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Transcript of Shah Manan Kanti
MATERIAL CHARACTERIZATION AND FORMING OF LIGHT WEIGHT
ALLOYS AT ELEVATED TEMPERATURE
THESIS
Presented in Partial Fulfillment of the Requirements for
the Degree Masters in the Graduate
School of the Ohio State University
By
MANAN K. SHAH, B.S
Mechanical Engineering Graduate Program
The Ohio State University
2011
Thesis Committee:
Dr. Taylan Altan, Advisor
Dr. Jerald Brevick
Copyright by
Manan K. Shah
2011
ii
ABSTRACT
The increase in using light weight alloys such as aluminum and magnesium
sheet materials is accompanied by many challenges in forming these alloys due
to their unique mechanical properties and/or low formability. 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, elevated temperature biaxial Viscous Pressure Bulge (VPB) tests
were conducted for Aluminum (AA 5182) and Magnesium (Mg AZ61 L) alloys
and the resulting flow stress curves were obtained. Using the Surface Response
Method that evaluates the error function gave the prediction of flow stress
coefficients K, n and m that fit the Power Law Equation. Results of this work
predict the flow stress data under a variable strain rate and thus cannot be
directly compared with other results which were conducted under a constant
strain rate. 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 light weight alloys to be used as an input to FE models.
iii
The sheet hydroforming with punch (SHF-P) process offers great potential for
low and medium volume production, especially for forming: (1) lightweight
sheet materials such as aluminum and magnesium alloys and (2) thin gage high
strength steels (HSS). Aluminum and Magnesium alloys are being increasingly
considered for automotive applications, primarily due to their lightweight and
high strength-to-weight ratios. However, there is limited experience-based
knowledge of process parameter selection and tool design for SHF-P of these
materials. Thus, there is a need for a fundamental understanding of the
influence of process parameters on part quality.
A Sheet Hydroforming with a Punch (SHF-P) process was successfully simulated
using the FE software Pamstamp 2G 2009. 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.
iv
Dedicated to my family
v
ACKNOWLEDGEMENT
I am sincerely grateful to my advisor, Dr. Taylan Altan for his supervision
during my Masters studies at the Center for Precision Forming. 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 support.
Special thanks to the sponsors of this research: General Motors (G.M.), Dr. John
Carlsey, for supporting the Warm Bulge Test and Sheet hydroforming project.
Special thanks to Interlaken Technology Corporation (ITC), Dr. Patrick Cain, for
working with CPF and providing technical support for the elevated temperature
sheet bulge test project.
I thank my colleagues of the CPF, Dr. Partchapol Sartkulvanich, Eren Billur, Jose
Gonzalez-Mendez, Deepak Ravindran, Ambikapathy Naganathan, Nimet
Kardes, Yurdaer Demiralp, Adam Groseclose, and Soumya Subramonian for
their assistance and encouragement.
vi
VITA
July 2, 1987 Born, Mumbai, India
2005-2009 B.S, Mechanical Engineering
The Ohio State University
2009-2011 Graduate Research Associate
Center for Precision Forming (formerly ERC/NSM),
Columbus, OH-USA
PUBLICATIONS
Shah M., Billur E., Sartkulvanich P., Carsley J., Altan T., (2011), ―Cold and Warm
Hydroforming of AA5754-O Sheet: FE Simulations and Experiments‖,
Numisheet 2011 Conference, (In the progress of publication)
Shah M., Sartkulvanich P., (2011), ―Process Simulations in Sheet Metal Forming‖,
Chapter for ASM Sheet Metal Forming Handbook, Editor: Prof. Taylan Altan (In
Progress)
Serhat K., Shah M., (2011), ―Warm Forming‖, Chapter for ASM Sheet Metal
Forming Handbook, Editor: Prof. Taylan Altan (In Progress)
FIELD OF STUDY
Major Field: Mechanical Engineering (Design and Manufacturing)
vii
NOMENCLATURE
Latin Letters dc Diameter of die cavity (Bulge test) Engineering strain in axial direction (Tensile test) The objective Error function to be minimized
Clamping force (Bulge test) hd Dome height (Bulge test) The measured dome height at time t (Experimental)
The simulation dome height at time t (FE output) Strength Coefficient Strain rate sensitivity exponent Strain hardening exponent p Bulging pressure (Bulge test) Rc Die corner radius (Bulge test) Rd Radius of curvature at dome apex (Bulge test) Time point at which simulation and experiment were
compared to Initial sheet thickness (Bulge test) td Instantaneous thickness at dome apex (Bulge test)
Greek Letters
Effective strain True strain in thickness direction (Tensile test, Bulge test) Principle strains in the sheet surface (Bulge test) Principle strain in the sheet thickness direction (Bulge test) Effective stress Principal stresses in the sheet surface (Bulge test)
Principal stress in the sheet thickness direction (Bulge test)
viii
TABLE OF CONTENTS
ABSTRACT ii
ACKNOWLEDGEMENT v
VITA vi
LIST OF FIGURES xi
LIST OF TABLES xiv
CHAPTER 1 Introduction 1
1.1 Sheet Hydroforming 1
1.2 Forming technology at Elevated Temperature (ET) 4
1.3 Forming of Light Weight Sheet Materials 7
1.3.1 Aluminum (Al) alloys 7
1.3.2 Magnesium (Mg) alloys 9
CHAPTER 2 Objectives and Approach 11
2.1 Objectives 11
2.2 Approach 11
2.3 Organization of the thesis 13
CHAPTER 3 Background and Literature Review 14
ix
3.1 Principles of Sheet Hydroforming with a Punch (SHF-P) 14
3.1.1 Process Window in SHF-P Process 17
3.1.2 Challenges in Warm hydroforming 19
CHAPTER 4 Determination of the flow stress for Aluminum and Magnesium
sheet alloys at Elevated Temperature 21
4.1 Biaxial Viscous Pressure Bulge (VPB) Test 21
4.2 Previous work on determining the flow stress data of sheet material at elevated
temperature 24
4.2.1 Virginia Commonwealth University (VCU), USA [Koc 2007] 24
4.2.2 ERC/NSM (OSU), USA [Al-Nasser 2009] 26
4.3 Determination of the flow stress at elevated temperature using the FE Inverse
Analysis Technique 28
4.3.1 Description of the FE inverse analysis technique 28
4.3.2 Experimental Setup and Results (Machine and Tool Design) 31
4.3.3 Finite Element Method (FEM) Database used for Surface Response Method
36
4.3.4 Results from the FE inverse analysis technique 40
4.3.5 Conclusions 47
CHAPTER 5 Cold and Warm Hydroforming of AA 5754 Sheet: FE Simulations
and Experiments 49
5.1 Model Part and Tools Geometry 50
5.2 Experimental Results 53
5.3 Finite Element Method (FEM) Setup 57
5.4 Comparison of FE predictions with experimental results 60
5.5 Conclusions 66
x
CHAPTER 6 Case studies in sheet metal forming at elevated temperature 68
6.1 Warm Forming of MgAZ31B sheet alloy 68
6.1.1 Summary of Inputs for PAMSTAMP v. 2009 Simulation 69
6.1.2 Results for FE Simulations and comparison with experiments 70
6.1.3 Conclusion 75
6.2 Hot Stamping/Forming of 22MnB5 Steel to form experimental part 76
6.2.1 Objective 76
6.2.2 FE Setup 76
6.2.3 FE Results and comparison with the experimental data 77
6.2.4 Future Work 79
CHAPTER 7 Discussion, Conclusion and Future Work 80
7.1 Discussion and Conclusions 80
7.1.1 Determination of the flow stress at elevated temperature 80
7.1.2 Design of Sheet hydroforming with Punch Process (SHF-P) 82
7.2 Future Work 83
7.2.1 Determination of flow stress at elevated temperature 83
7.2.2 Simulation of SHF-P Process 83
REFERENCES 85
xi
LIST OF FIGURES
Figure 1.1-(a) Conventional Deep Drawing, (b) Fluid Forming (Sheet Hydroforming with
Punch) [Maki and Walter 2007] ......................................................................................... 2
Figure 1.2-(a) Schematic of Sheet Hydroforming with Punch [Aust, 2001], (b) Sheet
Hydroforming with Die [Jager, 2005] ................................................................................ 3
Figure 1.3-Stylish body shape for the Pontiac Solstice [Maki and Walter 2007] ............... 4
Figure 1.4- True stress-strain curves of AA5182-O at several elevated temperatures for
the rolling direction [Abedrabbo 2007] .............................................................................. 8
Figure 1.5-Activation of additional sliding planes for magnesium at elevated
temperatures [Doege 2001] ............................................................................................... 10
Figure 1.6- Effect of temperature on the flow stress curve of MgAZ31B alloy
[Neugebauer 2006]............................................................................................................ 10
Figure 3.1- Schematic illustration of the SHF-P process [Aust 2001] ............................. 14
Figure 3.2-Schematic of the warm hydroforming process [Groche 2002] ....................... 15
Figure 3.3- Process window in the SHF-P Process [Palaniswany 2007] .......................... 18
Figure 4.1- Viscous Pressure Bulge (VPB) test tooling [Al-Nasser 2009]....................... 22
Figure 4.2- Geometrical features of the VPB test [Al-Nasser 2009] (nomenclature is
before chapter 1) ............................................................................................................... 22
Figure 4.3- Hydraulic Bulge test setup with Feedback control loop [Koc 2007] ............. 25
Figure 4.4- Schematic of the Fluid-based Elevated Temperature Biaxial Bulge Test
Apparatus [(AES), LLC] ................................................................................................... 26
Figure 4.5- Methodology to obtain K, n and m values by calculating the lowest error
function (E) ....................................................................................................................... 30
Figure 4.6- Bulge height profile at various time steps (tn) ................................................ 30
xii
Figure 4.7- Gas bulge tooling with 2 Cameras and data acquisition systems [provided by
Interlaken] ......................................................................................................................... 32
Figure 4.8- Experimental pressure vs. Bulge Height for AA 5182 sheet samples formed at
Pressure Rate = 0.5 MPa/sec at various temperatures (30, 200, 250, 300 and 350 degree
Celsius) ............................................................................................................................. 34
Figure 4.9- Experimental Strain vs Time data for AA5182 @ 200⁰C for PR=0.5 MPa/sec
........................................................................................................................................... 35
Figure 4.10- Calculated Strain Rate (s-1
) vs Time for AA5182 @ 200⁰C for PR=0.5
MPa/sec ............................................................................................................................. 36
Figure 4.11- FE Setup Sketch ........................................................................................... 38
Figure 4.12- FE Input for Pressure vs time (for 3 Pressure Rates) ................................... 39
Figure 4.13- FE outputs (Bulge Height vs time and Strain vs time) collected at apex for
every combination of k, n and m and stored in the FE Database ...................................... 40
Figure 4.14- Comparison of Bulge Height vs. Pressure curve at (a) Temperature =30⁰C
and (b) 200⁰C for a linear Pressure Rate= 0.5 MPa/sec ................................................... 41
Figure 4.15-Flow stress curves for AA5182 obtained using Surface Response Method for
PR=0.5 MPa/sec (at variable Strain Rate) ........................................................................ 43
Figure 4.16- Flow stress curves for MgAZ61L obtained using Surface Response Method
for PR=0.5 MPa/sec (at variable Strain Rate) ................................................................... 44
Figure 4.17- Flow stress data obtained using the calculated Bulge Test (B.T.) data
(Surface Response) and Tensile Test (T. T.) data from [Abedrabbo 2007] ..................... 45
Figure 4.18- True stress-True Strain data for AA5182-O obtained using tensile tests at
260 ⁰C for several strain rate values [Abedrabbo 2007] ................................................... 46
Figure 5.1- Schematic of the tooling for SHF-P experiments: (a) initial setup (b) after
deformation, where ri = initial blank radius, Dd = draw depth and h = bulge height. ...... 51
Figure 5.2- Pressure flow schematic to heat or cool the tooling ....................................... 52
Figure 5.3- Pressure flow schematic to form the part using the SHF-P process by
controlling pressure with the relief valve.......................................................................... 53
Figure 5.4- Position of thermocouples on the ITC hydroforming machine ...................... 57
xiii
Figure 5.5- Experimental output Pot pressure vs time for part formed at elevated
temperature (150 ⁰C)- Sample # 33 .................................................................................. 60
Figure 5.6- Thickness profile along the curvilinear length measured by the mechanical
indicator and compared with FE results for Sample #5 at room temperature (Punch
Stroke= 1.35 in, BHF = 6.81 kip, pot pressure = 304.7 psi) ............................................. 61
Figure 5.7- FE setup for the initial clearance of 1 mm between the blank holder and sheet
........................................................................................................................................... 62
Figure 5.8- (a) experimental workpiece, (b) Pam-Stamp result of quarter model, (c)
comparison part profile from FEM and experiment, for the SHF-P of Sample #33 (punch
stroke = 1.50 in, average temperature = 150C, pot pressure = 1494 psi) ........................ 63
Figure 5.9- Thickness profile along the curvilinear length measured by the mechanical
indicator and compared with FE results for Sample #33 (punch stroke = 1.50 in, average
temperature = 150C, pot pressure = 1494 psi) ................................................................ 64
Figure 5.10- Comparison of flange perimeter measurement and prediction between initial
blank and final part after SHF-P at room (Sample#5) and elevated (Sample#33)
temperatures ...................................................................................................................... 66
Figure 6.1- Schematic of warm forming tooling [Kaya 2008] ......................................... 70
Figure 6.2- Temperature vs Punch stroke at Point (P1) using variable HTC [CASE 1m:
Draw Ratio= 3, Punch stroke=65 mm , Forming velcity= 5 mm/sec] .............................. 72
Figure 6.3- Comparison of the results from FE simulations and experiments of CASE 1m,
for thinning distribution and punch load vs. stroke .......................................................... 73
Figure 6.4- Comparison of the results from FE simulations and experiments of CASE 4m,
for thinning distribution and punch load vs. stroke .......................................................... 74
Figure 6.5- Steps in the Forming stage at a) Initial position and b) Final position .......... 78
xiv
LIST OF TABLES
Table 1.1- Significant variables in the Warm Forming Process [Kaya 2008] .................... 6
Table 3.1- Summary of possible defects in the hydroforming process. Recreated based on
[Palaniswamy 2007 and Yadav 2008] .............................................................................. 18
Table 3.2- Data required as input to FEM for accurate process simulation of the warm
sheet hydroforming process [Yadav 2008] ....................................................................... 20
Table 4.1- Summary of the tests performed at elevated temperature [Al-Nasser 2009] .. 26
Table 4.2-Summary of the experimental tests performed at room and elevated
temperature at ITC ............................................................................................................ 33
Table 4.3 Simulation Geometry Parameters ..................................................................... 37
Table 4.4- Flow Stress Coefficients Material Input Set .................................................... 38
Table 4.5-Predicted flows stress coefficients K, n and m for AA5182 at PR =0.5 MPa/sec
........................................................................................................................................... 42
Table 4.6- Predicted flows stress coefficients K, n and m for MgAZ61L at PR =0.5
MPa/sec ............................................................................................................................. 44
Table 5.1- Input parameters for SHF-P tests at room temperature (punch velocity=0.075
in/sec) ................................................................................................................................ 54
Table 5.2- Input parameters used to conduct warm SHF-P test at elevated temperature of
about 150°C (cycle time = 20 sec) .................................................................................... 55
Table 5.3- Comparison of experimental input to the output readings and measurements at
room temperature (initial flange perimeter, fi= 53.41 in) ................................................. 55
Table 5.4- Comparison of experimental input and output readings and profile
measurements, for SHF-P experiments at elevated temperature (Initial flange perimeter,
Fi = 53.41 in) .................................................................................................................... 56
Table 5.5- Input parameters for FE simulations of SHF-P ............................................... 59
xv
Table 5.6- Percent thinning affected by the applied pot pressure while keeping the other
process parameters constant (BHF ≈ 2.2 kiPs, punch stroke = 0.56 in, cycle time = 20 sec,
average temperature = 150°C) .......................................................................................... 65
Table 6.1- Thermal and mechanical data used for warm forming simulations of Mg
AZ31-O [Braga 2008] ....................................................................................................... 69
Table 6.2- Test conditions from [Braga 2008] were selected for preliminary simulations
........................................................................................................................................... 71
Table 6.3- Material Properties for 22MnB5 Sheet............................................................ 77
Table 6.4- Process Parameters in Hot stamping- Forming operation only ....................... 77
1
CHAPTER 1 Introduction
Due to the need to significantly reduce the part weights in automotive
manufacturing, the use of lightweight materials becomes very important.
Unfortunately, these materials are often associated with limited room
temperature formability. Due to this fact, production of large, complex sheet
metal components using forming technology frequently requires increased
expenditures. In order to find a solution to counter the disadvantages mentioned
above, the use of elevated temperatures as a process parameter in forming
operations represents a potential solution approach.
1.1 Sheet Hydroforming
In Sheet hydroforming with a Punch (SHF-P), also known as hydromechanical
deep drawing (HMD), the female die used in conventional stamping is replaced
by a pressure pot as seen in Figure 1.1. The sheet is deep drawn to form over the
punch surface, as the counter pressure is exerted on the sheet by the pressurizing
fluid. During the SHF-P, the friction at the punch sheet interface prevents the
sheet from sliding over the punch surface, thus giving a more uniform wall
thickness and increased deep drawability. Some other considerable advantages
of this process are: (1) it eliminates the need for a female die, thus lowering tool
costs; (2) it may reduce the number of stamping operations to form complex
parts and (3) it eliminates sidewall wrinkles during forming due to fluid
pressure, thug giving a better surface quality.
2
Figure 1.1-(a) Conventional Deep Drawing, (b) Fluid Forming (Sheet Hydroforming with
Punch) [Maki and Walter 2007]
This innovative forming technology (hydroforming) offers an additional
potential for weight reduction in automobiles when used with lightweight
materials like aluminum and magnesium alloys. However, the high alloy
percentages in aluminum alloys and the hexagonal structure of magnesium, lead
to a relatively low formability of these sheet materials at room temperature.
Thus, a promising strategy for the enhancement of the formability is the
conduction of the forming processes at elevated temperatures below the
recrystallization temperature [Geiger 2001].
Forming at elevated temperature will lower forming forces and increase the
ductility of the work piece as additional slip planes become active, especially for
magnesium alloys. Furthermore, while forming aluminum alloys springback is
an issue and can be drastically reduced when formed at elevated temperatures.
3
Sheet Hydroforming is conducted as Sheet Hydroforming with Punch (SHF-P)
and Sheet Hydroforming with Die (SHF-D) as seen in Figure 1.2. In the SHF-P
process, the sheet metal is forced against the punch by the hydraulic pressure,
whereas in the SHF-D process, the sheet metal is forced against the die by the
hydraulic pressure.
Figure 1.2-(a) Schematic of Sheet Hydroforming with Punch [Aust, 2001], (b) Sheet
Hydroforming with Die [Jager, 2005]
Sheet hydroforming has fewer restrictions, when forming complicated parts,
which allows styling designers and manufacturing engineers more flexibility
during the design process. For example in Pontiac Solstice ®, GM chose sheet
hydroforming (SHF-P) to manufacture its hood, door, deck lid and body
assemblies as seen in Figure 1.3 [Maki and Walter 2007].
(a) (b)
4
Figure 1.3-Stylish body shape for the Pontiac Solstice [Maki and Walter 2007]
A counter pressure deep-draw approach with a reverse toggle draw orientation,
called fluid forming is used to form Solstice‘s panels. During this process, the
punch with the shape of the part draws the sheet metal into a pressure vessel and
the change in fluid volume naturally builds a counter pressure. A relief valve
controls fluid pressure throughout the stroke. The limitation of conventional
deep drawing is localized thinning at the punch shoulder radius as shown in
Figure 1.1 (a). However, in Figure 1.1 (b), the water pressure pushed the sheet
firmly to the walls of the punch during the forming process and an increase in
friction along the wall ensures uniform thinning along the length of the wall
instead of one local area.
1.2 Forming technology at Elevated Temperature (ET)
The use of temperature opens up the possibility of significantly increasing the
ductility of the material and the associated forming capability. On the other
5
hand, it also offers the possibility of significantly reducing the yield point and
hence the forming forces and pressures required. In order to be able to fully
exploit the potential of temperature-supported forming processes and guarantee
economic production of complex component geometries, the related challenges
must be faced. Some of these include [Neugebauer 2006]:
1) Identification of suitable temperatures or temperature distributions
2) Integration of the temperature-supported forming process within the
overall process chain
3) Regulation of the temperature or temperature distributions within a
satisfactory time limit
4) Qualification of the FE simulation for use as an effective design tool
5) Ensuring safety in the workplace
6) Guaranteeing economic viability
With the increasing importance of temperature in various sheet metal forming
operations, a distinction has been adopted in practice. The forming process can
be classified based on the forming characteristics of materials below and above
recrystallization temperature. 1) Warm forming can be defined as the forming
operation below recrystallization temperature in which the yield point and
forming strength of the work piece are distinctly reduced. 2) In the hot
forming/stamping operation, permanent strengthening of the work piece can be
achieved [Neugebauer 2006].
Compared to room temperature forming, elevated temperature forming brings
many complexities which require a systems approach. Similar to other well-
established processes, it is also important to consider this process as a system. A
fundamental understanding of the relationship between the input and output
6
variables of the system is essential for developing a robust, productive and
economical manufacturing process. Issues that affect the warm forming process
are summarized in Table 1.1.
Table 1.1- Significant variables in the Warm Forming Process [Kaya 2008]
Sheet material and blank
Flow stress as a function of strain, strain rate,
temperature and microstructure (constitutive
equation)
Formability as a function of strain, strain
rate, temperature and microstructure
(forming limit curves)
Surface texture
Thermal / physical properties (density,
melting point, specific heat, thermal
conductivity and expansions, resistance to
corrosion and oxidation)
Initial conditions (composition, temperature,
history / pre-strain)
Plastic anisotropy
Property variation within the coil (rolling
technique) from same production line
Property variation for the same material from
different suppliers
Blank size, location, and thickness
Equipment used
Mechanical/Hydraulic/Servo Press
Constant/variable speed / production rate
Force / energy capabilities
Rigidity and accuracy
Tooling
Geometry of tools
Heating/cooling techniques
Insulation (between heated tooling and press)
Binder forces and application method
(hydraulic/air or servo motor driven cushion
pins)
Surface conditions
Material / heat treatment / hardness
Condition at tool/material interface
Lubricant type and temperature
Insulation and cooling characteristics of the
interface layer
Lubricity and frictional shear stress
Ease of lubricant application and removal
Deformation Zone
Deformation mechanics and model used for
analysis
Metal flow, velocities, strain (kinematic),
strain rate
Stresses (variation during deformation)
Temperatures (heat generation and transfer)
Product
Geometry
Increased dimensional accuracy/tolerances
compared to room temperature forming
Surface finish
Microstructure, metallurgical and
mechanical properties
Environment
Available man power
Air, noise and wastewater pollution
Plant and production facilities and control
Safety
Appropriate metal fire extinguishing systems
(for possible Mg fire)
7
1.3 Forming of Light Weight Sheet Materials
Because of the close correlation between vehicle weight and fuel consumption,
there is huge potential for meeting this challenge by employing measures to
improve performance capability and increase the effectiveness of engines, but
above all by reducing the weight of components. The objective of lightweight
construction design concepts is to minimize the dead weight of a construction
without having an effect on its function, or safety. In addition to condition-
related and form-related or structure related lightweight construction, the use of
lightweight construction materials constitutes one of the most promising
strategies capable of contributing to the fulfillment of this task [Geiger 2001].
Examples of sheet metal materials that exhibit lightweight construction are
aluminum, magnesium or thin high-strength steel materials, and some titanium
alloys.
1.3.1 Aluminum (Al) alloys
Aluminum alloys offer the largest weight reduction after Magnesium alloys, but
their formability is also low at room temperature. Al sheet alloys with yield
strengths comparable to those of low carbon steels are less formable by current
processes used in the automotive industry. When attempting to form Al alloy
parts on dies normally used for steels, splits often develop in the regions
subjected to severe stretching or drawing. In today‘s practice, sections from Al
alloy tubes are only used for calibration (i.e. expanded with very limited amount
of strain; 4% to 6% versus 35% to 40% in steels) due to their low formability. The
reason for the lower formability of two-phase alloys, as opposed to single-phase
alloys or pure metals, is that the strengthening effect of the second-phase reduces
8
ductility. This is particularly apparent in Al alloys. Thus thoughts have turned to
forming at elevated temperatures [Shehata 1978].
[Abedrabbo 2007] conducted uniaxial tests for Aluminum alloys at several
elevated temperatures in the range of 25–260 ⁰C. To study the strain-rate
sensitivity of the material, uniaxial tests were performed under several strain
rates (0.001–0.08 s-1) at each temperature. 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. As
temperature increases, flow stress of the material decreases with a corresponding
increase in the elongation to failure (see Figure 1.4). This is due to the increase in
the mobility of the solutes which eliminates the serrated flow behavior.
Figure 1.4- True stress-strain curves of AA5182-O at several elevated temperatures for
the rolling direction [Abedrabbo 2007]
9
[Li 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.
1.3.2 Magnesium (Mg) alloys
Mg and Al are 78% and 65% lighter per unit volume than Fe respectively.
Magnesium has the highest strength-to-weight ratio of all commercially available
structural materials. Another important factor is the ease of fabrication and
joining. Magnesium is quite easy to form; often, operations that require several
steps for steel can be done in only one step for Mg. But due to the hexagonal
closed packed (hcp) crystal lattice structure at room temperature, magnesium
provides only low ductility for cold forming operations. At temperatures above
225⁰ C, additional sliding planes are activated (see Figure 1.5) thus increasing
ductility and lowering the yield stress, besides the conventional temperature
effect on ductility and yield stress [Yadav 2008]. Figure 1.6 shows the effect of
temperature on the flow stress curve of MgAZ31B alloy (Thickness= 1.3 mm).
10
Figure 1.5-Activation of additional sliding planes for magnesium at elevated
temperatures [Doege 2001]
Figure 1.6- Effect of temperature on the flow stress curve of MgAZ31B alloy
[Neugebauer 2006]
Due to this raised ductility of Mg alloy and its growing importance in the
automotive industry, many investigations are underway to get a better
understanding of the material behavior. Thus, it is very important to have a
reliable test which could predict the flow stress of this material at elevated
temperatures.
11
CHAPTER 2 Objectives and Approach
2.1 Objectives
1) The overall objective of this study is to determine the flow stress of
Aluminum and Magnesium alloy sheet materials, of interest to the
automotive industry, at room and elevated temperatures, respectively.
2) In addition improve the sheet hydroforming process of aluminum alloys
using FE simulations and validated by experimentation. More
specifically, the goal was to establish an efficient method for estimating
the process parameters (Blank Holder Force (BHF), pot pressure) that are
used for room and elevated temperature SHF-P processes to produce
defect-free parts.
2.2 Approach
The following tasks were performed to achieve the objective (1) of the study: To
determine flow stress of Aluminum and Magnesium alloys at elevated
temperature.
1) To analyze formability of the following aluminum alloys: AA 5182, AA
5754 (at room and elevated temperature) by FEM simulations in the code
DEFORM 2D.
12
2) To create a FEM Database for several values of K, n and m, chosen based
on [Abedrabbo 2007]. This database would include the bulge height, strain
of the bulge at the apex point at several time steps during the Viscous
Pressure Bulge (VPB) test.
3) To establish a Surface Response (SR) methodology to approximate the
flow stress data for the VPB test of aluminum and magnesium alloys at
elevated temperature. The flow stress data should be defined by the
power law equation . This methodology takes the bulge height
vs pressure, and strain from the FE simulations at various time steps and
compares it to the experimental bulge height vs pressure, and strain.
4) To program the methodology in MATLAB. Thus the following steps are
conducted: reading experimental data, comparing experimental data vs
FE database, calculation of the error function (difference between the
experimental and the FE data for the bulge height and strain)
5) To determine the lowest error function for the several combinations of K,
n and m by plotting the surface response.
Approach for objective (2) - Establish a method to improve the warm
hydroforming of light weight alloys using FE simulations and experiments:
1) To analyze formability of the aluminum alloy AA5754-O by FE
simulations using the FE code PAMSTAMP.
2) Conduct experiments to find the process parameters (blank holder force,
pot pressure) that are suitable for SHF-P process.
13
3) Understand the working of the ITC Hydroforming machine located at the
G. M. Technical Center (Interlaken UniTEST software, Fluid Pressure
Control System and Temperature Control System-Mokon System).
4) Measure the experimental samples either by CMM or height gauge
measurement system to compare them with the FE results.
2.3 Organization of the thesis
The following tasks were performed to achieve the objectives of the study:
1) Conduct a literature review on the Sheet Hydroforming process at room
and elevated temperature (Chapter 3)
2) Review the previous work/literature on determining the flow stress data
at elevated temperature (Chapter 4)
3) Develop a method to determine the flow stress of light weight alloys at
elevated temperature using the FE inverse analysis technique (Chapter 4)
4) Conduct experimental tests of different Aluminum and Magnesium alloys
at elevated temperature using the bulge test at ITC and applying the
surface response methodology to obtain the flow stress data (Chapter 4).
5) Suggest a methodology for designing process parameters (Pot pressure,
blank holder force) in SHF-P of AA5754-O by using FE simulation and
experiments (Chapter 5).
6) Conduct case studies on non-isothermal forming using the FE code PAM-
STAMP: i) Warm forming of MgAZ31 alloy and ii) Hot
Forming/Stamping of 22MnB5 Steel (Chapter 6)
14
CHAPTER 3 Background and Literature Review
3.1 Principles of Sheet Hydroforming with a Punch (SHF-P)
For the sheet hydroforming with punch (SHF-P) forming method, a sheet blank
is deep drawn against a counter pressure from compressed fluid inside the pot,
as presented in Figure 3.1, rather than against a female die as in conventional
stamping operations. The medium in the pressure pot can be either ―passive‖
(pressure generated due to incompressibility of the medium during forward
stroke of the punch) or ―active‖ (pressure generated by an external pump) as
defined by [Aust 2001].
Figure 3.1- Schematic illustration of the SHF-P process [Aust 2001]
For the warm hydroforming method, the sheet and the flange portion of the die
and the blank holder are heated to the required temperature (see Figure 3.2). The
15
pressurizing fluid may be maintained at slightly higher than room temperature,
while the punch is cooled. During the process, the lower temperature of the
punch cools the portion of the sheet that is in contact with the punch and
increases its load carrying capacity. Thus, failure caused by excessive thinning is
postponed and the process yields a higher limiting draw ratio (LDR) than those
obtained from deep drawing at room temperature [Groche 2002].
Figure 3.2-Schematic of the warm hydroforming process [Groche 2002]
The most common defects encountered during the SHF-P process are wrinkling,
excessive thinning (leading to fracture) and leaking of the pressurized fluid
during forming. Conventionally, the process parameters are estimated by
performing trial and error experiments which requires considerable time and
effort. Therefore, the present research focuses on the use of finite element (FE)
simulations along with physical experiments to estimate the optimum blank
holder force (BHF) vs. punch stroke and optimum pressure vs. punch stroke that
is needed to form a part successfully. This preliminary study assumes
16
isothermal conditions in the analysis of SHF-P at elevated temperatures
(meaning all tooling components, blank and fluid were heated to approximately
the same temperature).
Following are the benefits of the SHF-P process compared to conventional
stamping [Al-Nasser 2009]:
1) SHF-P gives higher limiting draw ratio (LDR) than conventional
stamping, since the pot pressure separates the sheet from the die corner
radius, so no friction energy is consumed at this location. The process
helps to lower the punch force and increases the LDR.
2) SHF-P has lower tooling cost: As mentioned earlier in the CHAPTER 1,
the Solstice body is a complicated deep-drawn component, which
undergoes three fluid forming/hydroforming operations as compared to
five stamping operations. Also, elimination of the female die results in
lower tool cost and lower die development time.
3) Pot pressure reduces/eliminates side wall wrinkling.
4) Better surface quality can be achieved as the outer surface of the sheet is
in contact with fluid only, thereby reducing the chance of tool marks.
5) Also a higher dimensional accuracy can be achieved for simple
symmetric parts.
Disadvantages of the hydroforming process [Al-Nasser 2009]:
1) Higher cycle time/ lower production rate. Sheet hydroforming is
slower than conventional stamping, because it takes time to control fluid
17
pressure and refill the die with fluid. Because of this, sheet hydroforming
is more suitable for small-lot production—from 5,000 to 40,000 vehicles
per year.
2) As a result of pot pressure, both the required ram and blankholder force
are larger than in conventional stamping (larger presses required).
3) Dimensional tolerances, especially at corner radii, may not be attainable
without a solid die.
3.1.1 Process Window in SHF-P Process
A successfully formed part will be characterized by minimum thinning and no
wrinkles, and will be formed without leaking/ minor leakage. In the SHF- P
process, the two main process parameters, the pot pressure and blankholder
force (BHF), should be optimized to successfully create a part. 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‖
as shown in Figure 3.3.
18
Figure 3.3- Process window in the SHF-P Process [Palaniswany 2007]
Table 3.1- Summary of possible defects in the hydroforming process. Recreated based on
[Palaniswamy 2007 and Yadav 2008]
# Type of Defect Cause Avoided/Postponed
1 Flange wrinkling -BHF too small
2 Side wall wrinkling -Insufficient pressure
-Punch geometry
-Excessive flange wrinkling
3 Fracture -High BHF
-Insufficient Pot Pressure
-Increasing Pot Pressure
-Decreasing BHF
19
4 Leaking of the pressurized medium
-Low BHF -Increase BHF or Reduce Fluid Pressure
5 Bulging against drawing direction
-Excessive fluid pressure -Decreasing the pressure
Table 3.1 summarizes the possible defects in the SHF-P process, explaining the
reasons for occurrence and possible methods of avoiding or postponing the
defects.
[Meinhard 2005] stated that small BHF should be applied at the beginning of the
process and then increased toward the end of the process, because the sheet
thickens as it flows in the flange and parts of the flange loose contact with the
tools at the end of the stroke, thus wrinkling may occur. 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.
3.1.2 Challenges in Warm hydroforming
According to the previous research conducted at ERC/NSM, the results for the
warm forming using finite element simulations were compared with the
experimental results available in [Droder 1999] literature. DEFORM 2D and 3D
codes were used to simulate cylindrical cup and rectangular pan geometries
using magnesium alloys. The results from the simulations predicted a higher
punch force and thinning distribution as compared to the experimental results.
For accurate finite element simulation of the warm sheet hydroforming process,
the mechanical and thermal changes in the workpiece need to be modeled as
shown in Table 3.2. Material flow stress data and material anisotropy are needed
20
over the range of forming temperatures (25 to 300⁰ C), along with strain rate
sensitivity. Heat transfer coefficient and friction between the workpiece and the
tools are also needed.
Table 3.2- Data required as input to FEM for accurate process simulation of the warm
sheet hydroforming process [Yadav 2008]
Mechanical data (for sheet) Thermal data (for sheet,
forming medium and hard
tools)
Process data
-Young‘s Modulus
-True stress-strain data
(function of temperature
and strain rate)
-Yield surface (function of
temperature)
-Anisotropy coefficients
(function of temperature)
-Thermal expansion
-Thermal conductivity
-Heat capacity
-Heat transfer
-Heat dissipation
-Friction between sheet and
tools
-Temperature (sheet and
tools)
-Interface pressure
-Process parameters
(forming pot pressure,
applied blank holder force)
Currently, in most commercially available FE codes, the interface of heat transfer
coefficient is assumed to be constant. But the heat transfer between the sheet and
the tools is dependent on the interface contact pressure. Since contact pressure
varies with location, the heat transfer coefficient should be an input as a function
of pressure [Yadav 2008]. PAMSTAMP version 2011 is capable of conducting
non-isothermal simulations using the heat transfer coefficient as a function of
pressure and/or gap. Additionally, it gives a user the option to input the
Young‘s Modulus (E), Poisson‘s ratio (υ), thermal density, thermal conductivity,
and specific heat capacity as a constant or as a function of temperature.
21
CHAPTER 4 Determination of the flow stress for Aluminum
and Magnesium sheet alloys at Elevated Temperature
4.1 Biaxial Viscous Pressure Bulge (VPB) Test
For the determination of flow curves at elevated temperatures and constant
strain rates, a particularly suitable measure is the viscous pressure bulge (VPB)
test. In comparison with tensile testing, this allows higher true strains to be
obtained. The higher true strains that can be reached in hydraulic bulge testing
as compared with tensile testing considerably reduce the required extrapolation
of the flow curve values for the numerical simulation based on finite elements.
Figure 4.1 is a schematic of the tooling used in the VPB test at Ohio State
University (OSU). 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 4.1] 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
22
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 4.2 shows the details of the geometrical features of the VPB
test tooling.
Figure 4.1- Viscous Pressure Bulge (VPB) test tooling [Al-Nasser 2009]
Figure 4.2- Geometrical features of the VPB test [Al-Nasser 2009] (nomenclature is
before chapter 1)
(a) Before Forming (b) After Forming
Upper die
Lower die
Potentiometer
Test Sample
Viscous Medium
Stationary Punch
Pressure Transducer
23
The membrane theory is usually used to calculate the flow stress from the
experimental data [Gutscher 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 1
Under balanced biaxial tension, which is the case in the bulge test, the formula
reduces to:
Equation 2
The average compressive stress in the thickness direction is -p/2. Using Von-
Mises yield criterion, the effective stress and effective strain can be calculated:
√
Equation 3
Equation 4
√
Equation 5
Equation 6
It can be noticed from Equations 4 and 6 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
24
the bulging pressure, measured using a pressure transducer and the dome
height, measured using a potentiometer.
4.2 Previous work on determining the flow stress data of sheet material at
elevated temperature
4.2.1 Virginia Commonwealth University (VCU), USA [Koc 2007]
[Koc 2007] used a non-contact sensor (ARAMIS system) in calculating strains at
the dome apex. At elevated temperatures, the influence of strain rate in
deformation needs consideration. Thus the author suggests, in characterizing
material properties, it is essential to collect data at constant strain rate. Through
flow control, this study focused on obtaining a near constant strain rate at the
dome apex during the bulging process. Flow stress was calculated using the
membrane theory assumptions (spherical dome shape) discussed in Section 4.1.
25
Figure 4.3- Hydraulic Bulge test setup with Feedback control loop [Koc 2007]
In this study, magnesium alloy AZ31B-O blanks were bulged at four different
temperatures (room, 100, 200, and 300°C) and at two different strain rates (0.0013
and 0.013 s-1). The test results revealed the effects of temperature and strain rate
on the sheet formability as well as the failure mode. In general, better sheet
formability (i.e., more elongation, lower flow stress) could be obtained when
forming processes were carried out at elevated temperatures or at low forming
rates. The premature shear fracture (i.e., die corner rupture) could be prevented
when bulging above 200°C and at the lower strain rate.
26
4.2.2 ERC/NSM (OSU), USA [Al-Nasser 2009]
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 4.4 shows a schematic of the machine design.
Figure 4.4- Schematic of the Fluid-based Elevated Temperature Biaxial Bulge Test
Apparatus [(AES), LLC]
Table 4.1- Summary of the tests performed at elevated temperature [Al-Nasser 2009]
Material Thickness
(mm)
Temperature (oC) Pressurization rate (in3/sec)
# of samples/ condition 200 230 260
AA5754-O 1 √ √ √ 0.2 and 2 3
AA5182-O 1 √ √ √ 0.2 and 2 3
AA3003-O 1 √ √ √ 0.2 and 2 3
LVDT
Sensors
Heat Exchanger
Fluid
Preheater
Hydraulic
Power
Supply
Computer
Controller
Fluid Pressure
Intensifier
Hydraulic Ram
Hydraulic Ram
Bulge Test
Specimen
Fluid Tank
Die Seal Plate
Fluid
Heater
27
Optimization Technique:
Since the material at elevated temperature is strain rate sensitive, two samples,
one pressurized fast (2 in3/second), and the other pressurized slow (0.2
in3/second) were tested and the resulting dome height evolutions were
compared with FE simulations run with the corresponding pressure vs. time
curves. 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.
Conclusions:
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 [Abedrabbo 2006]. This discrepancy
may be due to different reasons:
1) Problems of leakage and pre-bulging were observed in the experiments
2) The data in the literature is a tensile data, while data in this study is a bulge
test data (biaxial)
3) The optimization methodology needs to be further improved.
28
4.3 Determination of the flow stress at elevated temperature using the FE
Inverse Analysis Technique
As opposed to the previous studies/methods to determine the flow stress
coefficients at elevated temperature, this FE Inverse Analysis technique does not
require the assumption that the bulge profile needs to be spherical at the apex
location.
Different methods of heating the sheet in hydraulic bulge testing exist. Most
common method is holding the sheet between heated tools and applying air or
gas for obtaining the deformation. Another approach in hydraulic bulging of
sheets is to conduct the test under a heated liquid bath. In our study, a gas
pressure elevated temperature biaxial bulge system was used, which is designed
and developed by Interlaken (ITC).
4.3.1 Description of the FE inverse analysis technique
At CPF, we developed a technique to approximate flow stress data of lightweight
alloys through Viscous Pressure Bulge (VPB) test at elevated temperatures. This
technique should be capable to use experimental data (bulge height and strain)
from a VPB test to meet our objective (1)- to calculate the flow stress in terms of
the power law equation , where is the stress, is the strain, is the
strain rate and K, n and m are coefficients that shape the flow stress of the
material.
1) In light of this objective (1), a methodology called Surface Response (SR)
Approach, which is based on Inverse Analysis, has been proposed. This
29
methodology takes advantage of the optical measuring fixture developed
by Interlaken (ITC) and the capabilities of Finite Element Modeling.
2) The Finite Element tool is used to conduct a wide number of simulations
of the VPB test of a lightweight alloy under a wide range of values for
coefficients K, n and m. The ranges of K, n and m are taken from the
tensile tests at elevated temperature conducted by [Abedrabbo 2007]. By
doing this we are mapping the different bulge forming behaviors that the
alloy can present under different temperature and pressure conditions.
The FE simulation output of interest are the bulge height, strain at the
apex of the bulge profile and the pressure rate.
3) This Surface Response approach can be described as taking the
experimental data from VPB test for a given material and comparing it
with the different simulations conducted in the FE code. The simulation
that resembles the most to the experimental behavior of the VPB test will
provide the best approximation for that material to the power law
equation.
4) Transferring this idea to a more systematical approach, an extensive Finite
Element Database is built. This database contains bulge height and strain
distribution along the apex of the bulge and at different pressure level. An
error function is defined in the methodology that compares every
experimental variable/output (i.e. bulge height, etc.) with its equivalent in
the FE database at the same bulge location and pressure level (see Figure
4.5 and Figure 4.6). An error function is calculated for every combination
of K, n and m that exists in the database. The minimum error function is
selected as the best approximation and its corresponding values of K, n
and m assumed as the resulting flow stress coefficients.
30
Figure 4.5- Methodology to obtain K, n and m values by calculating the lowest error
function (E)
Figure 4.6- Bulge height profile at various time steps (tn)
Bulge height, Hexp vs TimeOne experimental output is
compared with FE output for
every combination (Kj, nj
and mj)Strain, Sexp vs Time
FE Output
Comparison
Every comparison
results in an error
function (E1, E2,
…, Ej)
Bulge height, HFE vs Time
Strain, SFE vs Time
Experimental Output
31
Equation to calculate the Error function (Ej) calculated for every combination of
Kj, nj, mj:
√∑(
)
4-1
Where,
Hexp(t)= Bulge Height at time t- Experimental measurement, HFE(t)= Bulge Height at time
t from FE simulation j, j= number of simulations
4.3.2 Experimental Setup and Results (Machine and Tool Design)
Figure 4.7 shows a schematic of the machine design at ITC, which consists
essentially of the tools (the forming upper and lower die, 2 camera systems, light
source, and 2 data acquisition systems. One of data acquisition systems (on the
left) collects experimental data for bulge height, strain, thickness and curvature
of the formed sample. The other system (on the right) controls the gas pressure
either by setting either pressure or strain limits. Thus, forcing the gas pressure to
drop immediately as one of these limits has reached.
Experimental test procedure:
The steps to conduct a test are as follows:
1) Prepare a speckle pattern on sample for the correct use of cameras.
2) Gas tank and pump should be turned on. Set the controls for linear pressure ramp input and maximum pressure/strain limit.
3) Both dies should be at required temperature.
32
4) Position the sample and close the dies as much as possible without clamping, wait 3 to 5 minutes to allow heating of the sample.
5) Apply clamping force and open the controlled gas inlet, confirm that pressure control command and pressure reading match.
6) Initialize optical gauge and start recording.
7) Proceed with bulge. It will stop according to maximum pressure or maximum strain criteria.
8) Extract sample.
9) Enter to post-processor, and compute all pictures to obtain all necessary information such as bulge height, strain, thickness and curvature of the bulge profile.
Figure 4.7- Gas bulge tooling with 2 Cameras and data acquisition systems [provided by
Interlaken]
2 cameras
Upper die
Lower die
Light
source
Lock bead
Gas
pressure
inlet
Gas bulge tooling with camera
Bulge height (Hexp)
Strain (Sexp)
Test is controlled by
either strain/ pressure
limit, meaning that
pressure input stops
when reaching one of
these stopping criteria
33
The pressure input selected were linear ramps (see Figure 4.12) based on the
discussions and the preliminary experimental results from the sponsor. Three
pressure rates; 0.1 MPa/sec (14.5 psi/sec), 0.5 MPa/sec (72.5 psi/sec) and 2.5
MPa/sec (362.5 psi/sec) were selected that accounted for a wide range of strain
rates.
The tooling dies (upper and lower) are made of A2 tool steel and are heated by
the heat bands. The heating time was quite fast (e.g. dies reach 200C in 20 min).
The optical system consisted of two cameras mounted on a fixture on top of the
dies. The optical system needed sporadic calibration for accuracy of results.
Post-processing the data required importing all pictures taken by the cameras,
selecting an area to analyze, and compute the parameters of interest. Post-
processing data was obtained for each test including: bulge height, strain,
pressure, thickness and curvature of the bulge. The average time to conduct one
test from preparation to post processing was around 20 min.
Testing Matrix
Table 4.2-Summary of the experimental tests performed at room and elevated
temperature at ITC
Material Thickness
(mm)
Temperature (oC) Pressurization rate (MPa/sec)
# of samples/ condition
25 150 200 250 300 350
AA5182-O
1.1 √ - √ √ √ √ 0.1, 0.5, 2.5 2
Mg AZ61L
1.1 - √ √ √ √ - 0.1, 0.5 2
Figure 4.8 shows the plot for experimental Bulge Height, Hexp vs Pressure, Pexp
for AA 5182 formed at a linear pressure rate of 0.5 MPa/sec. This experimental
34
data will be used to compare with the FE output of Bulge Height vs Pressure.
The combination of k, n and m which calculates the minimum error value will be
used to obtain the flow stress data of the material.
Figure 4.8- Experimental pressure vs. Bulge Height for AA 5182 sheet samples formed at
Pressure Rate = 0.5 MPa/sec at various temperatures (30, 200, 250, 300 and 350 degree
Celsius)
Post-processing the experimental data gives the Strain vs time (see Figure 4.9) at
the apex location on the formed sample. This strain vs time data can be further
differentiated on small time intervals to calculate the Strain Rate vs Time as
shown in the equation below:
0
5
10
15
20
25
30
0 2 4 6 8 10
Bu
lge
Hei
ght,
Hex
p (
mm
)
Pressure, Pexp (MPa)
350 C
300 C
250 C
200 C
30 C
35
t= time step S
exp (t
2) = Experimental strain at time step (t
2)
Sexp
(t1) = Experimental strain at time step (t
1)
The purpose of obtaining the data for Strain (ε) vs time and calculating the Strain Rate
( ) vs time is to give the flow stress in terms of the Power Law Equation.
Figure 4.9- Experimental Strain vs Time data for AA5182 @ 200⁰C for PR=0.5 MPa/sec
0
0.05
0.1
0.15
0.2
0.25
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Stra
in (
mm
/mm
)
Time (sec)
Experimental data: Strain vs Time
36
Figure 4.10- Calculated Strain Rate (s-1
) vs Time for AA5182 @ 200⁰C for PR=0.5
MPa/sec
4.3.3 Finite Element Method (FEM) Database used for Surface Response
Method
Several methods for building the flow stress data through FEM have been
implemented. The selected approach for this work defines a VPB test database
obtained from FE simulations. This FE database includes: time, pressure, bulge
height and strain at the apex of the formed sample. The database intends to cover
ranges of coefficients K, n and m that would describe the flow stress of aluminum
0
0.05
0.1
0.15
0.2
0.25
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Stra
in R
ate
(sec
-1)
Time (sec)
Calculated data: Strain Rate vs Time
37
and magnesium alloys at different temperatures. The FE database is an essential
part of the determination of flow stress.
The Viscous Pressure Bulge (VPB) Test is simulated in the Finite Element code
DEFORM-2D with an axisymmetric model and the geometry parameters
mentioned in Table 4.3:
Table 4.3 Simulation Geometry Parameters
diameter of the cavity, dc 105.66 mm
Die Radius, Rc 6.35 mm
Initial Sheet Thickness, t0 1 mm
Based on the conducted literature review on aluminum alloys flow stress at
elevated temperatures, the material properties used for the project are provided
by the following work by [Abedrabbo 2006]. [Abedrabbo 2006] presents the
resulting K, n and m coefficients obtained from tensile tests for aluminum alloys
(AA3003-H111, AA5182-O and AA5754-O) at different material temperatures,
ranging from room temperature up to 260 °C.
The values for the flow stress coefficients K, n and m have the following ranges:
70-550 MPa, 0.08-0.32 and 0.01-0.1 respectively. With the purpose of building a
FE database that maps through the spectrum of values, the ranges are discretized
and combined. Thus, the VPB test is simulated for various ranges of K, n and m
at different temperatures. Table 4.4 lists the ranges of coefficients that are
simulated in DEFORM-2D, the number of simulations is defined by number of
possible combinations of these coefficients.
38
Table 4.4- Flow Stress Coefficients Material Input Set
K n m
70 0.08 0
130 0.14 0.01
190 0.2 0.035
250 0.26 0.05
310 0.32 0.065
430 0.085
550 0.1
Figure 4.11 shows the setup of the FE Simulation in DEFORM-2D with the
geometrical parameters indicated.
Figure 4.11- FE Setup Sketch
39
Since this is a strain rate sensible process due to temperature, it is important to
simulate the VPB test at different strain rates. Three inputs of pressure have been
selected, these being: 2.5 MPa/sec (362.5 psi/sec), 0.5 MPa/sec (72.5 psi/sec),
and 0.1 MPa/sec (14.5 psi/sec), all of them in linear increment. In result, for each
pressure rate (Pressure vs time) a set of simulations as mentioned in Table 4.4
should be conducted. The pressure rates are applied as boundary conditions
along the sheet inner sheet profile as shown in Figure 4.12.
Figure 4.12- FE Input for Pressure vs time (for 3 Pressure Rates)
0
1
2
3
4
5
6
7
8
9
10
0 20 40 60 80 100
Pre
ssu
re (
MP
a)
Time (sec)
FE Input-Pressure vs Time
Pressure Rate=0.1 MPa/sec Pressure Rate=0.5 MPa/sec
Pressure Rate=2.5 MPa/sec
40
The simulations listed will assemble the FE database for a given pressure rate.
The other FE model parameters (geometry, symmetry, step size, etc.) should
remain the same. Once the FE simulations are finished, the following data will be
extracted from every simulation: time, pressure, instantaneous height at the apex
of the bulge (HFE) and instantaneous strain (SFE) at the apex of the bulge (see
Figure 4.13).
Figure 4.13- FE outputs (Bulge Height vs time and Strain vs time) collected at apex for
every combination of k, n and m and stored in the FE Database
4.3.4 Results from the FE inverse analysis technique
To simplify the process of matching one experimental data of Pressure vs Bulge
Height to several combinations of K, n and m from the FE output (Pressure vs
Bulge Height) we developed a code using MATLAB. This code would calculate
the error function (Ej) using the Equation shown below. Using this equation, the
K
n
n1 n2 n3 n4 … nj
K1
K2
K3
K4
…
Kj
m1
m2
…mj
m
0 10 20 30 40 50 60 700
5
10
15
20
25
30
35
40
Radial Coordinate (mm)
Bul
ge H
eigh
t (m
m)
tn
t2
t1
Bulg
e H
eig
ht (m
m)
Radial Coordinate (mm)
r0 r1 r2 r3 r4 r5
FE Database
For every combination of Kj, nj and mj,
Bulge Height (HFE) vs time, and Strain (SFE)
vs time output is collected at apex point
41
MATLAB code would compute the error function (Ej) [see Equation 4-1] for
every combination of K, n and m in the FE database. Finally, MATLAB would
give out the corresponding combination of K, n and m that matched the
experimental data of Bulge Height vs Pressure closest.
Figure 4.14 shows the comparison of the Bulge Height vs Pressure curve at a)
Room temperature (30 ⁰C) and b) at 200 ⁰C for linear Pressure Rate = 0.5
MPa/sec. The values of K and n tend to decrease with increase in temperature
and the m value increases with an increase in temperature.
Figure 4.14- Comparison of Bulge Height vs. Pressure curve at (a) Temperature =30⁰C
and (b) 200⁰C for a linear Pressure Rate= 0.5 MPa/sec
0 1 2 3 4 5 60
5
10
15
20
25
Pressure vs Height
Pressure (MPa)
Heig
ht
(mm
)
FE database approximation
experimental data
0 1 2 3 4 5 6 70
5
10
15
20
Pressure vs Height
Pressure (MPa)
Heig
ht
(mm
)
FE database approximation
experimental data
K=430 n=0.08 m=0.05K=550 n=0.20 m=0
Bulge Height vs Pressure Bulge Height vs Pressure
42
The same methodology has been applied to the experimental data obtained at
ITC for AA 5182 and MgAZ61L at several temperatures and the corresponding
flow stress coefficients (K, n and m) are listed in Table 4.5 and Table 4.6,
respectively. Please note that currently the MATLAB code is programmed to
approximate the experimental test to the existing K, n and m coefficients in the
current FE database (listed in Table 4.4). Using the strain and calculated strain
rate values we have plotted the flow stress for AA 5182 (see Figure 4.15) and
MgAZ61L (see Figure 4.16) alloys for various temperatures by curve fitting them
in the Power Law Equation.
Table 4.5-Predicted flows stress coefficients K, n and m for AA5182 at PR =0.5 MPa/sec
Temperature (⁰C)
K (MPa)
n m Strain Rate (s-1)
30 550 0.2 0 0.005-0.05
200 430 0.08 0.05 0.008-0.16
250 430 0.08 0.085 0.002-0.08
300 310 0.08 0.065 0.003-0.18
350 250 0.14 0.035 0.004-0.095
43
Figure 4.15-Flow stress curves for AA5182 obtained using Surface Response Method for
PR=0.5 MPa/sec (at variable Strain Rate)
0
50
100
150
200
250
300
350
400
450
0 0.05 0.1 0.15 0.2 0.25
Tru
e St
ress
(M
Pa)
True Strain
AA5182 at PR= 0.5 MPa/sec (Variable Strain Rate)
30 C 200 C 250 C 300 C 350 C
30 C
200 C
250 C
300 C
350 C
44
Table 4.6- Predicted flows stress coefficients K, n and m for MgAZ61L at PR =0.5
MPa/sec
Temperature (⁰C) K (MPa) n m Strain Rate (s-1)
150 430 0.08 0.01 0-0.023
200 430 0.08 0.05 0-0.020
250 250 0.08 0.035 0-0.052
300 250 0.08 0.085 0-0.055
Figure 4.16- Flow stress curves for MgAZ61L obtained using Surface Response Method
for PR=0.5 MPa/sec (at variable Strain Rate)
0
50
100
150
200
250
300
350
400
0 0.02 0.04 0.06 0.08 0.1
Tru
e S
tre
ss (
MP
a)
True Strain (mm/mm)
Mg AZ61L @ Pressure Rate= 0.5 MPa/sec
300 C 250 C 200 C 150 C
150 C
200 C
250 C 300 C
45
Using the tensile data available in the literature for AA 5182 alloy for a constant
Strain Rate of 0.0083 s-1, we have used this flow stress data to compare the
behaviour of the flow stress curve obtained from the bulge tests using the
Surface Response Method (see Figure 4.17). Our purpose here, is not to match the
flow stress data obtained using the 2 tests (tensile and bulge), but to see the trend
of the flow stress curves at various temperatures for AA 5182 material. When we
try to carefully look at the data obtained from the 2 tests (tensile vs bulge) at the
same temperature, we see that there seems to be a shift in the flow stress data
obtained for the bulge tests and this shift is consistent across all the three
temperatures (30, 200, 250 ⁰ C) as shown in this Figure 4.17.
Figure 4.17- Flow stress data obtained using the calculated Bulge Test (B.T.) data
(Surface Response) and Tensile Test (T. T.) data from [Abedrabbo 2007]
0
50
100
150
200
250
300
350
400
450
0 0.05 0.1 0.15 0.2 0.25
Tru
e S
tre
ss (
MP
a)
True Strain
30 C 200 C 250 C
Tensile Test_250 C Tensile Test_200 C Tensile Test_30 C
BT_30C
BT_200C
BT_250C
TT_30C
TT_200C
TT_250C
46
Please note that the Figure 4.10 plots the data for Strain Rate vs time for AA 5182
material, so we can clearly see that the bulge tests were not conducted at a
constant strain rate value, whereas the tensile tests obtained from [Abedrabbo
2007] were conducted at a constant strain rate value= 0.0083 s-1. Figure 4.18
shows the true stress-true strain curves for the AA5182-O material at 260 ⁰C in
the rolling direction at different strain rates (0.008, 0.01, 0.05, and 0.08 s-1) using
the uniaxial tests. As seen in the figure, the material became more strain rate
sensitive with increase in temperature and tends to shift upwards with the
increase in strain rate value.
Figure 4.18- True stress-True Strain data for AA5182-O obtained using tensile tests at
260 ⁰C for several strain rate values [Abedrabbo 2007]
47
4.3.5 Conclusions
Experimental tests at elevated temperature for AA 5182 and MgAZ61L alloys
were conducted at ITC using gas as pressure media. These tests were carried out
under a linear pressure rate. The test equipment was still in its development
phase at ITC and the ultimate goal of the testing device would be to conduct the
bulge tests under a constant strain rate even at elevated temperature by
implementing a feedback loop in the device that controls the pressure vs time.
Currently, the equipment is capable of post-processing the bulge profile, strain,
pressure, thickness even after the sample is burst during forming. This is possible
because the camera device takes a lot of images at very small time intervals to
capture the data till the step until the sample bursts.
Our objective at CPF was to use the given experimental data to predict the flow
stress behavior of the material at elevated temperature. Thus, a Surface Response
method to determine flow stress data at elevated temperature through VPB tests
has been developed. This methodology can be applicable only when we have the
means to correctly measure the bulge height, strain and strain rate, as in our case
with the device at ITC. Surface response method calculates a minimum of an
Error function (Ej) using an application code developed in MATLAB, by
comparing the experimental result (Pressure vs Bulge Height) with FE database.
Flow stress data currently predicted for AA 5182 and Mg AZ61L alloys using the
experimental data taken from ITC at a linear Pressure Rate of 0.5 MPa/sec.
Keeping the pressure rate constant does not mean that the strain rate remains
constant as seen from Figure 4.10. Thus, we cannot make a direct comparison of
the flow stress data obtained in this bulge test study with the tensile test data
available in the literature which were carried out under a constant strain rate.
48
The approximations of the flow stress coefficients given by the Surface Response
Method depend a lot on the density of the FE database.
49
CHAPTER 5 Cold and Warm Hydroforming of AA 5754 Sheet:
FE Simulations and Experiments
Warm hydroforming technique has the advantages of both hydroforming and
warm forming. These enable complex parts to be produced with materials those
have poor formability with less force/pressure compared to conventional
methods. In warm hydroforming process, the pressurized fluid medium is
usually hydraulic oil. Oil – when compared to gas – has higher thermal capacity
and higher pressures can be applied easily [Billur 2008].
When designing a warm hydroforming setup up to 300ºC (using oil as the fluid
medium), following concerns should be addressed [Novotny 2003]:
1. Key components, such as pumps, valves, sealing elements, etc. should be
suitable for both high pressure and temperature.
2. In order to have constant temperature during forming (isothermal
forming), heating is necessary for both the fluid medium and the dies.
3. For safety of operator, guards for splash should be properly designed. In
case of any burst in the work piece, hot oil should not contact the operator
or nearby people.
4. Vapor of lubricants and/or the pressurizing fluid should be removed
50
5.1 Model Part and Tools Geometry
The schematic of the tooling is presented in Figure 5.1. The lower die consisted of
three main components including the pressure pot, lower post (fixed in the
center) and blank holder. The upper die consisted of the punch and the spring
setup which allowed the punch to travel to a maximum stroke of 1.5 in (38 mm).
The purpose of the lower post was to create a reverse bulge at the center of the
deformed part when forming a part by conventional deep drawing without
using fluid pressure. However, necessary modifications of the deep drawing
tooling restricted the travel distance of the punch. In these SHF-P tests, the lower
post did not touch the sheet and the fluid pressure can be considered as the only
active force that forms the reverse bulge into the center recess of the punch.
51
Figure 5.1- Schematic of the tooling for SHF-P experiments: (a) initial setup (b) after
deformation, where ri = initial blank radius, Dd = draw depth and h = bulge height.
A Mokon heating system was used to control the forming fluid temperature.
With the fill and vent valves open, fluid will circulate through the tool (see Figure
5.2) to heat up the tooling along with the band heaters and cartridges. The
system includes a reservoir that maintains fluid at temperature and available for
filling and draining the tool cavity through the fill and vent valves. Dynalene
600, synthetic oil, was used as the fluid for building up forming pressure in the
pot cavity.
ir
dDh
Punch
Post
Die
Blankholder
Blank
(a)
Initial setup
(b)
After Deformation
52
Figure 5.2- Pressure flow schematic to heat or cool the tooling
While conducting our experiments for the SHF-P process, the part was formed
by conducting the following steps:
1) Close the bypass, vent and relief valve
2) Relief valve is programmed to a certain limit pressure
3) Tool cavity is sealed with the clamped sample
4) During the process, the punch moves down, displaces oil and builds
pressure, and at the same time, the relief valve helps to release pressure if
it exceeds the pressure limit value as shown in Figure 5.3.
The displaced oil from the tool follows the path of the 1) fill valve, 2) relief valve,
3) in from process and 4) Mokon system.
53
Figure 5.3- Pressure flow schematic to form the part using the SHF-P process by
controlling pressure with the relief valve
5.2 Experimental Results
Prior to forming tests at room and elevated temperatures, preliminary FE
simulations were conducted to establish initial test parameters (BHF, punch
velocity, and pot pressure) that could be used as experimental inputs. The sheet
material was AA 5754 with an initial diameter, di, and thickness, ti, of 17 in (432
mm) and 0.039 in (1.0 mm), respectively. Table 5.1 lists the input parameters for
the room temperature experiments.
In the preliminary FE experiments of the room temperature SHF-P process, the
pot pressure was maintained at approximately 300 psi (2.07 MPa) for BHF of 5.6
kips (25 kN). With the downward movement of the punch, the punch displaced
oil causing an increase in counter pressure. As this pressure approached the set
54
limit of 300 psi (2.07 MPa), the relief valve cycled to maintain a steady pot
pressure.
Table 5.1- Input parameters for SHF-P tests at room temperature (punch velocity=0.075
in/sec)
Sample # BHF (kip) Pot Pressure (psi) Punch stroke (inch)
5 5.6 300 1.35
6 5.6 300 1.13
In the case of experimental tests conducted at elevated, the maximum pot
pressure input for the relief valve was set to limiting pressure levels as listed in
Table 5.2. Initially, the same process parameters that were used for room
temperature forming were used (pot pressure of 300 psi (2.07 MPa) and BHF of
5.6 kip (25 kN)), but the part consistently failed around the punch corner region.
Therefore, new process conditions were used by applying a lower BHF, around 1
kip (4.45 kN), and increase in the pot pressure input.
A set of samples were formed at a constant BHF and draw depth of 0.56 in (14
mm), but with variable pressure limits of 500, 1000 and 2000 psi (3.4, 6.9 and 13.8
MPa), to study the effect of forming pressure on the part shape. For the pressure
limit of 2000 psi (13.8 MPa), the sample parts were further drawn to depths of
0.7, 1.0 and 1.5 in (17.8, 25.4 and 38.1 mm), to measure the amount draw-in.
55
Table 5.2- Input parameters used to conduct warm SHF-P test at elevated temperature of
about 150°C (cycle time = 20 sec)
Sample # Pot Pressure (psi) BHF (kip) Punch Stroke (inch)
21 500 1 0.56
27 1000 1 0.56
28 2000 1 0.56
29 2000 1 0.70
30 2000 1 1.00
33 2000 1 1.50
Table 5.3 compares input (entered at the control panel) and output values (BHF
and pot pressure measured from sensors inside the press machine) and the
measured draw depth, Dd, of the formed part at room temperature. Since the
output values of BHF fluctuated throughout the punch stroke, an average value
of BHF was calculated. Measured flange perimeter, Ff, draw depth, Dd, and the
bulge height, h, are presented in Table 5.3.
Table 5.3- Comparison of experimental input to the output readings and measurements at
room temperature (initial flange perimeter, fi= 53.41 in)
EXPERIMENTAL
INPUT EXPERIMENTAL OUTPUT
Sample
#
BHF
(kip)
Pot
Pressure
(psi)
Punch
stroke
(in)
BHF
(kip)
Pot
Pressure
(psi)
Flange
Perimeter,
Ff (in)
Draw
Depth,
Dd (in)
Bulge
Height,
h (in)
5 5.6 300 1.35 6.78 304.7 49.1 1.349 0.353
6 5.6 300 1.13 6.81 307.5 50.1 1.083 0.333
Table 5.4 compares the input and output values (BHF and forming pressure) and
the measured draw depths, Dd, of the samples formed at elevated temperature.
The steady BHF output obtained from the experimental results is higher than the
56
experimental input value. This may be because the BHF (clamp load) was very
small relative to the press capacity. Also, this load was measured using pressure
transducers, which are placed on either side of the actuator‘s piston and the cross
sectional areas of the piston areas are then considered to calculate the load.
Thus, it gave only approximation for measurement of a very small load. The
comparison of output values of pot pressure for samples 21, 27, and 28 indicates
that a maximum of 842.5 psi (5.8 MPa) was needed to draw this part to a depth of
0.56 in (14 mm). In order to draw the part to a depth of 1.5 in (38 mm), the
required pot pressure was increased to 1494 psi (10.3 MPa), keeping the BHF to
the same value of 2.2 kip (9.8 kN).
Table 5.4- Comparison of experimental input and output readings and profile
measurements, for SHF-P experiments at elevated temperature (Initial flange perimeter,
Fi = 53.41 in)
EXPERIMENTAL INPUT EXPERIMENTAL OUTPUT
Sample
#
BHF
(kips)
Pot
Pressure
(psi)
Punch
Stroke
(inch)
BHF
(kips)
Pot
Pressure
(psi)
Flange
Perimeter,
Ff (in)
Draw
Depth,
Dd (in)
21 1 500 0.56 2.19 595.3 52.3 0.578
27 1 1000 0.56 2.21 834.6 51.9 0.570
28 1 2000 0.56 2.21 842.5 52.1 0.573
29 1 2000 0.70 2.23 977.5 51.8 0.715
30 1 2000 1.00 2.19 1140.1 50.2 1.025
33 1 2000 1.50 2.22 1494.4 47.9 1.514
The temperature of the tooling (die, blank holder and punch) was controlled by
two dual channel Watlow F4 temperature controllers using resistance heaters.
The fourth Watlow channel was used to monitor the oil temperature with a
thermocouple positioned inside the lower die. Thermal data was collected for
57
each component of the tooling using thermocouples that were embedded in the
tooling as shown in Figure 5.4. Due to the constraints of the machine, it was very
difficult to obtain isothermal conditions within a 10C range. Results indicate
that the temperatures of the blank holder, die and oil ranged from 127 to 140C,
while the punch temperature was measured to be 157C.
Figure 5.4- Position of thermocouples on the ITC hydroforming machine
5.3 Finite Element Method (FEM) Setup
The part geometry was designed at General Motors as representative of a
challenging feature to form with aluminum by conventional stamping. The
58
AA5754 sheet blank was 0.039 in (1 mm) in thickness (ti) and 17 in (432 mm) in
diameter (di). The FE model was created using PAM-STAMP 2G, Ver. 2009,
which enabled input of the material model as a function of temperature and
strain rate simultaneously. Only one quarter of the geometry was modeled since
the tooling and part geometries were axisymmetric.
For all temperatures, the process was modeled using the Aquadraw Module in
PAM-STAMP 2G, which allows efficient control of pressure input in the tool
cavity, based on compressed fluid volume and maximum pressure limit to be
applied on the blank. To create a simplified model and replicate the elevated
temperature deformation, an ‗isothermal condition‘ was assumed. By
approximation, the FE model was set up at 150C (whereas temperature readings
of tools and fluid ranged from 127 to 157C).
The input parameters used during the simulation are summarized in Table 5.5.
The major difference between simulation of this process at room and elevated
temperature conditions is the input of material properties. As the material at
elevated temperature is strain rate sensitive, the deformation speed at different
regions of the blank in the simulation should take into account the influence of
strain rate.
[Abedrabbo 2007] conducted tensile tests and applied the Fields and Backofen‘s
material model (power law equation) to describe the stress-strain behavior of AA
5754. Flow stress data was input as a function of strain, strain rate and
temperature, in tabular format in PAM-STAMP 2G.
mnK
Where:
K = 503.7-0.592*T (for T = 25-93C) and 641.3-1.829*T (for T = 93-260C)
59
n = 0.3304 -0.000529*T (for T = 25-93C) and 0.4048-0.001192*T (for T = 93-260C)
m = 0.00118*exp (0.0161*T) (for T = 25-260C)
Table 5.5- Input parameters for FE simulations of SHF-P
Mechanical Properties
Blank material AA5754
Flow stress (obtained by tensile test) [Abedrabbo 2007]
Young‘s Modulus (E) 69 GPa
Poisson‘s ratio (ν) 0.3
R0, R45, R90 1 (material assumed isotropic)
Interface Condition
Friction coefficient µ (blank/ tools) 0.12
Mesh
Element type Shell (Belytschko-Tsay )
Object type
Blank Elastic, Plastic
Tools Rigid
Sheet Hydroforming with Punch (SHF-P)
Aquadraw Activate
Bulk Modulus, K 50 GPa
Pot Pressure Experimental output (see Figure 5.5)
Blank Holder stroke Experimental output
Punch stroke Room temp=1.35 in
Elevated temp= 1.50 in
Punch Velocity 0.074 in/sec
60
Figure 5.5- Experimental output Pot pressure vs time for part formed at elevated
temperature (150 ⁰C)- Sample # 33
5.4 Comparison of FE predictions with experimental results
The results from room temperature FE simulations have been summarized below
for Sample #5 (BHF = 6.8 kip, pot pressure = 304.7 psi and punch stroke = 1.35
in). For comparison of the thickness profile generated from the FE simulations,
the mechanical indicator (Mitutoyo) was used to measure thickness along the
curvilinear length of the formed sample. Figure 5.6 presents the thickness
distribution along the curvilinear length of the part. Note that the maximum
thinning location occurred near the punch corner region (location #4) for the part
formed at room temperature.
0
200
400
600
800
1000
1200
1400
1600
0 5 10 15 20 25
Po
t P
ress
ure
(p
si)
Time (sec)
Pot pressure vs Time
61
Figure 5.6- Thickness profile along the curvilinear length measured by the mechanical
indicator and compared with FE results for Sample #5 at room temperature (Punch
Stroke= 1.35 in, BHF = 6.81 kip, pot pressure = 304.7 psi)
For FE analysis at elevated temperature, Sample #33 (BHF= 1 kip (4.45 kN), pot
pressure = 2000 psi (13.8 MPa) and punch stroke=1.5 in (38 mm)) was selected.
The results of SHF-P at the elevated temperature of 150C are presented in Table
5.4. The BHF prediction of the FE simulation for Sample #33 indicates some
fluctuation, but the average value remains close to the experimental output. The
FEA input of BHF force did not work in PAM-STAMP because forming pressure
is balanced by blank holder only, but in reality the punch force adds to BHF to
balance the forming pressure. So in simulation, the forming pressure caused the
0 25 50 75 100 125 150 175 200 2250.78
0.82
0.86
0.90
0.94
0.98
1.02
1.06
1.10
Curvilinear Length (mm)
Thic
kness (
mm
)
FE Output
Measured
0 25 50 75 100 125 150 175 200 2250.78
0.82
0.86
0.90
0.94
0.98
1.02
1.06
1.10
Curvilinear Length (mm)
Thic
kness (
mm
)
1
2
34
56
7
8
1 2
3
45
67
8
Maximum thinning location
62
blank holder to open up. Therefore, input blank holder stroke of 1 mm was used
in the FE simulations at elevated temperature (instead of BHF) that was close to
the recorded blank holder stroke in ITC data file, as indicated in Figure 5.7.
Figure 5.7- FE setup for the initial clearance of 1 mm between the blank holder and sheet
Figure 5.8 is a comparison of the part profile measurement using the CMM and
the FE results of SHF-P for sample #33. For the CMM measurement of the
experimental sample, a significant bend in the reverse bulge region of the part
was observed. This bend in the part may be due to springback and distortion
from thermal contraction after part was removed from the press and cooled to
room temperature.
63
Figure 5.8- (a) experimental workpiece, (b) Pam-Stamp result of quarter model, (c)
comparison part profile from FEM and experiment, for the SHF-P of Sample #33 (punch
stroke = 1.50 in, average temperature = 150C, pot pressure = 1494 psi)
(a)
(b)
0 25 50 75 100 125 150 175 200
0
5
10
15
20
25
30
35
40
Radial Distance (in)
Part
Depth
(in
)
0
--
--0.00
1
--
--0.20
2
--
--0.40
3
--
--0.60
4
--
--0.80
5
--
--1.00
6
--
--1.20
7
--
--1.40
--1.60FEA
CMM
0 25 50 75 100 125 150 175 200
0
5
10
15
20
25
30
35
40
Radial Distance (in)
Part
Depth
(in
)
0
--
--0.00
1
--
--0.20
2
--
--0.40
3
--
--0.60
4
--
--0.80
5
--
--1.00
6
--
--1.20
7
--
--1.40
--1.60
0 25 50 75 100 125 150 175 200
0
5
10
15
20
25
30
35
40
Radial Distance (mm)P
art
Depth
(m
m)
0
--
--0.00
1
--
--0.20
2
--
--0.40
3
--
--0.60
4
--
--0.80
5
--
--1.00
6
--
--1.20
7
--
--1.40
--1.60FEA
CMM
0 25 50 75 100 125 150 175 200
0
5
10
15
20
25
30
35
40
Radial Distance (mm)P
art
Depth
(m
m)
0
--
--0.00
1
--
--0.20
2
--
--0.40
3
--
--0.60
4
--
--0.80
5
--
--1.00
6
--
--1.20
7
--
--1.40
--1.60
0 25 50 75 100 125 150 175 200
0
5
10
15
20
25
30
35
40
Radial Distance (in)
Part
Depth
(in
)
0
--
--0.00
1
--
--0.20
2
--
--0.40
3
--
--0.60
4
--
--0.80
5
--
--1.00
6
--
--1.20
7
--
--1.40
--1.60FEA
CMM
0 25 50 75 100 125 150 175 200
0
5
10
15
20
25
30
35
40
Radial Distance (in)
Part
Depth
(in
)
0
--
--0.00
1
--
--0.20
2
--
--0.40
3
--
--0.60
4
--
--0.80
5
--
--1.00
6
--
--1.20
7
--
--1.40
--1.60
height Bulge h
Dd
= D
raw
Dep
th
(c)
64
Figure 5.9- Thickness profile along the curvilinear length measured by the mechanical
indicator and compared with FE results for Sample #33 (punch stroke = 1.50 in, average
temperature = 150C, pot pressure = 1494 psi)
Figure 5.9 presents the comparison of the thickness profile of Sample #33 formed
at elevated temperature. The thickness profile for the FE simulation matches
fairly well with the measurements. FE results predict that maximum thinning
occurred near the reverse bulge region (position 8) along the curvilinear length.
Another set of tests were simulated to determine the effect of pot pressure on the
formed part geometry. The formed samples are # 23, 27 and 28, for BHF ~2.2 kip
(9.8 kN), cycle time = 20 sec, 0.56 in (14 mm) punch stroke and variable pressure
limits of 500, 1000 and 2000 psi (3.4, 6.9 and 13.8 MPa). From Table 5.6, it can be
0 25 50 75 100 125 150 175 200 2250.90
0.92
0.94
0.96
0.98
1.00
1.02
1.04
1.06
1.08
1.10
Curvilinear Length (mm)
Thic
kness (
mm
)
1
2
3
4
5 6 7
8
9
FE Output
Measured
0 25 50 75 100 125 150 175 200 2250.90
0.92
0.94
0.96
0.98
1.00
1.02
1.04
1.06
1.08
1.10
Curvilinear Length (mm)
Thic
kness (
mm
)
0.88
0.9
0.92
0.94
0.96
0.98
1
1.02
1.04
1.06
1.08
0 50 100 150 200 250
Thic
kne
ss (
mm
)
Curvilinear Length (mm)
Thickness profile along the curvilinear length for Sample 33 (BHF= 2.22 kip, Pot Pressure limit= 2000 psi, Punch Stroke= 1.50 in)
Experimental measurements with Error bar FE profile
12
3
4
5 6 78
91
2
3
4
5 6 7
Maximum
Thinning Location
65
inferred that with an increase in the input pot pressure limit, the maximum
thinning along the part would increase. However, there is not a significant
experimental difference in percent thinning between 1000 and 2000 psi (6.9 and
13.8 MPa), because the physical output for the maximum pressure only attained
about 840 psi (5.8 MPa), regardless of the value input at the control panel. In
order to form a part at elevated temperature (ET) for a draw depth (Dd) of 0.56 in
(14 mm) and 2.2 kip (9.8 kN) BHF, a maximum of 592.5 psi (4.1 MPa) pot
pressure should be used to achieve the least thinning percentage ~ 6.5%.
Table 5.6- Percent thinning affected by the applied pot pressure while keeping the other
process parameters constant (BHF ≈ 2.2 kiPs, punch stroke = 0.56 in, cycle time = 20 sec,
average temperature = 150°C)
Sample
#
Set pot
pressure
(psi)
Max.
thinning
(%)
Max.
thinning
location
Max. output
pot pressure
(psi)
23 500 6.54 Reverse bulge
region 592.5
27 1000 8.51 Reverse bulge
region 834.6
28 2000 8.56 Reverse bulge
region 842.5
The results compared in Figure 5.10 indicate that the flange perimeter
measurements, Ff from the experimental and FE predictions match very well.
There was only a small difference (0.5%) in the values of the final flange
perimeter determined by FE simulation and experimental measurement.
66
Figure 5.10- Comparison of flange perimeter measurement and prediction between initial
blank and final part after SHF-P at room (Sample#5) and elevated (Sample#33)
temperatures
5.5 Conclusions
FE modeling of the SHF-P process at room and elevated temperatures with the
assumption of isothermal conditions was completed using PAM-STAMP 2G Ver.
2009. Simulation results compared favorably with experimental measurements.
The experimental values of the process parameters (i.e. fluid pressure) were
input into the FE model to emulate similar conditions. The final flange perimeter
(Ff) predictions for both room and elevated temperature were within ± 0.5% of
the experimental results. For the elevated temperature case, there was some
difference in the part profile in the reverse bulge region. This difference could be
caused by artifacts of springback and thermal distortion as the part cooled to
room temperature or by thermal gradients within the part during the forming
Initial Perimeter SHF-P at Room Temp SHF-P at Elevated Temp44
46
48
50
52
54
1118
1168
1219
1270
1321
1372
(Sample #5)
Fla
nge P
erim
ete
r (in)
(Sample #33)
Initial Perimeter SHF-P at Room Temp SHF-P at Elevated Temp44
46
48
50
52
54
1118
1168
1219
1270
1321
1372
(Sample #5)
Fla
nge P
erim
ete
r (in)
(Sample #33)
FE Output
Measured
Initial Perimeter SHF-P at Room Temp SHF-P at Elevated Temp44
46
48
50
52
54
1118
1168
1219
1270
1321
1372
(Sample #5)
Fla
nge P
erim
ete
r (m
m)
(Sample #33)
Initial Perimeter SHF-P at Room Temp SHF-P at Elevated Temp44
46
48
50
52
54
1118
1168
1219
1270
1321
1372
(Sample #5)
Fla
nge P
erim
ete
r (m
m)
(Sample #33)
Measured
FE Output
67
process. The maximum thinning for the room temperature drawn part was
predicted to occur near the punch corner region. For elevated temperature,
however, the maximum thinning location occurred within the reverse bulge
region of the part. Simulation of thickness strain or thinning distribution across a
curvilinear length of the part matched reasonably well with the experimental
measurements. This study also shows that the SHF-P at elevated temperature
can form a cup with larger cup height and better reverse bulge profile than SHF-
P at room temperature.
68
CHAPTER 6 Case studies in sheet metal forming at elevated
temperature
6.1 Warm Forming of MgAZ31B sheet alloy
In warm forming, the punch is cooled in order to selectively cool the sheet that
comes in contact with the punch, while the flange is kept at higher temperature
to promote easy material flow into the die. Having the right temperature
distribution in the part during forming, is a key factor in improving formability
with the warm forming process. The use of FE simulations will help in a
systematic development of elevated temperature forming processes minimizing
the number of the expensive and time-consuming experimental tryouts.
Non-isothermal stamping processes of these materials have been done at
ERC/NSM in the past using the commercial codes DEFORM 2D, DEFORM 3D
[Palaniswamy 2004, Kaya 2008], commercial code LS-DYNA 9.70 [Spampinato
2006] and PAM-STAMP 2G 2007 [Braga 2008]. There are still unsolved issues in
the non-isothermal FE simulations of elevated temperature sheet forming
processes, namely, (a) reliability of flow stress data, (b) yield function, (c)
interface heat transfer coefficient (d) friction coefficient between sheet and tools
[Braga 2008].
69
In this study the new version of commercial FE code PAM-STAMP 2G 2009 has
been used to simulate warm deep drawing of magnesium alloy AZ31B-O, since it
is now able to conduct heat transfer calculations and allows modeling the flow
stress as function of strain rate and temperature simultaneously. Flow stress data
is input in a tabular form and can be extrapolated linearly beyond the given
input strain values. Temperature distribution, punch load-stroke curves and
thinning distributions in the sheet obtained in experiments [Kaya 2008],
[Spampinato 2006] were compared with FE simulation results for various
forming conditions.
6.1.1 Summary of Inputs for PAMSTAMP v. 2009 Simulation
Values of thermal properties, contact definitions and other material property
inputs for PAM-STAMP are summarized in Table 6.1. Please note that the values
are similar to those used in [Braga, 2008].
Table 6.1- Thermal and mechanical data used for warm forming simulations of
Mg AZ31-O [Braga 2008]
Thermal conductivity 77 W m-1C-1
Specific heat capacity 1020 J kg-1 C-1
Heat Transfer Coefficient (HTC) sheet-punch
1 kW m-2 C-1 HTC sheet-die
HTC sheet-blank holder
Fraction of mechanical work converted to heat 95%
Friction coefficient sheet-punch
0.04 (PTFE film Vac-Pak HT-620) Friction coefficient sheet-die
Friction coefficient sheet-blank holder
Young‘s modulus E (room temperature) 45 GPa
Poisson‘s ratio 0.35
70
6.1.2 Results for FE Simulations and comparison with experiments
Figure 6.1 gives a schematic view of the warm forming tooling used in Kaya‘s
study [Kaya, 2008]. Blank is initially placed on the bottom die/blank holder. The
top ram moves down till it touches the blank and dwells. During this dwell time,
the blank is heated to the required temperature by the heated die and blank
holder. After the dwelling period, the top ram moves further down against the
stationary punch (which is cooled to room temperature) to form the sheet.
In this study, only forming operation was simulated, while analyses of heat
transfer during dwelling and change in tool temperatures were neglected. In FE
simulations, it assumed that a blank was heated to uniform temperatures of 250-
300 C, according to the measurement given in Kaya‘s study [Kaya, 2008].
Although the punch could be gradually heated up by the blank in reality,
simulation assumed tool temperature as constant and above room temperature,
about 60-70 C. Test conditions were simulated, as shown in Table 6.2.
Figure 6.1- Schematic of warm forming tooling [Kaya 2008]
71
Table 6.2- Test conditions from [Braga 2008] were selected for preliminary simulations
Case
no.
Draw
Ratio
(Sheet diam. /
punch diam.)
Die-blank
holder
Temperature
[⁰C]
Punch
Temperature
[⁰C]
Stroke
(cup
height)
[mm]
Forming
velocity
[mm/s]
Blank
holder
force [kN]
1m 3.0 300 70 65 5 Linearly
increasing
from 1.1 to
4
2m
3m 2.7 55 35
4m 2.8 12
5m 2.7 250 60 48 10
Figure 6.2 shows a comparison of the temperature on the bottom cup during the
process between the experimental results and 4 simulations with different HTC
values (HTC= 1 and 4 kW/m2/C) and PAM-STAMP versions (2007 and 2009).
Same value of HTC was considered for all contacts (i.e. sheet-punch, sheet-die,
sheet- blankholder). The values of HTC were chosen following our previous
work in [Kaya, 2008; Braga, 2008]. From Figure 6.2, simulation with HTC of 1
kW/m2/C predicted the sheet temperature close to the experiment and this HTC
value was applied for all warm forming simulations for Mg alloy. Also from
Figure 6.2, there is no difference in temperature predictions between 2 different
versions of PAM-STAMP.
72
Figure 6.2- Temperature vs Punch stroke at Point (P1) using variable HTC [CASE 1m:
Draw Ratio= 3, Punch stroke=65 mm , Forming velcity= 5 mm/sec]
73
Figure 6.3- Comparison of the results from FE simulations and experiments of CASE 1m,
for thinning distribution and punch load vs. stroke
Figure 6.3 shows the thinning distributions and load-stroke curves for Case 1m
(drawing ratio = 3, forming velocity = 5 mm/s, initial sheet temperature = 300
C, stroke = 65 mm). Comparison was made between the results from simulation
using PAM-STAMP ver. 2007 and PAM-STAMP ver. 2009, and the experimental
data. Both PAM-STAMP versions are able to predict thinning distribution very
close to the experiment. However, PAM-STAMP ver. 2009 predicts stamping
load closer to the experiment. PAM-STAMP ver. 2007 overestimates the
maximum load by 67%. This may be due to the assumptions of constant strain
rate throughout stamping process and uniform strain rate for the whole regions
of the sheet. This limitation has been resolved in PAM-STAMP ver. 2009.
74
Figure 6.4 shows similar comparison for another case, Case 4m (drawing ratio =
2.8, forming velocity = 12 mm/s, initial sheet temperature = 300 C, stroke = 55
mm). Again, PAM-STAMP ver. 2009 predicts load closer to the experiment than
PAM-STAMP ver. 2007.
Figure 6.4- Comparison of the results from FE simulations and experiments of CASE 4m,
for thinning distribution and punch load vs. stroke
75
6.1.3 Conclusion
By using the PAM-STAMP 2G ver. 2009, the accuracy of the predictions
improved significantly by introducing a material model to describe flow stress as
function of both temperature and strain rate simultaneously. In particular, the
punch load results match closely with experimental using PAM-STAMP ver.
2009, which were predicted 50% higher than the experimental results in the
previous version (ver. 2007) of PAM-STAMP, possibly due to the constant strain
rate assumption used in the material model at elevated temperature.
For magnesium alloy AZ31B-O, the best value of the interface heat transfer
coefficient (HTC= 1 kW/m2/C) was chosen by comparing the experimental cup
bottom temperature during the process with the simulations results.
76
6.2 Hot Stamping/Forming of 22MnB5 Steel to form experimental part
In this case study, we will see the non-isothermal hot forming of 22MnB5 sheet to
form an automotive part. Hot stamping/forming is the second category of
forming above recrystallization temperature as mentioned earlier. The actual
process cycle for hot stamping involves: 1) Heating of the blank to its
austenization temperature, 2) Transferring the blank from the furnace to the die,
3) Forming operation and 4) Quenching of the formed part by holding it within
the tools after the forming process is completed.
6.2.1 Objective
The objective of this study was to develop a method through finite element
simulations using PAM-STAMP to perform the Hot Stamping- Forming
operation only.
Specific objectives were to:
a) Predict the flow of material during deformation of the blank.
b) Estimate the thinning distributions along a section of the final part and
compare them with the experimental results.
6.2.2 FE Setup
The 3-D surface parts of the geometry were provided by the sponsor company.
These models were then input to Altair Hypermesh software to generate a
refined mesh in the curved regions of the part. The material properties listed in
Table 6.3 and the process parameters listed in Table 6.4 are obtained from the
literature [Numisheet 2008].
77
Table 6.3- Material Properties for 22MnB5 Sheet
Material property Symbol Value
Young‘s Modulus E 100 GPa (constant)
Poisson‘s ratio ν 0.3 (constant)
Flow stress data for 22MnB5
Function of Temperature and Strain rate
[Numisheet 2008]
Thermal conductivity k 32 W/mK (constant)
Specific heat capacity cp 650 J/KgK (constant)
Heat transfer coefficient-between sheet and tooling
HTC Function of pressure
[Numisheet 2008]
Table 6.4- Process Parameters in Hot stamping- Forming operation only
Process Condition Symbol Value
Upper die and blank holder velocity
V Assumed constant
Lower die
Constrained in all directions
Temperature of blank at the beginning of forming
process Tf
Above austenization temperature ~ 700-750 °C
Temperature of tooling-upper die and lower die
Tt 30 ⁰C (assumption)
Coefficient of friction µ 0.4 (constant)
6.2.3 FE Results and comparison with the experimental data
The FE prediction of the material flow under the given setup and process
condition is shown schematically in Figure 6.5. The lower die is held stationary;
78
whereas the upper die and blank holder move down to deform the work piece.
In this FE setup, the distance between the upper and the lower die minus the
initial thickness of the blank was used as the stopping criteria.
Figure 6.5- Steps in the Forming stage at a) Initial position and b) Final position
The thinning distribution obtained from simulation was compared with
experimental data along one section of the formed part. It was found that the
overall trend of the thinning distribution predicted by the simulation closely
follows the experimental thinning distribution. The maximum thinning
calculated by the FE model is approximately 10.1%, which is quite close to the
experimental values of maximum thinning (approximately 13%). Thus, overall
thinning predictions can be considered to be in fairly good agreement.
Upper die
Lower die
Blank Holder Blank
79
6.2.4 Future Work
Following are the activities that could be performed in the near future on this
topic/ case study:
1) Since PAM-STAMP 2G 2011 can now handle heat transfer within the tools,
quenching simulations can be done for this case study and the results will
be validated against experimental data.
2) Finally, the microstructure analysis on the quenched part can be carried
out. This feature is built-in with the material model in PAM-STAMP 2G
2011.
80
CHAPTER 7 Discussion, Conclusion and Future Work
7.1 Discussion and Conclusions
7.1.1 Determination of the flow stress at elevated temperature
Experiments:
Experimental tests at elevated temperature were conducted for AA5182 and
MgAZ61L alloys at ITC using gas as pressure medium.
Experimental data of Pressure vs Bulge Height could be obtained for
samples which burst during forming. This was possible using the
sophisticated camera device which took a lot of pictures during the forming
process. And then using these images the data for Pressure, Strain, Bulge
height and thickness could be found.
Experiments could be controlled at a linear Pressure Rate of 0.1, 0.5 and 2.5
MPa/sec and stopped either by specifying a pressure or a strain limit.
FE Inverse Analysis Technique:
Surface Response method to determine flow stress data at elevated
temperature through VPB tests has been developed
81
Surface response method calculates a minimum of an Error function (Ej)
by comparing the experimental result (Pressure vs Bulge Height) with FE
database
Flow stress data has been predicted for AA 5182 and Mg AZ61L alloys
using the experimental data taken from ITC at a linear Pressure Rate of
0.5 MPa/sec
The approximated K, n, and m values were limited to the flow stress
coefficients that were simulated using the FE code and stored in the FE
database. Because of this limitation, the MATLAB code predicted different
combinations of K, n and m values at the same temperature conditions.
Further, expanding the FE database to include more combinations of K, n
and m could result in a better prediction of the flow stress coefficients.
The corresponding flow stress curves obtained by applying the surface
response methodology to the elevated temperature bulge test predicted a
higher flow stress data when compared to the data available in the
literature [Abbedrabbo 2006 and Abbedrabbo 2007] obtained using tensile
tests at a constant strain rate. This discrepancy may be due to different
reasons. First, the sample pre-bulging observed in the experiments.
Second, data in the literature was tensile data conducted at a constant
strain rate = 0.0083 s-1.
82
7.1.2 Design of Sheet hydroforming with Punch Process (SHF-P)
Experiments:
Experiments were conducted using Sheet hydroforming with Punch at
room and elevated temperature at the G.M. Tech Center for AA 5754-O
alloy. The process parameters (blank holder and pot pressure) have been
recorded earlier that were used to form these samples.
Flange perimeter measurements, bulge height, part profile and thickness
measurements on the formed samples were taken in order to compare
them with the FE predictions.
FE Simulations:
FE simulations were conducted for SHF-P at room and elevated
temperature using the isothermal assumption using the code PAM-
STAMP. The FE predictions were then compared to the experimental
measurements to validate the results.
Results show that the FE predictions of final flange perimeter, location of
the maximum thinning and part profile seem to match fairly well to the
experimental measurements taken
83
7.2 Future Work
7.2.1 Determination of flow stress at elevated temperature
Apply the same Surface Response Methodology to predict the flow stress
coefficients at Pressure Rate of 0.1 and 2.5 MPa/sec
Compare the flow stress data obtained using the Surface Response
method with the data available in the literature
Extend the FE database to more combinations of K, n and m
To develop the capability on the experimental device to control the strain
at the dome apex by controlling the flow rate of the pressurizing medium.
7.2.2 Simulation of SHF-P Process
Since the tooling (blank holder, lower die, punch and fluid) temperatures
used to conduct the experiments during the actual forming process were
not isothermal, ranging from 127 to 157C, elevated temperature FE
simulation was attempted using a non-isothermal model that considered
heat transfer. In this non-isothermal model, the initial temperature
conditions and the heat transfer coefficients were the required inputs of
the FE model, but this exceeded the capability of the FE code. The current
software used for this study did not allow modeling of the hydroforming
process (using the Aquadraw module) and heat transfer simultaneously.
There was also difficulty to define the heat transfer condition between the
fluid and the blank under non-isothermal conditions. ESI Group (USA) is
improving the capability of the PAM-STAMP code in order to model the
warm SHF-P process.
84
Future research in the continuation of this study would include additional
experimentation and FE analysis at higher forming temperatures (250C)
and warm forming of other materials (e.g. Mg alloys) using solid dies.
Furthermore, non-isothermal conditions will be modeled to study the
benefit of using a punch that is cooler than the remaining tooling
environment to enhance warm forming of sheet metal.
85
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