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

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

Introduction 3 3

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

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

“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

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

Approach: Draw-Bend Test

Draw-Bend Testing 9 9

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, 4.8 , 6.4, 11.1, 19.1 mm) 10 10

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

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

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

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

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 = - 0.07 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

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

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

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

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

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

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

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

(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

Constitutive Equations 24 24

1D Constitutive Equation

Comparison in Tensile Range (25oC)

Large-Strain Comparison (25oC)

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)

Simulated Tensile Test (50oC) 29

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

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

Large-Strain Comparison (DP780)

Large-Strain Comparison (DP980)

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

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

Role of Thermal Effects (Type III)

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

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

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

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

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

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

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

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

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

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

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

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

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

Effect of Strain Rate (DP780)

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

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.

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

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

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

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

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

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

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

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

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

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

Jump Tests: DP590(B)-CR-1.4mm 63 63

Measurement of Strain Rate Sensitivity 1% 4% 64

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

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

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

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

Tensile Test Simulation

Draw-Bend Simulation