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 Centerat Lewis Field

E-mail: Noel.N.Nemeth@grc.nasa.gov

Life Prediction Branch

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

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

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)

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

CARES/Life Structure

Reliability EvaluationComponent reliability analysis determines “hot spots” and the

risk of rupture intensity for each element

Parameter EstimationWeibull and fatigue parameter

estimates generated fromfailure data

Finite Element InterfaceOutput from FEA codes

(stresses, temperatures, volumes)read and printed toNeutral Data Base

Transient Life Prediction TheoryFor 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

Transient Life Prediction Theory -Slow Crack Growth and Cyclic Fatigue Crack Growth Laws

Power Law: - Slow Crack Growth (SCG)

t),(K A(t) = dt

t),da( N(t)Ieq

Combined Power Law & Walker Law: SCG and Cyclic Fatigue

- Denotes location and orientation

t),(K ))(R1(f(t)A

t),(K g(t)A = dt

t),da(

N(t)Ieq

)t(Qc2

N(t)Ieq1

Transient Life Prediction Theory -Power Law

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t

B

t

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t

tP

V

V

V

V

VjNVim

ViNVjm

Vj

Vj

VkVj

VjVk

Vk

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General reliability formula for discrete time steps:

33n22n1nnn yx

!3

2n1nnyx

!2

1nnynxxyx

Binomial Series Expansion:

(x + y)n xn + nxn-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

Transient Life Prediction Theory - Slow Crack Growth Modeled With Power Law

Computationally efficient transient reliability formulafor cyclic loading- simplified version

Computationally efficient transient reliability formulafor cyclic loading- simplified version

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dB

tZ

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tZ

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TT

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load

time

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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

EXAMPLE: Thermal Shocked Disks in Fast-Fracture

DATA: Material: Silicon Nitride SN282Information 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

-450-350-250-150-5050150250350450

0 2 4 6 8 10

Distance from Center [mm]

Tang

entia

l str

ess

[MP

a] 0.65

0.0

0

200

400

600

800

1000

1200

0 2 4 6 8 10

Distance from Center [mm]

Tem

pera

ture

[C

]

0.65

Thermal Shocked Disks in Fast-FractureDisk #3 Transient Temperature & Stress Profile Over 0.65 Seconds

Ceramic Sample

Nd:YAGLaser

Steerablemirrors

Temperature vs: Time Iso-lines

Tangential Stress vs: Time Iso-lines

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0.10 0.20 0.30 0.40 0.50 0.60 0.70Time [seconds]

Pro

babi

lity

of F

ailu

re

Disk #9

Disk #3

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 200 400 600 800

Stress [MPa]

Pro

babi

lity

of F

ailu

re3-Point BarDisk

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 Pf prediction

(mv = 8.72)

mV = 11.96,V = 612.7 MPa Bar exp.data

Disk exp. datamV = 6.91,

V = 345.9 MPa

Size Effect

EXAMPLE: Diesel Engine Si3N4 Exhaust Valve (ORNL/Detroit Diesel)

DATA: Material: Silicon Nitride NT551Information 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/TM1999/332. 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/TM13253. 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 loadingVersus transient loading of a Diesel engine exhaust valve for the power law and a combined power & Walker law

0

500

1000

1500

2000

2500

0 0.01 0.02 0.03 0.04

Time (sec)

Pres

sure

(psi

)

Pressure load applied to face of a ceramic valve over

the combustion cycle

Pressure load applied to face of a ceramic valve over

the combustion cycle

Thermaldistribution

Thermaldistribution

First principalstress at maximum

applied pressure

(MPa)

First principalstress at maximum

applied pressure

(MPa)

Loading and Stress Solution of Diesel Engine Exhaust Valve

Silicon Nitride NT551 Fast Fracture and SCG Material Properties

T (C) m 0V

(MPa.mm3/m)

Average strength

(MPa)

N B(MPa2.sec)

Q A2A1

20 9.4 1054 806 31.6 5.44e5  3.2 0.65

700 9.6 773 593 87 1.12e4 3.2 0.65

850 8.4 790 577 19 1.13e6 3.2 0.65

Power Law Parameters (NT551): N and BCyclic Fatigue Parameters: Q and A2A1

Note: Cyclic fatigue parameters are assumed values for demonstration purposes only

Diesel Engine Si3N4 Exhaust Valve

Batdorf, SERR criterion with Griffith crack

Transient and static probability of failure versus combustion cycles(1000 hrs = 1.14E+8 cycles)

Diesel Engine Si3N4 Exhaust Valve

Transient reliability analysis with proof testing capabilityProof test: 10,000 cycles at 1.1 load level

Batdorf, SERR criterion with Griffith crack

EXAMPLE: Predict material reliability response of an alumina assumingtime varying Weibull & Fatigue Parameters

DATA: Material: AluminaSpecimen: 4-pt flexure (2.2mm x 2.8mm x 50mm -- 38mm and 19mm bearing spans)

Test Type: Static FatigueTemperature: 10000 CSource: 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 withdiscrete time steps (10 steps per decade on a log scale)spanning 8 orders of magnitude. Applied load is constantbut Weibull and fatigue parameters allowed to vary with each time step.

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)

10000 C

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 interpolatedwith log of time -No extrapolationoutside of range

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 interpolatedwith log of time -No extrapolationoutside of range

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.