1. Draw-Bend Fracture Prediction with Dual-Phase Steels
R. H. Wagoner
September 25, 2012
AMPT
Wollongong, Australia

2. Outline Background – Shear Fracture, 2006
DBF Results & Simulations, 2011
Intermediate Conclusions
Practical Application, 2012
Ideal DBF Test
Recommended Procedure
No Ideal Test?
Results, 2

3. Background – Shear Fracture, 20063 3

4. Shear Fracture of AHSS – 2005 Case
Jim Fekete et al, AHSS Workshop, 2006

5. Shear Fracture of AHSS - 2011
Forming Technology Forum 2012 Web site:

6. Unpredicted by FEA / FLD
Stoughton, AHSS Workshop, 2006 6

7. Shear Fracture: Related to Microstructure?
Ref: AISI AHSS Guidelines

8. Conventional Wisdom, 2006 Shear fracture… Notes:
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.

9. 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] 9 9 9

10. 2. DBF Results & Simulations, 201110 10

11. 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
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
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

12. DBF Failure Types Type I: Tensile failure (unbent region)
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) 12 12

13. DBF Test: Effect of R/t 13

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. 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

18. Front Stress vs. Front Displacement18

19. Displacement to Maximum Front Load vs. R / t19

20. Is shear fracture of AHSS
brittle or ductile? 20 20

21. Fracture Strains: DP 780 (Typical)21 21

22. Fracture Strains: TWIP 980 (Exceptional)22 22

23. Directional DBF : DP 780 (Typical)23 23

24. Directional DBF Formability: DP980 (Exceptional)24 24

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.) 25

26. 3. Practical Application - 201226 26

27. 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 27

28. Ideal DBF Test: Plane Strain, High Rate28

29. Ideal Test Results - Stress29

30. Ideal Test Results - Strain30

31. How to Use Practically: Bend, Unbend Regions31

32. Practical Application of SF FLD – (1) Direct
For each element in contact
Known: R, t  e*membrane
Predicted Fracture: eFEA > e*membrane 32

33. Practical Application of SF FLD – (2) Indirect
For each element drawn over contact
Known: (R, t)contact  Pmax  s*PS tension  e*PS tension
Predicted Fracture: eFEA > e*PS tension
Wu, Zhou, Zhang, Zhou, Du, Shi: SAE 33

34. Calculation: Indirect Method
Example: von Mises Yield, Hollomon Hardening
Von Mises: 𝝈 ∗ 𝑷𝑺𝑻 = 𝟑 𝟐 𝑷 𝒎𝒂𝒙 𝑨
Hollomon: 𝝈=𝑲 𝜺 𝒏
So: 𝝈 ∗ 𝑷𝑺𝑻 = 𝟑 𝟐 𝑲 𝜺 ∗ 𝑷𝑺𝑻 𝒏  𝜺 ∗ 𝑷𝑺𝑻 = 𝟐 𝟑 𝝈 ∗ 𝑲 𝟏/𝒏 34

35. Recommended Procedure with Industrial FEA
Use adiabatic law in FEA, use rate sensitivity
Classify each element based on X-Y position (tooling)
Bend (plane-strain)
After bend (plane-strain)
General (not Bend, not After)
Apply 4 criteria:
FLD (Bend, After)
Direct SF (Bend)
Indirect SF (After)
Brittle Fracture* (All?) 35

36. 4. No Ideal Test?
(What to do?) 36 36

37. e*membrane = f(R/t) What is Needed? Pmax = f(R/t) (PS, high-speed DBF)37

38. 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

39. Adiabatic Constitutive Equation39

40. Peak Stress, Plane-Strain: DP98040

41. Membrane Strains at Maximum Load41

42. Analytical Model: Model vs. Fit42

43. Analytical Model: Model vs. Fit43

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.) 44

45. Thank you. 45 45

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
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 46

47. Extra Slides 47 47

48. DP Steels 48 48

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

50. Simulated D-B Test: Effect of Draw Speed50

51. DBF Formability: DP980(A), RD vs. TD (Typical)
* Directional Formability: TD=RD 51 51

52. DBF Formability: DP980(D), RD vs. TD (Exceptional)
* Directional Formability: RD>TD 52 52

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

54. DBF Interpretation: Plane-strain vs. Tension54

55. Inner and Outer Strains at Maximum Load55

56. Membrane Strains (R/t Affected Only)56

57. R/t-Affected Membrane Strains vs. t/R57

58. Forming Limit Diagram
Ref: Hosford & Duncan 58

59. PS T-M Model: Model vs. Fit59

60. PS T-M Model: Model vs. Fit60

61. 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 61 61

62. Ref: AISI AHSS Guidelines
AHSS vs. HSLA
Ref: AISI AHSS Guidelines 62