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

R. H. Wagoner 3

1. Background – Shear Fracture, 2006

R. H. Wagoner 4

Shear Fracture of AHSS – 2005 Case

Jim Fekete et al, AHSS Workshop, 2006

R. H. Wagoner 5

Shear Fracture of AHSS - 2011

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

R. H. Wagoner 6

Unpredicted by FEA / FLD

Stoughton, AHSS Workshop, 2006

R. H. Wagoner 7

Shear Fracture: Related to Microstructure?

Ref: AISI AHSS Guidelines

R. H. Wagoner 8

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]

R. H. Wagoner 10

2. DBF Results & Simulations, 2011

R. H. Wagoner

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

R. H. Wagoner

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

R. H. Wagoner

DBF Test: Effect of R/t

13

R. H. Wagoner 14

“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

R. H. Wagoner 15

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

R. H. Wagoner

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

R. H. Wagoner 17

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

R. H. Wagoner

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

R. H. Wagoner

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

R. H. Wagoner 20

Is shear fracture of AHSS brittle or ductile?

R. H. Wagoner

Fracture Strains: DP 780 (Typical)

21

R. H. Wagoner

Fracture Strains: TWIP 980 (Exceptional)

22

R. H. Wagoner

Directional DBF : DP 780 (Typical)

23

R. H. Wagoner

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

R. H. Wagoner 25

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.)

R. H. Wagoner 26

3. Practical Application - 2012

R. H. Wagoner

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.

27

R. H. Wagoner

Ideal DBF Test: Plane Strain, High Rate

28

R. H. Wagoner

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)*

R. H. Wagoner

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)*

R. H. Wagoner

How to Use Practically: Bend, Unbend Regions

31

R. H. Wagoner

Practical Application of SF FLD – (1) Direct

32

For each element in contact

Known: R, t ε*membrane

Predicted Fracture: εFEA > ε*membrane

R. H. Wagoner

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.

R. H. Wagoner

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

R. H. Wagoner

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?)

R. H. Wagoner 36

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

R. H. Wagoner

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)

R. H. Wagoner 38

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

R. H. Wagoner

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

R. H. Wagoner

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)

R. H. Wagoner

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

R. H. Wagoner

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

R. H. Wagoner

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

R. H. Wagoner 44

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.)

R. H. Wagoner 45

Thank you.

R. H. Wagoner 46

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.