NOTE FOR REVIEWERS
This proposal relies heavily on breakthrough results and techniques from the prior
NSF project. It is vital to read the “Results from Prior Support” section of this
proposal before reviewing the remainder. This section, often seen as a formality, here
forms a major part of this proposal. The current proposal capitalizes on these advances,
extends them, adds novel developments, and applies all of these to the newest materials
being considered by automakers, including the first so-called “3rd Generation AHSS.”
BACKGROUND
Some classes of advanced high strength steels (AHSS), for example dual-phase (DP)
steels, are being used currently by automakers for their impressive combinations of
strength (for service performance) and ductility (for manufacturing, forming). They offer
many societal advantages via reduced vehicle mass and increased strength: energy
conservation, safety improvement, and reduced environmental impact.
However, widespread adoption of other, even more promising AHSS grades has been
limited by poorly-understood sheet-forming properties in the areas of springback and
shear fracture [1, 2]. (“Shear fracture” is the unexpected, premature failures occurring in
sharp bending regions). An estimate from the 1990’s for traditional steels put the
economic impact of springback among U.S. automakers at $50 million/ year. [3] This has
no doubt been multiplied by several times now for AHSS.
DP steels are the most widely used of the various AHSS available. These materials
feature coarse (composite-like) microstructures of a soft ferrite matrix and hard
martensite “islands.” The internal stress concentrations produce early yield, high work
hardening, and thus high tensile ductility (relative to the expectation for their ultimate
tensile strengths).
While the properties of DP steels are remarkable, unexpected problems were encountered
by automakers and steelmakers once pre-production tests began. The critical problem was
the unpredictability of springback and shear fracture. In 2007, at the start of the current
project, here referred to in short as Formability and Springback 1, these problems were
attributed by conventional wisdom to special micro-mechanisms related to the special
microstructure of DP steels. Many projects concerned with that aspect were initiated,
including Formability and Springback 1. That project was focused on revealing those
mechanisms and using the knowledge gained to guide the development of a new,
improved, generation of AHSS by collaborating with another NSF project at the
Colorado School of Mines (CMMI-0729114).
As outlined in the next section, Formability and Springback 1 upended the conventional
wisdom. For a variety of DP steels tested and simulated, the formability and springback
behavior could be predicted accurately by employing properly formulated constitutive
equations and simulation methods. Only continuum models were needed. The details of
R. H. Wagoner
Formability and Springback 2
Page 2
the microstructures were irrelevant for most of the materials, except in one isolated case
likely related to improper processing.
The proposed work will extend the results and methods developed in Formability and
Springback 1 to more complex, and even more promising, AHSS. Materials to be tested
and simulated include the following:
 TRIP (transformation induced plasticity) steel
 TWIP (twinning induced plasticity) steel
 CP (complex phase) steel
 QP steel (quench and partition, a 3rd-Generation AHSS developed in part by CMMI0729114).
Because these alloys feature complexities such as microstructural transformations during
forming, developing and verifying the application of appropriate constitutive models will
be even more challenging.
The materials will be provided by the industrial partners (Auto/Steel Partnership and its
members, particularly General Motors and Chrysler). QP steels in small quantities will be
provided by the Colorado School of Mines and in larger quantities by Chrysler (originally
from Bao Steel USA, the first company to produce significant quantities of this 3rdGeneration AHSS).
RESULTS FROM PRIOR SUPPORT
Formability and Springback 1: “Sheet Formability and Springback of AHSS,” CMMI0727641, 10/07-3/11, R. H. Wagoner, $337,262. Collaborative with CMMI-0729114,
Colorado School of Mines.
Formal Outcomes: References attributed to Formability and Springback 1: [1-18]
Project Publications include 12 publications in print (1 peer-reviewed [1], 11 conference
proceedings [2-12]), 3 publications submitted and currently under review [13-15] and 3
publications under preparation [16-18].
The following personnel were developed in to Formability and Springback 1 as listed:
 Ji Hoon Kim was a Post-Doc, now a Research Scientist, Korea Institute of
Materials Science. Constructed a coupled, thermo-mechanical, finite element
model of the draw-bend test. [1, 3, 4, 7-12, 15, 16, 18]
 Ji Hyun Sung received his Ph. D. in Winter 2010, now a Senior Researcher, Korea
Institute of Industrial Technology. Formulated H/V model and conducted various
DBS/ DBF experiments. [1, 3-11, 15, 16, 18]
 Hojun Lim received his Ph. D. in Spring 2010, now a Post-Doc at OSU.
Conducted DBS tests and time-dependent springback of AHSS. [5, 6, 9, 16]
 Li Sun, graduate research assistant, is supported at OSU. Performed nonproportional path testing and formulated QPE model [9, 12, 14]
2
R. H. Wagoner
Formability and Springback 2
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 Kun Piao, graduate research assistants, is supported at OSU. Developed elevated
temperature C/T testing fixtures and conducted experiments and simulations of
tensile tests. [17]
 Mike Gram received his M. S. in Summer 2010. Developed a set of material
guidelines for fineblanking high strength steels. [2, 13]
Technical Summary: Advances made by Formability and Springback 1 can be
summarized as follows (and are presented in detail in the remainder of this section):
1) Novel Draw-Bend Springback (DBS) and Failure (DBF) Tests. [18] The drawbend test has two important characteristics not otherwise available: a) it
reproduces the conditions of a sheet forming operation as the sheet is drawn into
the die cavity, and b) it allows precise control and recording of draw-in
displacements, sheet tension, and friction conditions over a wide variety of
bending ratios and rates. These tests correlate with sheet forming practice and are
amenable to thermo-mechanical finite element simulation. Use of these tests led
directly to the remaining advances in this project. The DBS test was previously
devised whereas the DBF test was modified to give much more reproducible and
revealing results.
2) H/V Model. [1] This new 1-D plastic constitutive model relates flow stress to
strain, strain-rate, and temperature. It captures in particular the critical change of
strain-hardening over temperature ranges generated in sheet forming operations
by deformation-induced heating. These temperatures are typically up to 100 deg.
C for AHSS vs. 30 deg. C for traditional steels. This model proved essential for
understanding the DBF formability as well as tensile ductility of DP steels.
3) QPE Model. [14] This novel approach answers the question of how to treat
nonlinear unloading following deformation, as is observed widely. It introduces a
new class of strain, “quasi-plastic-elastic” (QPE) strain that is reversible like
elastic strains but energy absorbing like plastic strains. Previous methods relied on
modified elastic moduli (sometimes depending on forming strain) that had no
clear method for general application (for arbitrary 3-D loading and paths) and
which were found to be inadequate for predicting springback accurately.
Simulations of DBS results gave predictions within the experimental scatter when
using the QPE model, but not for other proposed constitutive approaches.
Each of these advances is introduced in this section, along with references to the principal
results and conclusions. These are the starting points for the research proposed here.
Draw-Bend Fracture (DBF) and Draw-Bend Springback (DBS) Tests [18]: The
draw-bend test, originally developed for measuring friction and wear [19-22], was
developed by the PI’s group for springback [23] and fracture applications [24]. The
principles of the test are shown in Fig. 2 (a). A strip of sheet metal (typically 25mm or
3
R. H. Wagoner
Formability and Springback 2
Page 4
50 mm wide by approximately 750 mm long) is formed around a circular tool (typically
fixed and lubricated) and then subjected to boundary conditions applied by a dualactuation control system through grips fixed to the ends of the strip specimen.
In Formability and Springback 1, two versions of the test were used. First, a novel
version of the DBF test was developed and used extensively [18]. It was shown to be
more reproducible and consistent than previous tests. The boundary conditions are as
follows: V1= constant velocity, V2= constant velocity lower than V1. Thus, there is no
reversal of strip motion (which is inherent in past control schemes but contrary to
industrial practice). Mechanically, the test looks much like a tensile test with bending and
unbending superimposed on the fixed extension rate of the specimen.
The DBF test reliably reproduced three kinds of failures and the transitions among them
for DP steels. The three types, shown in Fig. 1 (b), are as follows: Type I (tensile
fracture), Type II (mixed fracture), and Type III (shear fracture). For the boundary
conditions that reproduce industrial practice most closely, i.e. V1 > 50 mm/s, V2 = 0
mm/s, only Types I and III are typically observed, and the transition in type and in
displacement to failure indicate the susceptibility of shear fracture (as opposed to tensile
fracture as is well-represented and understood routinely by forming limit diagrams [2529]).
R

F1, V1
Uf
F2, V2
Figure 1: Schematic and variables of the draw-bend tests (left side) and the three
types of fractures observed in the draw-bend fracture (DBF) test (right side).
The game-changing breakthrough in the understanding of shear fracture occurred when it
was noticed that the occurrence of shear fractures increased dramatically at higher
pulling speeds. And, it should be noted, the highest tested strain rates (2-3/s) are several
times smaller than industrial strain rates (typically 10/s).
This observation led to the postulate that deformation-induced heating was the critical
factor promoting unpredicted shear fractures of AHSS. The theory was that AHSS,
because of their high energy product (work per volume under the stress-strain curve to
fracture), produce significantly more heat than traditional steels. Furthermore, at the high
industrial forming rates, the deformation is nearly adiabatic.
4
R. H. Wagoner
Formability and Springback 2
Page 5
Figure 2: Temperature change measurement with an infrared camera: (a) setup of FLIR-A40
infrared camera, (b) thermal image of DP980 (A) [1]
This theory has now been confirmed by infrared thermographic measurements (Fig. 2),
and comparison with a series of thermo-mechanical FE simulations using two other
developments made in Formability and Springback 1: a) the H/V constitutive model
(next section), and b) measured thermal properties (heat transfer coefficients, plastic
work conversion efficiency, etc.).
These developments have been presented (or are in progress) in several key publications
[1, 3, 4, 7, 15, 18], but an outline of the evidence is presented here. First, Fig. 2 (b) shows
temperature rises near (but not at) the fracture surface up to about 94 deg. C. For the three
grades of DP steels tested at various rates and R/t ratios, the measured temperatures
agreed with the independently-simulated ones to within 5 deg C. Second, the
displacements to failure were predicted to within an average of 15% error thermomechanically, as compared with 65% error isothermally, Table 1. Isothermal, low rate
simulations and measurements of formability are standard industrial procedures, hence
the unpredictability of shear fracture using these technologies.
Table 1: Comparison of the observed and predicted failure elongation and error for
the draw-bend formability of three grades of DP steels.
Material
R/t=2.2,3.3,4.5,5.7
DP 590
DP 780
DP 980
Average
Measured
U1
44 mm
31 mm
22 mm
Isothermal FE
U1
Error
61 mm
44%
49 mm
68%
37 mm
83%
65%
Thermo-Mech FE
U1
Error
46 mm
6%
33 mm
7%
27 mm
31%
15%
H/V Model [1]: Deformation-induced temperature rises affects formability via the
temperature-sensitivity of the plastic flow stress. While this has been safely ignored
during most of the 110 years or so of mass production by sheet forming, the new AHSS
exhibit much higher forming temperatures. By extensive isothermal tensile testing, the
critical aspect of AHSS behavior was identified as the sensitivity of strain hardening to
temperature. Unfortunately, existing temperature-dependent constitutive equations for
plasticity did not capture this aspect adequately.
5
R. H. Wagoner
Formability and Springback 2
Page 6
Therefore, an empirical 1D plasticity constitutive form describing the flow stress as a
function of strain, strain-rate, and temperature was developed in Formability and
Springback 1 [1]. The function consists of three multiplicative functions describing (a)
strain hardening (f), (b) strain-rate sensitivity (g), and (c) temperature sensitivity (h) as
follows:
(1)
s = s (e , e ,T ) = f (e ,T )× g (e )× h (T )
The functions g and h are standard forms, but the function f is novel. It combines, using a
linear combination coefficient a, the two typical novel strain hardening forms fh
(Hollomon or power-law hardening [30] and fv (Voce or saturation model hardening [31]:
(2)
f ( , T )   f H  (1   ) fV
The parameter  is allowed to vary linearly with temperature, such that at low
homologous temperatures the expected power-law hardening is obtained (i.e. =1) while
at higher temperatures a saturation stress is observed (i.e. =0).
The forms shown in Eqns. (1) and (2) have been shown to reproduce the tensile behavior
of DP steels accurately, Fig. 3, even in the post-uniform (necking) region. The H/V
model improves not only on the non-isothermal behavior (Fig. 3 (a)), but also the
isothermal behavior (Fig. 3 (b)) by extrapolating more accurately to higher strains
encountered in the post-uniform strain regime.
Engineering Stress (MPa)
1000
800
Initial Temp: 25 deg. C
Nonisothermal
dε/dt: 10-3 /s
DP980
DP780
DP590
600
400
200
0.00
Experiment
Voce
H/V
Hollomon
Engineering Stress (MPa)
800
1200
Experiment
600
Voce
400
0.10
0.15
0.20
0.25
Engineering Strain
(e
DP590
200
f
o
100 C (isothermal)
-3
d/dt =10 /s
0
0.05
H/V
0.30
0.35
0
0.05
0.1
FE
-e
Hollomon
Expt
)/e
f
Expt
f
X 100%
Voce: -8%
H/V: 2%
Hollomon: 39%
0.15
0.2
0.25
0.3
Engineering Strain
Figure 3: Comparison of tensile data and FE simulations using selected constitutive
models: (a) nonisothermal tests, and (b) isothermal tests.
Table 2 compares the predicted tensile elongations to failure using standard isothermal
models (Hollomon and Voce) and proposed non-isothermal models (Lin-Wagoner [32],
Rusinek-Klepaczko [33]). All of the models were fit to the same data using the fit
techniques recommended by the proposers of each model. The prediction accuracy of
the new H/V Model average is within 5% engineering strain, as compared with 19-42%
error for previous constitutive descriptions.
Table 2: Accuracy of simulated total tensile elongations for isothermal tensile tests
The numbers represent averaged percentage errors for tests at 25, 50, and 100 C.
Matl.
Lin-Wagoner
model [32]
Rusinek-Klepaczko
model [33]
Hollomon
model [30]
Voce
model [31]
H/V
model [1]
6
R. H. Wagoner
DP590
DP780
DP980
Avg.
Formability and Springback 2
19
21
18
19
30
47
50
42
23
21
29
24
Page 7
19
22
23
21
3
5
6
5
The most compelling evidence is the highly accurate thermo-mechanical prediction of
draw-bend failures using the H/V Model, Table 2. This deformation and these failures
occur in a distinct complex strain state involving much higher strains.
QPE Model [14]: Springback of AHSS has been a significant problem inhibiting their
adoption since their inception. Not only is the springback larger, in many cases
comparable to that of aluminum alloys, it has been resistant to simulation and prediction.
Research in Formability and Springback 1 clarified two aspects of the problem:
1. DP steels show the largest “variable modulus effect” [34-45] ever reported, with
unloading occurring at an effective Young’s modulus up to 22% less than the
published value. [36]
2. Contrary to traditional steels, DP steels exhibit time-dependent springback [16]. That
is, the springback magnitude changes for months following forming.
For the first time, a consistent description of nonlinear unloading (“QPE Model”) was
proposed and developed. It was also implemented, tested, and verified. The QPE model
introduces a third component of strain that is recoverable (elastic-like) but energy
dissipative (plastic-like). In a natural way it produces nonlinear loading and unloading
curves following stress/strain path changes. It is a general 3-D model implemented in FE
codes that allows prediction of unloading behavior that depends on strain path and
residual stress.
The QPE model captures accurately all known features of the so called modulus effect, as
shown in Fig. 4 (a). The initial unloading following plastic deformation occurs
elastically according to the handbook value of Young’s modulus, until some critical
stress is reached. At that point, a new constitutive behavior representing QPE is entered,
with corresponding nonlinear unloading and energy absorption. Reloading follows a
similar process, again transitioning from elastic behavior to QPE behavior and finally to
plastic/elastic/QPE behavior at yielding.
Fig. 4 (a) shows that the model fits the measured behavior accurately, whereas typical
chord models or complex elastic-plastic models do not. Fig. 4 (b) and Table 3 show that
springback predictions based on the QPE constitutive behavior are much more accurate
than existing models.
7
R. H. Wagoner
Formability and Springback 2
1200
Page 8
50
DP980-10-3
DP980-QPE-fine
DP980-DE
plastic model
DP980-1.43
0
-50
800
Y (mm)
True Stress (MPa)
1000
C /3-Param
0
600
-100
-150
Measure d
DP980(D)
Back force: 0.6y
V: 25.4 mm/s
R=6.35 mm, t=1.45 mm
R/t=4.38
Secant modulus
Model
0
Chaboche Model
56.09
400
43.87
-200
Chord m odel
54.66
200
0
QPE Model
0
EXP: 53.9
-250
0
QPE model
0
0.032
0.034
0.036
0.038
True Strain
0.04
-300
-200
0.042
-150
-100
-50
0
50
X (mm)
Figure 4: Comparison of QPE Model with existing constitutive approaches for DP
980: (a) unloading and reloading following tensile deformation, (b) draw-bend
springback prediction.
Table 3: Draw-bend springback simulation accuracy for various constitutive
models.
DP 980
Chord/ Iso
C0/ Chaboche
Chord/ Chaboche
QPE/ Chaboche
(Fb=0.3, 0.6, 0.8, 0.9)
18.0
8.5
5.3
2.6
A new phenomenon, time-dependent springback, was discovered by the PI’s group in the
late 1990’s [23]. It was found to occur for aluminum sheet-forming alloys but not typical
sheet-forming steels of that period. It was attributed to room-temperature creep driven by
high residual stresses [46].
Work under the auspices of Formability and Springback 1 showed that all of the AHSS
tested (DP600, DP800, DP980 and TRIP780) exhibited time-dependent springback, thus
making accurate prediction of the effect more complicated. The early shape changes
were proportional to log time for the first few days to weeks following forming, after
which the rate of change diminished relative to that behavior. The rate of time-dependent
shape change of AHSS was approximately ½ of that observed for the aluminum alloys.
Preliminary residual stress driven creep simulation using shell elements with von Mises
yield function and isotropic hardening showed good qualitative agreement for initial and
time-dependent springback.
PROPOSED WORK
The results introduced in the previous section redefine the current understanding about
the formability and springback of DP steels. They provide a way forward for solving the
application problems of other advanced alloys; those advances will be leveraged fully in
the new work. They do not, however, directly answer all of the most pressing questions
about other AHSS. The current proposal thus focuses on two major objectives:
8
R. H. Wagoner
Formability and Springback 2
Page 9
a) applying the previously-devised techniques to newer alloys to clarify their behavior
and predictability with respect to formability and springback, and
b) developing new, better ways to determine the behavior of each class of alloys.
Technical Need: While Formability and Springback 1 showed that the unexpected
forming and springback behavior DP steels is not related to their unique microstructural
characteristics, one set of tests for one material and one direction (among the 15
combinations tested) contradicted this conclusion. One DP 980 steel from one supplier
exhibited brittle fracture, but only in the transverse direction (TD). This has now been
attributed to a mistake in processing, but the new materials may exhibit very different
behavior in this regard.
Two lessons were learned:
1. Brittle fracture of some microstructures can occur and may in fact be significant
among other advanced alloys. This means that the newer classes of AHSS must be
tested and simulated to draw similar (or contrary) conclusions. Furthermore, multidirectional testing of new AHSS is required to explore microstructural anisotropies
(which were generally absent in DP steels).
2. For practical application as well as improved fundamental understanding, it will be
beneficial to measure the local formability, i.e. a critical strain where ductile strain
localization turns into fracture. This will be addressed by combining digital image
correlation (DIC) techniques with DBF tests.
There was no reliable way at the time of Formability and Springback 1 to measure the
plastic flow stress at the critical combination of high strain (well beyond the uniform
tensile limit) and at elevated temperatures. This made the accurate extrapolation of tensile
hardening to large strains, made possible by the H/V Model, essential. This aspect will be
addressed in the current work by conducting elevated-temperature balanced biaxial bulge
tests which are being developed collaboratively at the Pohang Institute of Science and
Technology.
Formability and Springback 1did not address local fracture problems, rather it focused on
the influence of continuum constitutive behavior (which was found sufficient if all its
facets were measured accurately enough). In order to gain a more fundamental
understanding of the transition from plastic localization to fracture, local measurements
will be taken in the proposed work. Digital image correlation (DIC) will be used in
conjunction with existing DBF tests, as well as a new DBF method to be developed that
promises to be more sensitive and also more amenable to DIC analysis.
Project Overview: Therefore, the three new aspects of the proposed project are as
follows
1. The new work extends the advances to newer, more complex materials:
 TRIP steel (transformation induced plasticity)
 TWIP steel (twinning induced plasticity)
 CP steel (complex phase)
9
R. H. Wagoner
Formability and Springback 2
Page 10
 QP steel (quench and partition, the first 3rd-Generation AHSS)
2. The new work develops novel techniques to refine the constitutive modeling and local
fracture criterion:
 Non-proportional path testing (tension/ compression), incorporation in 3-D
constitutive equations
 Elevated-temperature balanced biaxial bulge testing
 Digital image correlation (DIC) of DBF specimens; local fracture criterion
 New design for draw-bend fracture test
 Measurement of draw-bend formability vs. direction
3. Formulation of research formability data and simulations into practical guidelines for
industrial application.
Project Schedule: The plan for the proposed work is as follows:
Year 1: Materials/ Sheet characterization
 Material characterization (uni-axial, tension-compression, compression-tension,
loading-unloading tests) for various temperatures, orientations (RD and TD), and
strain rates.
 Balanced bi-axial bulge tests (room temperature and elevated temperature).
 Materials scatter tests.
 Sheet characterization (center to edge effect).
Year 2: Constitutive modeling/ DBF and DBS testing
 Devise a DBS test to characterize springback of candidate materials.
 Devise a DBF test for various tool radii and v1/v2 ratio to generate failure map.
 Conduct DBF test for different orientations (anisotropy effect).
 Setup 3D DIC with DBF tests for imaging local strains.
Year 3: Prediction of formability and springback
 Simulation of springback using QPE model.
 Simulation and prediction of post-uniform deformation of AHSS using thermomechanical model (H/V model).
 Establish practical guidelines to be used for industrial application.
Materials: The newer, even more advanced materials to be used in the proposed work
will likely have even more complex constitutive behavior. This is likely because in
general they rely on complex microstructures and deformation-induced structural changes
to achieve even higher combinations of strength and tensile ductility.
Table 4 shows candidate alloys. At least one alloy of each class will be subjected to a
full regimen of testing and simulation. A brief description of the principles of each alloy
is as follows:
10
R. H. Wagoner
Formability and Springback 2
Page 11
 TRIP steel is similar to a DP steel, except it has retained austenite at room
temperature that can transform to martensite during deformation, thus imparting high
strain hardening, particularly at high strains. The transformation rate depends not only
on strain, but also on temperature (and thus indirectly on strain rate) [1]. TRIP alloys
are being used in limited applications today.
 TWIP steel is similar to TRIP steel, except that the transformation that occurs during
straining is twinning rather than a phase change. TWIP steels currently have the
highest energy products of any sheet forming alloys, but their complex hardening
properties have so far inhibited their adoption.
 CP steels have extremely fine microstructures of ferrite, bainite, martensite, and
precipitation hardening phases. They offer modest formability with strengths up to
approximately 1000 MPa, while also producing bake hardening (in the standard paint
bake cycle used for automobiles) with an additional 70 MPa strength.
 QP steels represent the first available 3rd-Generation AHSS, as developed by the
collaborative project to Formability and Springback 1 at the Colorado School of
Mines (CMMI-0729114). Small quantities will be provided by CSM for testing; the
first large quantities of QP1000 are being acquired by the Auto/Steel Partnership from
Bao Steel USA. They will be provided to the project by A/SP or Chrysler. QP steels
are promising because the retain austenite by novel processing rather than by adding
large amounts very expensive alloying elements such as Ni or Mn.
Alloy
TRIP
TRIP
TRIP
TWIP
CP
CP
CP
CP
Q-P steel
Yield/UTS (MPa)
350/600
400/700
450/800
450/1000
500/800
700/800
800/1000
1000/1200
UTS 1000
Elongation (%)
29-33
24-28
26-32
50-54
10-24
10-15
8-13
8-10
?
Table 4: Typical mechanical properties for candidate alloys
Tension-Compression Testing: A new apparatus developed by the PI enables
continuous, large strain tension/ compression tests of sheet alloy specimen at elevated
temperatures, Fig. 5 [2, 3]. Using this novel device, complex hardening behavior of
candidate AHSS will be measured at range of strain rates and temperatures (up to 200C).
Fig. 6 shows one example of non-proportional path testing (tension/ compression) for DP
980 and prediction by QPE model [4]. In order to reproduce complex hardening effects
like Fig. 7, Geng and Wagoner model was introduced [5] to reproduce the strainhardening behavior adequately. Similar to Formability and Springback 1, obtained
experimental data will guide constitutive developments for candidate materials.
11
R. H. Wagoner
Formability and Springback 2
Page 12
1200
Monotonic tension
Absolute True Stress (MPa)
1000
800
C-T tests
600
DP980-1.43
400
200
0
0
Figure 5: Setup for tension/ compression test
at elevated temperature [3]
0.05
0.1
0.15
0.2
Accumulated Absolute True Strain
0.25
Figure 6: Comparison of QPE model predictions
with monotonic tension and compression-tension (CT) tests [4]
Elevated-Temperature Balance-Biaxial Bulge Testing: Previously, a roomtemperature bulge test was conducted to extrapolate the plastic flow stress beyond the
uniform tensile limit [6]. Fig. 7 shows comparison of three models, Hollomon, Voce and
H/V model, fitted for DP590 at small strain range from the tensile test. Three forms
reproduced measured stress-strain data equally well in the fit range, but the agreement
was best for the H/V model in large strain area, Fig. 7.
1000
DP590(B), RD
Hollomon <>=4MPa
-3
Effective Stress (MPa)
Strain Rate=10 /sec
900
o
25 C
H/V <>=1MPa
800
Bulge Test (r=0.84, m=1.83)
Voce <>=1MPa
700
Tensile Test
Fit
Range
600
0.1
Extrapolated, Bulge Test Range
0.2
0.3
0.4
0.5
0.6
0.7
Effective Strain
Figure 7. Large strain verification of H/V model [6]
The elevated-temperature balanced biaxial bulge tester, capable of testing up to 150 deg.
C will be used to test candidate materials at Pohang Institute of Science and Technology.
Balanced biaxial bulge results will test and verify H/V model’s prediction in large strain
area.
Digital image correlation (DIC) of DBF specimens: A three-dimensional digital image
correlation (3D DIC) photogrammetry is a non-contact measurement technique used to
determine the 3D shape, displacement, and full-field strain of tested sample [7]. A
12
R. H. Wagoner
Formability and Springback 2
Page 13
random pattern, generally using spray paint, is applied to the surface of the specimen and
the cameras save images of random patterns. These cameras have 1624 pixel by 1224
pixel resolution and can capture images at a maximum frame rate of 19 fps which is fast
enough for most experiments conducted on a servohydraulic load frame, Fig. 6 (b). Once
the camera images are saved, the pictures are uploaded into a digital image-processing
package to create a set of 3D coordinates for the imaging area. More detailed description
of the 3D DIC will be provided in the Facilities section.
3D DIC
R
Control of restraining force
(1) Load rate control mode
(2) Speed control mode
Uf
V1
(1)
F
V2 (2)
Specimen width: 25.4mm
Roller radii: 3.2, 4.8, 6.4, 7.9, 9.5, 11.1, 14.3, 19 mm
Figure 8: Draw-bend test (a) schematic of test and springback measures along with 3D DIC device.
(b) Two Point Grey GRAS-20S4M-C cameras for 3D DIC analysis
In the previous project, Formability and Springback 1, strain field of the sheet sample
was measured before and after the forming at GM to investigate fracture strain. In this
project, 3D DIC device will be attached to draw-bend tester to monitor the real-time local
strains of the sample during the forming, Fig. 8 (a). This novel experiment will provide
full strain fields of the sheet sample undergoing forming process that can be directly
compared with the draw-bend simulations and will lead the way to improved
implementation of fracture criteria for advanced high strength steels.
New design for DBF test: Draw-bend tester equipped with two-actuator velocity control
(dual-displacement control) and newly designed grips successfully reproduced three
types of forming failure for DP steels [8, 9]. A new version of DBF is envisioned that
will be developed and tested. In contrast to basic DBF test where the one side of sheet
sample is pulled at faster rate to draw the sample over the tool radius, formability of sheet
metal can be examined by pulling the sample with the same rate at each end but in
opposite direction (i.e., v1=-v2 from Fig. 8 (a)). A novel DBF testing has an advantage
that less material is required to perform the test (15 in. compared to 25 in. for regular DB
testing) and more amenable to analysis using DIC techniques because of the limited
surface displacements.
Measurement of draw-bend formability vs. direction: While most grades of DP steels
exhibited very little plastic anisotropy, one DP980 showed that the shear fracture
formability in the transverse direction (TD) was around 1/2 that of that in the rolling
13
R. H. Wagoner
Formability and Springback 2
Page 14
direction (RD), Fig. 9. The presumed cause of this high anisotropy is the alignment and
continuity of hard, brittle martensite particles. In a similar way, the formability for range
of sheet orientations will be tested for newer alloys. The information will be the first of
its kind, and will provide material data that will improve the accuracy of the fracture
prediction for complicated stamped parts.
Elongation to Fracture (mm)
30
0o
25
15o
30o
45o
20
60o
15
10
75o
DP980
R/t = 3.3
5
0
0
RD
RD
30
60
Angle to RD (degree)
90o
90
TD
Figure 9: Formability of DP980 for range of orientations
Practical guidelines for industrial application: In order to translate draw-bend fracture
information to industrial practice, two plane-strain models were constructed for DP
steels: one numerical (FE), and other analytical [9]. By assuming localized necking
initiate at the maximum tensile force, stress (and strain)-based failure criteria were
obtained and showed good agreement with each other, Fig. 10. The criteria obtained by
these simple models can be used to design the forming processes that exploit the real
formability of AHSS. In a similar manner, this procedure will be applied to newer alloys
to provide practical guidelines for industrial applications.
0.8
FE (rate sensitive, =0.06)
FE (rate insensitive, =0)
1200
1000
FE (finite width)
800
Analytical
600
DP980-1.43mm
Failure Strain at Outer Surface
Engineering Tensile Stress (MPa)
1400
0.6
Analytical
0.4
FE (rate sensitive, =0.06)
0.2
FE (rate insensitive, =0)
DP980-1.43mm
0
0
2
4
6
8
R/t
10
12
14
0
2
4
6
8
10
12
14
R/t
Figure 10. Failure criteria obtained by the plane-strain finite element and analytical
procedures (a) stress-based, and (b) strain-based.
14
R. H. Wagoner
Formability and Springback 2
Page 15
BROADER IMPACT
Broader impacts in three principal areas are anticipated: 1) Benefits to Society, 2)
Learning and Broadened Participation, and 3) Dissemination of Results.
Benefits to Society: Advanced materials with high specific strengths offer many societal
benefits in the form of better product performance, cost, safety (personal security),
energy savings, emissions (especially greenhouse gases), reliability and durability. In
spite of these strong driving forces, adoption of these materials is limited by unknowns
associated with design and manufacturing. These unknowns introduce uncertain tooling
and tryout costs, and uncertain product lead times which effectively bar their widespread
adoption and conferring of the potential benefits to mankind. Two kinds of potential
societal impact can be anticipated for replacing traditional HSLA steels with AHSS: 1)
energy savings, and 2) environmental impact.
Learning and Broadened Participation: The collaboration between OSU and GM will
provide exciting broadening opportunities for the funded Ph. D students. The PI will
develop educational modules that can be incorporated into MSE 661: Ferrous Metallurgy.
Dissemination of Results: The PI is committed to wide dissemination of results in peerreviewed journals, conference proceedings and lectures, graduate theses/ dissertations,
and undergraduate project reports.
REFERENCES
Note: References are numbered within each section of the proposal, as shown.
REFERENCES FROM NOTE FOR REVIEWERS SECTION
1.
Demeri, M.Y., Forming of advanced high strength steels, in ASM handbook, S.L.
Semiatin, Editor. 2006, ASM International: Materials Park: OH, USA.
2.
Horvath, C.D., Fekete, J.R. Opportunities and challenges for increased usage of
advanced high strength steels in automotive applications. in International
conference on advanced high strength steels for automotive applications. 2004.
Golden, CO, USA: Association of Iron and Steel Engineers.
3.
Wenner, M.L., Private communication. General Motors Corporation, March,
1996
REFERENCES FROM RESULTS FROM PRIOR SUPPORT SECTION
1.
Sung, J.H., Kim, J. H., Wagoner, R. H., A Plastic Constitutive Equation
Incorporating Strain, Strain-Rate, and Temperature. Int. J. Plasticity, vol. 26, pp.
1746-1771
15
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Formability and Springback 2
Page 16
2.
Gram, M., Wagoner, R. H. in Proc. NUMISHEET 2008. 2008. Interlaken
Switzerland.
3.
Kim, J.H., Sung, J. H., Wagoner, R. H. Thermo-Mechanical Modeling of DrawBend Formability Tests. in Proc. IDDRG: Mat. Prop. Data for More Effective
Num. Anal. 2009. Colo. School Mines.
4.
Kim, J.H., Sung, J. H., Matlock, D. K., Kim, D., Wagoner, R. H. Predicting Shear
Failure of Dual-Phase Steels. in NUMIFORM 2010, Proc. 10th Int. Conf. Numer.
Meth. Ind. Form. Proc. 2010.
5.
Lim, H., Lee, M. G., Sung, J. H., Wagoner, R. H. Time-dependent Springback. in
Procs. 11th Esaform 2008Conference on Material Forming. 2008: Springer.
6.
Padmanabhan, R., Sung, J. H., Lim, H., Oliveira, M. C., Menezes, L. F., Wagoner,
R. H. Influence of Draw Restraining Force on the Springback in Advanced High
Strength Steels. in Procs. 11th Esaform 2008Conference on Material Forming.
2008: Springer.
7.
Sung, J.H., Kim, J. H., Wagoner, R. H. Accurate Constitutive Equation for Dual
Phase Sheet Steels,. in Proc. IDDRG 2009, Proc. IDDRG: Mat. Prop. Data for
More Effective Num. Anal. 2009. Colo. School Mines.
8.
Wagoner, R.H., Kim, J. H., Sung, J. H. Formability of Advanced High Strength
Steels. in Proc. Esaform 2009. 2009. U. Twente, Netherlands.
9.
Wagoner, R.H., Sun, L., Sung, J. H., Kim, J. H., Lim, H., Schroth, J. G., Matlock,
D. K. Draw-Bend and Springback of Advanced High Strength Steels and Related
Constitutive Model. in Proceedings of 2009 NSF Engineering Research and
Innovation Conference. 2009. Honolulu, Hawaii.
10.
Wagoner, R.H., Sung, J. H., Kim, J. H. The Formability of Dual-Phase Steels. in
Proc. 2009 International Symposium on Automobile Steel (ISAS09). 2009. Dalian,
China.
11.
Wagoner, R.H., Kim, J. H., Sung, J. H., Formability of Advanced High Strength
Steels. Int. J. Mater. Forming, 2009. 2: p. 359-362.
12.
Sun, L., Kim, J. H., Wagoner, R. H. Non-Proportional Loading of Dual-Phase
Steels and its Constitutive Representation. in Proc. IDDRG 2009, Proc. IDDRG:
Mat. Prop. Data for More Effective Num. Anal. 2009. Colo. School Mines.
13.
Gram, M., Wagoner, R. H. , Fineblanking of High Strength Steels: Control of
Material Properties for Tool Life. J. Mat. Proc. Techol., Submitted.
14.
Sun, L., Wagoner, R. H., Complex Unloading Behavior: Nature of the
Deformation and Its Consistent Representation. Int. J. Plasticity, Accepted.
15.
Kim, J.H., Sung, J. H., Wagoner, R. H., Simulating the Shear Fracture of DualPhase Steel. Int. J. Plasticity, Submitted.
16.
Lim, H., Lee, M. G., Sung, J. H., Kim, J. H. Wagoner, R. H., Time-Dependent
Springback of Advanced High Strength Steels. Int. J. Plasticity To be submitted.
16
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Formability and Springback 2
Page 17
17.
Piao, K., Lee, J. K., Kim, H. Y., Wagoner, R. H., An Elevated Temperature
Tension / Compression Test for Sheet Material. Int. J. Plasticity, To be submitted.
18.
Sung, J.H., Kim, J. H., Wagoner, R. H. , The Draw-Bend Fracture of Dual-Phase
Steels. J. Mater. Proc. Technol, To be submitted.
19.
Demeri, M.Y., The stretch-bend forming of sheet metal. Journal of Applied
Metalworking, 1981. 2: p. 1-3.
20.
Vallance, D.W., Matlock, D. K., Application of the bending-under-tension friction
test to coated sheet steels. Journal of Materials Engineering and Performance,
1992. 1: p. 685-694.
21.
Wenzloff, G.J., Hylton, T. A., Matlock, D. K., A new procedure for the bending
under tension friction test. Journal of Material Engineering and Performance,
1992. 1: p. 609-613.
22.
Haruff, J.P., Hylton, T. A., Matlock, D. K., Frictional response of
electrogalvanized sheet steels. The Physical Metallurgy of Zinc coated steel, 1993.
23.
Carden, W.D., Springback after drawing and bending of metal sheets. 1997, The
Ohio State University: Columbus.
24.
Damborg, F.F., Wagoner, R. H., Danckert, J., Matlock, D. K. Stretch-bend
formability. in MP2M-Cener Seminar. 1997. Danish Technical University.
25.
Embury, J.D., Duncan, J. L., Formability maps. Annual Review of Materials
Sscience, 1981. 11: p. 505-521.
26.
Burford, D.A., Wagoner, R. H., A more realistic method for predicting the
forming limits of metal sheets. Forming limit diagrams: concepts, methods, and
applications 1989.
27.
Graf, A., Hosford, W. F., Calculations of forming limit diagrams. Metallugical
Transactions A, 1990. 21A: p. 87-94.
28.
Rees, D.W.A., Factors influencing the FLD of automotive sheet metal. J. of
Materials Processing Technology, 2001. 118: p. 1-8.
29.
Bleck, W., Deng, Z., Papamantellos, K., Gusek, C. O., A comparative study of the
forming-limit diagram models for sheet steels. J. of Materials Processing
Technology, 1998. 83: p. 223-230.
30.
Hollomon, J.H., Tensile deformation. Transactions of AIME, 1945. 162: p. 268–
290.
31.
Voce, E., The relationship between stress and strain for homogeneous
deformation. Journal of the Institute Metals, 1948. 74: p. 537-562.
32.
Lin, M.R., Wagoner, R.H., Effect of temperature, strain, and strain rate on the
tensile flow stress of I. F. steel and stainless steel type 310. Scripta Metallurgica,
1986. 20: p. 143-148.
33.
Rusinek, A., Klepaczko, J.R., Shear testing of a sheet steel at wide range of strain
rates and a constitutive relation with strain-rate and temperature dependence of
the flow stress. Int. J. Plasticity, 2001. 17: p. 87-115.
17
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Page 18
34.
Morestin, F., and Boivin, M. , On the necessity of taking into account the
variation in the Young modulus with plastic strain in elastic-plastic software.
Nuclear Engineering and Design, 1996. 162: p. 107-116.
35.
Augereau, F., Roque, V., Robert, L., and Despaux, G., Non-destructive testing by
acoustic signature of damage level in 304L steel samples submitted to rolling,
tensile test and thermal annealing treatments. Materials Science and Engineering
a-Structural Materials Properties Microstructure and Processing, 1999. 266: p.
285-294.
36.
Cleveland, R.M., and Ghosh, A. K., Inelastic effects on springback in metals.
International Journal of Plasticity, 2002. 18: p. 769-785.
37.
Caceres, C.H., Sumitomo, T., and Veidt, M., Pseudoelastic behaviour of cast
magnesium AZ91 alloy under cyclic loading-unloading. Acta Materialia 2003. 51:
p. 6211-6218.
38.
Luo, L.M., and Ghosh, A. K., Elastic and inelastic recovery after plastic
deformation of DQSK steel sheet. Journal of Engineering Materials and
Technology-Transactions of the Asme, 2003. 125: p. 237-246.
39.
Yeh, H.Y., and Cheng, J. H., NDE of metal damage: ultrasonics with a damage
mechanics model. International Journal of Solids and Structures 2003. 40: p.
7285-7298.
40.
Yang, M., Akiyama, Y., and Sasaki, T. , Evaluation of change in material
properties due to plastic deformation. Journal of Materials Processing
Technology, 2004. 151: p. 232-236.
41.
Perez, R., Benito, J. A., and Prado, J. M. , Study of the inelastic response of TRIP
steels after plastic deformation. ISIJ International, 2005. 45: p. 1925-1933.
42.
Pavlina, E.J., Levy, B. S., Van Tyne, C. J., Kwon, S. O., and Moon, Y. H. , The
Unloading Modulus of Akdq Steel after Uniaxial and near Plane-Strain Plastic
Deformation. Engineering Plasticity and Its Applications: From Nanoscale to
Macroscale. 2009, Singapore: World Scientific Publ. Co. PTE LTD. 698-703.
43.
Yu, H.Y., Variation of elastic modulus during plastic deformation and its
influence on springback. Materials & Design, 2009. 30: p. 846-850.
44.
Zavattieri, P.D., Savic, V., Hector, L. G., Fekete, J. R., Tong, W., and Xuan, Y. ,
Spatio-temporal characteristics of the Portevin-Le Chatelier effect in austenitic
steel with twinning induced plasticity. International Journal of Plasticity, 2009.
25: p. 2298-2330.
45.
Andar, M.O., Kuwabara, T., Yonemura, S., and Uenishi, A. , Elastic-Plastic and
Inelastic Characteristics of High Strength Steel Sheets under Biaxial Loading and
Unloading. ISIJ International, 2010. 50: p. 613-619.
46.
Wang, J.F., Wagoner, R. H., Carden, W. D., Matlock, D. K., Barlat, F., Creep and
anelasticity in the springback of aluminum. Int. J. Plasticity, 2004. 20: p. 22092232.
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REFERENCES FROM PROPOSED WORK SECTION
1.
Talyan, V., Wagoner, R. H., Lee, J. K., Formability of stainless steel. Metall.
Mater. Trans. A, 1998. 29A: p. 2161-2172.
2.
Boger, R.K., Wagoner, R. H., Barlat, F., Lee, M. G., Chung, K., Continuous,
large strain, tension/ compression testing of sheet materials. International Journal
of Plasticity, 2005. 21: p. 2319-2343.
3.
Piao, K., Lee, J. K., Kim, H. Y., Wagoner, R. H., An Elevated Temperature
Tension / Compression Test for Sheet Material. Int. J. Plasticity, To be submitted.
4.
Sun, L., Wagoner, R. H., Complex Unloading Behavior: Nature of the
Deformation and Its Consistent Representation. Int. J. Plasticity, 2010. Accepted.
5.
Geng, L.M., Wagoner, R. H., Role of plastic anisotropy and its evolution on
springback. Int. J. Mech. Sci., 2002. 44 (1): p. 123-148.
6.
Sung, J.H., Kim, J. H., Wagoner, R. H., A Plastic Constitutive Equation
Incorporating Strain, Strain-Rate, and Temperature. Int. J. Plasticity, vol. 26, pp.
1746-1771
7.
Gilat, A., Schmidt, T. E., Walker, A. L., Full field strain measurement in
compression and tensile split Hopkinson bar experiments. Experimental
Mechanics, 2009. 49: p. 291-302.
8.
Sung, J.H., Kim, J. H., Wagoner, R. H. , The Draw-Bend Fracture of Dual-Phase
Steels. J. Mater. Proc. Technol, To be submitted.
9.
Kim, J.H., Sung, J. H., Matlock, D. K., Kim, D., Wagoner, R. H. Predicting Shear
Failure of Dual-Phase Steels. in NUMIFORM 2010, Proc. 10th Int. Conf. Numer.
Meth. Ind. Form. Proc. 2010.
19