Characterization of Void Growth in High Temperature Fatigued Copper through USANS
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Characterization of Void Growth in High Temperature Fatigued
Copper through USANS
Guangjun Cheng Stephen Fenimore
Rohan Hule Jinkee Lee
Christopher MettingMaria Torija
Outline
• USANS• Problem background• Experimental design• Analysis• Results• Conclusions
USANS Capabilities
Graphite Filter
Sapphire Filter
Premonochromator
Monochromator
Monitor
Sample Changer
Main Detector
Analyzer
Transmission
Detector Isolation Table
Apertures
Scale: 1 m PCD Simplified Layout3.CV5
• Low q range– 3x10-5 Å-1 < q < 0.01 Å-1
• Particle Diameter: 0.1 μ m < D < 10 μm
Problem Background
• Fatigue causes voids in copper lattice
• Voids grow nucleate at grain boundaries
• Lead to mechanical failure
• Relationship between stress and void growth
Stress Axis
fatigue_cavity.CV5
Void
Grain Boundary (Diamond Configuration)
Experimental Design
• Fatigue conditions– 405 oC– 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
Reduced Slit Smeared USANS DataSlope= -1 (plate)
Slope= -3 (Porod)
Porod Scattering, 100,000 cycles
0 100
1 10 -7
2 10 -7
3 10 -7
4 10 -7
5 10 -7
6 10 -7
7 10 -7
8 10 -7
0 100 5 10 -4 1 10 -3 1.5 10 -3 2 10 -3 2.5 10 -3
q•d
s/d
(q)
Å-1
cm-1
q (Å-1 )
blue_Porod.gra
3
Intercept ~surface area/sample volume-3
Invariant
0
0.5
1
1.5
2
2.5
3
3.5
4
0 100 5 10-4 1 10-3 1.5 10-3 2 10-3 2.5 10-3
q•d
/d
(q)
Å-1
cm-1
q (Å-1 )
blue_invariant.gra
Area under curve ~ Volume Fraction
Modified Guinier (plate)
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
0 100 5 10 -7 1 10 -6 1.5 10 -6 2 10 -6 2.5 10 -6 3 10 -6 3.5 10 -6 4 10 -6
ln(q
•d
s/d
(q))
Å-1
cm-1
q2 (Å-2 )
blue_mGuinier.gra
m= -T2/12
Results
Number of Cycles
25,000 50,000 100,000
Surface area/Sample volume (cm2/cm3) 160 240
Volume fraction 5.80E-04 1.70E-03 2.90E-03
Average diameter (m) 0.60 0.72
Average volume (m3) 0.11 0.20
Number of voids/sample volume (cm-3) 1.50E+10 1.40E+10
Plate thickness (m) 0.36 0.55 0.63
Comparison with prior workScripta Met. 24 (1990) 227-232
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
HURRAY for USANS!
Thanks to John Barker, Man-Ho Kim, and David Mildner
Questions?
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dqddTsQI
Vq
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HVA
SAcor
)(1)(
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)/)(()(
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Data reduction for USANS:Smearing corection
Scattering for non-interacting particles
2
3
22
)()cos(sin31),(
)(/)(
qRqRqRqRdr
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qPNVdqd
pV
riq
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PPS
Particle Volume fraction- Invariant
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dqqddq
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ddqQ S
q
VI
V
Interfacial Surface Area
424 /2/)(lim qSqCqdd
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