NASA/TM--1998-208648

U.S. ARMY

,/,X," _3 _ ARL-MR-418

/_/.d .z /_O

RESEARCH LABORATORY

Simulation of Crack Propagation in Engine

Rotating Components Under Variable

Amplitude Loading

P.J. Bonacuse

U.S. Army Research Laboratory, Lewis Research Center, Cleveland, Ohio

L.J. Ghosn

Case Western Reserve University, Cleveland, Ohio

J. Telesman and A.M. Calomino

Lewis Research Center, Cleveland, Ohio

P. Kantzos

Ohio Aerospace Institute, Cleveland, Ohio

October 1998

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NASA / TM--1998-208648

U.S. ARMY

ARL-MR-418

RESEARCH LABORATORY

Simulation of Crack Propagation in Engine

Rotating Components Under Variable

Amplitude Loading

P.J. Bonacuse

U.S. Army Research Laboratory, Lewis Research Center, Cleveland, Ohio

L.J. Ghosn

Case Western Reserve University, Cleveland, Ohio

J. Telesman and A.M. Calomino

Lewis Research Center, Cleveland, Ohio

P. Kantzos

Ohio Aerospace Institute, Cleveland, Ohio

Prepared for the Symposium of the Applied Vehicle Technology Panel

sponsored by the NATO/AGARD

Toulouse, France, May 11-15, 1998

National Aeronautics and

Space Administration

Lewis Research Center

October 1998
NASA Center for Aerospace Information

7121 Standard Drive

Hanover, MD 21076

Price Code: A03

Available from

National Technical Information Service

5285 Port Royal Road

Springfield, VA 22100

Price Code: A03

lrt ii,
Simulation of Crack Propagation in Engine Rotating Components

Under Variable Amplitude Loading

P.J. Bonacuse

Materials Research Engineer

U. S. Army Research Laboratory

L. J. Ghosn

Resident Research Associate

Case-Western Reserve University

J. Telesman and A. M. Calomino

Materials Research Engineers

NASA Lewis Research Center

P. Kantzos

Senior Research Associate

Ohio Aerospace Institute

21000 Brookpark Rd., MS 49-7

Cleveland, OH 44135

U.S.A.

Abstract

The crack propagation life of tested specimens has been repeatedly shown to strongly depend on the

loading history. Overloads and extended stress holds at temperature can either retard or accelerate the

crack growth rate. Therefore, to accurately predict the crack propagation life of an actual component, it is

essential to approximate the true loading history. In military rotorcraft engine applications, the loading

profile (stress amplitudes, temperature, and number of excursions) can vary significantly depending on the

type of mission flown. To accurately assess the durability of a fleet of engines, the crack propagation life

distribution of a specific component should account for the variability in the missions performed

(proportion of missions flown and sequence). In this report, analytical and experimental studies are

described that calibrate/validate the crack propagation prediction capability for a disk alloy under variable

amplitude loading. A crack closure based model was adopted to analytically predict the load interaction

effects. Furthermore, a methodology has been developed to realistically simulate the actual mission mix

loading on a fleet of engines over their lifetime. A sequence of missions is randomly selected and the

number of repeats of each mission in the sequence is determined assuming a Poisson distributed random

variable with a given mean occurrence rate. Multiple realizations of random mission histories are

generated in this manner and are used to produce stress, temperature, and time points for fracture

mechanics calculations. The result is a cumulative distribution of crack propagation lives for a given, life

limiting, component location. This information can be used to determine a safe retirement life or

inspection interval for the given location.

Introduction

The U. S. Army is changing its life management philosophy for critical rotating components in rotorcraft

turbo-shaft engines. A 'safe-life' approach has been the Army's traditional means of determining

component retirement lives. For 'safe-life,' a minimum calculated fatigue crack initiation life dictates when

the component is retired from service. Although the 'safe-life' approach tends to be conservative and

relatively easy to implement, it also suffers from several shortcomings, i.e.: 1) most components are

retired with significant remaining crack initiation life, 2) unforeseen damage, such as scratches incurred

during disassembly/assembly, is ignored, and 3) there is no established 'early warning' mechanism to

identify changes in use and errors in life prediction.

NASAYI'M-- 1998-208648 1
The U. S. Air Force has pioneered a very different life management philosophy. The Air Force's

methodology emphasizes planned inspections to detect damaged components while safely maximizing

the use of undamaged components. This approach has often been termed retirement for cause (RFC).

The RFC approach is based on fracture mechanics as the means of determining component lives. In

RFC, preexisting flaws are assumed to exist at a size just below the detection threshold of the chosen

inspection technique. The crack propagation life from this threshold to a fracture critical size is calculated

for all high stress locations to determine the life limiting component location. Planned inspection intervals

for these high stress locations are set to a fraction of the predicted life of the life limiting location to ensure

that all propagating cracks are discovered well before they might cause component failure. The U. S.

Army is adopting a tailored version of this approach.

Loading of rotorcraft engines, and in particular military rotorcraft engines, is typically far more variable than

in fixed, wing aircraft. Army rotorcraft perform a number of different missions with often very different

loading histories. This variation in component loading can have a marked influence on the crack

propagation life. For example, rapid excursions to high power settings can cause overloads that may

retard crack growth rates. Conversely, many small stress excursions at high R-ratios can significantly

shorten lives. This additional variability in load history can have a strong influence on the expected life

distribution. Given that the Army utility helicopters are used in a variety of missions and the impending

implementation of RFC, the effect of this variation on crack propagation life should be quantified.

A methodology is presented herein for predicting the distribution in the crack propagation lives of rotorcraft

engine rotating components subjected to realistic mission loading histories. The methodology for

determining the mission mix is based on direct Monte Carlo simulation of the engine loading given that the

engine will likely be used in multiple aircraft performing a variety of missions. The development of this

methodology is predicated upon the ability to accurately model fatigue crack growth under variable

amplitude loading. The crack propagation life prediction code, FASTRAN II, was used to perform the life

calculations. In order to calibrate and confirm the effectiveness of this code, an experimental program

was devised and performed. Results are presented that validate the underlying crack propagation model.

Fatigue Crack Growth Under Variable Amplitude Loading

Models that predict load interactions for cracks propagating under variable amplitude loading, fall into two

broad categories. The first group may be classified as overload plastic zone type models, which include

the Willenborg [1] and Wheeler [2] models. These models calculate the effective crack driving force as a

function of the ratio of the overload plastic zone size to the plastic zone size due to the current load

amplitude as well as the location of the crack tip in relation to the overload plastic zone. Models of this

type are widely used, especially by the engine companies who have invested significant effort in tailoring

these models to their requirements.

The other class may be called crack closure models. They are based upon the original finding by Elber [3]

who showed that crack regions behind the crack tip can close prior to reaching the minimum load. The

stress intensity range over which the crack tip is open, termed AKe,, is assumed to be the true crack

driving force. The premature closure of the crack tip region is due to the crack growing through previously

plastically deformed material which can come into contact behind the crack tip. The effective stress

intensity factor range (_Ke, = Kmax - Ko) will therefore be somewhat smaller (Ko > Kmin) than that computed

without accounting for this effect. A model of this type is used in this work. The effective stress intensity

factor range, AKe,, is given by:

AKoff = Y . (c,,_, - Go),_-a Eq. 1

where a is the crack depth, Y is a geometric correction factor, Cmaxis the maximum stress, and Gois the

stress at crack closure.

NASA/TM-- 1998-208648 2
The cyclic crack growth rate, assuming a Paris Law, is related to the effective stress intensity range by

(Eq. 2):

d% N = C(AKe, )m Eq. 2

where C and m are material constants. The magnitude of the crack closure stresses (_o) is a function of

the applied loading history, the crack tip constraint and the size and magnitude of the crack wake field

behind the crack tip. A widely recognized crack propagation life prediction code, based upon the crack

closure model, is FASTRAN II developed by Newman [4] at the NASA Langley Research Center.

The attractiveness of the crack closure model for engine applications is its ability to accurately predict

crack growth of small flaws. Rotating engine components, such as disks, are highly stressed due to their

high rotational speed. Because of these conditions, the critical crack size which results in failure is

considerably smaller than typically encountered in airframe components. The crack closure models have

been shown [5] to reliably predict the early stages of crack development where the crack wake is not yet

fully developed and thus the z&Ke, is greater than would be predicted by the overload plastic zone type

models. Thus the authors believe that the crack closure models are appropriate where the critical crack

sizes are relatively small i.e., lifing of engine rotating components.

The crack propagation analysis program FASTRAN II was used to estimate crack propagation lives in this

study. The program contains a library of stress intensity solutions for a variety of crack geometries. The

solution chosen for the sample problem examined in this report was a uniaxialiy loaded surface crack in a

prismatic body (Figure 1). The overall dimensions of this prismatic body approximate the dimensions of

the appropriate cross section of the second stage gas generator turbine disk in the UH-60 Blackhawk

utility helicopter's TT00 engine. This solution was also used to perform crack propagation calculations for

the Kb bar specimens used in the experimental program. Stress amplitudes and temperatures were taken

from calibrated thermal and stress analyses of this component. The failure criterion used by FASTRAN II

to discontinue the crack propagation analysis was a calculated stress intensity factor range in excess of

90% of the input material fracture toughness (K_c).

I

I

i

I

I

\ \

r

Figure 1: Schematic of prismatic body with surface crack,

The loading histories analyzed in this study were a randomized mix of utility helicopter mission histories.

The U. S. Army has specified that the UH-60 Blackhawk helicopter performs ten different missions at

three different ambient conditions yielding a total of 30 distinct engine histories (Table I). The purpose of

specifying these mission profiles was to enable more realistic fatigue life calculations. It is well known that

minor excursions (load ranges less than maximum minus minimum) cause additional damage both in

crack initiation and propagation. Table I describes the specified portion of the overall engine life spent in

each of these missions.

NASA/TM-- 1998-208648 3
Mission

Table I: Army Mission Mix Specification

Ambient Conditions

Temp. 15 °C 35 °C 35 °C

Elevation Sea Sea

Level Level

Troop Assault 5.10

Resupplying 3.30

Aeromed Evacuation 10.50

Replacing Units 3.00

Transport of Recon. 2.30

Reinforce/Reposition • 4.70

Tro____££_Extraction 2.60

Aerial Command Post 2.00

Sling Load 3.80

Training 7.60

Totals 44.90

All values in % of engine operating life

5.80

3.80

11.90

3.40

2.70

5.40

3.00

2.20

4.30

8.60

51.10

1220

m

0.50

0.30

0.90

0.30 ' 6170

0.20 . 5120

0.40 !10,50

0.20 5,_

0.20 4.40

0.30

0.70

4,00

Totals

11

7140

231_

Calibration and Validation of Crack Growth Algorithm

To validate the accuracy of the FASTRAN II crack propagation analysis code for variable amplitude

loading of a turbine disk alloy at elevated temperature, an experimental program (10 specimens)was

performed. The purpose of the experimental program was twofold. The first was to generate relevant

baseline data necessary to calibrate the crack closure model used by the FASTRAN I1 program. The

second was to generate variable amplitude loading experimental data that could be directly compared with

FASTRAN II predictions.

Mechanical Testing Procedure

All specimens were cut from a single retired Ren6 95 disk (Fig. 2). Ren6 95 is a powder metallurgy,

nickel-base superalloy that is used for most of the gas generator turbine rotating components in the

UH-60 Blackhawk's T700 engine. The experiments were performed at 400 °C to more closely simulate the

engine operating environment at the fracture critical locations: the disk bore and bolt/cooling air holes.

Fatigue crack growth testing was performed with an axially loaded Surface cracked specimen geometry,

the Kb bar (Fig. 3). The Kb bar geometry was thought to be more representative of the actual flaws and

high applied stresses expected in turbine disk applications tha6 the_more Conventional compact tension

specimen geometry. The gage-secti_on dimensions of the Kb bar specimen were nominally 10.2 mm wide

by 4.3 mm thick. Crack lengthsw_ere monitored with a direct-cur_rent- electric-potential (DCEP) technique.

DCEP in this program was calibrated using marking cycles, heat tinting, and post failure crack length

measurements. Testing was performed on a computer controlled, servo-hydraulic, test frame equipped

with a clamshell furnace.

NASA/TM-- 1998-208648

I[| l i
Figure 2: Fatigue crack growth specimen blank locations; TTO0 Stage 2 gas generator turbine disk.

÷

Figure 3: Kb Bar specimen instrumented for elevated temperature crack propagation experiment. Inset is

a close up of an EDM notch with spot welded DCEP probes.

The cracks in the specimens were not allowed to propagate through the specimen thickness. The

experiments were stopped at a crack depth where the accuracy of the analytical solution for the DCEP

calibration was expected to degrade (approximately 50-60% through thickness).

NASA/TM-- 1998-208648 5
Calibration Experiments

To properly calibrate the crack closure model, constant amplitude fatigue crack growth experiments were

performed at three different R ratios (R = CmJCmax):0.05, 0.5 and 0.7. In Figure 4, the experimental data

from these calibration experiments is displayed as a function of the applied crack driving force, AKapp.

Figure 5 shows the same data set corrected for crack closure with Newman's formulation for the effective

crack driving force, AKe,. This formulation is used by the FASTRAN II software to estimate the effect of

crack closure on the crack propagation rate. The stress intensity geometric correction formula for the Kb

bar specimen was taken from Newman and Raju [6].

1 0 "2

o

E

Z

1 0 -3

10 .4

10 .5

10 6

[]

O

R = 0.05

R =0.5

R=0.7

i

4 6 8 10 20 40 60

AKap p [MPa°mm '/2]

Figure 4: da/dN vs. AKappfor Rer_ 95 at 4008C.

As seen in Figure 4, the R=0.05 data is considerably different than the 0.5 and 0.7 data, showing slower

crack growth rates for the same ,SKapp. This difference is expected since at a 0.05 R-ratio, the crack

closes at a higher applied stress than the minimum stress. But when the stress intensity factor range is

corrected for the early closure of the crack faces (AKeff -- (Kmax- Kcwsure) < (Kmax - Kmin)) using Newman's

formulation [4], there is a better correlation between the three different R-ratios, (see Fig. 5). Hence, the

AK_, parameter plotted in Figure 5 represents a true measure of the actual crack driving force,

independent of the applied load ranges. The curve fit of the crack growth rate versus the effective stress

intensity factor range, determined from these three constant amplitude experiments, is supplied to

FASTRAN II for use in predicting the variable amplitude loading experiments.

NASA/TM-- 1998-208648 6

!I1 1
5

E

E

Z

"o

e5

1 0 .2

10-3

1 0 .4

10-5

1 0 6

/k R = 0.05

[] R =0.5

© R =O.7

Curve Fit

4 6 8 10 20 40 60

AKef f (Newman) [MPa°mm V2]

Figure 5: da/dN vs. AKe_ for Ren_ 95 at 4008C.

Validation Experiments

The variable amplitude loading experimental program, consisted of 5 experiments. Three different

repeating load sequences were applied to Kb bar test specimens at 400 °C. Load sequence 1 (LS 1) (Fig.

6a) closely resembles the Army specified training mission. Load sequence 2 (LS 2) (Fig. 6b) is essentially

the same as sequence 1 with a few additional large excursions (each roughly equivalent to a take-off -

ground idle excursion). Load sequence 3 (LS 3) (Fig. 6c) was run to test the extremes of the crack

closure model's predictive capability. It includes excursions covering various ranges of loading R ratio.

The FASTRAN II analysis of the three loading spectra showed excellent agreement with the experimental

results. Comparison of the experimentally observed crack depth versus the number of mission spectra

repeats applied with the FASTRAN II predictions for each of the three spectra are shown in Figure 7. Only

the data from one experiment for each loading spectrum is displayed. The predicted crack depths

faithfully replicate those observed in the experiments. The predicted final crack depths were all within a

factor of 1.5 of the experimentally observed values (Fig. 8).

NA SA/TM-- 1998-208648 7
X

E

13_

13_

m

_

5 10 15

Loading Points

Figure 6a: Experimental Loading History 1 (LS i).

20

X

E

tl

n

_

_

f I t i

5 10 15 20

Loading Points

Figure 6b: Experimental Loading History 2 (LS 2).

25

NASA/TM-- 1998-208648 8

I[| ili_
X

EL

0 -

0 5 10 15 20

Loading Points

Figure 6c: Experimental Loading History 3 (LS 3).

i i

25 30 35

E

E

.E

Q.

D

tJ

O

2.5

2.0

1.5

1.0

0.5

/ !

1 Prediction

2 Experiment

2 Prediction

3 Experiment

3 Prediction

t i i

0 1000 2000 3000 4000 5000

Number of Missions

Figure 7: Correlation of FASTRAN II mission mix predictions with experimental crack depth data.

NASA/TM-- 1998- 208648 9
E

"2 1 0 s

Q,)

(/)

"ID

(D

_ lO 4

z

< 10 a

rr

I--

<

IJ10 2

° " ° • "7

;7"

1.5x _

.

• ._/

,4...

0 2 10 3 10 4 10 5

Experimental Missions

Figure 8: Experimental vs. predicted crack propagation lives for block loaded Kb bar FCG specimens.

In order to evaluate/demonstrate the need to correct the crack driving force for load interactions, the crack

growth data were modeled using a Miner's type (linear) summation of all the different cyclic segments

without regard for load interactions. The crack growth rates for a given load excursion, at a given R ratio,

were calculated using Walker's methodology [7] for evaluating the influence of the load ratio. The Walker

model uses ,_Kapp as the crack driving force. The results of the analysis, performed on the LS 3 spectrum

(Fig. 6c) are presented in Figure 9. As shown, the crack growth rate calculated using this linear

summation approach is substantially faster than was experimentally measured, amply demonstrating the

presence of load interaction effects.

Also, an analysis of the minor cycles' influence on the crack growth behavior was performed. This

analysis consisted of a FASTRAN II run with a single load excursion from the minimum stress to the

maximum stress and back down to the minimum stress (all the minor cycles removed from the load

history). As shown in Figure 9, the major excursion in the load histories could only account for a small

fraction of the observed crack growth. Thus, the minor cycles' contribution to crack growth, for this

particular spectrum, is significant.

NASA/TM-- 1998-208648 10

It|11i
3.0

E 2.5

E

{.-

B. 2.0

(D

O

o 1.5

},_

o

1.0

0.5

(_) Experiment

FASTRAN w/o minor cycles

.... Walker Correction - No Closure

J

J

J

I

i i

0 1000 2000 3000 4000 5000

Number of Missions

Figure 9: Influence of crack closure and minor cycles on the predicted crack propagation rate. The LS 3

spectrum was used in displayed results.

Simulation of Mission Mix Histories

Given that the FASTRAN II crack propagation analysis code proved successful in predicting the crack

growth behavior for the various spectrum loading sequences, it was deemed an appropriate tool for the

study of mission mix history on the overall fatigue crack growth life.

There are several ways to interpret the Army's mission mix specification. The most literal interpretation is

that each engine will experience the exact mission fractions and ambient conditions specified in the

mission mix. In practice, this is highly improbable. It is far more likely that the mission mix is an estimate

of the flee_.__!t usage. This would mean that an appropriate fraction of the fleet would experience the

specified missions, for example, 0.5% of the fleet flying time (given a fleet of 2000 aircraft, one aircraft

might fly this mission continuously or two aircraft half the time, etc.) will be used for the troop assault

mission on a 35 °C day from a base at 1220 m. Therefore, the more severe missions (as well as the

more benign missions) are not spread evenly to all engines. This leads to a larger variance in the

distribution of the expected crack propagation lives. In addition, the longer the interval between changes

in mission for the engines, the larger the spread in the fatigue lives.

In describing this simulation technique several terms will be used that require unambiguous definition: A

mission is a loading sequence that approximates the loading imposed on a component during a single

rotorcraft flight, from engine start-up, through takeoff and flight maneuvers, to landing and engine shutdown. A block is defined as a number of sequentially repeated missions of the same type (e.g., any

number of repeated Troop Assault missions all at sea level standard conditions would be considered a

block). A block of missions is intended to simulate the repeated use of an engine for a specific mission

while stationed with a unit. The block length is defined as simply the number of repeated missions in a

block. A realization is defined as a sequence of blocks that terminates with component failure. A

realization can be thought of as the simulated loading history of a single engine.

To determine the crack propagation life of a component, all potentially life limiting (high stress) locations

are analyzed to predict the crack growth life from a flaw of a known size (as determined by the resolution

and reliability of the inspection technique). The feature chosen for this crack propagation simulation was

the bore of the second stage gas generator turbine disk. A crack propagating from this location would

eventually lead to a catastrophic uncontained engine failure. To estimate the effect of the random mission

NASA/TM-- 1998-208648 11
mix loading, a direct Monte Carlo simulation technique was formulated. This method involved generating

a number of blocks of mission loading sequences that were then fed into the FASTRAN II crack

propagation analysis code (Fig. 10). This was repeated (16-64 realizations) with new randomly generated

sequences of mission blocks to get a distribution of crack propagation lives.

Realization 1 I #3 I #9 I #17 1#71 ... I #14 X£_"

Realization 2 [#2_7 I #1 t #6 I #13 I #6 I #12 I ... I #5 v,-,_"_'-

Realization 3 I_8 @ 011 I #21 I #9 1#41 #27 I ... I #30 X_ _, _6

time ." _,_o

Realization N I.-__1_ #18 I #6 I #29 I #7 I ... ] #4 v/,, _

#1 Troop Assault SLS

#2 Resupply SLS

#3 Aeromed. Evac. SLS

#4 Replacing Units SLS

#5 Trans. of Recon. SLS

#6 Reinforce/Repos. SLS

#7 Troop Extract. SLS

#8 Aerial Comm. Post SLS

#9 Sling Load SLS

#10 Training SLS

#11 Troop Assault 35°C

#12 Resupply 35°C

#13 Aeromed. Evac. 35°C

#14 Replacing Units 35°C

#15 Trans. of Recon. 35°C

#16 Reinforce/Repos. 35°C

#17 Troop Extract. 35°C

#18 Aerial Comm. Post 35°C

#19 Sling Load 35°C

#20 Training 35°C

#21 Troop Assault 35°C HA

#22 Resupply 35°C HA

#23 Aeromed. Evac. 35°C HA

#24 Replacing Units 35°C HA

#25 Trans. of Recon. 35°C HA

#26 Reinforce/Repos. 35°C HA

#27 Troop Extract. 35°C HA

#28 Aerial Comm. Post 35°C HA

#29 Sling Load 35°C HA

#30 Training 35°C HA

Figure 10: Schematic of random mission block loading. Note both the random selection of missions and

the variation in the block length.

Several assumptions have been made to simplify the FASTRAN II simulation and to fill in for certain

unknowns about the actual usage of the engine. First, it was assumed that the engines are 'pooled' at the

depot. By this it is meant that an engine returned to the depot for maintenancewill not necessarily return

to the original 'owner' but will go to the first unit requiring an engine. This allows us to model the selection

of each block of missions with an appropriately partitioned uniform random variable. The probability of

selecting a particular mission and ambient condition is directly linked to the fraction of time the engine is

expected to spend performing that mission/ambient condition combination as described by the Army

mission mix specification (Table I).

Another, and perhaps oversimplifying, assumption is that, while stationed with a unit, the aircraft will

perform one mission exclusively. For example, aircraft stationed at a training facility perform only the

training mission. It was also assumed that the block length (number of missions between removal of the

engines for overhaul at the depot) could be modeled as a Poisson process. The purpose of using a

Poisson distributed random variable, as opposed to a fixed block length, was to more closely model the

actual engine usage (the T700 has no scheduled overhaul interval). A Poisson process is defined as a

discrete process where the intervals between events are exponentially distributed. The probability

distribution is defined by (Eq. 3):

P(x) - e- _ Eq. 3

x!

where P(x) is the probability that x events occur and X is the mean number of events. This equation may

be solved for the number of events, x, and may be used to generate a Poisson distributed random

variable. The Poisson distribution parameter, X, for the purposes of this simulation, is equal to the mean

block length and the random variable, x, will be defined as the Poisson distributed block length. The

method of generating a Poisson distributed random variable was taken from Press et al. [8].

NASA/TM-- 1998-208648 12

ll| !li_
The simulation method was used to execute six runs of 16 realizations each using various values for the

mean block length, ;L(Table II). An additional run of 64 realizations with X = 165 missions, was performed

as a measure of the sample to sample variability. The first row of Table II, labeled I, = 1, was actually run

with the block length fixed to one mission. This is roughly analogous to running the 30 missions, in

proportion to the mission mix specification, on each of the engines.

Table I1:Simulation Results

X

[missions

/block]

1

Realizations

16

33 16

66 16

99 16

132 16

165 16

165 64

Mean

[hrs]

8496

8522

8520

8662

8607

8578

8476

Standa_ -3c Life

Deviation [hrs]

[hrs]

182.1 7950

315.3 7576

628.4 6472

715.0 6517

1176.1 5078

1344.0 4546

772.1 6160

The increase in the dispersion of the simulated crack propagation lives as the expected number of

repeated missions between change of mission increases is clearly shown in Figure 11.

0.25

0.20

.m

•"= 0.15

..o

0

n 0.10

0.05

0.00

4000

one mission

f_ X=33 X=99

' X= 165

• -3c

165 ? I _._"

T, 2.4H6000 8000 10000 12000

Time to Failure [hrs]

Figure 11: Normal distributions derived from simulation results. The labeled drop lines indicate life at

mean minus 3 standard deviations for each distribution.

The last row of Table II shows the results of a repeat of the X = 165 mission simulation with 64

realizations. The standard deviation in this sample was considerably smaller than in the 16 realization

simulation run at the X = 165 missions. The reason for this difference in the variance cannot be readily

explained. However, it should be noted that the variance is likely to fluctuate from one sample to the next,

especially when the sample size is relatively small. The difference in the simulated standard deviations

may simply illustrate the sample to sample variation in the variance and may indicate that 16 realizations

of the randomized mission loading sequence is inadequate to provide a reasonable estimate of the

underling population's standard deviation. In spite of this discrepancy the trend of increasing variance with

simulated block length seems to hold true.

NASA/TM-- 1998-208648 13
Discussion

If one ignores the loading interaction that may occur in changing missions (variation in the maximum and

minimum stresses from one type of mission to the next is small when compared to the variations in the

loads within each mission), a linear summation approach might be used to calculate the mission mixed

loading crack propagation life distribution. Given the calculated crack propagation lives for each of the

missions, an analytical distribution function for the probability of failure can be derived if the following

question can be answered: What fraction of the possible combinations of mission blocks, of Poisson

distributed length, lead to failure in a given time, t? Numerical integration of the probability density function

is possible but the number of combinations is daunting. For example: given a Poisson distribution

parameter for the block length, X, of 165 missions and assuming an average mission length of 1.46 hours

per mission, at 3675 hours of component operation there would be approximately 15 blocks of missions

flown, each block with one of the 30 possible missions. Assuming no distribution in the fatigue lives of the

individual missions, i.e., each mission contributes exactly 1/(total mission cycles to failure for a specific

mission) fractional damage to the component and assuming that each block is equally possible and

independent, there can be 301Sor 1.4x10 22 possible combinations. In calculating the probability of failure

at longer operating times, the number of mission blocks increase and the number of possible

combinations grows exponentially. With the additional complications that the missions are not equally

probable, the length of the individual missions are not constant, and the number of missions per block is

also variable, this becomes an increasingly difficult problem to solve in closed form. If it is assumed that

the loading interaction that can occur in changing missions has a marked effect on fatigue crack growth, a

closed form analytical solution does not seem feasible.

The results of this study indicate a strong dependence of the crack propagation life on the mission

sequence and particularly on the mean block length (expected number of mission repeats between engine

removal for overhaul). The expected crack propagation fife variance caused by the mission mix loading

will necessitate a reduction in the estimated lower bound crack propagation life. If not accounted for in the

current component life estimates, retirement lives and/or inspection intervals will need to be shortened.

A basic assumption driving this simulation technique is that the mission sequence has strong effect on

crack propagation rate. If it can be demonstrated that the effect of the mission sequence on the crack

propagation rate is negligible, or that the mission loading inthe prescribed mission mix is not conducive to

significant 'mission to mission' load interactions, an analytical solution or a simplified (less computationally

intensive) simulation technique might be utilized.

The intrinsic (material dependant) variability in the crack propagation life could also be incorporated into

the simulation. This would require an additional random variable to account for the experimentally

observed scatter in the crack propagation rate.

Given that the Army specified mission mix is an estimate of the actual usage, that the fleet usage is likely

to evolve with time, and that there can be significant pilot topilot variation in how the aircraft are flown, the

contribution to the variability in crack propagation due to these loading variations can potentially be large.

Accounting for this loading variability could lead to unacceptably short inspection intervals, increased

inspection costs, and a large impact on fleet readiness. To mitigate the loading history uncertainty, a

strong argument can be made for onboard monitoring of the aircraft usage. This could allow for a 'realtime' calculation of the available crack propagation life. A more aggressively used engine could be pulled

for inspection or retirement, even though the original life estimates (based on the expected usage) would

indicate that it was still safe to operate. Conversely, a lightly used engine might not be removed as often

for costly inspection/overhaul or outright replacement.

NASA/TM-- 1998-208648 14

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Summary and Conclusions

The FASTRAN II crack propagation analysis code, which is based on the crack closure model, accurately

predicts crack propagation in surface cracked K_ bar specimens under variable amplitude loading.

A method of estimating crack propagation life distribution of helicopter engine rotating components

subjected to thirty different missions of varying severity, length, and probability of occurrence, has been

developed. This method utilizes several random variables to generate simulated engine histories that are

then fed into the FASTRAN II crack propagation analysis code.

There is a direct correlation between the mean number of missions between removal for

inspection/overhaul and the variance in the predicted crack propagation lifetimes. Extra caution is

therefore necessary when determining the retirement life or a safe inspection interval for critical rotating

components. A more accurate accounting of the actual usage of the engines would also seem prudent.

This might include onboard monitoring of engine usage.

References

1. Willenborg, J., Engle, R., and Wood, H., "A Crack Growth Retardation Model Using an Effective

Stress Concept," AFFDL-TM-71-1-FRB, Wright-Patterson Air Force Base, Ohio, January 1971.

2. Wheeler, O. E., "Crack Growth Under Spectrum Loading," J. of Basic Eng. Trans. ASME, p. 181,

March 1972.

3. Elber, W., 'q-he Significance of Fatigue Crack Closure," Damage Tolerance of Aircraft Structures,

ASTM STP-486, 1971, pp. 230-242.

4. Newman, J. C., FASTRAN-II - A Fatigue Crack Growth Structural Analysis Program, NASA TM104159, Feb. 1992.

. Newman, J. C., Jr., "Prediction of Fatigue Crack Growth under Variable Amplitude and Spectrum

Loading Using a Closure Model," Design of Fatigue and Fracture Resistant Structures, ASTM STP761, P. R. Abelkis and C. M. Hudson, eds., 1982, pp. 255-277.

o Newman, J. C. and Raju, I. S., "Stress-Intensity Factor Equations for Cracks in Three-Dimensional

Finite Bodies Subjected to Tension and Bending Loads," Computational Methods in the Mechanics of

Fracture, S. N. Atluri, Ed., Elsevier Science, 1986, pp. 311-334.

. Walker, K., 'q-he Effect of Stress Ration During Crack Propagation and Fatigue for 2024-T3 and 7075-

T6 Aluminum," Effects of Environment and Complex Load History on Fatigue Life, ASTM STP 462,

American Society for Testing and Materials, 1970, pp. 1-14.

8. Press, W. H., Flannery, B. P., Teukolsky, S. A., and Vetterling, W. T., Numerical Recipes, Cambridge

University Press, 1986.

NASA/TM-- 1998-208648 15
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1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORT TYPE AND DATES COVERED

October 1998 Technical Memorandum

4. TITLE AND SUBTITLE 5. FUNDING NUMBERS

Simulation of Crack Propagation in Engine Rotating Components Under Variable

Amplitude Loading

6. AUTHOR(S)

P.J. Bonacuse, L.J. Ghosn, J. Telesman, A.M. Calomino, and P. Kantzos

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

NASA Lewis Research Center

Cleveland, Ohio 44135-3t9t

and

U.S. Army Research Laborafory

Cleveland, Ohio 44135 3191

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

Washington, DC 20546-0001

and

U.S. Army Research Laborator3.,

Adelphi, Maryland 20783-1145

WU-505-23-0M_00

ILl61102AH45

8. PERFORMING ORGANIZATION

REPORT NUMBER

E-11366

10. SPONSORING/MONIToRING

AGENCY REPORT NUMBER

NASA TM--1998-208648

ARL-MR-418

11. SUPPLEMENTARY NOTES

Prepared for the Symposium of the Applied Vehicle Technology Panel sponsored by NATO/AGARD, Toulouse, France,

May 11-15, 1998. P.J. Bonacuse, U.S. Army Research Laboratory, Lewis Research Center, Cleveland, Ohio; L.J. Ghosn,

Case Western Reserve University, Cleveland, Ohio, 44 ! 06; J. Telesman and A.M. Calomino, Lewis Research Center,

Cleveland, Ohio; P. Kantzos, Ohio Aerospace Institute, Cleveland, Ohio, 44142. Response person, P.J. Bonacuse, organization code 0300, (216) 433-3309.

12a. DISTRIBUTION/AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE

Unclassified - Unlimited

Subject Category: 39 Distribution: Nonstandard

This publication is available from the NASA Center for AeroSpace Information, (301) 621 0391)

13. ABSTRACT (Maximum 200 words)

The crack propagation life of tested specimens has been repeatedly shown to strongly depend on the loading history. Overloads and

extended stress holds at temperature can either retard or accelerate the crack growth rate. Therefore, to accurately predict the crack

propagation life of an actual component, it is essential to approximate the true loading history. In military rotorcraft engine applications,

the loading profile (stress amplitudes, temperature, and number of excursions) can vary significantly depending on the type of mission

flown. To accurately assess the durability of a fleel of engines, the crack propagation life distribution of a specific component should

account for the variability in the missions performed (proportion of missions flown and sequence). In this report, analytical and

experimental studies are described that calibrate/validate the crack propagation prediction capability for a disk alloy under variable

amplitude loading. A crack closure based model was adopted to analytically predict the load interaction effects. Furthermore, a

methodology has been developed to realistically simulate the actual mission mix loading on a fleet of engines over their lifetime. A

sequence of missions is randomly selected and the number of repeats of each mission in the sequence is determined assuming a Poisson

distributed random variable with a given mean occurrence rate. Multiple realizations of random mission histories are generated in this

manner and are used to produce stress, temperature, and time points for fracture mechanics calculations. The result is a cumulative

distribution of crack propagation lives for a given, life limiting, component location. This information can be used to determine a safe

retirement life or inspection interval for the given location.

14. SUBJECT TERMS

Crack closure; Crack propagation; Fracture mechanics; Monte Carlo method; Simulation

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