INCREASING RUPTURE PREDICTABILITY FOR ALUMINUM

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INCREASING RUPTURE PREDICTABILITY FOR ALUMINUM Influence of anisotropy Daniel Riemensperger, Adam Opel AG Paul Du Bois, PDB 2 www.opel.com

CONTENT Introduction/motivation Isotropic & anisotropic material models Rupture criterion Conducted tests for characterization Validation Comparison Conclusion 3

INTRODUCTION / MOTIVATION Reducing weight + growing safety standards More ultra high strength materials Ductility and hardening as a safety buffer is diminished Rupture prediction essential for CAE driven product development Rupture prediction is limited by physical noises like material or geometry deviations by the applied numerical material and rupture model. Will the introduction of Anisotropy push this limitation? 4

Anisotropy DIRECTION DEPENDENCY Young's modulus A 90 A Yield strength 45 Hardening 0 Rolling direction Flow, necking and rupture Lankford coefficient R R = ε yy ε zz = ε yy ν ε xx = ε yy (ε xx + ε yy ) Ratio of lateral vs. thickness strain z x y z A - A 5

Force [N] Anisotropy TESTED ALUMINUM SHEET Young's modulus uniaxial tests Yield strength Hardening Flow, necking and rupture 0 45 90 Lankford coefficient R 0 ~R 45 ~R 90 ~0.5 displacement [mm] Transversely isotropic Model handling same as isotropic 6

force force Comparison Von Mises vs Barlat YIELD CRITERION Von Mises (*MAT_024): σ 1 Hosford(isotropic) / Barlat(anisotropic) (*MAT_036): test sim σ 2 7 displacement Von Mises displacement Hosford σ 1 = 2 σ 2 (η = 1 3 )

true stress [MPa] Comparison Von Mises vs Barlat NECKING BEHAVIOR Von Mises curve is reverse engineered yield curves necking point σ = σ Barlat curve is purely test based pt of rupture Barlat Von Mises plastic strain [-] 8 test simulation ( 0.5 mm)

Rupture criterion TRIAXIALITY Capture stress state in one value (The Lode angle parameter is not needed for elements following plane stress ) For plane stress(s ZZ =0, t XZ =0, t YZ =0) follows : Definition : h = hydrostatic stress deviatoric stress compression shear tension -2/3-1/3 0 1/3 2/3 9

Damage accumulation GISSMO ε eq.pl. D = ΔD D = 1 IP deleted D 0 =1E-12 ε f (η) LCSDG rupture starts D crit = D(ε crit η ) Δε p ECRIT localization starts η 10 D = D crit σ = σ D = 1 σ = 0 Eq. plastic strain at rupture is not equal to ε f (η) Coupling reduces the strength of the element prior to element deletion ductile fracture

l = 50mm r = 80mm r = 5mm Triaxality tests TEST GEOMETRIES Shear specimen Tensile ratio Notched specimen Principles : Plane stress as long as possible (b/t>4) Scalability of element size r = 80mm l = 8mm η = 0.577 Homogenous triaxiality in deformed area No local thickness reduction η~0 η~0.15 η~0.3 η = 0.4 0.55 11

Triaxality tests TEST GEOMETRIES - SHEAR Optimized radii and offsets to focus the load onto the center Symmetrical specimen : lateral deformation does not effect the test equipment Asymmetrical specimen : lateral deformation is test equipment 8 8 dependent Different rupture modes can be triggered for the same material 12

l = 50mm r = 80mm r = 5mm Triaxality tests TEST GEOMETRIES Shear specimen Tensile ratio Notched specimen Principles : Plane stress as long as possible (b/t>4) Scalability of element size r = 80mm l = 8mm η = 0.577 Homogenous triaxiality in deformed area No local thickness reduction Internal moment dissipation η~0 η~0.15 η~0.3 η = 0.4 0.55 13

Barlat with GISSMO smooth l=50mm double shear 0 double shear 35 double shear tensile eq. plastic strain [-] lcsdg ecrit 1st eroded element 2nd eroded element notched r=80mm, l=8mm notched r=80mm notched r=5mm 14 0 1/3 2/3 Triaxiality [-] Test

Von Mises with GISSMO smooth l=50mm double shear 0 double shear 35 double shear tensile eq. plastic strain [-] lcsdg ecrit 1st eroded element 2nd eroded element notched r=80mm, l=8mm notched r=5mm 15 0 1/3 2/3 Triaxiality [-] Test

true stress Comparison VON MISES VS BARLAT Yield curves Damage curves eq. plastic strain [-] lcsdg Barlat lcsdg Von Mises ecrit Barlat ecrit Von Mises true plastic strain Lankford coefficient R (1) 0.5 16 0 1/3 2/3 Triaxiality [-]

16.5 Three point bending test SETUP, TEST Small roll formed beam with continuous laser welds 250 mm 10.75 21.5 Rotational free cylindrical rests Cylindrical impactor 17

Three point bending test SETUP, SIMULATION Beam : Discretization [mm]: 0.5 (also 1.0, 1.5, 2.25, 4.5 not part of this presentation) Fully integrated shell elements (type 16) Laser weld as solid w/ constrained contact Rests : Rotational free 18 Double precision

Three point bending test TEST RESULTS Force [kn] 8 400 mm/min 20 mm/min 6 4 2 5 tests / 2 velocities Good reproducibility Only little strain rate dependency Variation in rupture deflection 19 0 10 20 30 Displacement [mm]

Three point bending test TEST RESULTS VS SIMULATION Force [kn] 8 Von Mises Barlat 6 4 2 Yielding is too soft Rupture too late Barlat and Von Mises similar 20 0 10 20 30 Displacement [mm]

Three point bending test ADDITIONAL TEST EVALUATION HV hardness Uniform, but for weld line Inner and outer radius Smaller than intended (1.5 mm < 2.3 mm) Overall geometry Angles and lengths deviate Geometry has to be adjusted 21

Three point bending test ADDITIONAL TEST EVALUATION HV hardness Uniform, but for weld line Inner and outer radius Smaller than intended (1.5 mm < 2.3 mm) Overall geometry Angles and lengths deviate Geometry has to be adjusted 22

Three point bending test ADDITIONAL TEST EVALUATION HV hardness Uniform, but for weld line Inner and outer radius nominal adjusted 10 mm Smaller than intended (1.5 mm < 2.3 mm) Overall geometry Angles and lengths deviate Geometry has to be adjusted 23

Three point bending test TEST RESULTS VS SIMULATION 8 6 von Mises Barlat Model geometry adjusted to test Process simulation mapped Friction set to µ=0.1 from 0.2 Force [kn] 4 2 Best rupture prediction Von Mises Too optimistic Barlat Still optimistic but close to test 24 0 10 20 30 Displacement [mm]

Three point bending test TEST RESULTS VS SIMULATION Von Mises Test Barlat 25

Three point bending test TEST RESULTS VS SIMULATION Bottom view Triaxiality Plastic strain Rupture imminent Barlat Von Mises 26

CONCLUSION An accurate yield criterion and flow law are fundamental, Von Mises law is not sufficient in this study Introduction of out of plain anisotropy has improved results significantly without increasing the model complexity Geometrical detail and process data have an immense impact on validation We need every piece of the puzzle 27

Daniel Riemensperger THANK YOU. 28