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Structural Design Parameters for Germanium
Jon Salem, Richard Rogers and Eric BakerNASA GRC
15th Department of Defense Electro-Magnetic Windows Symposium
May 18th 2016
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https://ntrs.nasa.gov/search.jsp?R=20160012342 2018-09-17T08:02:03+00:00Z
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Germanium• Good electromagnetic transmission in 2-15 μm range.
Used for specialty windows; solar cells; substrates.
• Space Act Agreement with an industrial partner to determine the transient reliability of a proprietary, thermally and mechanically loaded, Ge window, along with the input design properties.
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Germanium
• Brittle transition metal.• Relatively soft.• Behaves like a soft, brittle ceramic.• Stress corrosion cracking?• What is the fracture toughness?
Objective
Measure mechanical propertiesPerform transient reliability analysis.
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Material• Single crystal beams• Polycrystalline disks (2” & 5”Φ):
• Coarse, variable grain structure – not ideal for testing.
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25 mm25 mm
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Anisotropy• Anisotropy factor A* measures relative magnitude of
elastic anisotropy exhibited by a crystal. A* = 0 for isotropic materials, A* = 0 to 1 for many single crystals.
• Running mechanical test on off-axis planes can be problematic if the anisotropy is large.
• Relatively low A* - proceed…………. 5
Total Anisotropy Factor (Ac*+As
*)
0 5 10 15 20 25A
ppro
xim
ate
Stre
ss/S
erie
s S
tress
(Pla
te C
ente
r)
0.98
1.00
1.02
1.04
1.06
1.08Tetragonal and Trigonal Materials, {010}
BaTiO3
In
SnTiO2
Sapphire
Quartz
Anisotropy Factor A*0 2 4 6 8 10 12 14 16 18
App
roxi
mat
e S
tress
/Ser
ies
Stre
ss(P
late
Cen
ter)
1.00
1.02
1.04
1.06
1.08
1.10Cubic materials, {100}
NiAl
-SiC
GaPGeSi
MgO
Diamond
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• E<111> = 154.8 ± 0.9 GPa• E<110> = 138.3 ± 0.2• E<100> = 103.1 ± 0.6
• Epoly = 131, vpoly = 0.21
Young’s Modulus- impulse excitation -
Ge McSkimin Bogardus McSkimin Mason Average NASA % Diff.
Young’s Modulus (GPa)E<100> = 104. 4 102.0 102.2 103.7 103.1 103.1 0.0%E<110> = 138.7 136.7 137.0 138.0 137.6 138.3 0.5%E<111> = 155.8 154.2 154.5 155.1 154.9 154.8 -0.1%
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}Aggregate Constants
Formula E (GPa)
v
Voigt 135 0.20Hashin 133 0.21Shtrikman 132 0.21Reuss 129 0.21
• Well oriented germanium….
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Procedure - Fracture Toughness -
• Three standard test methods (C1421):
• Different crack size and crack formation history.• Different effort.• Some methods don’t work well on some materials.
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W
B
ao
a3a2a1
a1
a
2c
1= a1 /Wo= ao /W
=( a1+a2+a3) /3W
h Remove4.5h to 5h
Precracked Beam(SEPB)
Chevron Notch Beam(CNB)
Surface Crack Flexure(SCF)
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Fracture Toughness
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• Essentially similar on all planes.
• KIscf{jkl} = 0.74 ± 0.02 MPam.
• KIpb{100, 110} = 0.68 ± 0.04 MPam.
• ~10% difference between SCF and SEPB. Plasticity?
• Practical value of KI{jkl} = 0.68 ± 0.02 MPam.
Method {100} {110} {111}SEPB 0.67 ± 0.04 0.68 ± 0.01 0.72 ± 0.02
CNB 0.67 ± 0.03 0.69 ± 0.02 0.75 ± 0.03
SCF 0.74 ± 0.02 0.74 ± 0.02 0.74 ± 0.02
0.3 mm
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SCF Fracture Surfaces
• {100} is conchodial and exhibits cathedral Wallner lines.
• The most planar surface occurs on the {110}. • {111} is planar but tends to exhibit cleavage
steps.• Secondary orientation was not fixed.
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{100}
<100>
{111}
<110>
Precrack
0.5 mm
{110}
<100>
0.5 mm
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Cathedral Orientation
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<100>
<110>
• Peak of cathedral corresponds to the <100> {100}.
{100}
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CNB Fracture Surfaces
• Ambient lighting:
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{110}Smooth,
Flat -Cleavage
{111}Stepped,
Flat –Cleavage
{100}Smooth,
Rounded -Conchoidal
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CNB Fracture Surfaces
• Oblique lighting:
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{110}Fine Wallner lines
Flat
{111}Stepped
Flat
{100}Smooth, dimples,
Rounded
Pores or inclusions?
0.3 mm
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0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0 1 2 3 4
Fracture Tou
ghne
ss, M
Pam
L/t
Data of Jaccodine
Cut off
KI{111} Data of Jaccodine• Reported an energy equivalent value of 0.55 MPam.• Used DCB w/ fracture mechanics solution that did not
include L/t effects.• Reanalysis gives KI{111} = 0.69 ± 0.02 MPam (4):
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Engineering value ~0.68 ± 0.02 MPamfor low index planes
R.J. Jaccodine, “Surface Energy of Germanium and Silicon,” J. Electrochemical Soc., Vol. 110, No. 6, June,
1963, pp. 524-527.
Valid range
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Strength Testing
• Constant Stress Rate Tests(5 MPa/s)
• Biaxial Flexure ring-on-ring (ROR)• ~400 grit as-ground surfaces in
distilled, deionized water • ~Polished surface in lab air
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ASTM C1499
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Fracture Strength & Weibull Statistics
• Polished m = 6; ground m = 9; spurious damage m = 4.• Scale effect evident: 168 vs 215 MPa.• Strength of 235 MPa is predicted vs 215 MPa (10%).
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θ m #/S
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Biaxial Fracture Patterns (polished)• Repetitive pattern that makes fractography difficult:
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Fracture Path- ground disk -
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Grinding Crack
#14-3, 36.1 MPa
Grain Boundary
Grinding Lay
Grinding Lay
8 mm
Grain Boundary
Grinding Crack
(#15-2)
• Crack initiated at a grinding scratch. • Transited to a low index planes.• Deflected at a grain boundary.
25 mm
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• Crack initiated from a semi-elliptical crack emanating from a scratch.
• Turned onto the {111} plane:
• Opportunity to estimate the fracture toughness!• KI{hkl} = 0.73 MPa√m.• Why did the crack turn?
Fracture Path in a Polished ROR Disk
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9o from {110}
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Preferred Fracture Plane• The fracture toughness on low index planes is similar, so why is
the {111} the preferred propagation plane?• The {111} is the stiffest direction, and stiff directions exhibit high
stresses under displacement controlled situations (NiAl):
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• Stress concentration where the load ring intersects the stiff direction! Anisotropy changes the stress distribution.
Ring loading Pressure loading
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Pressurized Plate• Applying pressure avoids contacts:
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Stress, MPa0 10 20 30 40 50 60 70 80 90 100
0102030405060708090
100
Stre
ss, M
Pa
Tangential Stress, r/Rs = 0.2Radial Stress, r/Rs = 0.2
Tangential Stress, r/Rs = 0.8Radial Stress, r/Rs = 0.8
<100
>
<110>
<111>
Isotropic
• For a pressurized plate, the stress concentrations at stiff directions are not exhibited. Better test!
{110}
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Pressurized Plate (POR)
• Measured strength is ~20% greater than expected from the ROR data because the stress concentration has been removed. ROR is conservative.
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Fracture Toughness – semi-elliptical cracks on high index planes -
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• For polished specimens, KI = 0.77 ± 0.04 MPa√m (0.73-0.83).• For grinding cracks, KI = 0.87 ± 0.04 MPa√m (0.80 – 0.90).• Higher due to random orientation and transition to {111}.• Caveat: local stress not precisely known…..
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Slow Crack Growth - Experimental Approach -
• Constant Stress Rate Testing “dynamic fatigue”- ASTM C1368
• Strength based approach with advantages & disadvantages:
- rapid test; simple geometry- samples the inherent, small flaws- statistical scatter (many specimens needed)- averaging of fatigue regions
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Experimental Procedure
• Constant Stress Rate Tests(5 to 5 x 10-4 MPa/s)
• Biaxial Flexure (Ring-on-ring)• Distilled, deionized water • ~400 grit as-ground surfaces• ~10 tests per stress rate• ~40 tests
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Slow Crack Growth Analysis
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• Parameter extraction via regression:
1121 nn
if nB 2
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22
2
2
2
nYAK
nAYKB *
Icn
Ic
• Crack growth function:
• Constant stress rate testing:
]KK[AAK =
dtda = v n
IC
InI *
Dloglog1n
1log 1010f10
2ni1010 1nBlog
1n1Dlog
(Slope ) (Intercept )
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Constant Stress Rate Curve
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• Still some scatter.• Medians clarify the trend.• Slope is negative to zero n > 100, no measurable SCG.
Ge
Russian Silica, Water
Quartz-silica, water
Corning 7980, water
.Stress Rate, , MPa/s
0.0001 0.001 0.01 0.1 1 10 100
Stre
ngth
, Sf ,
MPa
20
30
40
5060
80
100
Medians
Water
Tosoh Fused Silica
Russian Silica, Water
Quartz-silica, water
Corning 7980, water
.Stress Rate, , MPa/s
0.001 0.01 0.1 1 10 100
Stre
ngth
, Sf ,
MPa
20
30
40
50607080
10
100
Inert Strength
Water
p = 0.15
p = 10-8
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Summary and Conclusions• Ge exhibits similar fracture toughness of KI = 0.68 ±
0.02 MPa√m on low index planes. Lower than Si!
• Randomly oriented cracks exhibit higher apparent toughness, but turn and propagate on the stiff {111} directions due to higher stresses (?)…..FEA.
• Natural cleavage plane appears to be the {110}.
• Weibull modulus varies from m = 4 (spurious) to m = 9 (ground).
• Strength varies from Sf = 40 MPa (ground) to 160 MPa (polished).
• Ge exhibits a Weibull scale effect, but does not exhibit measurable SCG.
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Summary and Conclusions• Aggregate, polycrystalline Young’s modulus and
Poisson’s ratio are Epoly = 131 GPa, vpoly = 0.21. • ROR loading results in stress concentrations at the
stiff directions of single crystals.
• From a stress state point-of-view, a lower strength measurement is expected………
• However, from an effective area perspective, a high strength should be measured.
• Pressure loading (POR) is a better test method for single crystals, because it avoids stress concentrations, but it is more effort……
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Potential Future Work
• Cyclic fatigue testing• Finite element analysis of ROR specimens• Testing of more pressure-on-ring specimens• Further SCF testing• SCG testing in other environments
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