1. Characterization of Void Growth in High Temperature Fatigued Copper through USANS Guangjun Cheng Stephen Fenimore Rohan Hule Jinkee Lee Christopher Metting Maria Torija

2. Outline USANS Problem background Experimental design Analysis Results Conclusions

3. USANS Capabilities Low q range –3x10 -5 Å -1 < q < 0.01 Å -1 Particle Diameter:0.1 μ m < D < 10 μm

4. Problem Background Fatigue causes voids in copper lattice Voids grow nucleate at grain boundaries Lead to mechanical failure Relationship between stress and void growth

5. Experimental Design Fatigue conditions –405 o C –17 cycles/second –Max stress amplitude: 34 MPa Monitor void growth by varying the number of fatigue cycles –25,000; 50,000; 100,000 cycles USANS to examine growth shape and size

6. Reduced Slit Smeared USANS Data Slope= -1 (plate) Slope= -3 (Porod)

7. Porod Scattering, 100,000 cycles 3 Intercept ~surface area/sample volume -3

8. Invariant Area under curve ~ Volume Fraction

9. Modified Guinier (plate) m= -T 2 /12

10. Results Number of Cycles 25,00050,000100,000 Surface area/Sample volume (cm 2 /cm 3 )160240 Volume fraction5.80E-041.70E-032.90E-03 Average diameter (  m) 0.600.72 Average volume (  m 3 ) 0.110.20 Number of voids/sample volume (cm -3 )1.50E+101.40E+10 Plate thickness (  m) 0.360.550.63

11. Comparison with prior work Scripta Met. 24 (1990) 227-232

12. Conclusions USANS proved to be a powerful tool for this investigation Average volume increases with cycle number Number of nucleation sites is independent of the number of cycles

13. HURRAY for USANS! Thanks to John Barker, Man-Ho Kim, and David Mildner Questions?

14. Data reduction for USANS: Smearing corection

15. Scattering for non-interacting particles

16. Particle Volume fraction- Invariant

17. Interfacial Surface Area