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Characterization of Void Growth in High Temperature Fatigued Copper through USANS. Guangjun Cheng Stephen Fenimore Rohan Hule Jinkee Lee Christopher Metting Maria Torija. Outline. USANS Problem background Experimental design Analysis Results Conclusions. Low q range - PowerPoint PPT Presentation
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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?
duuqdd
dd
dqddTsQI
Vq
V
S
HVA
SAcor
)(1)(
)2)(2(
)/)(()(
22
0
Data reduction for USANS:Smearing corection
Scattering for non-interacting particles
2
3
22
)()cos(sin31),(
)(/)(
qRqRqRqRdr
VRqP
qPNVdqd
pV
riq
P
PPS
Particle Volume fraction- Invariant
3
62
00
2
34)0(
)(1)(
R
R
dd
dqqddq
qdqq
ddqQ S
q
VI
V
Interfacial Surface Area
424 /2/)(lim qSqCqdd
Pq
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