1. Plasticity and Failure of Advanced High Strength Steels
R.H. Wagoner, Ji Hyun Sung, A. Madeshia, Ji Hoon Kim

2. Outline Introduction Draw-Bend Testing Constitutive Equations
Draw-Bend Simulations
Conclusions

3. Introduction 3 3

4. NSF Workshop on AHSS (October 2006)70
L-IP 60
AUST. SS
TWIP 50 IF
IF- HS
Elongation (%)
Elongation (%) 40
Mild
ISO
ISO 30 BH
TRIP
CMn 20
HSLA
DP, CP 10
MART
300
600
600
900
1200
1600
Tensile Strength (MPa)
R. W. Heimbuch: An Overview of the Auto/Steel Partnership and Research Needs [1] 4 4 4

5. Unexpected Forming Failures
Comparison between FE / FLD simulation and practice.
Stoughton, AHSS Workshop, 2006

6. “Shear Failure?” FLD Tensile localization map (+ biaxial) AHSS
“Shear failure” at die radii, minimal width or thickness strain
Lou, XY, Int. J. Plasticity,
23, 1, 2007, 84
Mg AZ31B Al 6013
(Shear type) (Tensile localization) 6 6

7. Jim Fekete et al., AHSS Workshop, 2006
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 7

8. Approach: Draw-Bend Test

9. Draw-Bend Testing 9 9

10. Draw-Bend Fracture Testing
Start
Max. Finish V1 R
317.5 mm
190.5 mm
435.5 mm
V2 = aV1
u1 = V1 Dt
R: 1/8, 3/16, 1/4, 7/16, 3/4 inch
(3.2, , 6.4, 11.1, 19.1 mm) 10 10

11. Phenomenological Failure Types
Type I
Type II
Type III
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) 11 11

12. Failure Types: DP590(B)-CR-1.4mm
R/t = 2.27 , V1 = 2.54 mm/s, e = 0.37 , de/dtmax = 0.22 /s II I
III
DXc = 6mm
V2/V1 = 0
= 0.96
DXc = 17mm
= 0.92
V2/V1 = 0.25
DXc = 43mm
= 0.89
V2/V1 = 0.50

13. Transition: Type II  III (DP590)
R/t = 2.57, V1 = 127 mm/s, em = 0.33 , de/dtmax = 7.95 /s II
III
III
III
V2/V1 = 0.25
V2/V1 = 0.20
V2/V1 = 0.20
V2/V1 = 0.10
DXc = 24
DXc = 20
DXc = 20
DXc = 16
= 0.94
= 0.93
= 0.93
= 0.95

14. Infrared Temperature Measurements
Tmax ~ 50 to 100oC near fracture
Type III
Differential temperature rise along the width

15. IR Results - Type III (Fracture) t = - 0.07 s t = 0 s t = 0.07 s
100
200
300
400
500
600
700
800 20 30 40 50 60 70 80
0.2
0.4
0.6
0.8 1
Time (sec)
Front stress
Back stress 2 3 4
C_ DP590
2.65
R/t
25.4 mm w V2
127 mm/s V1
t = s
t = 0 s
t = 0.07 s
t = 0.14 s
Calibration
Material
V1 (mm/s)
TTC
(oC)
TFLIR e
(emissivity) DT
DP590(C)-GA-1.75mm
127
60.25
53.8
0.7
6.5

16. Controlled Draw-Bend Parameters
R/t em= ln(1+tsheet/R), em=tsheet/R
V1 emax~ em/DD, DD~3tsheet/V1 (FEA)
V2/V1 related to DXc at failure .
Observed Role of Parameters
R/ti ( emh & de/dtmax h ) IgIII
V2/V1h ( DXch ) IgIII
V1h ( de/dtmax h) IgIII

17. Definition of Normalized Stress
Maximum Pull Force / Original Area
s =
Ultimate Tensile Strength (at e = 0.7/s) .

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

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

20. Failure Types (V2/V1=0) DP590(C)-GA-1.75mm R/t (em) g V1 (mm/s) i 127
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 25
0.95
0.98
0.97
2.5
0.91
0.94
0.93
Key
Type I
Type II
Type III
DP590(B)-CR-1.4mm
R/t (em) g
V1 (mm/s) i
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
2.5
0.94
0.97
0.93

21. Failure Type Map (DP780, V2/V1=0)21

22. Failure Type Map (TRIP780, V2/V1=0)22

23. (R/t)*1 and (R/t)*2 for D-P Steels (V2/V1=0)
Shear / Tensile Transition, (R/t)*1 [ = f (matl, V1) ]
V1(mm/s)
51(127)
13(25)
2.5
DP590(B)-CR-1.4 6 3 2
DP780(D)-GI-1.4
DP980(D)-GA-1.45 11 4
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
DP780(D)-GI-1.4 5
DP980(D)-GA-1.45 23 23

24. Constitutive Equations24 24

25. 1D Constitutive Equation

26. Comparison in Tensile Range (25oC)

27. Large-Strain Comparison (25oC)

28. Thermo-Mechanical FE Simulation
Tinitial = 25oC
Grip
hmetal, air = 20 W/m2K
Sample
hmetal,metal = 5 kW/m2K
Abaqus Standard (V6.7)
3D solid elements (C3D8RT), 2 layers
Von Mises, isotropic hardening
Symmetric model
Grip
Gage region (2% taper)

29. Simulated Tensile Test (50oC)29

30. Predicted Ductility (ef): DP590
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%)
* ef is defined by measured fractional load drop at failure 30

31. Predicted Ductility (ef): DP 590, 780, 980
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%) 31 31

32. Large-Strain Comparison (DP780)

33. Large-Strain Comparison (DP980)

34. Draw-Bend Simulations (Coupled Thermo-Mechanical FEM)
Note: Test results are shown for fixed roller and lubricated condition. 34 34

35. FE Draw-Bend Model U2, V2 hmetal,air = 20W/m2K Abaqus Standard (V6.7)
3D solid elements (C3D8RT), 5 layers
Von Mises, isotropic hardening
Symmetric model
m = 0.08
hmetal,metal = 5kW/m2K
U1, V1

36. Role of Thermal Effects (Type III)

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

38. R/t = 7.9, V1=127mm/s, V2/V1=0 (Type I)
Temperature (oC)
117mm
52oC
ep=0.16
99oC, ep=0.41
(93oC measured)
Type I
F=Fmax
U1=46mm
F=0.9Fmax
U1=61mm

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

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

41. R/t = 3.4, V1=127mm/s, V2/V1=0.5 (Type II)
Temperature (oC)
Type II
10mm
101oC, ep=0.38
(93oC measured)
157oC
ep=0.65
F=Fmax
U1=61mm
F=0.9Fmax
U1=67mm

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

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

44. R/t = 3.4, V1=127mm/s, V2/V1=0 (Type III)
Temperature (oC)
Type III
155oC
ep=0.72
87oC, ep=0.39
(80oC measured)
F=Fmax
U1=44mm
F=0.9Fmax
U1=46mm

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

46. Observed vs. Simulated Failure (DP590)
DP590(B)-CR-1.4mm
Key: Type I, Type II, Type III
V2/V1=0
R/t g
V1 (mm/s) i
2.3
3.4
4.5
7.9
13.5
127
0.96
0.99
1.00 25
2.5
0.97
0.98
V2/V1=0.5
R/t g
V1 (mm/s) i
2.3
3.4
4.5
7.9
13.5
127
0.86
0.93
0.96
0.99 25
0.95
0.98
2.5
0.88
0.94 46

47. Observed vs. Simulated Failure (DP780)
DP780(D)-GI-1.4mm
Key: Type I, Type II, Type III
V2/V1=0
R/t g
V1 (mm/s) i
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
2.5
V2/V1=0.5
R/t g
V1 (mm/s) i
2.3
3.4
4.5
7.9
13.5 51
0.83
0.87
0.91
0.93
0.94 13
0.82
0.90
0.92
2.5
0.88 47

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

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

50. Effect of Strain Rate (DP780)

51. Conclusions
Note: All test results are shown for fixed roller and lubricated condition. 51 51

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.

53. Definition of Normalized Stress
sUTS (DP590(C)) = 614 MPa
sUTS (DP590(B)) = 642 MPa
sUTS (DP780(D)) = 835 MPa
sUTS (TRIP780(D)) = 875 MPa
sUTS (DP980(D)) = 1014 MPa 53 53

54. Failure Type Map (V2/V1=0): DP590(B)54

55. Failure Type Map (V2/V1=0): DP780(D)55

56. Failure Type Map (V2/V1 = 0): DP980(D)56 56

57. Failure Type Map (V2/V1=0.5): DP590(B)57

58. Failure Type Map (V2/V1=0.5): DP780(D)58

59. Failure Type Map (V2/V1 = 0.5): DP980(D)59 59

60. Summary: (R/t)*1 varies with material and V1
Shear / Tensile Failure Transition, (R/t)*1: 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
DP980(D)-GA-1.45 11 4
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 6
DP780(D)-GI-1.4 11
DP980(D)-GA-1.45 13 60 60

61. Summary: (R/t)*2 almost independent of material
Maximum Stress Transition, (R/t)*2: V2/V1=0
V1(mm/s)
51(127)
13(25)
2.5
DP590(B)-CR-1.4 5 3
DP780(D)-GI-1.4 4
DP980(D)-GA-1.45
Maximum Stress Transition, (R/t)*2: V2/V1=0.5
V1(mm/s)
51(127)
13(25)
2.5
DP590(B)-CR-1.4 4 3
DP780(D)-GI-1.4 5
DP980(D)-GA-1.45 61 61

62. Effect of Roller Condition (V2/V1 = 0): DP780(D)
(R/t)*1 line
for fixed roller
Free roller
Fixed roller
Fixed
Free
(R/t)*1 line
for free roller
* Direction of roller effect agrees with FE simulation (V2/V1=0 only) 62 62

63. Jump Tests: DP590(B)-CR-1.4mm63 63

64. Measurement of Strain Rate Sensitivity1% 4% 64

65. W. Gan, Unpublished Result, 2008
Preliminary Results: Interrupted Tests A B C D E F
W. Gan, Unpublished Result, 2008 65

66. 1D Constitutive Equation: DP590(B)-CR-1.4mm
H=1.07e-4
m=0.0043 α
Hollomon
Voce
α1=0.743
K=1065
σo=666.7
α2=0.0035
n=0.182
A=0.5096
B=19.71 66

67. 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 equation 2. Use with isothermal FEA

68. Hardening Curve under Adiabatic Condition
: temperature increase caused by adiabatic deformation heating

69. Tensile Test Simulation

70. Draw-Bend Simulation