https://ntrs.nasa.gov/search.jsp?R=20160010277 2018-04-24T03:01:31+00:00Z National Aeronautics and Space Administration Slow Crack Growth of Germanium Jon Salem NASA GRC ICACC, January 2016 www.nasa.gov 1
National Aeronautics and Space Administration Germanium • Good electromagnetic transmission in 2-15 μ m range. Specialty window material: www.nasa.gov 2
National Aeronautics and Space Administration Germanium • Brittle transition metal. • Relatively soft. • Behaves like a soft, brittle ceramic. • Stress corrosion cracking? • What is the fracture toughness? www.nasa.gov 3
National Aeronautics and Space Administration Material • Single crystal beams • Coarse gained disks (2” & 5” Φ ): 25 mm • Variable grain structure – not ideal for testing. www.nasa.gov 4
National Aeronautics and Space Administration 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. 1.08 1.10 Tetragonal and Trigonal Materials, {010} Approximate Stress/Series Stress Approximate Stress/Series Stress Cubic materials, {100} In NiAl 1.06 1.08 (Plate Center) (Plate Center) BaTiO 3 1.04 -SiC 1.06 1.02 1.04 GaP Quartz Sn Ge Si TiO 2 MgO 1.00 1.02 Diamond Sapphire 0.98 1.00 0 5 10 15 20 25 0 2 4 6 8 10 12 14 16 18 Anisotropy Factor A* * + A s * ) Total Anisotropy Factor ( A c • Relatively low. Running mechanical test on off-axis planes is problematic if the anisotropy is large. www.nasa.gov 5
National Aeronautics and Space Administration Young’s Modulus - impulse excitation - Aggregate Constants GPa E v • E <111> = 154.8 ± 0.9 GPa } 135 0.20 Voigt • E <110> = 138.3 ± 0.2 133 0.21 Hashin • E <100> = 103.1 ± 0.6 132 0.21 Shtrikman 129 0.21 Reuss • E poly = 131, v poly = 0.21 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% • Well oriented germanium…. www.nasa.gov 6
National Aeronautics and Space Administration Procedure - Fracture Toughness - • Three standard test methods (C1421): Precracked Beam Chevron Notch Beam (SEPB) (CNB) 1 = a 1 /W =( a 1 +a 2 +a 3 ) /3W o = a o /W Surface Crack Flexure (SCF) W a 1 2 c a 1 a 2 a 3 a a o Remove h 4.5h to 5h B • Different crack size • Different crack formation history • Different effort www.nasa.gov 7
National Aeronautics and Space Administration Loading Configuration - Fracture Toughness - S i PUSH ROD BALL B Strain Gage S o TEST S i 40 SPECIMEN 35 30 S o Force (N) 25 Displacement Transducer 20 15 10 SUPPORT 5 ROD 0 0 50 100 150 200 250 300 350 400 Backface Strain (µ m/m) • Relatively simple fixtures: test frame, load cell, recording device. 8 www.nasa.gov 8
National Aeronautics and Space Administration Fracture Toughness Method {100} {110} {111} SEPB 0.68 ± 0.04 0.68 ± 0.01 < 0.74 SCF 0.74 ± 0.02 0.74 ± 0.02 0.74 ± 0.02 CNB In progress In progress In progress • Essentially the same on all planes • K I scf{jkl} = 0.74 ± 0.02 MPa m • K I pb{100, 110} = 0.68 ± 0.04 MPa m • ~ 10% difference between SCF and SEPB. Plasticity? • Practical value of K I {jkl} = 0.70 ± 0.02 MPa m. www.nasa.gov 9
National Aeronautics and Space Administration SCF Precracks {100} {110} <100> <100> Precrack {111} » {100} exhibit cathedral Wallner lines. » The most planar surface occurs on the {110}. <110> » {111} tends to exhibit cleavage steps. » Secondary orientation was not fixed. www.nasa.gov 10
National Aeronautics and Space Administration Cathedral Orientation {100} <100> <110> • Peak of cathedral corresponds to the <100> {100}. www.nasa.gov 11
National Aeronautics and Space Administration K I {111} Data of Jaccodine • Reported an energy equivalent value of 0.55 MPa m. • Used DCB w/ fracture mechanics solution that did not include L/t effects. • Reanalysis gives K I {111} = 0.72 ± 0.05 MPa m (6) w/ trend toward 0.67 MPa m: 1.0 Engineering value Fracture Toughness, MPa m 0.9 ~0.68 MPa m 0.8 0.7 for low index planes 0.6 0.5 Data of Jaccodine 0.4 Cut off Valid range 0.3 0.2 R.J. Jaccodine, “Surface Energy of 0.1 Germanium and Silicon,” J. Electrochemical 0.0 Soc., Vol. 110, No. 6, June, 1963, pp. 524- 0 1 2 3 4 527. L/t www.nasa.gov 12
National Aeronautics and Space Administration 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 ASTM C1499 www.nasa.gov 13
National Aeronautics and Space Administration Fracture Strength & Weibull Statistics θ m #/S • 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%). www.nasa.gov 14
National Aeronautics and Space Administration Biaxial Fracture Patterns (polished) • Repetitive pattern that makes fractography difficult: www.nasa.gov 15
National Aeronautics and Space Administration Fracture Path - ground disk - #14-3, 36.1 MPa (#15-2) Grinding Lay Grain Boundary 8 mm Grinding Crack Grinding Crack Grinding Grain Lay Boundary 25 mm • Crack initiated at a grinding scratch. • Transited to a low index planes. • Deflected at a grain boundary. www.nasa.gov 16
National Aeronautics and Space Administration Fracture Path in a Polished ROR Disk • Crack initiated from a semi-elliptical crack emanating from a scratch. • Turned onto the {111} plane: 9 o from {110} • Opportunity to estimate the fracture toughness! • K I {hkl} = 0.73 MPa √ m. • Why did the crack turn? www.nasa.gov 17
National Aeronautics and Space Administration 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 strain controlled situations…… Isotropic <100> Tangential Stress, r/R s = 0.2 Radial Stress, r/R s = 0.2 Tangential Stress, r/R s = 0.8 100 Radial Stress, r/R s = 0.8 90 80 <111> 70 Stress, MPa 60 50 40 30 {110} 20 10 <110> 0 0 10 20 30 40 50 60 70 80 90 100 Stress, MPa Stress concentration where the load ring But, for a pressurized plate, the stress intersection the stiff direction. concentrations are not exhibited. www.nasa.gov 18
National Aeronautics and Space Administration Fracture Toughness – semi-elliptical cracks on high index planes - • For polished specimens, K I = 0.77 ± 0.04 MPa √ m (0.73-0.83). • For grinding cracks, K I = 0.87 ± 0.04 MPa √ m (0.80 – 0.90). • Higher due to random orientation and transition to {111}. • Caveat: local stress not precisely know….. www.nasa.gov 19
National Aeronautics and Space Administration 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 www.nasa.gov 20
National Aeronautics and Space Administration 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 www.nasa.gov 21
National Aeronautics and Space Administration Slow Crack Growth Analysis • Crack growth function: da K n n I v = = AK A [ ] * I dt K IC • Constant stress rate testing: n K K n 2 2 1 1 2 2 n B n 2 1 Ic Ic B f i * AY n A Y n 2 2 2 2 • Parameter extraction via regression: 1 1 log log log D n 2 log D log B n 1 10 f 10 10 10 10 i n 1 n 1 (Slope ) (Intercept ) 22 www.nasa.gov 22
National Aeronautics and Space Administration Constant Stress Rate Curve Tosoh Fused Silica Ge Quartz-silica, water 100 Quartz-silica, water 100 Corning 7980, water Russian Silica, Water Corning 7980, water Russian Silica, Water 80 80 70 60 60 Strength, S f , MPa Strength, S f , MPa 50 50 40 40 30 30 20 20 Inert Strength Medians Water Water 10 0.0001 0.001 0.01 0.1 1 10 100 0.001 0.01 0.1 1 10 100 . . Stress Rate, , MPa/s Stress Rate, , MPa/s • Still some scatter. • Medians clarify the trend. • Slope is negative to zero; n > 100, no measurable SCG. www.nasa.gov 23
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