1. Predicting the Shear Failure of Dual-Phase Steels
Numiform 2010, Pohang, Korea
June 16, 2010
R. H. Wagoner, J.H. Kim1, J. Sung2, D. K. Matlock3, D.Y. Kim1
The Ohio State University
1KIMS, S. Korea
2Dongbu Steel, S. Korea
3Colorado School of Mines, USA

2. Outline Background Results Practical Application
Draw-Bend Fracture Test
Thermo-Mechanical (T-M) FEM
H/V Constitutive Equation
Results
Practical Application
Problems with Direct Use
Adiabatic Const. Eq.
Plane-strain FE Model
Analytical Model
Framework for R/t-Affected Failure
Conclusions 2

3. Background 3 3

4. Jim Fekete et al, AHSS Workshop, 2006
Shear Fracture of AHSS
Jim Fekete et al, AHSS Workshop, 2006

5. Unpredicted by FEA / FLD
Stoughton, AHSS Workshop, 2006 5

6. Draw-Bend Fracture Test
Background:
Draw-Bend Fracture Test 6 6

7. Draw-Bend Fracture Test (DBF): V1, V2 Constant
190.5 mm
Start
444.5 mm (10”)
V2 = aV1
Max. Finish R
190.5 mm
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
a = V2/V1: 0 and 0.3
Start
444.5 mm(10”) uf V1
Max. Finish
Wagoner et al., Esaform, 2009 7 7

8. 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) 8 8

9. Thermo-Mechanical FEM
Background:
Thermo-Mechanical FEM 9 9

10. FE Draw-Bend Model: Thermo-Mechanical (T-M)
U2, V2
hmetal,air = 20W/m2K
Abaqus Standard (V6.7)
3D solid elements (C3D8RT), 5 layers
Von Mises, isotropic hardening
Symmetric model
m = 0.04
hmetal,metal = 5kW/m2K
Kim et al., IDDRG, 2009
U1, V1

11. Selected Materials 11 11

12. H/V Constitutive Equation
1. Background:
H/V Constitutive Equation 12 12

13. “H/V” Constitutive Framework
Special:
Standard:
Sung et al., Int. J. Plast. 2010

14. “H/V” Constitutive Eq.: Large-Strain Verification14

15. FE Simulated Tensile Test: H/V vs. H, V15 15

16. Predicted ef, H/V vs. H, V: 3 alloys, 3 temperatures
Standard deviation of ef: simulation vs. experiment
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%) 16 16

17. 2. Results 17 17

18. Thermo-Mechanical Simulation
DP mm, V1=51mm/s, V2/V1=0, R/t=4.5

19. Isothermal Simulation
DP mm, V1=51mm/s, V2/V1=0, R/t=4.5

20. Front Stress vs. Front Displacement20

21. Displacement to Maximum Front Load vs. R / t21

22. Interim Conclusions
Deformation-induced heating dominates the error in predicting shear failures (FLD/FEM).
Damage also occurs, but is a smaller effect for most alloys. [Exception: DP 980(D) TD]
New constitutive equation is essential. (Large-strain accuracy, incorporate T in strain hardening.)
Most shear failures are predictable.
(But impractical: solid elements, T-M model.) 22

23. 3. Practical Application Problems with Direct Use23 23

24. DBF Test and FE vs. Industrial Practice and FE
~Plane strain
High rate / adiabatic Shell elements / Iso-T FE FLD – large R/t, low rate
Fracture?
Draw-Bend Test,
25mm Strip Width 24

25. DBF Formability: DP980(A), RD vs. TD
* Directional Formability: TD=RD 25 25

26. DBF Formability: DP980(D), RD vs. TD
* Directional Formability: RD>TD 26 26

27. 3. Practical Application
Adiabatic Const. Eq. 27 27

28. Simulated D-B Test: Effect of Draw Speed28

29. Adiabatic Constitutive Equation29

30. 3. Practical Application
Plane-Strain FE Model 30 30

31. FE Plane Strain DBF Model
U2, V2 = 0
Abaqus Standard (V6.7)
Plane strain solid elements (CPE4R), 5 layers
Von Mises, isotropic hardening
Isothermal, Adiabatic, Thermo-Mechanical
U1, V1

32. Plane Strain DBF Test
DP mm, R/t=3.4 32

33. 3. Practical Application Analytical Model (PS, Adiabatic)33 33

34. Analytical Plane Strain Bending Model
Fracture Criterion: Fracture occurs at Tmax for given R, to
Yoshida, 2003
Wagoner, 2007 34

35. Analytical Model Results for DP780 vs. PS FE35

36. DBF Interpretation: Plane-strain vs. Tension36

37. Analytical Model vs. DBF: DP98037

38. Framework for R/t-affected Failure
(Preliminary) 38 38

39. Inner and Outer Strains at Maximum Load39

40. Membrane Strains at Maximum Load40

41. Membrane Strains (R/t Affected Only)41

42. R/t-Affected Membrane Strains vs. t/R42

43. Analytical Model: Model vs. Fit43

44. Analytical Model: Model vs. Fit44

45. PS T-M Model: Model vs. Fit45

46. PS T-M Model: Model vs. Fit46

47. Next Steps
Simulate adiabatic limit strains – PS, 3-D, solid, shell. Add to framework.
Add simple fracture limit (emax?).
Apply R/t criterion to a) DBF results, b) practical forming problems (GM). 47

48. Conclusions
Simple models clarify DBF results. Three failure mechanisms: tension, R/t localization, fracture
Maximum tension load determines failure by plastic localization (Yoshida 2003, Hudgins 2010)
Promising framework introduced for predicting R/t-affected localization failures. 48

49. 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
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 (ISDN )
R. H. Wagoner and M. Li: Simulation of Springback: Through-Thickness Integration, Int. J. Plasticity, 2007, Vol. 23, Issue 3, pp
M. R. Tharrett, T. B. Stoughton: Stretch-bend forming limits of 1008 AK steel, SAE technical paper No , 2003.
M. Yoshida, F. Yoshida, H. Konishi, K. Fukumoto: Fracture Limits of Sheet Metals Under Stretch Bending, Int. J. Mech. Sci., 2005, 47, pp 49

50. Thank you ! 50

51. Material Parameters DP590 DP780 DP980 H (MPa) 1051 1655 1722 n 0.179
DP590
DP780
DP980
H (MPa)
1051
1655
1722 n
0.179
0.213
0.154
V (MPa)
643.9
752.1
908.1 A
0.576
0.265
0.376 B
22.44
30.31
39.64 b
2.67 E-4
5.78 E-4
3.86 E-4 a1
0.818
0.507
0.586 a2
1.93 E-3
1.87 E-3
1.49 E-3 a
2.0 E-3
3.0 E-3
2.1 E-3
1.03 E-2
1.15 E-2
8.6 E-3
(/s)
0.001
TRT(°C) 25 51

52. Material Properties Orientation Thickness (mm) UTS (MPa) 0.2% YS eu
(%) et n
r**
YS/UTS
DP590(B)-CR-1.4mm RD
1.35
605
352
15.9
23.2
0.21
1.02
0.58 TD
1.37
616
359
15.8
1.25 DD
620
351
16.3
23.6
0.83
0.57
DP780(D)-GI-1.4mm
1.40
815
499
12.7
17.9
0.19
0.87
0.61
810
486
12.9
17.2
0.18
0.69
0.60
803
480
18.1
0.89
DP980(D)-GA-1.45mm
1.43
1022
551
9.9
13.3
0.15
0.82
0.54
1021
584
9.4
0.13
0.80
986
511
1.04
0.52
TRIP780(D)-GA-1.6mm
1.60
857
471
14.9
19.2
0.22
0.81
0.55
1.57
860
501
13.9
18.4
1.20
844
481
21.3
1.03 52

53. Analytical Model – Curvilinear Derivation
Fracture Criterion: Fracture occurs at Tmax for given R, to 53

54. Uf: A More Sensitive Measure of Formability54 54

55. Peak Front Stress vs. Bending Ratio (R/t): DP 78055

56. Peak Front Stress vs. Bending Ratio (R/t): DP 98056

57. Peak Front Stress vs. Bending Ratio (R/t): DP 59057

58. Measured vs. Predicted Failure Types
V1 (mm/s)
R/t = 2.3
3.4
4.5
5.7
6.8
7.9
10.2
13.6
DP RD 51
III (III)
I (I) 13
2.5
I (III)
DP RD
III (I)
DP RD
V2/V1=0
Values in the parentheses are predicted ones.

59. Simplified FE Results 59