dept. of materials science and engineering, the ohio state university plasticity and failure of...

Center forAdvancedMaterials andManufacturing ofAutomotiveComponents

Dept. of Materials Science and Engineering,

The Ohio State University

Plasticity and Failure of Advanced High Strength Steels

R.H. Wagoner, Ji Hyun Sung, A. Madeshia, Ji Hoon Kim

R. H. Wagoner 2

Outline

• Introduction

• Draw-Bend Testing

• Constitutive Equations

• Draw-Bend Simulations

• Conclusions

R. H. Wagoner 3

Introduction

R. H. Wagoner 444

NSF Workshop on AHSS (October 2006)E

lon

gati

on (

%)

Tensile Strength (MPa)

0

10

20

30

40

50

60

70

0 600 1200300 900 1600

DP, CP

TRIP

MART

HSLA

IF

Mild

IF- HS

BHCMn

ISO

Elo

nga

tion

(%

)

600

TWIPAUST. SS

L-IP

ISO

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

R. H. Wagoner 5

Unexpected Forming Failures

Stoughton, AHSS Workshop, 2006

Comparison between FE / FLD simulation and practice.

R. H. Wagoner 66

“Shear Failure?”

• FLD– Tensile localization map

(+ biaxial)

• AHSS– “Shear failure” at die

radii, minimal width or thickness strain

Mg AZ31B Al 6013 (Shear type) (Tensile localization)

Lou, XY, Int. J. Plasticity,23, 1, 2007, 84

6

R. H. Wagoner 7

Project Objectives

• Produce and characterize fractures at die radii (“shear

failure”)• Develop a new formability criterion (with bending)

Jim Fekete et al., AHSS Workshop, 2006

R. H. Wagoner 8

Approach: Draw-Bend Test

R. H. Wagoner 9

Draw-Bend Testing

R. H. Wagoner 10

Draw-Bend Fracture Testing

Sta

rt

Max. Finish

Max

. F

inis

h

V1

Start

R

317.5 mm190.5 mm

19

0.5

mm

43

5.5

mm

V2 = V1

u1 = V1 t

R: 1/8, 3/16, 1/4, 7/16, 3/4 inch (3.2, 4.8 , 6.4, 11.1, 19.1 mm)

R. H. Wagoner 11

Phenomenological 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)

R. H. Wagoner 12

• R/t = 2.27 , V1 = 2.54 mm/s, = 0.37 , ddtmax = 0.22 /s

II

I

III

Failure Types: DP590(B)-CR-1.4mm

V 2/V 1

= 0

V 2/V 1

= 0.25

V 2/V

1 =

0.5

0

Xc = 6mm

Xc = 43mm

Xc = 17mm = 0.92

= 0.89

max

max

= 0.96max

R. H. Wagoner 13

Transition: Type II III (DP590)• R/t = 2.57, V1 = 127 mm/s, m = 0.33 , ddtmax = 7.95 /s

V2/V1 = 0.25 V2/V1 = 0.20 V2/V1 = 0.10

II III III III

V2/V1 = 0.20

Xc = 24 Xc = 16Xc = 20Xc = 20

= 0.94 = 0.93 = 0.95max maxmax = 0.93max

R. H. Wagoner 14

Infrared Temperature Measurements• Tmax ~ 50 to 100oC near fracture • Type III

– Differential temperature rise along the width

R. H. Wagoner 15

IR Results - Type III

0

100

200

300

400

500

600

700

800

20

30

40

50

60

70

80

0 0.2 0.4 0.6 0.8 1

Time (sec)

Front stress

Back stress

1

2

3

4

C_ DP5902.65R/t

25.4 mmw0V2

127 mm/sV1

(Fracture)

t = - 0.07 s t = 0 s t = 0.07 s t = 0.14 s

Material V1 (mm/s)TTC (oC)

TFLIR (oC)

(emissivity) T

DP590(C)-GA-1.75mm 127 60.25 53.8 0.7 6.5

Calibration

R. H. Wagoner 16

• R/t ( m & ddtmax )IIII

• V2/V1 ( Xc )IIII

• V1 ( ddtmax )IIII

Controlled Draw-Bend Parameters

• R/t m= ln(1+tsheet/R), m=tsheet/R

• V1 max~ m/D, D~3tsheet/V1 (FEA)

• V2/V1 related to Xc at failure

Observed Role of Parameters

..

R. H. Wagoner 17

Definition of Normalized Stress

Maximum Pull Force / Original AreaMaximum Pull Force / Original Area

Ultimate Tensile Strength (at = 0.7/s)Ultimate Tensile Strength (at = 0.7/s)..

R. H. Wagoner 18

Effect of R/t (V1 = 127 mm/s, V2/V1 = 0)

6

*

1

R=

t

3

*

2

R=

t

R. H. Wagoner 19

Effect of Bend Strain Rate (V2/V1 = 0)

R. H. Wagoner 20

Failure Types (V2/V1=0)

R/t (m) V1 (mm/s)

1.7(0.46)

2.6(0.33) 3.7(0.24) 6.5(0.14) 11(0.09)

127 0.88 0.96 0.99 1.00 0.99

25 0.88 0.95 0.98 0.97 0.96

2.5 0.91 0.94 0.95 0.94 0.93

R/t (m) V1 (mm/s)

2.3(0.37) 3.4(0.26) 4.5(0.20) 7.9(0.12) 13.6(0.07)

127 0.92 0.95 0.99 0.96 0.98

25 0.92 0.98 0.98 0.95 0.96

2.5 0.94 0.97 0.97 0.93 0.94

DP590(C)-GA-1.75mm

DP590(B)-CR-1.4mm

KeyType IType IIType III

R. H. Wagoner 21

Failure Type Map (DP780, V2/V1=0)

R. H. Wagoner

22

Failure Type Map (TRIP780, V2/V1=0)

R. H. Wagoner 2323

(R/t)*1 and (R/t)*2 for D-P Steels (V2/V1=0)

V1(mm/s) 51(127) 13(25) 2.5

DP590(B)-CR-1.4 6 3 2

DP780(D)-GI-1.4 6 3 3

DP980(D)-GA-1.45 11 4 4

• Shear / Tensile Transition, (R/t)*1 [ = f (matl, V1) ]

• Maximum Stress Transition, (R/t)*2 [ not f (matl, V1) ]

V1(mm/s) 51(127) 13(25) 2.5

DP590(B)-CR-1.4 4 3 4

DP780(D)-GI-1.4 4 4 5

DP980(D)-GA-1.45 4 4 4

R. H. Wagoner 24

Constitutive Equations

R. H. Wagoner 25

)()(),( ThgTf

1D Constitutive Equation

sgm

/10,)()2 31

1

2

)]exp(1[0

BAf

Kf

Voce

nHollomon

CTTTHTh o25),(1)()1 00

CTTTwhere

ffTfo

VoceHollo

25);(:

)1(),()3

0021

R. H. Wagoner

Comparison in Tensile Range (25oC)

26

R. H. Wagoner

Large-Strain Comparison (25oC)

0 84 1 797( . , . )r m

27

R. H. Wagoner 28

Thermo-Mechanical FE Simulation

• Abaqus Standard (V6.7)• 3D solid elements (C3D8RT), 2 layers

• Von Mises, isotropic hardening• Symmetric model

Tinitial = 25oC

Gage region (2% taper)

Sample

hmetal, air = 20 W/m2K

Grip

hmetal,metal = 5 kW/m2K

Grip

R. H. Wagoner 29

Simulated Tensile Test (50oC)

0 0.05 0.1 0.15 0.2 0.25 0.30

200

400

600

800

En

gin

eer

ing

Str

ess

(M

Pa)

Engineering Strain

DP590(B)-CR-1.4mm

50oCIsothermal

d/dt =10-3/s

Measured FE SimulatedVoce

FE SimulatedHollomon

FE SimulatedH/V

R. H. Wagoner 30

Predicted Ductility (ef): DP590

* ef is defined by measured fractional load drop at failure* ef is defined by measured fractional load drop at failure

Temp Exp

ef*

Hollomon Voce Mixed

25℃ 0.247 0.274(11%) 0.184(-23%) 0.229(-10%)

50℃ 0.238 0.282(15%) 0.185(-19%) 0.228(-5%)

100℃ 0.195 0.278(43%) 0.184(-4%) 0.204(5%)

Std. Dev.(%) 0.056(24%) -0.048(-15%) 0.013(7%)

R. H. Wagoner

Predicted Ductility (ef): DP 590, 780, 980

31

Hollomon Voce H/V

DP590 0.04(14%) 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%)

R. H. Wagoner

Large-Strain Comparison (DP780)

0 97 1 807( . , . )r m

32

R. H. Wagoner

Large-Strain Comparison (DP980)

0 76 1 904( . , . )r m

33

R. H. Wagoner 34

Draw-Bend Simulations

(Coupled Thermo-Mechanical FEM)

Note: Test results are shown for fixed roller and lubricated condition.

R. H. Wagoner 35

FE Draw-Bend Model

hmetal,air = 20W/m2K

hmetal,metal = 5kW/m2K

= 0.08

U1, V1

U2, V2

• Abaqus Standard (V6.7)

• 3D solid elements (C3D8RT), 5 layers

• Von Mises, isotropic hardening

• Symmetric model

R. H. Wagoner 36

Role of Thermal Effects (Type III)

0

5

10

15

20

25

30

0 20 40 60 80 100

Fro

nt

Fo

rce

(k

N)

Front Displacement (mm)

DP590(B)-CR-1.4mmR/t=3.4, V

1=127mm/s, V

2/V

1=0

Solid Elem.

Measured Nonisothermalsimulation (Type III)

Isothermalsimulation (Type I)

R. H. Wagoner 37

R/t = 7.9, V1=127mm/s, V2/V1=0 (Type I)

R. H. Wagoner

R/t = 7.9, V1=127mm/s, V2/V1=0 (Type I)Temperature (oC)

F=Fmax

U1=46mmF=0.9Fmax

U1=61mm

52oC

117mm

p=0.16

Type I

99oC, p=0.41(93oC measured)

38

R. H. Wagoner 39

R/t = 7.9, V1=127mm/s, V2/V1=0 (Type I)

0

5

10

15

20

25

30

0 20 40 60 80 100

Fo

rce

(k

N)


DP590(B)-CR-1.4mmR/t=7.9, V

1=127mm/s, V

2/V

1=0

Nonisothermal, Solid Elem.

Back

Front

Measured

FE Simulated

R. H. Wagoner 40

R/t = 3.4, V1=127mm/s, V2/V1=0.5 (Type II)

R. H. Wagoner

R/t = 3.4, V1=127mm/s, V2/V1=0.5 (Type II)

Temperature (oC)

F=Fmax

U1=61mmF=0.9Fmax

U1=67mm


10mm

Type II

157oCp=0.65

41

R. H. Wagoner 42

R/t = 3.4, V1=127mm/s, V2/V1=0.5 (Type II)

0

5

10

15

20

25

30

0 20 40 60 80 100

Fo

rce

(k

N)


DP590(B)-CR-1.4mmR/t=3.4, V

1=127mm/s, V

2/V

1=0.5


Measured

FE Simulated

Back

Front

R. H. Wagoner 43

R/t = 3.4, V1=127mm/s, V2/V1=0 (Type III)

R. H. Wagoner


Temperature (oC)

F=Fmax

U1=44mmF=0.9Fmax

U1=46mm


155oCp=0.72

Type III

44

R. H. Wagoner 45


0

5

10

15

20

25

30

0 20 40 60 80 100

Fo

rce

(k

N)


DP590(B)-CR-1.4mmR/t=3.4, V

1=127mm/s, V

2/V

1=0


Measured

FE Simulated

Front

Back

R. H. Wagoner

Observed vs. Simulated Failure (DP590)

R/t V1 (mm/s) 2.3 3.4 4.5 7.9 13.5

127 0.96 0.99 1.00 1.00 1.00

25 0.96 0.99 1.00 1.00 1.00

2.5 0.97 0.98 0.98 0.98 0.98

DP590(B)-CR-1.4mm Key: Type I, Type II, Type III

R/t V1 (mm/s) 2.3 3.4 4.5 7.9 13.5

127 0.86 0.93 0.96 0.99 0.99

25 0.86 0.93 0.95 0.98 0.99

2.5 0.88 0.94 0.96 0.98 0.98

V2/V1=0.5

V2/V1=0

46

R. H. Wagoner

Observed vs. Simulated Failure (DP780)

R/t V1 (mm/s) 2.3 3.4 4.5 7.9 13.5

51 0.91 0.93 0.94 0.96 0.95

13 0.90 0.92 0.93 0.94 0.94

2.5 0.91 0.93 0.94 0.94 0.94

DP780(D)-GI-1.4mm

V2/V1=0.5

Key: Type I, Type II, Type III

R/t V1 (mm/s) 2.3 3.4 4.5 7.9 13.5

51 0.83 0.87 0.91 0.93 0.94

13 0.82 0.87 0.90 0.92 0.94

2.5 0.83 0.88 0.90 0.93 0.94

V2/V1=0

47

R. H. Wagoner

Effect of R/t (DP590, V2/V1 = 0)

48

R. H. Wagoner

Effect of R/t (DP780, V2/V1 = 0)

49

R. H. Wagoner

Effect of Strain Rate (DP780)

50

R. H. Wagoner 51

Conclusions

Note: All test results are shown for fixed roller and lubricated condition.

R. H. Wagoner 52

Conclusions

• Thermo-mechanical simulation predicts the formability of DP590, DP780.

• Damage mechanics is not required.

• Deformation-induced heating is a critical aspect.

• New constitutive form is needed for accurate predictions.

• Knowledge of strain hardening beyond eu is critical.

R. H. Wagoner 53

Definition of Normalized Stress

0.7/sdt/dσ/AF

σmaxUTS

omax

1

• UTS (DP590(C)) = 614 MPa

• UTS (DP590(B)) = 642 MPa

• UTS (DP780(D)) = 835 MPa

• UTS (TRIP780(D)) = 875 MPa

• UTS (DP980(D)) = 1014 MPa

R. H. Wagoner 54

Failure Type Map (V2/V1=0): DP590(B)

R. H. Wagoner 55

Failure Type Map (V2/V1=0): DP780(D)

R. H. Wagoner 5656

Failure Type Map (V2/V1 = 0): DP980(D)

R. H. Wagoner 57

Failure Type Map (V2/V1=0.5): DP590(B)

R. H. Wagoner 58

Failure Type Map (V2/V1=0.5): DP780(D)

R. H. Wagoner 5959

Failure Type Map (V2/V1 = 0.5): DP980(D)

R. H. Wagoner 6060

Summary: (R/t)*1 varies with material and V1

V1(mm/s) 51(127) 13(25) 2.5

DP590(B)-CR-1.4 6 3 2

DP780(D)-GI-1.4 6 3 3

DP980(D)-GA-1.45 11 4 4

• Shear / Tensile Failure Transition, (R/t)*1: V2/V1=0

• Shear / Tensile Failure Transition, (R/t)*1: V2/V1=0.5

V1(mm/s) 51(127) 13(25) 2.5

DP590(B)-CR-1.4 14 14 6

DP780(D)-GI-1.4 14 11 6

DP980(D)-GA-1.45 13 13 11

R. H. Wagoner 6161

V1(mm/s) 51(127) 13(25) 2.5

DP590(B)-CR-1.4 5 3 3

DP780(D)-GI-1.4 5 4 4

DP980(D)-GA-1.45 4 4 4

• Maximum Stress Transition, (R/t)*2: V2/V1=0

V1(mm/s) 51(127) 13(25) 2.5

DP590(B)-CR-1.4 4 3 4

DP780(D)-GI-1.4 4 4 5

DP980(D)-GA-1.45 4 4 4

• Maximum Stress Transition, (R/t)*2: V2/V1=0.5

Summary: (R/t)*2 almost independent of material

R. H. Wagoner 6262

Effect of Roller Condition (V2/V1 = 0): DP780(D)

Free rollerFixed roller

(R/t)*1 linefor free roller

(R/t)*1 linefor fixed roller

FreeFixed

* Direction of roller effect agrees with FE simulation (V2/V1=0 only)

R. H. Wagoner 63

400

500

600

700

800

0 0.03 0.06 0.09 0.12

Data 12

Tru

e Str

ess(

MPa)

True Strain

10-1/s 10-2/s10-2 /s 10-3/s

10-3/s 10-4/s

DP590(B)-CR-1.4mm

e=0.1

Jump Tests: DP590(B)-CR-1.4mm

R. H. Wagoner 64

Measurement of Strain Rate Sensitivity

1%1% 4%4%

m

mC

)(1

2

1

2

R. H. Wagoner 65

Preliminary Results: Interrupted Tests

AB C DE F

W. Gan, Unpublished Result, 2008W. Gan, Unpublished Result, 2008

R. H. Wagoner 66

1D Constitutive Equation: DP590(B)-CR-1.4mm

α Hollomon Voce

α1=0.743 K=1065 σo=666.7

α2=0.0035 n=0.182 A=0.5096

B=19.71

m=0.0043

CTTTHTh o2511 00 ),()()H=1.07e-4

CTTTwhere

ffTfo

VoceHollo

25

13

0021

);(

)(),()

sgm

/10,)()2 31

1

2

R. H. Wagoner

Commercial Sheet-Forming FE

• Problems with commercial sheet-forming FE: 1. No thermo-mechanical capability

2. No solid elements

• Solution to Problem 1:1. Calculate the adiabatic constitutive equation2. Use with isothermal FEA

R. H. Wagoner

Hardening Curve under Adiabatic Condition

0p

T dC

( , ) ( , , )adiabatic T

: temperature increase caused by adiabatic deformation heating

0

200

400

600

800

1000

1200

0 0.2 0.4 0.6 0.8 1

Flo

w S

tre

ss (

MP

a)

Plastic Strain

DP590(B)-CR-1.4mmd/dt=0.001/s

Adiabatic=843[1-0.44exp(-7.5)]

25oC=964[1-0.47exp(-3.9)]

R. H. Wagoner

Tensile Test Simulation

0

200

400

600

800

1000

1200

0 0.05 0.1 0.15 0.2

En

gin

eeri

ng

Str

ess

(MP

a)

Engineering Strain

DP780(D)-GI-1.4mm

Identical results:- T-M FE, d/dt=1/s- T-M FE, d/dt=1/s, adiabatic- FE, d/dt=1/s, adiabatic

FE (T=25oC), d/dt=1/s

*T-M = Thermo-Mechanical

R. H. Wagoner

Draw-Bend Simulation

0

0.2

0.4

0.6

0.8

1

1.2

-10 0 10 20 30 40 50 60

No

rmal

ize

d S

tres

s


DP780(D)-GI-1.4mmR/t=3.4, V

2/V

1=0

51mm/s(2/s)

Adiabatic lawV

1=51mm/s

(d/dt=2/s)

Isothermal (25oC)51mm/s(2/s)

2.5mm/s

(10-1/s)

0.025mm/s

(10-3/s)

10mm/s

(4X10-1/s)

Typical sheet forming rate:d/dt=10/s

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