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Probabilistic Analysis Techniques Applied to Lifetime Reliability Estimation of Ceramics

Probabilistic Analysis Techniques Applied to Lifetime Reliability Estimation of Ceramics. Stefan Reh Tamas Palfi Noel Nemeth * JANNAF Interagency Propulsion Committee – NGLT Advanced Materials and Safe Life December 1-5, 2003, Colorado Springs, Colorado. (Noel.N.Nemeth@nasa.gov).

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Probabilistic Analysis Techniques Applied to Lifetime Reliability Estimation of Ceramics

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  1. Probabilistic Analysis Techniques Applied to Lifetime Reliability Estimation of Ceramics Stefan Reh Tamas Palfi Noel Nemeth* JANNAF Interagency Propulsion Committee – NGLT Advanced Materials and Safe Life December 1-5, 2003, Colorado Springs, Colorado (Noel.N.Nemeth@nasa.gov) Glenn Research Center at Lewis Field

  2. Outline • Objective • Background - Why probabilistics… - CARES/Life - ANSYS Probabilistic Design System (PDS) - ANSYS/CARES/PDS • Example - Silicon nitride turbine stator blade • Conclusions

  3. Objective To predict the lifetime reliability (probability of survival) of brittle material components subjected to transient thermomechanical loading, taking into account stochastic variables such as loading, component geometry, and material properties.

  4. Radome • SOFH Fuel Cell • Oxygen Transport Membrane • Thermal Protection System • Ceramic Gun Barrel • Micro-Rocket

  5. Why Probabilistics… Brittle material strength is highly stochastic (Pressure membrane fracture strength vs: probability of failure) 3C-SiC – Recipe 1a &1b (Effect of changing suseptor) Amorphous Si3N4 Unfailed specimens (200 psi) Polycrystaline SiC 3C-SiC - Recipe 2 (Double growth rate)

  6. Why Probabilistics… Strength as a function of time is highly stochastic G. D. Quinn, “Delayed Failure of a Commercial Vitreous Bonded Alumina”; J. of Mat. Sci., 22, 1987, pp 2309-2318. Static Fatigue Testing of Alumina (4-Point Flexure) 10000 C

  7. Why Probabilistics… • For many applications the variability of other quantities or properties on component lifetime can be significant • MEMS devices - tolerance control of dimensions • Batch-to-batch variations in material properties • Probabilistic loading. • - magnitude of loads & loading directions (dental prosthetics) • - random vibrations (engine parts) Measured variation in film thickness can be significant for MEMS devices  Std. Dev.

  8. CARES/Life (Ceramics Analysis and Reliability Evaluation of Structures) Software For Designing With Brittle Material Structures • CARES/Life – Predicts the instantaneous and time-dependent probability of failure of advanced ceramic components under thermomechanical loading • Couples to commercial finite element software  ANSYS Weibull-Batdorf Stress-Volume Integration • Specimen rupture tests • Characterize material stochastic response Complex component life prediction

  9. CARES/Life Schematic & Capabilities Finite Element Interface Output from FEA codes (stresses, temperatures, volumes) read and printed to Neutral Data Base Parameter Estimation Weibull and fatigue parameter estimates generated from specimen rupture data • Reliability Evaluation • Component probability • of survival • Component “hot spots” • - high risk of failure • Volume flaw & surface analysis • PIA & Batdorf multiaxial models • Fast fracture reliability analysis • Time-/Cycle-dependent analysis • Multiaxial proof testing • Works with transient FE analysis

  10. Time-Dependent Life Prediction Theory -Slow Crack Growth and Cyclic Fatigue Crack Growth Laws Power Law: - Slow Crack Growth (SCG) Combined Power Law & Walker Law:SCG and Cyclic Fatigue

  11. Life Prediction TheoryFor Transient Mechanical & Thermal Loads • Methodology: • Component load and temperature history discretized into short time steps • Material properties, loads, and temperature assumed constant over each time step • Weibull and fatigue parameters allowed to vary between each time step – including Weibull modulus • Failure probability at the end of a time step and the beginning of the next time step are equal

  12. Transient Life Prediction Theory -Power Law General reliability formula for discrete time steps:

  13. CARES/Life Uses Results From Deterministic Finite Element Analysis CARES/Life predicts component lifetime probability of survival based on stochastic strength. It does not assess the effect on probability of survival from other stochastic variables related to the component - such as loads, geometry, and material properties.

  14. Material • Strength • Material Properties • Loads • Thermal • Structural Geometry/ Tolerances • Boundary Conditions • Gaps • Fixity ANSYS/PDS (Probabilistic Design System) Bringing Probabilistic Design into Finite Element Analysis Random input variables Finite-Element Model Statistical analysis of output parameters PDS Simulations • Deformations • Stresses • Lifetime • (LCF,...)

  15. ANSYS/PDS (Probabilistic Design System) Capabilities • General • - Free for ANSYS users • - works with any kind of ANSYS finite element model – including transient, • static, dynamic, linear, non-linear, thermal, structural, electro-magnetic, CFD .. • Probabilistic preprocessing • - Allows large number random input and output parameters • - modeling uncertainty in input parameters – Gaussian, log-normal, Weibull… • - random input parameters can be defined as correlated data • Probabilistic methods • - Monte Carlo  Direct & Latin Hypercube Sampling • - Response Surface Method  Central Composite & Box-Behnken Designs • Probabilistic postprocessing • - Histograms • - Cumulative distribution functions • - Sensitivity plots • Parallel, distributed computing

  16. ANSYS/CARES/PDS – Probabilistic Component Life Prediction ANSYS macros were developed to allows CARES/Life to run within PDS • CARES/Life uses results from • Deterministic FEA. Enabling • CARES/Life to work with PDS • Allows the effects of component • Stochastic variables to be • Considered in the life prediction • Stochastic loads, geometry & • material properties • Stochastic Weibull and fatigue • parameters  Simulates batch-to-batch • material variations or uncertainty in • measured parameters from specimen • rupture data

  17. EXAMPLE: Simplified Turbine Stator Vane in Startup and Shutdown OBJECTIVE: Explore the failure probability response of a turbine stator vane model from repeated startup/shutdown thermal loading - assuming stochastic thermal loads, material parameters, and Weibull & fatigue parameters Material: A generic silicon nitride DATA: MODEL: • ANSYS FEA analysis using 24151 solid tetrahedral elements • CARES/Life analysis - volume flaw failure mode & 17 time steps Red = clamped areas

  18. Temperature Dependent Material Properties Density: 3300 [kg/m3 ] Poisson’s ratio: 0.28

  19. Time profile of the transient thermal loads Transient FE analysis performed using 17 time steps Maximum vane temperature & principle stress as a function of time

  20. Steady state temperatures [°C] at time 75 seconds Location of maximum principal stress [Pa] at time 75 seconds

  21. CARES/Life Predictions From Deterministic Finite Element Analysis Weibull and fatigue parameters of the silicon nitride ceramic material Conditional probability of failure as a function of number of load cycles from CARES/Life and deterministic finite element analysis

  22. CARES/Life With PDS Analysis Random input variables for the PDS analysis

  23. Cumulative Distribution of the Conditional Failure Probability for 1,000 and 30,000 Cycles Monte Carlo simulation method (400 simulations)

  24. Failure Probability From Deterministic FE Analysis Versus Total Probability From PDS Analysis for 400 Simulations MCS = Monte Carlo RSM = Response Surface Method

  25. Convergence Behavior of the Monte Carlo Simulation Results 1000 cycles 30,000 cycles • Convergence behavior is significantly better at 30,000 cycles

  26. Sensitivity of Conditional Failure Probability 1,000 load cycles with Monte Carlo simulation

  27. Conclusions • A coupling of the NASA CARES/Life and the ANSYS Probabilistic Design System has been demonstrated for brittle material component life prediction. • This methodology accounts for stochastic variables such as loading, component geometry, material properties, and lifing parameters on component probability of survival over time. • The turbine vane example demonstrated that ignoring stochastic effects can lead to un-conservative design Acknowledgments: The authors would like to acknowledge NASA Next Generation Launch Technology (NGLT) program Propulsion Research & Technology (PR&T) project program manager, Mark D. Klem and Safe Life Design Technologies subproject manager, Rod Ellis. We also would like to acknowledge the generous cooperation and support of ANSYS Incorporated.

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