predicting the bending-affected fracture in sheet forming

Predicting the Bending-Affected Fracture in Sheet Forming

R. H. Wagoner*, C. Du**, D. Zhou** *The Ohio State University

** Chrysler Corporation

October 25, 2012

IABC Troy, Michigan, U.S.A.

R. H. Wagoner

Outline

1. Background – Shear Fracture, 2006 2. DBF Results & Simulations, 2011 Intermediate Conclusions 3. Practical Application, 2012

Ideal DBF Test Recommended Procedure

4. No Ideal Test? Results, Recommended Procedure

2

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1. Background – Shear Fracture, 2006

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Shear Fracture of AHSS – 2005 Case

Jim Fekete et al, AHSS Workshop, 2006

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Shear Fracture of AHSS - 2011

Forming Technology Forum 2012 Web site: http://www.ivp.ethz.ch/ftf12

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Unpredicted by FEA / FLD

Stoughton, AHSS Workshop, 2006

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Shear Fracture: Related to Microstructure?

Ref: AISI AHSS Guidelines

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Conventional Wisdom, 2006

Shear fracture… • is unique to AHSS (maybe only DP steels) • occurs without necking (brittle) • is related to coarse, brittle microstructure • is time/rate independent Notes: • All of these based on the A/SP stamping trials, 2005. • All of these are wrong. • Most talks assume that these are true, even today.

R. H. Wagoner 9 9 9

NSF Workshop on AHSS (October 2006) E

long

atio

n (%

)

Tensile Strength (MPa)

0

10

20

30

40

50

60

70

0 600 1200 300 900 1600

MART

Mild BH

Elo

ngat

ion

(%)

600

R. W. Heimbuch: An Overview of the Auto/Steel Partnership and Research Needs [1]

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2. DBF Results & Simulations, 2011

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References: DBF Results & Simulations J. H. Kim, J. H. Sung, K. Piao, R. H. Wagoner: The Shear Fracture of

Dual-Phase Steel, Int. J. Plasticity, 2011, vol. 27, pp. 1658-1676. J. H. Sung, J. H. Kim, R. H. Wagoner: A Plastic Constitutive Equation

Incorporating Strain, Strain-Rate, and Temperature, Int. J. Plasticity, 2010, vol. 26, pp. 1746-1771.

J. H. Sung, J. H. Kim, R. H. Wagoner: The Draw-Bend Fracture Test (DBF)

and Its Application to DP and TRIP Steels, Trans. ASME: J. Eng. Mater. Technol., (in press)

11

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DBF Failure Types

Type I

Type II Type III

65o

65o

V2

V1

Type I: Tensile failure (unbent region) Type II: Shear failure (not Type I or III) Type III: Shear failure (fracture at the roller)

12

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DBF Test: Effect of R/t

13

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“H/V” Constitutive Eq.: Large-Strain Verification

600

700

800

900

1000

0.1 0.2 0.3 0.4 0.5 0.6 0.7

Effe

ctiv

e St

ress

(MPa

)

Effective Strain

H/V <σ>=1MPa

DP590(B), RDStrain Rate=10-3/sec25oC

Tensile TestVoce <σ>=1MPa

Hollomon <σ>=4MPa

Bulge Test (r=0.84, m=1.83)

FitRange Extrapolated, Bulge Test Range

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0 0.05 0.1 0.15 0.2 0.25 0.3300

400

500

600

700

Engi

neer

ing

Stre

ss (M

Pa)

Engineering Strain

Experiment(D-B)

Voce HollomonH/V model

DP590(B), RDStrain Rate=10-3/s100oC, Isothermal

FE Simulated Tensile Test: H/V vs. H, V

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Predicted ef, H/V vs. H, V: 3 alloys, 3 temperatures

16

Hollomon Voce H/V

DP590 0.05 (23%) 0.05 (20%) 0.02 (7%)

DP780 0.03 (18%) 0.04 (22%) 0.01 (6%)

DP980 0.04 (30%) 0.03 (21%) 0.01 (5%)

Standard deviation of ef: simulation vs. experiment

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FE Draw-Bend Model: Thermo-Mechanical (T-M)

hmetal,air = 20W/m2K

hmetal,metal = 5kW/m2K

µ = 0.04

U1, V1

U2, V2

• Abaqus Standard (V6.7) • 3D solid elements (C3D8RT), 5 layers • Von Mises, isotropic hardening • Symmetric model

Kim et al., IDDRG, 2009

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Front Stress vs. Front Displacement

18

0

200

400

600

800

1000

0 20 40 60 80

Fron

t Str

ess,

σ1

Front Displacement, U1 (mm)

Measured

DP780-1.4mm, RDV

1=51mm/s, V

2/V

1=0

R/t=4.5

IsothermalSolid, Shell

T-M

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Displacement to Maximum Front Load vs. R / t

19

0

20

40

60

80

0 2 4 6 8 10 12 14

UM

ax. L

oad (m

m)

R / t

Type I

Type III

DP780-1.4mm, RDV

1=51mm/s, V

2/V

1=0

T-M, Solid

Measured

Isothermal, Solid

Isothermal, Shell

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Is shear fracture of AHSS brittle or ductile?

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Fracture Strains: DP 780 (Typical)

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Fracture Strains: TWIP 980 (Exceptional)

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Directional DBF : DP 780 (Typical)

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Directional DBF Formability: DP980 (Exceptional)

24

0

5

10

15

20

25

30

0 30 60 90

Elon

gatio

n to

Fra

ctur

e (m

m)

Angle to RD (degree)RD TD

DP980R/t = 3.3

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Interim Conclusions

• “Shear fracture” occurs by plastic localization.

• Deformation-induced heating dominates the error in predicting shear failures.

• Brittle cracking can occur. (Poor microstructure or exceptional tensile ductility, e.g. TWIP).

• T-dependent constitutive equation is essential.

• Shear fracture is predictable plastically. (Challenges: solid elements, T-M model.)

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3. Practical Application - 2012

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DBF/FE vs. Industrial Practice/FE

Ind.: Plane strain High rate ~Adiabatic FE: Shell Isothermal Static

DBF: General strain Moderate rates Thermo-mech. FE: Solid element Thermo-mech.

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Ideal DBF Test: Plane Strain, High Rate

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Ideal Test Results - Stress

29

400

600

800

1000

1200

0 2 4 6 8 10 12 14

Peak

Eng

inee

ring

Stre

ss (M

Pa)

Bending Ratio, R / t

DP780-1.4mm

Analytical PS Result

(UTS)

(R/t)*

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Ideal Test Results - Strain

30

0

0.1

0.2

0.3

0.4

0 2 4 6 8 10 12 14 16

True

Str

ain

Bending Ratio, R / t

Analytical PS ResultsDP 780 - 1.4mm

Outer Strains

Inner Strains

Center Strains(Membrane) FLD

o

(R/t)*

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How to Use Practically: Bend, Unbend Regions

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Practical Application of SF FLD – (1) Direct

32

For each element in contact

Known: R, t ε*membrane

Predicted Fracture: εFEA > ε*membrane

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Practical Application of SF FLD – (2) Indirect

33

For each element drawn over contact

Known: (R, t)contact Pmax σ*PS tension ε*PS tension

Predicted Fracture: εFEA > ε*PS tension

Wu, Zhou, Zhang, Zhou, Du, Shi: SAE 2006-01-0349.

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Calculation: Indirect Method

34

Example: von Mises Yield, Hollomon Hardening

Von Mises: 𝝈∗𝑷𝑷𝑷 = 𝟑𝟐𝑷𝒎𝒎𝒎 𝑨

Hollomon: 𝝈 = 𝑲 𝜺 𝒏

So: 𝝈∗𝑷𝑷𝑷 = 𝟑𝟐𝑲 𝜺∗𝑷𝑷𝑷

𝒏 𝜺∗𝑷𝑷𝑷 = 𝟐𝟑

𝝈∗

𝑲

𝟏/𝒏

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Recommended Procedure with Industrial FEA

35

1. Use adiabatic law in FEA, use rate sensitivity

2. Classify each element based on X-Y position (tooling) a) Bend (plane-strain) b) After bend (plane-strain) c) General (not Bend, not After)

3. Apply 4 criteria: a) FLD (Bend, After) b) Direct SF (Bend) c) Indirect SF (After) d) Brittle Fracture* (All?)

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4. No Ideal Test? (What to do?)

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What is Needed?

37

Pmax = f(R/t) (PS, high-speed DBF)

400

600

800

1000

1200

0 2 4 6 8 10 12 14

Peak

Loa

d (M

Pa)

Bending Ratio, R / t

0

0.1

0.2

0.3

0.4

0 2 4 6 8 10 12 14 16

Mem

bran

e St

rain

Bending Ratio, R / t

ε∗membrane = f(R/t) (PS, high-speed DBF)

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FE Plane Strain DBF Model

µ = 0.06

U1, V1

U2, V2 = 0

• Abaqus Standard (V6.7) • Plane strain solid elements (CPE4R), 5 layers • Von Mises, isotropic hardening • Isothermal, Adiabatic, Thermo-Mechanical

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0

400

800

1200

1600

0 0.2 0.4 0.6 0.8 1

True

Str

ess

(MPa

)

True Plastic Strain

DP980(D)-GA-1.45mmdε/dt=10-3/s

Adiabatic

25oC75oC

125oC

-5% -12%

Adiabatic Constitutive Equation

0p

T dC

εη σ ερ

∆ = ∫

( , ) ( , , )adiabatic Tσ ε ε σ ε ε= ∆

39

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Peak Stress, Plane-Strain: DP980

40

600

800

1000

1200

1400

0 2 4 6 8 10 12 14

Peak

Eng

inee

ring

Stre

ss (M

Pa)

R / t

DP980-1.43mm

Analytical Model,Plane StrainPS FE Model,

m=0, µ=0

UTS

DBF measured(RD, TD)

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Membrane Strains at Maximum Load

41

0

0.05

0.1

0.15

0.2

0.25

0 2 4 6 8 10 12 14 16

ε s, Tru

e M

embr

ane

Stra

in

Bending Ratio, R / t

Analytical Adiabatic ModelStopped at Maximum LoadDP590

DP780

DP980

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Analytical Model: Model vs. Fit

42

0

0.02

0.04

0.06

0.08

0.1

0 0.1 0.2 0.3 0.4 0.5 0.6

∆ε s, T

rue

Mem

bran

e St

rain

1 / Bending Ratio, t / R

Analytical Adiabatic ModelStopped at Maximum Load

DP590S = 0.167, ε

so = 0.138

DP780S = 0.198, ε

so = 0.101

DP980S = 0.221, εs

o = 0.088

−+

ε=

ε

maxmax

oss R

tRtS

Rt

Rt

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Analytical Model: Model vs. Fit

43

0

0.05

0.1

0.15

0.2

0.25

0 2 4 6 8 10 12 14 16

ε s, Tru

e M

embr

ane

Stra

in

Bending Ratio, R / t

Analytical Adiabatic ModelStopped at Maximum Load

DP590: S = 0.168, ε

so = 0.138

DP780: S = 0.198, εs

o = 0.101

DP980: S = 0.221, ε

so = 0.088

−+

ε=

ε

maxmax

oss R

tRtS

Rt

Rt

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Conclusions

• Shear fracture is predictable with careful testing or careful

constitutive modeling and FEA.

• “Shear fracture” occurs by plastic localization.

• “Shear fracture” is an inevitable consequence of draw-bending mechanics. All materials.

• Brittle fracture can occur, but is unusual. (Poor microstructure or

v. high tensile tensile limit, e.g. TWIP).

• T-dependent constitutive equation is essential for AHSS because of high plastic work. (But probably not Al or many other alloys.)

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Thank you.

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References

• R. H. Wagoner, J. H. Kim, J. H. Sung: Formability of Advanced High Strength Steels, Proc. Esaform 2009, U. Twente, Netherlands, 2009 (CD)

• J. H. Sung, J. H. Kim, R. H. Wagoner: A Plastic Constitutive Equation Incorporating Strain, Strain-Rate, and Temperature, Int. J. Plasticity, (accepted).

• A.W. Hudgins, D.K. Matlock, J.G. Speer, and C.J. Van Tyne, "Predicting Instability at Die Radii in Advanced High Strength Steels," Journal of Materials Processing Technology, vol. 210, 2010, pp. 741-750.

• J. H. Kim, J. Sung, R. H. Wagoner: Thermo-Mechanical Modeling of Draw-Bend Formability Tests, Proc. IDDRG: Mat. Prop. Data for More Effective Num. Anal., eds. B. S. Levy, D. K. Matlock, C. J. Van Tyne, Colo. School Mines, 2009, pp. 503-512. (ISDN 978-0-615-29641-8)

• R. H. Wagoner and M. Li: Simulation of Springback: Through-Thickness Integration, Int. J. Plasticity, 2007, Vol. 23, Issue 3, pp. 345-360.

• M. R. Tharrett, T. B. Stoughton: Stretch-bend forming limits of 1008 AK steel, SAE technical paper No.2003-01-1157, 2003.

• M. Yoshida, F. Yoshida, H. Konishi, K. Fukumoto: Fracture Limits of Sheet Metals Under Stretch Bending, Int. J. Mech. Sci., 2005, 47, pp. 1885-1896.