1. Fracture of Tungsten in a HAPL Chamber Jake Blanchard HAPL MWG Fusion Technology Institute University of Wisconsin September 2003

2. Outline Latest results for crack propagation in tungsten-coated steel walls Steel stresses as function of tungsten thickness Thoughts on how to measure mass loss in samples

3. Introduction In Albuquerque, I presented a fatigue analysis for a tungsten-coated, steel HAPL wall This analysis indicated that surface cracking can be expected within the first hour of operation This does not tell us whether cracks will reach the steel (this requires fracture mechanics)

4. Approach Place crack into structural model and calculate stress intensity factor for several crack depths If stress intensity goes to 0, cracks will stop Otherwise, the stress intensity determines the crack growth rate (per cycle) Unfortunately, no crack growth data for tungsten has been found

5. Fracture Mechanics Analysis of Tungsten Coating Crack tip Crack depth Tungsten Steel Contact surface Crack tip stress intensities during thermal cycling calculated using ANSYS J-integral fracture mechanics algorithm

6. Thermal Response of Structure Temperature Contours Near Surface at end of Pulse 6.5 m chamber 154 MJ target No gas 50 microns W

7. Stresses Resulting from Thermal Cycle Stresses at Maximum TemperatureStresses After Cool Down MPa

8. Stress Intensity Variation with Crack Depth 50, 100, and 200  m Tungsten coating thicknesses 500  m crack half spacing – single thermal cycle

9. Crack Tip Stress Intensity Variation with Crack Spacing Variation of Stress Intensity with Crack Spacing (Single Cycle) 50  m thick tungsten layer

10. Next Step What if crack reaches steel?

11. Stresses in Steel As long as we avoid yielding in the steel, the stress will always be compressive Hence, the stress limit will be defined such that yielding is avoided. Using the design stress as a limit will ensure this, with a safety factor

12. Allowable Stresses Temperature (C)Allowable Stress (MPa) 500268 650133 700111

13. Latest Results Chamber radius (m) Xe Pressure (mTorr) Target Yield (MJ) W Thickness (micron) Peak W Temp in 4 cycles (C) Peak Steel Temp in 4 cycles (C) Steel Temp Swing (C) Peak Steel Stress (MPa) 6.510154167251051085-300 6.510154250251048059-210 8.510300167241052096-340 8.510300250241049065-240

14. Conclusions Tungsten will crack and cracks may well reach the steel (results are inconclusive) Modeling a crack which has reached the steel may not be of any benefit Experiments will be the key Steel stress requirements lead us to tungsten thicknesses on the order of 200 microns

15. How to Measure Mass Loss Weigh Samples before and after Measure Remaining Thickness of Armor (Profilometry, Auger, RBS) Measure What Comes Off (Spectrometry/RGA) Measure velocity of vapor cloud (shadowgraphy or similar) Put layer of trace element at fixed depth

16. Crack Tip Stress Intensity Variation with Time and Crack Spacing (MPa-m 1/2 ) Variation of Stress Intensity for a 30  m Crack over 20 Thermal Cycles Variation of Stress Intensity with Crack Spacing for a 30  m Crack (Single Cycle) Stress intensity for a 30  m crack in a 50  m thick tungsten layer 100  m crack half spacing

17. Latest Results Chamber radius (m) Xe Pressure (mTorr) Target Yield (MJ) W Thickness (micron) Peak W Temp in 4 cycles (C) Peak Steel Temp in 4 cycles (C) Steel Temp Swing (C) Peak Steel Stress (MPa) Steel Stress Swing (MPa) 6.5101541002510550130-438410 6.510154167251051085-300270 6.510154250251048059-210180 7.5101541001840520100-330310 7.510154167184048065-230210 7.510154250184046045-160140 7.510154500184044018-8055 7.510300500319047035-150110 8.510300167241052096-340310 8.510300250241049065-240100 9.50300167248051088-310280 9.50300250248048059-212180 9.510300167189050078-270250 9.510300250189048053-190160

18. Designs That Work 150 MJ 6.5 meter radius 10 mTorr Xe 250 microns W 300 MJ 8.5 meter radius 10 mTorr Xe 250 microns W