draw-bend fracture prediction with dual-phase...

Draw-Bend Fracture Prediction with Dual-Phase Steels

R. H. Wagoner

September 25, 2012

AMPT Wollongong, Australia

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

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Shear Fracture of AHSS - 2011

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

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]

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

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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 =1MPa

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

Tensile TestVoce =1MPa

Hollomon =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

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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

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

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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

(mm

)

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)

21

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Fracture Strains: TWIP 980 (Exceptional)

22

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Directional DBF : DP 780 (Typical)

23

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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

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

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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.

27

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Ideal DBF Test: Plane Strain, High Rate

28

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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


Analytical PS ResultsDP 780 - 1.4mm

Outer Strains

Inner Strains

Center Strains(Membrane) FLDo

(R/t)*

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How to Use Practically: Bend, Unbend Regions

31

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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.

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?)

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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)


0

0.1

0.2

0.3

0.4

0 2 4 6 8 10 12 14 16

Mem

bran

e St

rain


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, T

rue

Mem

bran

e St

rain


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

, Tru

e M

embr

ane

Stra

in

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, T

rue

Mem

bran

e St

rain



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.

http://www.sciencedirect.com/science?_ob=IssueURL&_tockey=

R. H. Wagoner 47

Extra Slides

R. H. Wagoner

DP Steels

48

0

200

400

600

800

1000

1200

0 5 10 15 20 25

Engi

neer

ing

Stre

ss(M

Pa)

Engineering Strain (%)

DP590(B)-1.4mm

DP780(D)-1.4mm

DP980(D)-1.45mm

Strain Rate: 10-3/secRoom Temp.Rolling Direction

R. H. Wagoner 49

“H/V” Constitutive Framework

Special:

Standard:

( , , ) ( , ) ( ) ( )T f T g h Tσ σ ε ε ε ε= = ⋅ ⋅

( , ) ( ) (1 ( ))Hollo Vocef T T f T fε α α= + − ⋅

1 2( ) ( )RTT T Tα α α= − −n

Hollof Kε= [1 exp( )]Vocef A B Cε= − −

[log ]

0

( )a b

gε

εε

ε

+

=

( ) (1 ( ))RTh T D T T= − ⋅ − Sung et al., Int. J. Plast. 2010

R. H. Wagoner

Simulated D-B Test: Effect of Draw Speed

50

0

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20 25 30 35

F/F U

TS

Front Displacement (mm)

DP980(D)R/t=4.4, V

2/V

1=0

51mm/s(dε/dt=2.5/s)

Adiabatic

Isothermal

2.5mm/s(0.13/s)

0.001mm/s(5x10-3/s)

13mm/s(0.6/s)

R. H. Wagoner

DBF Formability: DP980(A), RD vs. TD (Typical)

51

* Directional Formability: TD=RD

0

10

20

30

40

50

2.2 3.4 4.5 5.5 6.6 7.8 10 13.3

Fron

t Dis

p. to

Fai

lure

(Uf,

mm

)

R/t

RDTD

DP980(A)V

1=51mm/sec

V2/V

1=0

R. H. Wagoner

DBF Formability: DP980(D), RD vs. TD (Exceptional)

52

* Directional Formability: RD>TD

0

10

20

30

40

50

60

2.2 3.3 4.4 5.4 6.6 7.7 9.9 13.1

Fron

t Dis

p. to

Fai

lure

(Uf,

mm

)

R/t

DP980(D)V

1=51mm/sec

V2/V

1=0

RD

TD

R. H. Wagoner

Analytical Model – Curvilinear Derivation

Rrn

Neutral liner

θ t

T T

lnn

r

rθε =

2 2ln

3 3ij ij

n

r

rε ε ε= =

53

Fracture Criterion: Fracture occurs at Tmax for given R, to

2 2 2( ) ( )3 3 3

n

n

rR t

r r

r dr dr rθθσ σ σ σ+

= − −

∫ ∫

0R tR t

R R

Trdr dθθ θθσ σ ξξ

++

=∂

=∂∫ ∫

2 2( ) ( )3 3

R t

r

r dr rθθσ σ σ+

= +

∫

Materially embedded coordinate :ξ

nr

rdr d dr

λ ξ ξ= =

0 2 2( ) ( )3 3

R t r dθθξ

σ ξ σ ξ σ ξξ

+ ∂ = + ∂

∫

0 2 2 2( ) ( )3 3 3

n

n

R t r rd dξ

θθξ ξ

σ ξ σ ξ σ ξ σ ξξ ξ

+ ∂ ∂ = − − ∂ ∂

∫ ∫

nr r>

nr r<

nξ ξ>

nξ ξ

R. H. Wagoner

DBF Interpretation: Plane-strain vs. Tension

400

600

800

1000

1200

0 2 4 6 8 10 12 14

Peak

Eng

inee

ring

Stre

ss (M

Pa)

R / t

DP780-1.4mm

Analytical Model,Plane Strain

Simplified FE Model,m=0, µ=0

UTS

54

R. H. Wagoner

Inner and Outer Strains at Maximum Load

55

0

0.1

0.2

0.3

0.4

0 2 4 6 8 10 12 14 16

True

Str

ain



DP590

DP780

Inner Strains

DP980

Outer Strains

R. H. Wagoner

Membrane Strains (R/t Affected Only)

56

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



DP590

DP780DP980

R. H. Wagoner

R/t-Affected Membrane Strains vs. t/R

57

0

0.05

0.1

0.15

0.2

0.25

0 0.1 0.2 0.3 0.4 0.5 0.6

∆ε s

, Tru

e M

embr

ane

Stra

in



DP590

DP780

DP980

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Forming Limit Diagram

58

Ref: Hosford & Duncan

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PS T-M Model: Model vs. Fit

59

-0.05

0

0.05

0.1

0.15

0.2

0.25

0 0.1 0.2 0.3 0.4

∆ε s

, Tru

e M

embr

ane

Stra

in


Plane Strain Thermo-Mechanical ModelStopped at Maximum Load DP590

S = 0.753, εs

o = 0.149

DP780S = 0.330, ε

so = 0.123

DP980S = 0.051, ε

so = 0.133

−+

ε=

ε

maxmax

oss R

tRtS

Rt

Rt

R. H. Wagoner

PS T-M Model: Model vs. Fit

60

0

0.1

0.2

0.3

0.4

0.5

0 2 4 6 8 10 12 14 16

ε s, T

rue

Mem

bran

e St

rain


Plane Strain Thermo-Mechanical ModelStopped at Maximum Load

DP590S = 0.753, ε

so = 0.149

DP780: S = 0.330, εs

o = 0.123

DP980: S = 0.051, εs

o = 0.133

−+

ε=

ε

maxmax

oss R

tRtS

Rt

Rt

R. H. Wagoner 61

Draw-Bend Fracture Test (DBF): V1, V2 Constant

Star

t

Max. Finish

Max

. Fin

ish

V1

Start

R

444.5 mm (10”) 190.5 mm

190.

5 m

m

444.

5 m

m(1

0”)

V2 = αV1

uf

Specimen width: 25mm Tool radius choices: 2/16, 3/16, 4/16, 5/16, 6/16, 7/16, 9/16, 12/16 inch 3.2, 4.8, 6.4, 7.9, 9.5, 11.1, 14.3, 19 mm α = V2/V1: 0 and 0.3

Wagoner et al., Esaform, 2009

R. H. Wagoner

AHSS vs. HSLA

62

Ref: AISI AHSS Guidelines

Draw-Bend Fracture Prediction with Dual-Phase SteelsOutlineSlide Number 3Shear Fracture of AHSS – 2005 CaseShear Fracture of AHSS - 2011Unpredicted by FEA / FLDShear Fracture: Related to Microstructure?Conventional Wisdom, 2006NSF Workshop on AHSS (October 2006)Slide Number 10References: DBF Results & SimulationsDBF Failure Types DBF Test: Effect of R/tSlide Number 14Slide Number 15Predicted ef, H/V vs. H, V: 3 alloys, 3 temperaturesFE Draw-Bend Model: Thermo-Mechanical (T-M)Front Stress vs. Front DisplacementDisplacement to Maximum Front Load vs. R / tSlide Number 20Slide Number 21Slide Number 22Slide Number 23Slide Number 24Interim ConclusionsSlide Number 26DBF/FE vs. Industrial Practice/FEIdeal DBF Test: Plane Strain, High RateIdeal Test Results - StressIdeal Test Results - StrainHow to Use Practically: Bend, Unbend RegionsPractical Application of SF FLD – (1) DirectPractical Application of SF FLD – (2) IndirectCalculation: Indirect MethodRecommended Procedure with Industrial FEASlide Number 36What is Needed?FE Plane Strain DBF ModelAdiabatic Constitutive EquationPeak Stress, Plane-Strain: DP980Membrane Strains at Maximum LoadAnalytical Model: Model vs. FitAnalytical Model: Model vs. FitConclusionsSlide Number 45ReferencesSlide Number 47DP SteelsSlide Number 49Simulated D-B Test: Effect of Draw SpeedSlide Number 51Slide Number 52Analytical Model – Curvilinear DerivationDBF Interpretation: Plane-strain vs. TensionInner and Outer Strains at Maximum LoadMembrane Strains (R/t Affected Only)R/t-Affected Membrane Strains vs. t/RForming Limit DiagramPS T-M Model: Model vs. FitPS T-M Model: Model vs. FitDraw-Bend Fracture Test (DBF): V1, V2 ConstantAHSS vs. HSLA

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