Structural Design Parameters for Germanium - NASA · National Aeronautics and Space Administration...

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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

22

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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Acknowledgements

• Thanks to Terry McCue for SEM fractography.• Thanks to the ISS Program and Penni Dalton for

funding & reviews.

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