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

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

Background 3 3

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

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

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

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

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

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

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

Selected Materials 11 11

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

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

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

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

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

2. Results 17 17

Thermo-Mechanical Simulation DP780-1.4mm, V1=51mm/s, V2/V1=0, R/t=4.5

Isothermal Simulation DP780-1.4mm, V1=51mm/s, V2/V1=0, R/t=4.5

Front Stress vs. Front Displacement 20

Displacement to Maximum Front Load vs. R / t 21

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

3. Practical Application Problems with Direct Use 23 23

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

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

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

3. Practical Application Adiabatic Const. Eq. 27 27

Simulated D-B Test: Effect of Draw Speed 28

Adiabatic Constitutive Equation 29

3. Practical Application Plane-Strain FE Model 30 30

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

Plane Strain DBF Test DP780-1.4mm, R/t=3.4 32

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

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

Analytical Model Results for DP780 vs. PS FE 35

DBF Interpretation: Plane-strain vs. Tension 36

Analytical Model vs. DBF: DP980 37

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

Inner and Outer Strains at Maximum Load 39

Membrane Strains at Maximum Load 40

Membrane Strains (R/t Affected Only) 41

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

Analytical Model: Model vs. Fit 43

Analytical Model: Model vs. Fit 44

PS T-M Model: Model vs. Fit 45

PS T-M Model: Model vs. Fit 46

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

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

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. 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. 49

Thank you ! 50

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

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

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

Uf: A More Sensitive Measure of Formability 54 54

Peak Front Stress vs. Bending Ratio (R/t): DP 780 55

Peak Front Stress vs. Bending Ratio (R/t): DP 980 56

Peak Front Stress vs. Bending Ratio (R/t): DP 590 57

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 DP590-1.4-RD 51 III (III) I (I) 13 2.5 I (III) DP780-1.4-RD III (I) DP980-1.45-RD V2/V1=0 Values in the parentheses are predicted ones.

Simplified FE Results 59