange. Therefore, the bead used can be called a lockbead rather
than a drawbead. In addition to these tools, another set of flat tools (flat die and
blankholder) will be made to benefit from the SHF-P process and to avoid the
complications associated with using a drawbead. Figure 6.2 is a 2D sketch of the
tools geometry and dimensions.
All dimensions are in
mm
(Drawing not to scale)
Figure 6.2 2D sketch of the tools geometry and dimensions. The sketch shows the
blank holder and the die with a lockbead. Another set of tooling similar to this,
but without a lockbead, will also be used
90
6.2
Approach and Methodology for Designing SHF-P Process using FE
Simulations
Design criteria: Eliminate defects (see Table 1), minimize side wall thinning, and
minimize material used.
Design variables: blank size, pot pressure vs. stroke, BHF vs. stroke.
General Procedure: trial and error FE simulations, experimental validation based
on thinning distribution, punch force, and defects observed.
6.2.1
General Approach
The blank radius will be initially estimated and may be changed later in the
process.
Small BHF and pot pressure will be used at the beginning of the stroke and will
be increased toward the end of the process. The BHF will be held at a constant
(low) value just sufficient to prevent wrinkling for about half the stroke (or more)
and will be increased linearly (to simplify) after that, up to the end of the stroke.
With respect to the pot pressure, the stroke is divided into three parts. In the first
part, the critical stroke, where the sheet is being bent about the punch and die
corner radii, and very little draw-in takes place, applying a high pot pressure will
stretch form (and excessively thin) the sheet. Therefore, a small constant pressure
value will be applied just to separate the sheet from the die corner radius (and
also to slightly increase the contact pressure of the sheet with the punch). In the
second part, the punch-die clearance decreases with the stroke and bulging
91
against the drawing direction becomes difficult. Therefore, the pot pressure will
be increased linearly (to simplify) up to a maximum pressure reached at about
half the stroke (more or less). The slope (how fast the pressure builds up)
depends on how fast the clearance changes with the stroke. The maximum
pressure reached also depends on other factors such as blankholder lifting. It
should be noted that the higher the pot pressure, the higher the BHF should be to
avoid lifting.
The discussion above is for drawing and SHF-P processes where the sheet is
allowed to draw-in from the flange. Another set of simulations will be made
where the sheet is totally clamped. This stretch forming process will be simulated
with different pot pressures to see how the maximum thinning in the part is
affected. These simulations are not included in the detailed methodology below.
6.2.2
Detailed Methodology
Step 1: Initial estimation of the blank radius
Based on the principle of volume constancy and ignoring thickness change, the
blank radius will be estimated using: Area initial =
= Area final
Note: The initial radius also depends on the BHF (the higher the BHF, the smaller
the initial radius), µ (the higher µ, the smaller the initial radius), punch-die
clearance (the higher the clearance, the smaller the initial radius), and on other
factors.
92
Preliminary simulations will be made to check the suitability of the selected
radius.
Step 2: Initial estimation of BHF curve by simulating an equivalent deep drawing
process (SHF-P with zero pot pressure)
- Simulate half to two third of the stroke. Find minimum (constant) BHF to avoid
flange wrinkling.
- Simulate the rest of the stroke. Increase the BHF linearly until the end of the
stroke. Find the minimum BHF (reached at end of stroke) without wrinkling.
Step 3: Optimizing pot pressure and BHF curves by simulating the SHF-P
process
- Estimate the critical stroke from previous simulations (stroke in which the sheet
only stretch bends about corner radii with very small flange draw-in).
- Simulate the SHF-P process up to the critical stroke. Find the minimum
pressure just to separate the sheet from the die corner radius. BHF should be
increased to avoid lifting.
- After the critical stroke, linearly increase the pressure up to a maximum value.
The higher the maximum pressure reached, without defect (see Table 1), the
better. Find the maximum pressure and the stroke at which it is reached. The
earlier the maximum pressure is reached, without defects, the better. The BHF
will have to be increased to prevent lifting.
93
- Simulate the rest of the process with a constant pressure. BHF from step 2 will
have to be increased to prevent lifting.
Step 4: Experimental Validation
Run experiments with the same conditions (pot pressure and BHF) to validate
simulation results. Compare the thinning distribution, punch force vs. stroke,
and the defects observed.
Step 5: Develop guidelines for designing SHF-P process, improve the suggested
methodology for designing SHF-P process, Quantify the improvement in the
thinning distribution attained by replacing the deep drawing process by the
SHF-P process.
6.3
FE Model using Pamstamp 2G 2007
Pamstamp 2G 2007 commercial FE software was used to simulate the process.
Since the tools are axisymmetric, only quarter geometry was modeled to reduce
the simulation time (see Figure 6.3 a and b). Aquadraw module was used to
model the SHF-P process (see Appendix A). The reverse punch and the die
corner radius are modeled as parts of the pressure pot.
Table 6.1 summarizes the parameters used in the FE model.
94
Punch
Symmetry
planes
Blankholder
Blank
Binder
Pot +reverse punch+die corner
(a)
Lockbead
(b)
Figure 6.3 FE model of the SHF-P (a) without a lockbead (b) with a lockbead.
Prepared using Pamstamp 2G 2007 (reverse punch and die corner radius are
parts of the pressure pot)
95
Blank Geometry
Varied (see section 6.4 for the
simulation Matrix)
1 mm
Blank radius
Thickness
Mechanical Properties
Flow stress/ AA5754-O (obtained
See Figure 6.5
by VPB test)
Young‟s Modulus (E)
70 GPa
Poisson‟s ratio (ν)
0.33
R0, R45, R90
1 (material assumed isotropic)
Interface Condition
Friction coefficient µ
0.1 (in deep drawing)
(blank/binder and blank/ blank
0.06 (in Hydroforming)
Holder)
Friction coefficient µ (blank/ punch)
0.12
Mesh
Element type
Shell (Belytschko-Tsay )
Tools element size/ number of
5 mm (6 element at radii)
elements at radii
Initial sheet element size
2 mm
Meshing
Adaptive Meshing (max. level 3)
Object type
Blank
Elastic, Plastic
Tools
Rigid
Aquadraw (for Details of FE modeling using Aquadraw, see Appendix
A)
Medium (Bulk Modulus, K)
Water (2.2 GPa)
Varied (see section 6.4 for the
Pot Pressure
simulation Matrix)
Locking stage (if exist)
Blankholder stroke
5.994 mm (see Figure 6.4-b)
Hydroforming Stage
Varied (see section 6.4 for the
BHF
simulation Matrix)
About 64.8 mm (see Figure 6.4–
Full punch stroke
a)
Table 6.1 Summary of the parameters used in the deep drawing and SHF-P FE
simulations
96
(a) A schematic showing the punch full stroke (flat die and blank holder are
shown)
(b) A schematic showing the locking stroke for the tool set with a lockbead
Figure 6.4 Schematics showing (a) the punch full stroke and (b) the locking stroke
(if a lockbead is used)
97
True Stress (MPa)
350
300
250
200
150
100
50
0
0.00
0.05
0.10
0.15
0.20
0.25
0.30
True Strain
Figure 6.5 Flow Stress curve of AA5754-O (1 mm) obtained using the VPB test
(data is not extrapolated) [Penter et al, 2008]
6.4
Simulation Matrix
6.4.1
Stretch Forming and hydroforming without Draw-In
#
1
2
Blank
radius
(mm)
265
265
BHF (KN)
Blank
holder
fixed
Blank
holder
fixed
Pot
Objective of running the
Pressure
simulation
(Bars)
Zero
To investigate the
possibility of excessive
thinning in the clamping
stage
To study the effect of pot
pressure on the stretch
forming process by
comparing with 2
To study the effect of pot
pressure on the stretch
forming process by
comparing with 1
100
Figure 6.6 Simulation matrix of stretch forming with and without pot pressure
98
6.4.2
Preliminary Simulation of Deep Drawing and Hydroforming with
Draw-In
#
1
2
3
4
Blank
radius
(mm)
176.3
176.3
176.3
176.3
BHF (KN)
60
140
140
140
Pot
Objective of running the
Pressure
simulation
(Bars)
Zero
Study the effect of BHF
Zero
40
Study the effect of Pot
pressure
Compare deep drawing
and SHF-P
Study the effect of Pot
pressure
60
Compare deep drawing
and SHF-P
Figure 6.7 Preliminary simulation matrix of deep drawing and SHF-P with drawin
99
6.4.3
Deep Drawing and Hydroforming with Draw-In (According to the
Proposed Methodology)
Blank
radius
(mm)
Pot
Pressure
Objective of running the
#
BHF curve (KN)
curve
simulation
(Bars)
Step 1: Initial estimation of the blank radius
1-1 203
60 (constant)
Zero
To check the suitability of the
calculated radius; 203 mm
1-2 215
60 (constant)
Zero
To make sure a flange is left after
forming
1-3 240
60 (constant)
Zero
To increase thinning (on purpose)
in order to see a considerable
difference when running SHF-P
simulations.
Step 2: Initial estimation of BHF curve – Deep Drawing Simulations
2-1 240
BHF curve 1a
Zero
To find minimum possible BHF
(without wrinkling) in the first half
2-2 240
BHF curve 2a
Zero
to two third of the stroke
2-3 240
BHF curve 3a
Zero
To find minimum possible BHF
a
curve to completely form the part
2-4 240
BHF curve 4
Zero
(without wrinkling)
Step 3: Optimizing the Pot Pressure and BHF curves – SHF-P Simulations
3-1 240
BHF curve 4*
35
Simulated up to the critical stroke
+ 50 KN to
(constant) to check the suitability of this
prevent lifting
pressure value.
Critical stroke was estimated from
previous simulations to be ~14 mm
3-2 240
BHF curve 4*
Pressure
To find the most suitable pressure
b
+ 50 KN to
curve 1
curve (which minimizes thinning)
prevent lifting
and BHF curve to prevent lifting
*
due to the pot pressure
3-3 240
BHF curve 4
Pressure
+ 80 KN to
curve 2b
prevent lifting
Figure 6.8 Simulation matrix of deep drawing and SHF-P with draw-in
(according to the proposed methodology)
a
For the BHF curves, see Figure 6.9
b
100
For the pot pressure curves, see Figure 6.10
40
No wrinkling
BHF curve 1
BHF curve 2
BHF (KN)
30
BHF curve 3
BHF curve 4
20
10
Start of wrinkling
0
0
10
20
30
40
Stroke (mm)
50
60
70
Figure 6.9 BHF curves used in simulating the deep drawing process with 240 mm
blank radius. Also shown (with a circle) the punch stroke at which the flange
started to wrinkle in the simulation (details can be found in the Results section)
250
Pot Pressure (Bars)
P1 (extra BHF = 50 KN)
200
P2 (extra BHF = 80 KN)
150
100
50
0
0
10
20
30
40
Stroke (mm)
50
60
70
Figure 6.10 Pot pressure curves used in simulating the SHF-P process with 240
mm blank radius and BHF curve 4 selected from deep drawing simulations plus
an addition force to prevent blankholder lifting because of the pot pressure. The
extra force applied is also shown for each curve
101
6.5
Results
6.5.1
Stretch Forming and hydroforming without Draw-In
At the end of the clamping stage, the maximum thinning observed in the
lockbead region was about 6.5%, which indicates that cracking in this region is
unlikely to occur. In the stretch forming stage (with and without pot pressure),
no draw-in was observed in the simulation. Therefore, the geometry of the
lockbead should be modified if sheet draw-in is required. Figure 6.11 compares
the thinning distribution in simulations with zero and 100 bars pot pressure, at a
punch stroke of 13 mm.
14
P=zero
P=100 bars
D
Thinning (%)
12
10
B
8
C
E
A
6
4
2
0
0
50
100
150
Curvilinear Length (mm)
200
Figure 6.11 Comparison of the thinning distribution in stretch forming
simulations with zero and 100 bars pot pressure, at a punch stroke of 13 mm. It
can be seen that thinning at punch corner radius (point D) increases with
pressure increase, indicating that SHF-P is detrimental if the sheet is totally
clamped (stretch forming). Other pressure values were tried and shown to give
similar results
102
6.5.2
Preliminary Simulation of Deep Drawing and Hydroforming with
Draw-In
Preliminary simulations of the deep drawing and SHF-P processes of AA5754-O
were made with a sheet 176.3 mm in radius. The drawing ratio calculated from
this radius is about 1.15. The reason for selecting this small radius was to utilize
the available tools (with lockbead) until a new tool set, without a lockbead, is
manufactured at GM R&D. A sheet with this radius will not interfere with the
lockbead.
Because of the small drawing ratio, the process window in the deep drawing
process was big. High BHF does not result in high sheet thinning and very low
BHF is required to see wrinkling in the simulation. Moreover, the flange was
small that the maximum possible punch stroke was about 20 mm. Two constant
BHF; 60, and 140 KN were used in the deep drawing simulations. A comparison
of the thinning distribution at 20 mm stroke in deep drawing is shown in Figure
6.12. Since thinning in all cases is relatively low and to be able to see thinning
reduction in the hydroforming process, the highest BHF (140 KN) was
intentionally selected when running the SHF-P simulations.
Figure 6.13 compares the thinning distribution at 20 mm stroke in SHF-P
simulations run with two constant pot pressures; 40 bars, and 60 bars.
Figure 6.14 shows the sheet bulging (in the punch-die clearance) against the
drawing direction for the same pressure values.
Figure 6.15 compares the thinning distribution (at 20 mm stroke) in deep
drawing and SHF-P. The BHF in both simulations is 140 KN.
103
BHF=60 KN
Thinning (%)
4
BHF=140 KN
D
3
E
2
1
0
-1 130
140
150
160
170
180
-2
-3
Curvilinear Length (mm)
Figure 6.12 Effect of BHF on the thinning distribution in deep drawing
simulation of 176.3 mm radius sheet (Material: AA5754-O). Two BHF were used;
60, and 140 KN. Thinning was recorded at 20 mm stroke. Only thinning in the
punch-die clearance is shown
P= 40 bars
Thinning (%)
6
P=60 bars
D
4
2
0
-2
-4
130
140
150
160
170
180
190
Curvilinear Length (mm)
Figure 6.13 Effect of pot pressure on the thinning distribution in SHF-P
simulation of 176.3 mm radius sheet (Material: AA5754-O). Two pot pressure
were used; 40, and 60 bars. 140 KN BHF was used in both simulations. Thinning
was recorded at 20 mm stroke. Only thinning in the punch-die clearance is
shown
104
Punch
Blankholder
Punch
Blankholder
Die
Die
Small sheet bulging
Big sheet bulging
(a) Pot pressure = 40 bars
(b) Pot pressure = 60 bars
Figure 6.14 Sheet bulging (in the punch-die clearance) against the drawing
direction in SHF-P simulations with two different pot pressures; 40 and 60 bars
(Material: AA5754-O). Excessive pot pressure stretch forms (and thins) the sheet
4
3
P=0 (Drawing)
Ddrawing
DSHF-P
2
Thinning (%)
P=40 bars (SHF-P)
Edrawing
1
0
-1 130
140
150
160
170
180
190
-2
-3
-4
Curvilinear Length (mm)
Figure 6.15 Comparison of thinning distribution at 20 mm stroke in deep
drawing and SHF-P (40 bars pot pressure) obtained by FE simulations (Material:
AA5754-O). The BHF in the two simulations is 140 KN. Thinning in SHF-P is
lower than deep drawing. Two necks form in deep drawing, while only one
forms in SHF-P
105
6.5.3
Deep Drawing and Hydroforming with Draw-In (According to the
Proposed Methodology)
Following are the results organized according to the steps in the proposed
methodology:
Step 1: Initial estimation of the blank radius
Based on the results shown in
Table 6.2, a blank radius of 240 mm was selected to prevent the blank edge from
moving past the die corner and also to see considerable thinning reduction when
simulating the SHF-P process (same process but with a pot pressure). Although
normally, the blank radius should be minimized, in this case and for research
purposes, the maximum was selected.
Ref. to
Simulation
Matrix
Blank
Radius
(mm)
Pot
BHF
Pressure
(KN)
(Bars)
Wrinkling
1-1
1-2
1-3
203
215
240
60
60
60
No
No
No
Zero
Zero
Zero
Punch
Blank
corner
moving
Thinning
past the
(%)
die corner
3.77
Yes
4.1
No
10
No
Table 6.2 Simulation results of applying step 1 of the proposed methodology;
Initial estimation of the blank radius. A preliminary BHF of 60 KN was used.
Step 2: Initial Estimation of the BHF Curve- Deep Drawing Simulations
Based on the results shown in
106
Table 6.3, BHF curve 4 was selected since it is the minimum BHF curve (of the
curves simulated) to completely form the part without wrinkling. For the
selected curve, maximum thinning at the punch corner at the end of the stroke is
8.6%, while the maximum thinning in the pocket is 22.3%.
Ref. to
Simulation
Matrix
Blank
Radius
(mm)
2-1
2-2
2-3
2-4
240
240
240
240
BHF curve
(KN)
BHF curve1a
BHF curve2a
BHF curve3a
BHF curve4a
Pot
Pressure
(Bars)
Stroke at
wrinkling
(mm)
Zero
Zero
Zero
Zero
19.5
47.5
53.5
No
Punch
corner
Thinning
(%) [if no
wrinkling]
8.6
Table 6.3 Simulation results of applying step 2 of the proposed methodology;
Initial estimation of the BHF curve.
a
For the BHF curves, refer to Figure 6.9
Step 3: Optimization of the BHF and Pot Pressure Curves
The critical stroke was estimated from previous simulations to be about 14 mm.
In the critical stroke, very small draw-in (~3.5 mm) was observed. 35 bars pot
pressure was found to be suitable for lifting the sheet from the die corner without
excessive bulging/ thinning. To prevent blank holder lifting due the pot pressure
in the punch-die clearance, a BHF 50 KN higher than the BHF curve 4.
According to the simulation matrix, simulations with two pressure curves were
made.
Figure 6.15 compares the thinning distribution at the end of the stroke for the
two pressure curves, as well as zero pressure curve (deep drawing).
107
BHF curve 4 (deep drawing)
30
P1
P2
B-C (pocket corners)
Thinning (%)
25
20
15
10
D (punch corner)
5
0
100
150
200
250
Curvilinear Length (mm)
300
Figure 6.16 Comparison of the thinning distribution at the end of the stroke
between deep drawing (with selected BHF curve 4) and SHF-P with two different
pressure curves (see simulation matrix). Note the considerable improvement in
thinning distribution when using SHF-P
108
CHAPTER 7
DISCUSSION, CONCLUSIONS AND FUTURE WORK
7.1
Discussion and Conclusions
7.1.1
Characterization of AHSS at Room Temperature
Tensile Test Results
Figure 4.6 shows that the engineering stress- strain curves of the five AHSS
grades tested become almost flat around the UTS for a wide strain range,
making it difficult to visually identify the instability point (Uniform
elongation). Thus, these values that are clearly identified for low carbon steels
are difficult to determine visually for AHSS.
As seen in Figure 4.9, DP 600 has the highest post-uniform elongation (about
10%). Although DP 780-HY has the lowest uniform elongation, it has the
second highest post-uniform elongation of about 9.5%.
As seen in
Table 4.2, DP 600 and DP 780-HY have the highest Average Anisotropy Ratio
(Strain Ratio) of about 1.00, while TRIP 780 has the lowest value (about 0.7).
TRIP 780 has the highest Planar Anisotropy (ΔR) of about 0.33, while DP 600
has the lowest value (about 0.001). Thus, non-uniform flow in the flange
region (earing) when forming TRIP 780 sheet can be an issue.
109
One of the problems faced during tensile testing is that necking and failure
for some materials at certain orientations occurred outside the gauge length.
This was the case for some samples of DP 780 at 45o and 90o, TRIP 780 at 45o,
and both DP 780-CR and DP 780-HY in all orientations. Since deformation is
uniform before the instability point and since the presented true stress- true
strain curves are plotted up to this point, the data obtained from these
samples was not discarded.
For TRIP steels, strain hardening at the beginning takes place by the
interaction of dislocations with second phases existing in the matrix. Later,
when the material starts to loose its hardening characteristics, the retained
austenite transforms to martensite (the strain at which phase transformation
takes place depends mainly on the amount of carbon in the alloy) [9]. As a
result, the alloy retains it hardening characteristic, which explains the delayed
necking of TRIP 780 in uniaxial tensile test as compared to other DP steels
with the same UTS (see Figure 4.7 and Figure 4.9). It can be seen from Figure
4.6 and Figure 4.7 that the flow stress curves of TRIP 780 have relatively low
slope at lower strains compared to other grades with the same UTS. Still, this
alloy has the largest values of both uniform and total elongation. This maybe
attributed to the transformation mentioned above.
It is reported that the austenite-to-martensite transformation of TRIP steels is
easier under biaxial tension than under compression [9]. Thus, if used in
drawing applications, TRIP steels shows relatively good performance since
the transformation strengthens the side wall, while the flange region stays
soft and easy to draw.
110
Bulge Test Results
Figure 4.16 and Figure 4.17 show how much flow stress data is lost when
ending the test at a pressure value slightly below the burst pressure.
Moreover, these figures illustrate the high strain values which can be
attained under balanced biaxial condition.
The dome height at fracture (bursting) in the VPB test can be used as a
measure of formability and therefore used as a quick and reliable acceptance
test of incoming raw material in the stamping plant. However, not many
samples were burst in this study so that burst height cannot be considered to
be reliable in describing and/or comparing the formability of the different
AHSS grades tested.
The negligible variation in the dome height vs. pressure curves, and
corresponding flow stress curves, among different samples of the same
material, indicate the consistency in their deformation behavior.
The combined FE-optimization methodology worked very well for the five
AHSS materials tested using the VPB test at room temperature. Flow stress
curves plotted from the K and n values obtained from LS-OPT output are
compared in Figure 4.19.
Comparison of Different Techniques
For all materials, stress levels obtained from the tensile test is lower than
levels obtained from the VPB test. For DP 780-HY, the two tests gave close
flow stress curves.
Table 7.1 below compares the stress levels in the tensile test and the bulge
test (calculated using the combined FE-Membrane theory methodology) at
111
a true strain value which corresponds to the instability point in the tensile
test. This particular point was selected for comparison because the
difference in the stress level between the two tests reaches it maximum at
this point. It can be seen that the percentage difference in stress level
between the VPB and the tensile tests can be as high as 17% as is the case
for TRIP 780.
True Strain at instability
(in the tensile test)
Maximum True Stress
Level obtained in the
Tensile Test (MPa)
True Stress level in VPB
test (MPa) (at a strain
value equals to the
instability strain in the
tensile test)
Maximum
Percent
difference between tensile
test and bulge test
DP 600
DP 780
DP780-CR
TRIP 780
0.154
0.84
0.10
0.138
681
946
904
935
747
1062
979
1094
9.7 %
12.3 %
8.3 %
17 %
DP 780-HY
0.765
911
956
4.9 %
Table 7.1 Comparison between the stress levels in the tensile and VPB tests
(calculated using the combined FE-Membrane theory methodology) at a strain
values equal to the true strain at the onset of necking in the tensile test
Depending on
and
, the corrected flow stress may increase,
decrease, or stay the same. It can be seen from Figure 4.20 through Figure
4.24 that there is almost no difference between the anisotropy-corrected
and uncorrected flow stress curves for both DP 780 and DP 780-HY, while
the biggest difference is for TRIP 780. This illustrates how correcting for
anisotropy may be important for some materials.
112
Theoretically speaking, the effective strain at instability under balanced
biaxial loading is twice the instability strain under uniaxial loading. It can
be seen from Table 7.2 below that data in the bulge test can be collected up
to a very high strain values compared to the tensile test. This is an
advantage of the bulge test, especially if the flow stress data is to be used
for FE simulation, since no extrapolations is needed as is the case when
using tensile data.
Maximum true strain that
can be obtained in tensile
test (at instability point)
Maximum true strain
obtained in the bulge test
(without extrapolation)
Percent difference
DP 600
DP 780
DP780-CR
TRIP 780
0.154
0.84
0.10
0.138
0.545
0.356
0.237
0.258
254%
324%
137%
88%
DP 780-HY
0.765
0.508
564%
Table 7.2 Comparison between the maximum true strain that can be obtained in
the tensile test and that obtained in the VPB test (calculated using the combined
FE-Membrane theory methodology)
Although we expect the percent difference in strain between the tensile
and bulge tests to be about 100%, we can see that it can be as low as 88%
(for TRIP 780) and as high as 564% (for DP 780-HY). This emphasizes the
importance of the bulge test because of its capability to provide data for a
bigger range of strain compared to the traditional tensile test. In addition,
some materials may behave differently (especially from the formability
point of view) under different loading conditions. DP 780-HY is an
obvious example. It should be noted that the data lost because of ending
113
the test before bursting decreased the percentages shown in Table 5.
Therefore, these percentages are not the maximum possible except for DP
600 and DP 780-HY since a sample accidentally burst while the
potentiometer is in use.
As shown in Figure 4.20 through Figure 4.24, and in Table 4.3, the
combined FE-optimization methodology showed very similar results to
the combined FE-Membrane theory methodology. Although working very
well, it is not recommended to use the optimization methodology to
determine the flow stress for the room temperature bulge test. The main
reason is the long time required to run the optimization; more than two
hours in this case, compared to few minutes in the combined FEMembrane theory methodology. Moreover, the need for two software (FE
and Optimization software) to apply this methodology makes this
methodology difficult to apply in the industry. However, results shown in
this study validates the optimization methodology when two design
variables (K and n) are used, which is promising to extend the same
approach to the elevated temperature bulge test, where strain rate
becomes important and three design variables (K, n and m) are involved.
The suitability of the Power Law Fit
Power law fit, with R2 values close to one, as is the case for all materials
tested, may not capture the hardening behavior of the material. This is
important because hardening is critical to predict thinning and necking in
FE simulations.
114
A suggested quick test is to check the degree to which the NSH curve
obtained from the fit data matches that obtained from the original data,
especially in the range below NSH equals to 1 where various types of
necking, for different states of stress, take place. The better the match, the
more likely a simulation with the fit curve will accurately predict thinning
and necking.
For DP 780-HY (Figure 4.28), the two curves are close in the region from 1
to 0.5. For DP 780, the two curves matched very well in the region from 1
to 0.5, although this is not expected since the data is not available up to
busting. However, fitting the power law to the extrapolated data gave nvalue equals to 0.111 which is close to the value used to generate Figure
4.26 (0.116). For TRIP 780 and DP 780-CR, a big amount of data was lost
because of ending the test before the burst pressure. For these two
materials, there is a big mismatch between the NSH curve obtained from
the original data and fit data, especially if the true strain value is
compared at NSH equals to 0.5.
It is not intended by using the NSH curve to predict necking. However, it
can be used to check whether the power law fit captures the hardening
behavior of the material or not. It is observed that obtaining incomplete
data results in a mismatch between the two curves. If this is the case, then
the original data should be used in the simulation.
The goodness of fit of the power law, as quantified by R2, is not a good
indicator of whether the power law describes the hardening behavior or
not. This is because curves are usually fit to data by the least square
method (by minimizing the difference in the stress level (not the curve
slope)). This is clear when comparing the R2 values in Table 4.3 which are
all close to 1, with the degree to which the two curves in Figure 4.25
115
through Figure 4.29 match, especially in the region below NSH equals to
one.
7.1.2
Characterization of Aluminum Alloys at Elevated Temperature
The optimal K, n, and m values (and corresponding flow stress curves)
obtained by applying the new methodology to the ET bulge test did not
match with the flow stress data available in the literature [Abbedrabbo et
al, 2006-a and Abbedrabbo et al, 2006-b]. This discrepancy may be due to
different reasons. First, the Leakage and sample pre-bulging observed in
the experiments. Second, data in the literature is a tensile data, while data
in this study is a bulge test data. Third, the optimization methodology
needs to be further improved.
For AA3003-O, increasing the temperature from 200 oC to 230 oC resulted
in a higher pressure which is not expected. The problems encountered in
the experiment may be responsible for this. However, this may also be
explained as follows. For strain rate-sensitive materials, the increase in
strength due to high strain rate may be higher than the decrease in
strength due to high temperature. This may take place in certain ranges of
temperatures and strain rates.
116
7.1.3
Design of SHF-P Process
Stretch forming and Hydroforming without Draw-In
Since the sheet is totally clamped (no draw-in), the sheet in the punch-die
clearance region is subjected to pure stretch forming. As a result,
increasing the pot pressure was detrimental to sheet thinning in this
region (see Figure 6.11). Thus, it is not recommended to use SHF-P if the
sheet is totally clamped.
Thinning in the punch base (between the pocket and punch corner radius)
decreased in the SHF-P. This is because the contact pressure is higher in
the presence of pot pressure, which increases the friction forces and
prevents (reduces) sheet stretching.
Preliminary Simulation of Deep Drawing and Hydroforming with Draw-In:
It can be seen from Figure 6.12 that two necks form in the deep drawing
process, one around the punch corner radius and the other around the
die corner radius. As expected, the higher the BHF, the higher the
thinning.
As clear from Figure 6.13 and
Figure 6.14, applying excessively high pot pressure at the beginning of
the process, where the clearance is large, will bulge the sheet against the
drawing direction in the punch-die clearance region. This will result in
high sheet thinning.
117
Figure 6.15 shows one neck and lower thinning in the SHF-P simulation
as compared to two necks and higher thinning in the deep drawing
process. In the SHF-P process, the sheet is separated from the die corner
radius. Thus, no neck forms at this region. Also, the sheet is pushed
against the punch. Thus, lower thinning occurs at this region. As a result,
thinning in the SHF-P is reduced and the neck shifts up the cup side wall.
Simulation of Deep Drawing and Hydroforming with Draw-In (According to the
Proposed Methodology):
Step 1: Initial Estimation of the Blank Radius
A blank radius of 240 mm was selected although the remaining flange
after forming is larger than the case of 215 mm radius (more material
waste). This was done on purpose, to increase thinning so that the effect of
using the SHF-P process can be appreciated.
Step 2: Initial Estimation of the BHF Curve
It can be seen from Figure 6.9 and
Table 6.3, that the required BHF to prevent wrinkling increases with the
stroke (i.e the tendency for wrinkling increases with stroke). Therefore,
applying an increasing BHF, instead of a constant and high BHF, will
reduce thinning and increase the LDR. In this study, a simple BHF curve
is suggested, where the force is constant up to 1/2 to 2/3 of the stroke and
then increases linearly until the end of the process.
BHF curve 4 (Figure 6.9) was selected and used in all SHF-P simulations.
However, it should noted that the optimal (minimum) BHF curve in deep
118
drawing is not sufficient to prevent wrinkling in SHF-P because the pot
pressure tends to lift the blankholder.
Step 3: Optimizing the Pot pressure and BHF Curves
It is observed from FE simulations that sheet draw-in in the flange is
higher in SHF-P compared to deep drawing. 3.5 mm difference was
observed between simulation 3-2 and 2-4 (see simulation matrix). This is
because of the lower thinning in SHF-P. Therefore, when designing a SHFP, the blank size should be slightly increased over the optimal size in deep
drawing.
At the beginning of the stroke, the punch-die clearance is large making it
easy for the sheet to bulge against the drawing direction and thin.
Therefore, only 35 bars was applied in the first 14 mm of the simulation,
just to separate the sheet from the die corner.
Two maximum pressures were reached; 200 bars and 100 bars (see Figure
6.10. 100 bars gave slightly better results indicating the 200 bars was
causing extra stretching in the clearance region.
Comparing deep drawing (simulation 4-2, see matrix) with SHF-P
(simulation 3-2, see matrix), it was possible to reduce the thinning at the
punch corner radius from 8.6% to 4.2% (about 51% reduction). This
considerable reduction is mainly a result of the high contact force at the
sheet-punch corner interface.
The maximum thinning in the pocket was reduced from 26% to 15.5% (in
practice, both values may cause fracture). When the reverse (solid) punch
is used to fill the pocket, extra force is required to overcome friction. This
force will be transmitted through the sheet and cause excessively thinning.
It should be noted that the pocket filling with a hydraulic medium is
similar to SHF-D process.
Another advantage observed in the simulations for the SHF-P is that the
sheet is taking the exact shape of the punch, where in deep drawing, a gap
is left between the sheet and the punch.
It was noticed in the deep drawing simulations that the sheet at the punch
base, especially at the unsupported region under the pocket, thins slightly
during the process even before stretch forming in the pocket. This
119
thinning history is another reason for the high thinning in the pocket in
deep drawing.
7.2
Future Work
Characterization of AHSS at Room Temperature:
The engineering stress-strain curve of AHSSs around the UTS is almost
flat. This means that a clear neck, and a change from a uniaxial to triaxial
state of stress, may not occur immediately after the UTS is exceeded. It is
interesting to check experimentally if the neck formation coincides with
the UTS. This may change the way of determining and reporting the
uniform elongation for this special steel family.
To further check the suitability of the power law fit, a sheet forming
process can be simulated with the original flow stress and with the power
law fit, and the results compared with the experimental data.
Characterization of Aluminum Alloys at Elevated Temperature:
To repeat the elevated temperature bulge test experiments of AA5754-O,
AA5182-O, and AA3003-O in order to get reliable data to be used as an
input to the optimization methodology.
To develop the capability to control the strain rate at the dome apex by
controlling the flow rate of the pressurizing medium.
To increase the tips radii of the probes used to prevent (reduce) sheet
penetration and therefore prevent probe deflection.
To simulate of the elevated temperature bulge test to understand the effect
of the rheological parameters; K, n, and m on the strain, strain rate, and
120
thickness distribution in the dome, as well as the shape of the dome. This
will help in selecting the best parameter to be measured and compared
with the simulation in the inverse analysis methodology.
The combined FE-optimization methodology is very promising for the
elevated temperature bulge test. However, it should be improved to be
more robust.
Simulation of SHF-P Process:
To run experiments at General Motors R&D to validate the simulation
results.
The conical punch has a very small conical angle, which makes it easier to
design the process since applying high pressure cannot bulge the sheet in
the punch-die clearance easily. Another punch with larger angle can be
made to make the design process more challenging and closer to reality.
121
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APPENDIX A AQUADRAW MODULE IN PAMSTAMP 2G 2007
(This appendix is adapted entirely from [Pamstamp manual, 2007])
Aquadraw
This option creates an aquadraw attribute for the blank which can be used to
model the forming process illustrated in figure below.
Note that the aquadraw process input data are not issued from a macrocommand, therefore the user must create all the necessary attributes and
conditions for each component (object) of the process. For further information,
please refer to the User's Guide.
The process makes use of conventional deep drawing tools, but the die is filled
with a relatively incompressible fluid such as water. Additional pumps and
valves may be included to prebulge the sheet and/or to control the maximum
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fluid pressure. During forming the pressure in the die cavity rises as the fluid is
compressed until the resultant force acting on the sheet is sufficient to lift the
blankholder. At this point fluid begins to escape via the gap between the binder
and sheet, relieving the pressure and reducing friction on the die side. A
continuous controlled lift of the blankholder during forming is generally
desirable and is known as a stable aquadraw regime.
i
Dialog Box
This dialog enables the user to define the parameters for the aquadraw attribute.
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Curve Selection
The
button allows the user to gain access to the 2D curve plotter which is
used to specify time varying pressure limits and flow rates into the cell.
Fluid Bulk Modulus
The Bulk modulus of fluid K is used to calculate the cell pressure p using the
formula:
where VC is the volume of the fluid cell and VF is the volume
of the fluid contained in the cell when uncompressed.
Normally the physical bulk modulus of the fluid should be specified, although in
special applications such as superplastic forming with strain rate control, an
artificial K value may be used. Very large values of K may lead to integration
stabilities, particularly if the fluid cell volume is small. However, in normal
applications with water or oil emulsions these problems seldom occur. If
encountered they can be cured by reducing the time step factor.
Volume Definition
Ideally, the fluid cell should be defined as a closed volume with shell elements
and the orientation of the elements should be such as to have their normal
pointing inwards.
Volume definition with:
The volume is defined between the blank an object selected
in this drop-down list, usually the die.
Axis for volume definition:
The direction of this axis is defined by a vector either by
using the help of the wizard or by typing its components in the text fields.
Warning, only one of the three main directions can be used (X-axis, Y-axis or Zaxis).
The volume of the fluid cell is calculated by summing up the contributions of
rectangular prisms drawn on each boundary segment with sides parallel to a
specified integration direction, as illustrated in figure below.
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Note
Surface elements whose normals are perpendicular to the integration axis do not
contribute to the volume sum and can be omitted. When symmetry has been exploited in
the model, it is often convenient to leave out surface boundaries on symmetry planes,
while choosing an integration axis which lies within them.
: This drop-down list defines whether the axis definition is done in the
Global or a user-defined system of axes.
Initial volume:
It can be defined by the user to avoid model positioning problem.
Optional
Volume flow rate curve:
Select in the drop-down list the curve that defines the
volume
flow rate.
Maximum fluid pressure curve:
Represents the maximum pressure the system can
develop within the fluid cell.
Maximum velocity curve:
The maximum sheet velocity should be limited to 10 m/s
to avoid unwanted inertia effects. Note that the average sheet velocity Vs is
related to the flow rate F by the approximate formula
, where Am is the
area of moving boundaries in the cell.
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Binder
This panel is used to specify the binder object. When the solver detects that the
contact force between blank and binder is zero, a stable aquadrawing regime is
assumed and the die pressure is subsequently held constant.
Binder identification:
Select in this drop-down list the object which represents the
binder.
Fluid pressure scale factor:
Function Buttons
OK:
Validates the selected parameters for the aquadraw process and closes the
dialog.
Cancel:
Closes the dialog without assigning any parameters to the aquadraw.
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