Characterization of Stress to Predict The Reliability of Brittle Materials TE Buchheit, SJ Grutzik, MC Teague, RL Johnson, SP Meserole, DR Tallant, & KG Ewsuk 40th ICACC Daytona Beach, Florida USA January 26, 2016 1 Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000. SAND No. 2011–XXXXP. ICACC-S1-014-2016 9:20-9:50 AM Coquina Salon D SAND2016-0659C Technical Symposium S1: Mechanical Behavior and Performance of Ceramics & Composites 40th International Conference and Exposition on Advanced Ceramics and Composites (ICACC) Brittle Materials Failure Presents A Reliability Concern in High Consequence Applications Electrical Feedthru Braze “catastrophic” brittle failure * Braze structure high strength, low ductility, low toughness Pin Alumina Alumina Stress 500 mm “graceful” ductile failure * Electronic Substrate high strength, high ductility, high toughness Metal Via Strain 2 LTCC 200 mm Brittle materials are susceptible to sudden catastrophic failure Sandia’s Interests & Capabilities To Predict Brittle Failure Align With The National Challenge Identified In 2012 NSF Workshop Sandia National Laboratories The Challenge Brittle Failure Prediction Is A Ceramic Material Grand Challenge Brittle Materials Performance & Reliability Are Critical To Sandia’s Mission Critical Capabilities 3D Microstructure Characterization & Multi-Scale Modeling/Simulation Core Capabilities In Materials Characterization & Modeling/Simulation Glass-to-Metal (GtM) Seals 2 mm Pin Glass Glass 3 Pin 5 mm Current State: Qualitative Stress-Based Predictions Stress o We Design To Avoid High Stress o Engineering Judgment Has Deficiencies • • • 4 Structure/Pr operties Failure Probability % ~ crit Limited by practical experience Neglects flaws/flaw populations Does not incorporate fracture mechanics Strength (MPa) Qualitative prediction of brittle failure based on engineering judgment/experience Future State: Quantitative Mechanics-Based Prediction of Brittle Failure & Reliability K ~ a1/2 ~ KIC Stress Structure/Pr operties Fracture Mechanics 5 Thermal Strain (%) 0.2 Fast Cool Slow Cool 0 -0.2 -0.4 Super-Cooled Liquid -0.6 -0.8 0 100 200 300 400 500 600 Temperature (C) Quantitative mechanicsbased brittle failure prediction Coordinated Stress, Fracture, & Structure/Props Experiments & Modeling Are Being Conducted Vision: Quantitative mechanics-based failure & reliability prediction Microstructure & Property Characterization & Modeling Micro- to ContinuumScale Stress Characterization & Modeling . Characterization & Modeling Crack propagation 6 Current State: Qualitative stressbased failure analysis (engineering judgment) Experimentally-Validated Modeling Tools Are Being Developed To Predict Crack Propagation Bi-material stress/crack growth specimen metal glass Steady State KII= 0 Position Crack Path Crack Origin initial crack Tested/Refined crack propagation force standard mesh /b = 0.0125 refined mesh /b = 0.00625 6 growth steps Simulated crack propagation with Sandia Sierra/SolidMechanics-Franc3D Semi-analytical solution for plane stress G=K2/E 2b 2 F(a / b) EG/3.14 a 3P(L S) 7 Emery & Reedy Method /b F(a/b) % from ref. soln. J-integral 0.01250 1.490 -0.3 J-integral 0.00625 1.493 -0.1 CZ analysis 0.01250 1.453 -2.8 CZ analysis 0.00625 1.486 -0.5 Crack Path Predictions Compare Favorably With Experiment 304 SSl Ef,= 193 Gpa, f =0.29, f =17.3e-6/OC hf=3.175 mm l=254 mm b=25 mm ao=15.9 mm Experiment Borosilicate/SS #11 (a0= 16 mm, Tf= -47°C) Borosilicate glass Es=64 Gpa, s= 0.20, s =3.25e-6/OC hs=31.75 mm Model 45 crack growth steps, (displacement mag 10x) 4.9 mm 8 Reedy & Grutzik Non-FEA predicts a steady state crack path 4.9 mm below the interface --- same as Sierra/SM-Franc3D Hutchinson & Suo IJSS 1989 Materials Behavior Characterization Enabled Model Development, Parameterization, & Validation 0.1 0.01 0.01 25 20 0.1 1 10 Frequency (Hz) G' Data G' Prony Fit G'' Data G'' Prony Fit 100 0.6 7 6 15 4 10 3 2 5 9 1 G'' (GPa) G' (GPa) 5 0.5 Displacement (mm) Simplified Potential Energy Clock (SPEC) Nonlinear Viscoelastic Model For Glass 400 C 430 C 460 C 490 C 520 C 550 C 1 6 Model Calibration 1st cool 30C/min Reheat 0.5C/min 2nd cool 30C/min SPEC Model 0.4 0.3 0.2 Symbols are data 5 Model Validation F= 0.81N F= 1.57N F= 4.89N F= 8.32N Creep Tref=460°C 4 3 Dashed = data Solid = SPEC model 2 1 0 0 50 100 150 Time (min) 200 250 0.6 Linear Thermal Strain (%) Characterization Linear Thermal Strain (%) Tan Delta 10 0.5 data C1 data C2 data C3 SPEC Model 0.4 0.3 0.2 0.1 0.1 0 0 100 200 300 400 500 0 100 200 300 -4 -3 -2 -1 0 1 2 3 4 Temperature (C) Time (min) Log(freq, rad/s) R.S. Chambers, Rajan Tandan, Mark E. Stavig, Characterization and calibration of a viscoelastic simplified potential energy clock model for inorganic glasses, J. Non-Cryst. Solids (2015), http://dx.doi.org/10.1016/j.jnoncrysol.2015.06.005 400 500 Improved Materials Models Have Enabled Stress/Strain Predictions With Engineering Accuracy The Physically-based SPEC Model Accurately Predicts Thermal Strain During Solidification Thermal Strain History 2 -0.2 -0.4 Elastic Solid -0.6 Viscous Liquid Actual Tg Legacy Tset -0.8 -1 100 200 300 400 500 Temperature (C) Legacy Modeling Employs Simplifying Assumptions/Approximation s 600 Max Principal Stress (ksi) Thermal Strain (%) 0 Legacy Thermal Strain Processing History 0.01 C/min Cooling FE Analysis with SPEC Model Predicts HigheratResidual Stress Stresses Pin/Glass Interface 1.5 1 0.5 0 Legacy Models - No History New Models - With History New Models - 0.01 C/min -0.5 0 100 200 300 400 500 600 o Temperature ( C) Enhanced Modeling Accounts for Time-Dependent Response & Process History Processing history affects GtM seal residual stress/predictions 10 Elisberg Coupled Experiments & Modeling Enable Better Stress Determination Stress Mapping Using Indentation Fracture c2 c4 Stress related crack length c3 20 Radial Stress (MPa) c1 Metal 0 -20 -40 -60 Concentric seal test geometry Experimental issue -80 Stress determined indirectly Modeling assumption Continuum-based material behavior 11 Chambers, Tandon, Jamison, Newton, & Buchheit 0 1 2 3 4 Radial Position (mm) 5 Experimental Measurements (3 test geometries) simulated result (SPEC+BCJ) Micro- To Continuum-Scale Stress Mapping Is Possible With SEM/EBSD And PL Spectroscopy SEM of polycrystalline AL2O3 EBSD map (0.5 m spacing) 20 µm PL Spectroscopy grid (2 µm spacing) R2 peak shift 692.91 692.9 692.89 692.88 692.87 12 Buchheit, McKenzie, Johnson & Meserole Glass-Bonded Sapphire Bicrystals Were Fabricated For EBSD & PL Spectroscopy Sputtered ~100 nm of Eagle glass (Corning) on polished surface of single crystals Placed glass side together in alumina boat Bonded by heating in air to 1600C at 20C/min, 1H hold Bonded Bicrystals • C-plane to C-plane, rotated 30 • A-plane to C-plane • M-plane to C-plane Bicrystal boundary Sapphire Single Crystal #1 (C-Plane) Sapphire Single Crystal #2 (M-Plane) 500 µm 13 Brown-Shaklee & Teague EBSD Was Used To Determine Exact Crystal Orientation For Stress Modeling & Calculation A-C Bicrystal Crystal #1 Crystal #2 Global X Crystal #1 (a-plane) x = [ 0.84832 -0.02183 0.52902] - [1.6 0 1 ] y = [ 0.52913 0.07101 -0.84556] - [ 1 0 1.6] z = [-0.01910 0.99724 0.07179] - [ 0 1 0 ] Crystal #1 Crystal #2 Crystal #1 Global Y Global Z Crystal #2 (C-plane, rotated) x = [ 0.01895 0.53775 -0.84289 ] - [ 0 1 1.6 ] y = [-0.03011 0.84297 0.537125] - [ 0 1.6 1 ] z = [ 0.99937 0.01520 0.032165] - [ 1 0 0 ] y x z y 14 Buchheit & McKenzie z x Crystal #2 Global y x z Stress In The Bicrystal Was Simulated Using ABAQUS FEA Material Parameters elastic constants S11= 497 GPa S44= 147 GPa S13= 116 GPa 0.5 mm Al2O3 Free surface S33= 501 GPa S12= 163 GPa S14= -22 Gpa - Goto et. al. Journal of Geophysical Research, 1989 Coefficients of thermal expansion α11 = 7.3e-06 1/C α33 = 8.2e-06 1/C Glass E=70 GPa =0.2 α =3.55e-06 1/C Z-displacement held to zero on bottom surface Simulation conditions T = -600C 0 nm glass bond layer Stresses in bicrystal are generated due to CTE mismatch and elastic anisotropy 15 Buchheit & Grutzik FE Stress Predictions Were Bounded By Modeling A 0 nm And 30 m Glass Bond Layer A-C bicrystal A-C bicrystal 0 nm glass layer 30 mmlayer glass=layer glass 30 um glass layer = 0 nm 120 AA-Crystal crystal C - crystal C Crystal ACrystal A Crystal C-Crystal Crystal C Stress (MPa) 80 40 0 -40 s11 11 s22 22 s33 33 Stress Pressure -80 -120 -0.4 -0.2 0 0.2 0.4 X Displacement from boundary Disp. from boundary (mm) (mm) s11 11 s22 22 s33 33 Stress Pressure -0.4 -0.2 0 0.2 0.4 Disp. fromfrom Boundary (mm) X Displacement boundary (mm) The same stress is predicted for a 0 nm to 5 m glass layer 16 Buchheit & Grutzik A State-Of-The-Art PL Spectroscopy Capability Has Been Developed To Map Multi-Scale Stress Map mm2 areas using thousands of spectra with micrometer-scale spatial resolution Focused laser beam for micro-scale spatial resolution Determine stress sensitive R1 (~694.24 nm) and R2 (~692.84 nm) Ruby (Al2O3:Cr3+) PL bands Automated specimen repositioning and spectra acquisition Process thousands of spectra in minutes (MATLAB, GRAMS, & LABSPEC) Wavelength resolution and stability to resolve peak shits to 0.001 nm (~3MPa) Instrument drift corrected to Ar lamp emission line NIST reference (696.5431 nm) Temperature stable to 0.1C (0.0007 nm peak shift) and temperature corrected Working to correct for Cr concentration (1 wt.% Cr – 4.8 nm peak shift) • R1 & R2 fluorescence peaks (positions, widths, & separations) are best fit with a Lorentzian or pseudo-Voigt fit • The Ar peak is best fit with a Gaussian fit 17 Johnson, Tallant, & Meserole R2 peak R1 peak Ar peak Spatially Resolved R1 & R2 Peak Positions Were Mapped In The A-C Bicrystal X Position R2 Peak Position A Crystal X Position C Crystal R1 Peak Position 18 Johnson Y Position Y Position A Reference Stress-Free R2 Peak Position Was Used To Determine Stress Related Peak Shifts A-C Bicrystal R2 Peak Position A-C Bicrystal R2 Peak Position Use this region for “bulk average” X Position Closest to A-C interface Far from interface “bulk” average = 692.8827 nm NIST standard = 692.84 nm 19 Johnson Y Position R1 & R2 Peak Shifts In the A-C Bicrystal Were Calculated Relative To A Stress-Free Reference R2 peak shift – single line scan C Crystal A Crystal C Crystal Peak Shift (nm) A Crystal R2 peak shift – average of 11 line scans Y Position X Displacement from (m) boundary (mm) Y Position X Displacement from (m) boundary (mm) Noise Is reduced by averaging peak shift line scans 20 Johnson Stress-Related Cr Band Peak Shifts In The A-C Bicrystal Were Mapped 21 Johnson A Crystal Larger peak shifts indicate higher stress regions X Position X Position Region near bicrystal boundary shows larger peak shifts R2 Peak Shift C Crystal R1 Peak Shift Y Position Y Position Measured Cr Fluorescence Peak Shifts Were Converted To Residual Stress 1 cm-1 = 200 MPa Piezospectroscopic Coefficients for Ruby Uniaxial Loading 11 33 22 Hydrostatic Coefficient 11 22 33 11 + 22 + 33 Modeling And Experiment Predict Similar Stresses In The Glass-Bonded A-C Bicrystal A-C bicrystal Stress: Simulation vs. Experiment Hydrostatic Stress 11 +σ22 + σ33) MPa Trace(σ(MPa) 200 Simulation Experimental Data 150 100 A Crystal C Crystal 50 0 -50 -100 -150 -200 23 -400 Buchheit, Grutzik, & Johnson -200 0 200 X Displacement from boundary (mm) 400 Experimentally-Informed Microstructure Modeling Capability Is Being Developed To Predict Stress 20 µm SEM of Al2O3 EBSD map ofAl2O3 Stress map of Al2O3 Al2O3 – Kovar Brazed Sample EBSD map of polycrystalline Si 1 µm Applied Tension 1.29 (GPa) 1.96 Kovar Al2O3 Measured area 19.5 mm Measurement Grid 3000 µm x 200 µm (10 µm spacing) Spectroscopic peak shift Von-Mises Stress Predicted stress Resultant stress calculation -100 0 100 FE simulation of micro-scale stress & (MPa) variation in a brittle material microstructure PL spectroscopy used for micro- to 24 Buchheit, Teague, Johnson, Tallant, Meserole, & Tandon continuum-scale stress measurement We Are Integrating Stress, Microstructure, & Fracture Mechanics To Predict Failure/Reliability Mechanics Model PL Spectroscopy • Surface initiated fracture Clarke FIB cuts create a strip under uniaxial stress • Crack shapes Zimmermann et. al, J. Am. Cer. Soc., 1998 Nakamura et al., J. Am. Cer. Soc., 2009 SEM/EBSD 25 Microstructure Map PL Peak Shift Principal stress Sierra/SolidMechanics-Frank3D Microstructure model Stress/fracture predictions