Expansion Jianhui Shang, Steve Hatkevich, Larry Wilkerson American - PowerPoint PPT Presentation

Experimental Study and Numerical Simulation of Electromagnetic Tube Expansion Jianhui Shang, Steve Hatkevich, Larry Wilkerson American Trim LLC, Lima, Ohio USA *Thank Professor Glenn Daehn and Mr. Geoffrey Taber of the Ohio State University for the velocity measurement using PDV, and Pierre L'eplattenier of Livermore Software Technology Corporation for LS-DYNA software support ICHSF 2012 April 24-26, 2012 – Dortmund, Germany 1

Motivation 1. Electromagnetic forming involves large deformation, high velocity and high strain rate. 2. Tube expansion is a simple 2D axisymmetric forming process. 3. Photon Doppler Velocimeter (PDV) enables the reliable measurement of high velocity. 4. Electromagnetism module of LS-DYNA allows the simulation of electromagnetic forming. 5. Combination of PDV and LS-DYNA can help the study of the dynamic behavior of aluminum alloys at high strain rate and high velocity. ICHSF 2012 April 24-26, 2012 – Dortmund, Germany 2

Procedure PDV Electromagnetic Tube Expansion Tube Expansion Velocity Experiment Rogowski coil Comparison Current through Coil Input Output LS-DYNA Electromagnetism Tube Expansion Simulation Velocity Input Determine if material properties are suitable Material Properties including Dynamic Behavior ICHSF 2012 April 24-26, 2012 – Dortmund, Germany 3

Basic Layout of Electromagnetic Forming High current switch Tube Coil + + Charging + + System Capacitor bank + + ICHSF 2012 April 24-26, 2012 – Dortmund, Germany 4

Experimental Set-up High current switch Tube Coil PDV + + Charging Probe A + + System Capacitor bank + + PDV Probe B Rogowski Coil Rogowski coil measures current; PDV measures expansion velocity. ICHSF 2012 April 24-26, 2012 – Dortmund, Germany 5

Capacitor Bank Used A 16kJ Magneform machine in OSU (1) Maximum charging voltage is 8.66kV; (2) Total capacitance is 426µF; (3) Internal inductance is around 100nH; ICHSF 2012 April 24-26, 2012 – Dortmund, Germany 6

Three-turn Coil OD: 61mm; Gap between turns: 1.8mm; 6.3mm x 6.3mm cross section ICHSF 2012 April 24-26, 2012 – Dortmund, Germany 7

Al6061-T6 Tube PDV probe B (10mm away from Probe A) PDV probe A (Middle of 3-turn coil) OD of Al tube: 63.5 mm; Wall thickness: 0.89mm; Length: 45mm ICHSF 2012 April 24-26, 2012 – Dortmund, Germany 8

Velocity and Current Measurements (0.8 kJ) 80 80 Velocity B 60 60 Velocity A Current 40 40 Velocity (m/s) Current (kA) 20 20 0 0 -50 50 150 250 350 450 -20 -20 -40 -40 Time (micro-second) ICHSF 2012 April 24-26, 2012 – Dortmund, Germany 9

2D Axisymmetric Modeling G10 holder Al tube At the Cu 3-turn coil At the beginning of end of simulation simulation Axisymmetric axe ICHSF 2012 April 24-26, 2012 – Dortmund, Germany 10

2D Axisymmetric Modeling (Closer look) PDV probe B(10mm away from Probe A) Cu 3-turn coil PDV probe A (Middle of 3-turn coil) Al tube Axisymmetric axe ICHSF 2012 April 24-26, 2012 – Dortmund, Germany 11

Johnson-Cook Strength Model Johnson-Cook strength model was selected, because of high strain rate in electromagnetic forming. σ = + ε + ε − n * m ( A B )( 1 C ln )( 1 T )  Model for A (MPa) B (MPa) C n m T m (K) Al 6061-T6 Model 1 [1] 324 114 0.002 0.42 1.34 925 Model 2 [2] 275 500 0.02 0.3 1.0 925 Model 3 [3] 293 121.3 0.002 0.23 1.34 925 Model 4 [4] 289.6 203.4 0.011 0.35 1.34 925 ICHSF 2012 April 24-26, 2012 – Dortmund, Germany 12

Comparison--- Velocity A (0.8 kJ) 90 Model 1 80 Model 2 Model 3 70 1 Model 4 60 Measurement Velocity (m/s) 3 50 2 40 30 4 20 10 0 0 10 20 30 40 50 60 70 80 90 100 Time (micro-second) ICHSF 2012 April 24-26, 2012 – Dortmund, Germany 13

Comparison --- Velocity B (0.8 kJ) 50 Model 1 45 Model 2 40 Model 3 Model 4 35 Velocity (m/s) Measurement 30 25 20 15 10 5 0 0 10 20 30 40 50 60 70 80 90 100 Time (micro-second) ICHSF 2012 April 24-26, 2012 – Dortmund, Germany 14

Strain and Strain Rate for Position A (0.8 kJ) 2500 0.08 Effective plastic strain rate Effective plastic strain rate 0.07 Effective plastic strain 2000 Effective plastic strain 0.06 0.05 1500 (/s) 0.04 1000 0.03 0.02 500 0.01 0 0 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 Time (micro-second) ICHSF 2012 April 24-26, 2012 – Dortmund, Germany 15

Stress-strain Plots for Position A (0.8 kJ) 700 Model 1 2 600 Model 2 Effective stress (MPa) 4 Model 3 500 Model 4 400 300 1 3 200 100 0 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 Effective plastic strain ICHSF 2012 April 24-26, 2012 – Dortmund, Germany 16

Parameters for J-C model σ = + ε + ε − n * m ( A B )( 1 C ln  )( 1 T ) Model for A (MPa) B (MPa) C n m T m (K) Al 6061-T6 Model 1 324 114 0.002 0.42 1.34 925 Model 2 275 500 0.02 0.3 1.0 925 Model 3 293 121.3 0.002 0.23 1.34 925 Model 4 289.6 203.4 0.011 0.35 1.34 925 (1) Strain rate sensitivity C should be small for Al 6061-T6; (2) Strain hardening has smaller effect than strain rate hardening in this case; ICHSF 2012 April 24-26, 2012 – Dortmund, Germany 17

Summary 1) PDV was applied for the velocity measurement and Ls- dyna electromagnetism module was applied for the simulation of the Al 6061-T6 tube EM expansion; 2) Comparison between the numerical and experimental results showed the good agreement; 3) Four different parameter sets for Johnson-Cook strength model were used in the numerical simulation. The results showed that the value of the strain rate sensitivity for Al 6061-T6 should be small; 4) Strain rate hardening has larger effect in EM expansion; ICHSF 2012 April 24-26, 2012 – Dortmund, Germany 18

Acknowledgement The authors would like to thank Professor Glenn Daehn and Mr. Geoffrey Taber of the Ohio State University for the experiment and the velocity measurement using PDV, and Pierre L'eplattenier of Livermore Software Technology Corporation for LS-DYNA software support. References of J-C strength model parameters: (1) Corbett, B.: Numerical simulations of target hole diameters for hypervelocity impacts into elevated and room temperature bumpers. International Journal of Impact Engineering 33 (2006), p. 431-440. (2) Elsen, A.; Ludwig, M.; Schaefer, R.; Groche, P.: Fundamentals of EMPT-Welding. Proceedings of 4th International Conference on High Speed Forming, Columbus, OH, 2010, p.117-126. (3) Rule, W.: A numerical scheme for extracting strength model coefficients from Taylor test data. International Journal of Impact Engineering 19 (1997), p.797-810. (4) Fish, J.: Al 6061-T6 - elastomer impact simulations. Technical report, 2005. ICHSF 2012 April 24-26, 2012 – Dortmund, Germany 19

Questions? ICHSF 2012 April 24-26, 2012 – Dortmund, Germany 20