1. R. H. Wagoner 1 Thermally-Enhanced Forming of Mg Sheets Midterm Report, Dec. 5, 2008 - May 31, 2009 Robert H. Wagoner R. Wagoner, LLC 144 Valley Run Place Powell OH 43065

2. R. H. Wagoner 2 One-Year Project Goals (from Research Agreement, signed December 5, 2008) Task “1. Formulate a simple, approximate, constitutive equation based on simple testing temperature at a range of temperatures, rates and strains that is suitable for implementation in commercial sheet-forming softward (LS-Dyna, PamStamp, etc.). ” Status: First fitting completed. (For Posco AZ31B material provided.) To be improved. Task “2. Develop a thermo-mechanical FE model of a simplified sample part to be specified by Posco.” Status: The simplified model has been constructed in Abaqus and preliminary testing has been done. Will perform simulations using Abaqus for comparison with Posco simulation using LS-Dyna or PamStamp. Will refine thermal model. Task “3. Using the constitutive equation of Goal 2 and the FE model of Goal 3, identify optimal thermally-assisted forming strategies for the sample part.” Status: Not started yet.

3. R. H. Wagoner 3 Summary Task I. Constitutive Equation Measurement -A. Tensile testing – AUSTEM Mg AZ31B -B. Screening of material (use 118-5) -C. Tensile testing - Posco Mg AZ31B -D. Fitting to 3 laws: H, V, H&V -E. Test with FEA simulation Task II. Postech/Posco Formability Test Simulation -A. Put in ABAQUS model -B. Modify B.C. for convergence -C. Preliminary simulation using Posco/Postech constitutive eq* * K. Oh and et al., “Development of New Formability Test for Sheet Materials using Axiomatic Design”, submitted to J. Mater. Proc. Tech.. 150 o C200 o C250 o C300 o C 10 -1 /sxxxx 10 -2.5 /sxxxx 10 -4 /sxxx

4. R. H. Wagoner 4 Summary of Properties of Mg sheets MaterialThickness (mm)YS (MPa)UTS (MPa) Ave.Standard Dev. Ave.Standard Dev. Ave.Standard Dev. 108-50.9960.00719752843 118-50.9730.00919732842 336-31.0200.00719622802 material used

5. R. H. Wagoner 5 Tensile Test Results: AUSTEM vs. Posco Mg AZ31B

6. R. H. Wagoner 6 Tensile Tests of Mg AZ31B at 150 o C & 200 o C

7. R. H. Wagoner 7 Tensile Tests of Mg AZ31B at 250 o C & 300 o C

8. R. H. Wagoner 8 Tensile Test Results: Posco Mg AZ31B

9. R. H. Wagoner 9 Tensile Tests of Mg AZ31B at 10 -1 /s & 10 -2.5 /s

10. R. H. Wagoner 10 Tensile Test of Mg AZ31B at 10 -4 /s

11. R. H. Wagoner 11 Constitutive Equation Framework Three versions: # Parameters (h(T) w/1 parameter) 1) Hollomon: 4 2) Voce: 5 3) H / V: 8 = 3 choices Hollomon: Voce: H / V:

12. R. H. Wagoner 12 Fitting Procedure Least squares fit to 4, 5, or 8 parameters, using tensile data from 0.02 – Software: SigmaPlot Starting parameters were varied in this order: K 1, K 2 = 50, 100, …, 1000 n = 0.05, 0.06, …, 0.5 m = 0.05, 0.06, …, 0.2 B = 0.01, 0.05,…, 0.5 C = 5, 10, …, 200 = 0.1, 0.2, …,1 Least squares fit => K1, n, m, K2, B, C,, (smallest standard dev.)

13. R. H. Wagoner 13 Choice of Temperature Function h(T) “T-1” “T-2” “T-exp”

14. R. H. Wagoner 14 Least-Squares Fits Para.H T-1 H T-2 H T-exp V T-1 V T-2 V T-exp H&V T-1 H&V T-exp K 1 (MPa) 2934404922000435 n 0.13760.13130.13040.64390.0943 K 2 (MPa) 5624204952000 B 0.71690.43020.45450.84180.8648 C 1.57266.73285.71930.16360.6974 m 0.0916 0.09170.09190.09160.09190.09170.0914 k0.73191.86030.73041.85121.83161.8594 k1k1 -0.5699-0.5629 k2k2 1.39511.3863 -0.08900.0103 0.86920.9006 Stand. Dev. 11 (MPa) 8 (MPa) 8 (MPa) 11 (MPa) 7 (MPa) 8 (MPa) 9 (MPa) 8 (MPa) (Current Best Eq.)

15. R. H. Wagoner 15 Fitting of Tensile Test at 150 o C & 200 o C

16. R. H. Wagoner 16 Fitting of Tensile Test at 250 o C & 300 o C

17. R. H. Wagoner 17 Test of Best-Fit Constitutive Equations FEM model, using ABAQUS software Uniform temperature distribution Solid element: C3D8R Material property: Voce Law – (T-2) Tensile test simulations:

18. R. H. Wagoner 18 Tensile test of Mg AZ31B – Voce (T-2)

19. R. H. Wagoner 19 Tensile test of Mg AZ31B – Voce (T-2)

20. R. H. Wagoner 20 PosTech / Posco Formability Test Simulation

21. R. H. Wagoner 21 Simulation of Stamping Process ABAQUS/Standard Material: 340BH* Thickness = 0.738 mm * Contact: Friction coefficient: 0.15* The z-coordinates of the nodes in blankholder which were not 0 were changed to 0. K. Oh and et al., Development of New Formability Test for Sheet Materials using Axiomatic Design, J. Mater. Proc. Tech. (submitted)

22. R. H. Wagoner 22 Current Results vs. Oh paper*, Fig. 14 Minor strain distribution Holding force = 300kN Drawing depth = 60 mm A B C D A B C D Oh paper * Fig. 14(c) Current results K. Oh and et al., Development of New Formability Test for Sheet Materials using Axiomatic Design, J. Mater. Proc. Tech. (submitted)

23. R. H. Wagoner 23 C D A B C D A B Current Results vs. Oh paper*, Fig. 14 Oh paper * Fig. 14(c) Current results Minor strain distribution Holding force = 300kN Drawing depth = 60 mm K. Oh and et al., Development of New Formability Test for Sheet Materials using Axiomatic Design, J. Mater. Proc. Tech. (submitted)

24. R. H. Wagoner 24 Thickness distribution Holding force = 100kN Drawing depth = 30 mm To be compared with Fig. 9 (a)* Thickness distribution Holding force = 300kN Drawing depth = 30 mm A B C D A B C D Current Results vs. Oh paper*, Fig. 9 To be compared with Fig. 9 (a)* K. Oh and et al., Development of New Formability Test for Sheet Materials using Axiomatic Design, J. Mater. Proc. Tech. (submitted)

25. R. H. Wagoner 25 A B C D K. Oh and et al., Development of New Formability Test for Sheet Materials using Axiomatic Design, J. Mater. Proc. Tech. (submitted) Current Results and Oh paper*, Fig. 9 To be compared with data for Fig. 9 (c)* Thickness distribution Holding force = 500kN Drawing depth = 30 mm

26. R. H. Wagoner 26 Note R. Wagoner LLC requests the original Oh data* for Figure 9 and possibly other draw depths and variables (thickness strain, von Mises strain) for comparison with current results. Also, as shown on the next slide, punch force vs. draw depths could be compared. The paper does not clearly show those results. K. Oh and et al., Development of New Formability Test for Sheet Materials using Axiomatic Design, J. Mater. Proc. Tech. (submitted)

27. R. H. Wagoner 27 Punch Force vs. Draw Depth CPU Time (hour) 100kN2.8 300kN2.7 500kN2.6 * K. Oh and et al., “Development of New Formability Test for Sheet Materials using Axiomatic Design”, submitted to J. Mater. Proc. Tech..

28. R. H. Wagoner 28 Conclusions Tensile tests of Posco Mg AZ31B have been carried out, 150 o C - 300 o C, 10 -1 /s - 10 -4 /s. A preliminary constitutive model reproduces measured tensile data with reasonable accuracy ( = 7 MPa) Further refinement of constitutive model is needed to reproduce large-strain tensile response better. The Oh formability test has been implemented and tested using Abaqus (material: 340BH). Additional data from Oh simulations are requested to permit additional verification. * K. Oh and et al., “Development of New Formability Test for Sheet Materials using Axiomatic Design”, submitted to J. Mater. Proc. Tech..