formability and springback of twip, trip and cp...

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

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

CMMI-0729114). 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 3rd-Generation AHSS).

RESULTS FROM PRIOR SUPPORT

Formability and Springback 1: “Sheet Formability and Springback of AHSS,” CMMI-0727641, 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 non-proportional path testing and formulated QPE model [9, 12, 14]

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]

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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 draw-bend 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 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 dual-actuation control system through grips fixed to the ends of the strip specimen.

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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 [25-29]).

Uf

F1, V1

R

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.

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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 thermo-mechanically, 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 Measured Isothermal FE Thermo-Mech FER/t=2.2,3.3,4.5,5.7 U1 U1 Error U1 Error

DP 590 44 mm 61 mm 44% 46 mm 6%DP 780 31 mm 49 mm 68% 33 mm 7%DP 980 22 mm 37 mm 83% 27 mm 31%Average 65% 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.

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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)

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]:

( , ) (1 )H Vf T f f (2) 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.

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]

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DP590 19 30 23 19 3DP780 21 47 21 22 5DP980 18 50 29 23 6Avg. 19 42 24 21 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.

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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 WORKThe 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:

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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, multi-directional 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)

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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 thermo-

mechanical 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: 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

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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 Yield/UTS (MPa) Elongation (%)TRIP 350/600 29-33TRIP 400/700 24-28TRIP 450/800 26-32TWIP 450/1000 50-54

CP 500/800 10-24CP 700/800 10-15CP 800/1000 8-13CP 1000/1200 8-10

Q-P steel UTS 1000 ?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 200C). 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 strain-hardening behavior adequately. Similar to Formability and Springback 1, obtained experimental data will guide constitutive developments for candidate materials.

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Figure 5: Setup for tension/ compression test at elevated temperature [3]

Figure 6: Comparison of QPE model predictions with monotonic tension and compression-tension (C-T) tests [4]

Elevated-Temperature Balance-Biaxial Bulge Testing: Previously, a room-temperature 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.

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 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

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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.

draw-bend tester to m

Control of restraining force(1) Load rate control mode(2) Speed control mode

F(1)

V2 (2)

Uf V1

R

3D DIC

Specimen width: 25.4mmRoller 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 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

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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.

RD

0o 15o30o

60o

45o

75o

90o

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, tThis procedure will be applied to newer alloys to provide practical guidelines for industrial applications.

Figure 10. Failure criteria obtained by the plane-strain finite element and analytical procedures (a) stress-based, and (b) strain-based.

BROADER IMPACT

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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 peer-reviewed 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

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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 Draw-Bend 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 Dual-Phase 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.

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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.

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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.

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.

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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. 2209-2232.

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.

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formability and springback of twip, trip and cp...

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