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

2. 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

3. R. H. Wagoner 3 1.Background – Shear Fracture, 2006

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

5. R. H. Wagoner 5 Shear Fracture of AHSS - 2011 Forming Technology Forum 2012 Web site: http://www.ivp.ethz.ch/ftf12http://www.ivp.ethz.ch/ftf12

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

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

8. R. H. Wagoner 8 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.

9. R. H. Wagoner 999 NSF Workshop on AHSS (October 2006) Elongation (%) Tensile Strength (MPa) 0 10 20 30 40 50 60 70 060012003009001600 DP, CP TRIP MART HSLA IF Mild IF- HS BH CMn ISO Elongation (%) 600 TWIP AUST. SS L-IP ISO R. W. Heimbuch: An Overview of the Auto/Steel Partnership and Research Needs [1]

10. R. H. Wagoner 10 2. DBF Results & Simulations, 2011

11. 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

12. R. H. Wagoner DBF Failure Types Type I Type II Type III 65 o 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

13. R. H. Wagoner DBF Test: Effect of R/t 13

14. R. H. Wagoner 14 “H/V” Constitutive Eq.: Large-Strain Verification

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

16. R. H. Wagoner Predicted e f, H/V vs. H, V: 3 alloys, 3 temperatures 16 HollomonVoceH/V DP5900.05 (23%)0.05 (20%)0.02 (7%) DP7800.03 (18%)0.04 (22%)0.01 (6%) DP9800.04 (30%)0.03 (21%)0.01 (5%) Standard deviation of e f : simulation vs. experiment

17. R. H. Wagoner 17 FE Draw-Bend Model: Thermo-Mechanical (T-M) h metal,air = 20W/m 2 K h metal,metal = 5kW/m 2 K  = 0.04 U 1, V 1 U 2, V 2 Abaqus Standard (V6.7) 3D solid elements (C3D8RT), 5 layers Von Mises, isotropic hardening Symmetric model Kim et al., IDDRG, 2009

18. R. H. Wagoner Front Stress vs. Front Displacement 18

19. R. H. Wagoner Displacement to Maximum Front Load vs. R / t 19

20. R. H. Wagoner 20 Is shear fracture of AHSS brittle or ductile?

21. R. H. Wagoner Fracture Strains: DP 780 (Typical) 21

22. R. H. Wagoner Fracture Strains: TWIP 980 (Exceptional) 22

23. R. H. Wagoner Directional DBF : DP 780 (Typical) 23

24. R. H. Wagoner Directional DBF Formability: DP980 (Exceptional) 24

25. 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.)

26. R. H. Wagoner 26 3. Practical Application - 2012

27. R. H. Wagoner 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

28. R. H. Wagoner Ideal DBF Test: Plane Strain, High Rate 28

29. R. H. Wagoner Ideal Test Results - Stress 29

30. R. H. Wagoner Ideal Test Results - Strain 30

31. R. H. Wagoner How to Use Practically: Bend, Unbend Regions 31

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

33. R. H. Wagoner Practical Application of SF FLD – (2) Indirect 33 For each element drawn over contact Known: (R, t) contact  P max   * PS tension   * PS tension Predicted Fracture:  FEA >  * PS tension Wu, Zhou, Zhang, Zhou, Du, Shi: SAE 2006-01-0349.

34. R. H. Wagoner Calculation: Indirect Method 34

35. 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?)

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

37. R. H. Wagoner What is Needed? 37 P max = f(R/t) (PS, high-speed DBF)  membrane = f(R/t) (PS, high-speed DBF)

38. R. H. Wagoner 38 FE Plane Strain DBF Model  = 0.06 U 1, V 1 U 2, V 2 = 0 Abaqus Standard (V6.7) Plane strain solid elements (CPE4R), 5 layers Von Mises, isotropic hardening Isothermal, Adiabatic, Thermo-Mechanical

39. R. H. Wagoner Adiabatic Constitutive Equation 39

40. R. H. Wagoner Peak Stress, Plane-Strain: DP980 40

41. R. H. Wagoner Membrane Strains at Maximum Load 41

42. R. H. Wagoner Analytical Model: Model vs. Fit 42

43. R. H. Wagoner Analytical Model: Model vs. Fit 43

44. 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.)

45. R. H. Wagoner 45 Thank you.

46. 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.Vol. 23, Issue 3 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.

47. R. H. Wagoner 47 Extra Slides

48. R. H. Wagoner DP Steels 48

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

50. R. H. Wagoner Simulated D-B Test: Effect of Draw Speed 50

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

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

53. R. H. Wagoner Analytical Model – Curvilinear Derivation 53 Fracture Criterion: Fracture occurs at T max for given R, t o

54. R. H. Wagoner DBF Interpretation: Plane-strain vs. Tension 54

55. R. H. Wagoner Inner and Outer Strains at Maximum Load 55

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

57. R. H. Wagoner R/t-Affected Membrane Strains vs. t/R 57

58. R. H. Wagoner Forming Limit Diagram 58 Ref: Hosford & Duncan

59. R. H. Wagoner PS T-M Model: Model vs. Fit 59

60. R. H. Wagoner PS T-M Model: Model vs. Fit 60

61. R. H. Wagoner 61 Draw-Bend Fracture Test (DBF): V 1, V 2 Constant Start Max. Finish V1V1 Start R 444.5 mm (10”) 190.5 mm 444.5 mm(10”) V 2 =  V 1 ufuf 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  = V 2 /V 1 : 0 and 0.3 Wagoner et al., Esaform, 2009

62. R. H. Wagoner AHSS vs. HSLA 62 Ref: AISI AHSS Guidelines