1. Predicting the Reliability of Ceramics Under Transient Loads and Temperatures With CARES/Life Noel N. Nemeth Osama M. Jadaan Tamas Palfi Eric H. Baker Symposium on Probabilistic Aspects of Life Prediction November 6-7, 2002, Miami Beach Florida Glenn Research Center at Lewis Field E-mail: Noel.N.Nemeth@grc.nasa.gov Life Prediction Branch

2. Outline  Objective  Background - CARES/Life  Theory - Power law & Walker law - Computationally efficient method for cyclic loading  Examples - Laser irradiated disk in thermal shock - Diesel exhaust valve - Alumina bar in static fatigue  Conclusions

3. Objective Develop a methodology to predict the time-dependent reliability (probability of survival) of brittle material components subjected to transient thermomechanical loading, taking into account the change in material response with time.  Transient reliability analysis

4. Fully Transient Component Life Prediction MOTIVATION: To be able predict brittle material component integrity over a simulated engine operating cycle REQUIRES: Life prediction models that account for: - transient mechanical & temperature loads - transient Weibull and fatigue parameters (temperature/time) Interface codes that transfer transient analysis finite element results into life prediction codes (CARES/Life)

5. 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 ANSYS, ABAQUS, MARC

6. CARES/Life Structure Reliability Evaluation Component reliability analysis determines “hot spots” and the risk of rupture intensity for each element Parameter Estimation Weibull and fatigue parameter estimates generated from failure data Finite Element Interface Output from FEA codes (stresses, temperatures, volumes) read and printed to Neutral Data Base

7. Transient Life Prediction Theory For Slow Crack Growth Assumptions: 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 over 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

8. Transient 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 - Denotes location and orientation

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

10. Binomial Series Expansion: (x + y) n  x n + nx n-1 y, when x >> y When x>>y the series can be approximated as a two term expression Binomial Series Approximation Used to Derive Computationally Efficient Solution For Cyclic Loading

11. Transient Life Prediction Theory - Slow Crack Growth Modeled With Power Law Computationally efficient transient reliability formula for cyclic loading - simplified version Computationally efficient transient reliability formula for cyclic loading - simplified version T T 2TZT load time

12. Combined Walker Law & Power Law for cyclic fatigue - Computationally efficient version with Z factor multiple Combined Walker Law & Power Law for cyclic fatigue - Computationally efficient version with Z factor multiple

13. EXAMPLE:Thermal Shocked Disks in Fast-Fracture DATA: Material: Silicon Nitride SN282 Information Source: Ferber, M., Kirchhoff, G., Hollstein, T., Westerheide, R., Bast, U., Rettig, U., and Mineo, M., “Thermal Shock Testing of Advanced Ceramics – Subtask 9.” International Energy Agency Implementing Agreement For a Programme of Research and Development on High Temperature Materials for Automotive Engines, prepared for The Heavy Vehicle Propulsion System Materials Program Oak Ridge National Laboratory for the U.S. Department of Energy, M00-107208, March 2000. MODEL: ANSYS FEA analysis using solid elements Disks were 20 mm diameter, 0.3 mm thick Disks were not constrained and were tested in vacuum Volume flaw failure assumed OBJECTIVE: Predict the failure response of laser induced thermal shocked disks from rupture data of simple beams in uniaxial flexure

14. Thermal Shocked Disks in Fast-Fracture Disk #3 Transient Temperature & Stress Profile Over 0.65 Seconds Ceramic Sample Nd:YAG Laser Steerable mirrors Temperature vs: Time Iso-lines Tangential Stress vs: Time Iso-lines

15. Predictions of failure probability vs: time & failure probability vs: peak stress in the disk Finite Element Model of Disk  Predictions based on Weibull parameters obtained from 3-point flexure bar data Prediction for a single time step CARES/Life disk #3 P f prediction (m v = 8.72) m V = 11.96,   V = 612.7 MPa Bar exp.data Disk exp. data m V = 6.91,   V = 345.9 MPa Size Effect

16. EXAMPLE:Diesel Engine Si 3 N 4 Exhaust Valve (ORNL/Detroit Diesel) DATA: Material: Silicon Nitride NT551 Information Source: Andrews, M. A., Wereszczak, A. A., Kirkland, T. P., and Breder, K.; “Strength and Fatigue of NT551 Silicon Nitride and NT551 Diesel Exhaust Valves,” ORNL/TM  1999/332. Available from the Oak Ridge National Laboratory 1999 Corum, J. M, Battiste, R. L., Gwaltney, R. C., and Luttrell, C. R.; “Design Analysis and Testing of Ceramic Exhaust Valve for Heavy Duty Diesel Engine,” ORNL/TM  13253. Available from the Oak Ridge National Laboratory, 1996 MODEL: ANSYS FEA analysis using axisymmetric elements Combustion cycle (0.0315 sec.) discretized into 29 load steps A 445 N (100 lb) spring pre-load applied to valve stem in open position. 1335 N (300 lb) on valve stem on closure. Thermal stresses superposed with mechanical stresses Volume flaw failure assumed OBJECTIVE: Contrast failure probability predictions for static loading Versus transient loading of a Diesel engine exhaust valve for the power law and a combined power & Walker law

17. Pressure load applied to face of a ceramic valve over the combustion cycle Thermal distribution Thermal distribution First principal stress at maximum applied pressure (MPa) First principal stress at maximum applied pressure (MPa) Loading and Stress Solution of Diesel Engine Exhaust Valve

18. Silicon Nitride NT551 Fast Fracture and SCG Material Properties T (  C)m  0V (MPa.mm 3/m ) Average strength (MPa) NB (MPa 2.sec) QA2A1 209.4105480631.65.44e5 3.20.65 7009.6773593871.12e43.20.65 8508.4790577191.13e63.20.65 Power Law Parameters (NT551): N and B Cyclic Fatigue Parameters: Q and A2A1 Note: Cyclic fatigue parameters are assumed values for demonstration purposes only

19. Diesel Engine Si 3 N 4 Exhaust Valve Batdorf, SERR criterion with Griffith crack Transient and static probability of failure versus combustion cycles (1000 hrs = 1.14E+8 cycles)

20. Diesel Engine Si 3 N 4 Exhaust Valve Transient reliability analysis with proof testing capability Proof test: 10,000 cycles at 1.1 load level Batdorf, SERR criterion with Griffith crack

21. EXAMPLE:Predict material reliability response of an alumina assuming time varying Weibull & Fatigue Parameters DATA: Material: Alumina Specimen: 4-pt flexure (2.2mm x 2.8mm x 50mm -- 38mm and 19mm bearing spans) Test Type: Static Fatigue Temperature: 1000 0 C Source: G. D. Quinn – J. Mat. Sci. – 1987 MODEL: Single element model of specimen inner load span (2.8mm x 19mm) with uniform uniaxial stress state (surface flaw analysis) Loading is static (non-varying) over time Weibull and fatigue parameters vary with the log of the time PROCEDURE: A single element CARES neutral file is constructed with discrete time steps (10 steps per decade on a log scale) spanning 8 orders of magnitude. Applied load is constant but Weibull and fatigue parameters allowed to vary with each time step.

22. EXAMPLE: Time Dependent Weibull & Fatigue Parameters 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) 1000 0 C

23. t = 1.6 sec., m = 29.4,  0  = 165.8, N = 6.7, B = 2711.1 t = 31.6 sec., m = 15.8,  0  = 152.7, N = 13.2, B = 9707.7 t = 1.0E+5 sec., m = 13.1,  0  = 127.3, N = 36.4, B = 2276.2 Parameters interpolated with log of time - No extrapolation outside of range

24. t = 1.6 sec., m = 29.4,  0  = 165.8, N = 6.7, B = 2711.1 t = 31.6 sec., m = 7.4,  0  = 263.3, N = 8.0, B = 2395.9 t = 316.2 sec., m = 4.5,  0  = 870.1, N = 9.0, B = 10,389.0 Parameters interpolated with log of time - No extrapolation outside of range

25. Conclusions  A computationally efficient methodology for computing the transient reliability in ceramic components subjected to cyclic thermomechanical loading was developed for power law (SCG), and combined power & Walker law (SCG & cyclic fatigue).  This methodology accounts for varying stresses as well as varying Weibull and fatigue parameters with time/temperature.  FORTRAN routines have been coded for the CARES/Life (version 6.0), and examples demonstrating the program viability & capability were presented.