Rachel Sharp Corinne Packard Isaac Feitler Hao Hu

1. Project Update April 10, 2003 Rachel Sharp Corinne Packard Isaac Feitler Hao Hu Massachusetts Institute of Technology 3.082

2. Today • Update on progress • Capacitor bank • Casting • Other machining • Calculations • Deformation mechanisms • Next steps

3. Week Revised Gantt Chart Vessel design and parts acquisition Capacitor bank acquisition Pressure Vessel assembly CAD Break Die printing Casting of mold Electrohydraulic test Funnel formation Final part formation Presentation preparation Pressure Vessel Capacitor Bank Mold Electrohydraulic forming Final Presentation

4. Capacitor Bank Update • Magneform machine has been supplied with power, and troubleshooting started but has not progressed very far. • Low-voltage, high capacitance 1kJ capacitor bank has been acquired. • We still expect measurable results, but we won’t know to what extent until we test it. • 1kJ capacitor bank for at least the time being. Time permitting, we may still pursue higher-energy deformation.

5. Creating the Dies • CAD files of dies created with Solidworks • Dies are printed 3D printer • From MIT & Z-corp • Prints composed of starch • Creation of Plaster Mold • Casting with Bronze

6. Lost Wax Casting • A positive print of final shape is created with 3D printing • Ceramic shells are created to surround the 3D print • Molten Bronze is poured into the shell • As the starch burns out, the molten bronze takes the shape of the positive die shape

7. Pressure Vessel Design Changes • Stainless steel pipe plugs replace cast iron plugs • Hole depth for pipe plugs is 0.7”  the min. wall thickness of the vessel is 0.5” • Inter-electrode spacing now 2.75” • Teflon insulation design slightly modified • Aluminum pipe purchased for testing of assembly without a die Machining has been slow due to the robustness of the materials used. Despite this, the vessel is nearly complete.

8. Raw Materials for Electrode Assembly

9. Final Electrode Assembly

10. Al Pipe Ring for Free Expansion

11. Drilling Electrode Holes in Pressure Vessel

12. Working in Edgerton Machine Shop

13. Part failure calculations

14. Leak-Before-Break Criteria • Wall thickness > critical crack size, and a crack in the vessel reaches the critical crack size, then the vessel will fail in a “fast fracture mode” • Wall thickness < critical crack size, then the crack will propagate through the wall and the vessel will leak (reducing the internal pressure) before a “fast fracture” can occur.

15. Calculations • Stress-intensity factor (also called fracture toughness) D. Broek, Elementary Engineering Fracture Mechanics, Martinus Nijhoff Publishers, 1982. Pg.393 ] • ac is critical crack size, sy is yield strength, agenerally is 1 in the worst case. • Solve for ac

16. Calculations, continued: • [D. Fryer,High Pressure Vessels, Chapman and Hall, 1997, p.123] • sY.P. is the yield strength in ksi • CVN is the Charpy V-notch adsorbed energy in ft-lbs • KIc is in ksi-in2 • For AISI 1045 steel, CVN varies widely with hardness. • We choose a low value of hardness (225 Brinell) and get a CVN of 38-48 at 50°F

17. Calculations, continued 2: • For CVN = 38, sY.P. = 55 ksi, KIc = 98.5: ac = 1” • Neglecting the holes for the electrodes which pierce the vessel completely, the thinnest and most crack prone area of the vessel is 0.5” thick • The vessel will leak before bursting at the areas we expect to be weakest and most crack-prone.

18. I. II. III. Strain and Deformation ε ε Sample responds to strain by necking Region II. Smaller area  greater σ Image from http://www.sri.com/poulter/fe_modeling/fem_figures/fig_wf3.html

19. Stopping the Downward Spiral • To overcome this weakening cycle, necking must be suppressed • Work Hardening • Phonon Drag Higher ε Lower A Higher σ

20. Work Hardening • At any strain rate- Stress causes dislocations to move Strain is the macroscopic result of dislocation activity In the necked region, ε is higher  dislocation activity is higher Image from http://newt.phys.unsw.edu.au/~epe/1250.L9/1250.L9.small.html

21. Work Hardening Increased dislocation activity creates tangles which increase the yield stress of the material Ultimately, increased ε increased σy, So if σy II > σy I, III , Regions I and III will yield first and necking will be suppressed.

22. ε ε V1 V1 V2 I. II. III. Phonon Drag “Inertial Effects” I=mv Smaller A in II  yielding in the region  V2>V1 What is the result of having a high strain rate?

23. Phonon Drag Back to dislocation movement- Stress lowers the activation energy required to make a dislocation move Remember that phonons are lattice vibrations. ┴ E ┴ moves * But there is still a critical time length when probability favors movement

24. Phonon Drag • At low strain rates, probability is not limiting • Dislocations move smoothly • At high strain rates, probability is limiting • Dislocation move jerkily Phonon Drag Coefficient, B, increases with temperature, is very different for different crystal systems, and has dependences on many other microscopic variables Phonon Drag must be the rate limiting step in order for this equation to hold!

25. Work Hardening Any strain rate Phonon Drag High strain rates Review of Deformation Mechanisms σy σy ε dε/dt At very high strain rates, Phonon Drag becomes an important factor and allows for greater elongation than work hardening alone