BARC/1992/E/036

7nIwo

A METHODOLOGY FOR ON LINE FATIGUL LIFE MONITORING:RAINFLOW CYCLE COUNTING METHOD

by

N. K. Mukhopadhyay, B. K. Dutta and H. S. KushwahaRcattor Engineering Division

1992

BARC/1992/E/036

GOVERNMENT OF INDIA£ ATOMIC ENERGY COMMISSIONo

UOS

A METHODOLOGY FOR ON LINE FATIGUE LIFE MONITORING:

RAINFLOW CYCLE COUNTING METHOD

by

N.K. Mukhopadhyay, B.K. Dutta, H.S. KushwahaReactor Engineering Division

BHABHA ATOMIC RESEARCH CENTREBOMBAY, INDIA

1992

BARC/1992/E/036

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10 Title and subtitle i A methodology for on line fatigue lifemonitoring i rainflow cycle countingmethod

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N.K. Mukhopadhyayj B.K. DuttaiH.S. Kushwaha

21 Affiliation of author <s) : Reactor Engineering Division,Bhabha Atomic Research Centre, Bombay

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60 Abstract :A realistic method is proposed for on line fatigue lifemonitoring of nuclear power plant components in a B.A.R.C. externalreport no. BARC/1992/E/019. Green's, function technique is used in online -fatigue life monitoring to convert plant data to stress versustime data. This technique converts plant data most efficiently tostress versus time data, lo compute the fatigue usage factor theactual number of cycles experienced by the component is to be foundout from stress versus time data. Using material fatigue popertiesthe fatigue usage factor is tn be computed from the number of cycles,(generally the stress response is very irregular in nature. To convertan irregular stress history to stress frequency spectra rainflowcycle counting method is used. This method is proved to be superiorto other counting methods and yields best fatigue estimates. A codehas been developed which computes the number of cycles experienced bythe component from stress time history using rainflow cycle countingmethod. This postprocessor also computes the accumulated fatigueusage factor from material fatigue properties. The present reportdescribes the development of a code to compute fatigue usage factorusing rainflow cycle counting technique and presents a real life casestudy.

70 Keywords/Descriptors i ON-LINE SYSTEMS| MONITORING* REACTORCOMPONENTS! ALGORITHMS* STRESSES) FATIGUE* S CODES) F CODES» B CODES)FINITE ELEMENT METHOD» GREEN FUNCTION) FORECASTING) STRAINS*LIFETIME) NUCLEAR POWER PLANTS) REACTOR MONITORING SYSTEMS

Additional descriptors t

RAINFLOW CYCLE COUNTING METHOD

71 Class No. t INIS Subject Categoryi E2200

99 Supplementary elements i

I-'

r

A METHODOLOGY FOR ON LIME FATIGUE LIFE MONITORING

RAINFLOW CYCLE COUNTING METHOD

N.K.Mukhopadhyay, B.K.Dutta, H.S.Kushwaha

Reactor Engineering Division

Bhabha Atomic Research Centre

Bombay 400-085, India

Introduction

A realistic method is proposed for on line fatigue life

monitoring of nuclear power plant components using available

plant instrumentations [1]. Superimposed single site Gxeen's

function technique is used to solve multiple site thermal

loading problem. It is shown that this technique converts plant

data to stress versus time data most efficiently. The different

steps in on line fatigue life monitoring are shown in Fig.1.

To compute the fatigue usage factor the actual number of

complete cycles experienced by the component is to be found out

from stress versus time data. Using material fatigue properties

the fatigue usage factor is to be computed from the number of

cycles. This present report describes the development of

methodologies for computing fatigue usage factor from stress

versus time data.

FATIGUE LIFE PREDICTION THEORY

The traditional S-N or load based life prediction method is

described first. A curve relating nomial stress and cyclic

life, called S-N curve is used to make load based life

predictions. This S-N curve is a material property and are

given in [2]. It is the stress range AS which primarilyi

governs the fatigue life of a component. The aean stress S •

only secondarily affect the fatigue life. Using Palmgren-Miner

rule a life estimate nay be Bade by ignoring the mean stresses

and using an appropriate S-N curve from completely reversed

loading.

n.

£-- -- =1 (1)

where n. is the number of cycles applied at stress range AS.,

and N. is the number of cycles to failure corresponding to AS..

This can also be Modified to account for the effect of Bean

nominal stresses by using the modified Goodman diagram. An

applied combination of stress amplitude S and mean stress Sci o

are considered equivalent to a completely reversed stress

amplitude S , which results in the same fatigue life. S is

expressed as

Sa(2)

(1 )

Su

where S is the ultimate tensile strength of the material. The

life prediction is then modified by using values of S with the

completely reversed S-N curves, in place of values S .

The earlier described life prediction theory is suitable

when the stress history is consisting of blocks of well defined

constant amplitude cycles. For a highly irregular nominal

stress history, care is to be taken in defining cycles. Cycle

is to be counted such that small stress excursions are

considered as temporary interruptions of larger stress

excursions, otherwise the significance of larger stress

excursions is lost and major errors in life prediction can

result [3]. Common cycle counting technique in use are range-

pair and rainflow cycle counting methods. They are quite

similar to each other and handle small excursions in desired

manner.

RAINFLOW CYCLE COUNTING METHOD

Rainflow cycle counting method has been proved to be superior

to other cycle counting methods and yields best fatigue

estimates. The most accurate fatigue life estimates are

obtained using an analysis based on the strain at the most

highly stressed / strained location. Using local stress-strain

concepts fatigue life is predicted by rainflow cycle counting

method.

The rainflow cycle counting method is explained in Fig.2.

An irregular loading history (stress-time history) is shown in

Fig.2(a). The load time history is plotted in such a way that

time axis is vertically downwards and the lines connecting the

strain peaks are imagined to be a series of pagoda roofs. This

is shown in Fig.2(b). Rain is injected at each point of stress

reversal in order and flows by gravity subject to the following

rules [3,5].

(i) For rain moving toward the left and down, the flow

disappears if it comes opposite to a reversal point farther to

the right than, or equal to, the one from which it started.

(ii) For rain moving toward the right and down, the flow

disappears if it comes opposite to a reversal point farther to

the left than, or equal to, the one from which it started.

(iii) The flow disappears to avoid meeting rain from a

roof above.

These rules are illustraed in Fig.2(b). Reversal point 1'

being equal to 1, so the rain flow from 1 disappears opposite

to 1' due to rule (i). Similarly rain flow from 2 disappears

opposite to 4 due to rule (ii), as reversal point 4 being

farther to the left than 2. Again the rain flow from 7

disappears under 6 due to rule (iii), to avoid meeting the rain

flowing down from 6.

Once the rainflow rules are followed for the entire

history, the horizontal length of each continuous rain flow is

taken to be the range of a half cycle. In most of the cases,

the majority of these half cycles will occur in pairs which may

be combined to form cycles. In Fig.2(b) all half cycles can be

paired, so that four full cycles are counted. The full cycles

correspond to stress excursions 2-3-2', 6-7-6', 5-8-5*, and 1-

4-1* .

For an irregular loading history life prediction is done

using Eqn.(1) after defining and counting the number of cycles.

For the example history of 2(a)

n. 1

N2-3 N6-7 N5-8 N1-4

where each n. is unity and the N. values correspond to the

stress ranges of Fig.2(b).

This method is also very efficient for a repeating stress

history. Cycle ratios are summed for only one repetition of the

history and then multiplied by the number of repetitions to

failure R. The criteria for a component to be safe against

fatigue failure is given below.

n.

N.

(4)

An irregular load history must be reduced into a series of

constant amplitude events for comparision with the smooth

specimen data as fatigue properties are determined from

constant amplitude testing. The concept of a cycle in an

irregular history is difficult to define. However, a reversal

can easily be defined as a change in sign in the loading. A

constant amplitude sinusoidal cycle would contain two

reversals. The apparent reason for the superiority of rainflow

cycle counting method is that it combines load reversals in a

manner that defines a cycle as a closed hysteresis loop. Each

closed hysteresis loop has a strain range and mean stress

associated with it that can be compared with the constant

amplitude fatigue data in order to compute fatigue damage. Any

counting technique that counts closed hysteresis loops is

equivalent to rainflow cycle counting method.

The simple stress-time and strain-time spectrums and the

corresponding stress/strain response are shown in Fig.2(c). The

four events in the stress/strain response that resemble

constant amplitude cycles are easily identified as A-D-A, C-B-

C, D-E-D and F-G-F. Rainflow cycle counting recognizes these

events as closed hysteresis loops and counts them cycles. The

small event B-C is treated as an interruption of the overall

event A-D. The principal idea behind rainflow cycle counting is

to treat snail events as interruptions of larger overall

events. It matches the highest peak and deepest valley, then

the next largest and smallest together, etc., until peaks and

valleys have been paired.

ALGORITHM OF RAINFLOW CYCLE COUNTING METHOD

Due to the great importance of rainflow cycle counting method

many different algorithms have been proposed in the literature

[4-7]. The algorithm presented by D.F.Socie [43 requires that

the entire load history be known before the counting process

starts. As a result, it is not suitable for on line data

processing since the entire load history is not known until the

end of the test. The one-pass rainflow cycle counting algorithm

presented by S.D.Downing and D.F.Socie [6] overcomes this

limitation. This can operate in on line data processing. A

rainflow cycle counting algorithm suitable for very long stress

histories even with a small computer for on line data

processing is described by G.Glinka and J.C.P.Kam [7],

The fundamental characteristics of rainflow cycle counting

method are its simplicity in algorithm. It is also compatible

with the corresponding stress/strain relation when it is

applied to a strain-time history. It is a wave analysing

procedure which takes into account the sequential order of

peaks and valleys while ignoring the time duration between the

successive peaks and valleys. A flow chart for rainflow cycle

counting algorithm is shown in Fig.3. A means of collecting

long term data, using microcomputer devices and interpreting

the data in a aanner useful to the engineer for fatigue

analysis is reported in [8]. A hard-wired logic for the

rainflow cycle counting algorithm is described and simulated in

[9]-

DEVELOPMENT OF CODES

A post processor SREGRE (Structural REsponse by GREen's

functions) is developed to compute the total temperature and

stress response from fluid temperature and flow histories using

superimposed single site Green's function technique [1]. This

post processor is modified to handle very long fluid

temperature variation histories. Very often the entire fluid

temperature history cannot be read into the computer because of

limitation of computer memory. Hence, the post processor is

modified to compute the temperature / stress response while

reading the input data. At each time step it compares the

responses and selects only the peaks and valleys as outputs.

A new post processor FRAIN (Fatigue usage factor by

RAINflow counting) is developed . From the peak and valley

stresses, this post processor finds out the number of complete

cycles experienced by the component using rainflow cycle

counting method. Using equations (1-4) this post processor

finds out the accumulated fatigue usage factor. S-N data for

different materials are taken from [2]. This post processor is

capable of performing rainflow counting without prior knowledge

of the whole stress history. Very often the entire stress

history which is to be analysed cannot be read at once because

of limitation of the computer memory. Here, the stress history

can be read and analysed by computer one block at a time

without reading the whole history at once. This enables small

computers to analyse very long stress histories because the

length of one block can be adjusted to the computer

capabilities.

A REAL LIFE CASE STUDY

A schematic of a portion of a plant that has been studied is

shewn in Fig.4. The temperature variation of fluid is

continuously monitored as it comes out of heat exchanger CHX-1.

This temperature is observed to be varying with time. The heat

exchanger is connected with the pipe by a reducer. Considering

stress distribution, this reducer is selected as the critical

component and this is studied.

The geometrical details are taken from [10]. The

geometrical details, material properties and fluid heat

transfer coefficient are shown in Fig.5. The reducer is

insulated from the surrounding and heat inleak is negelected.

Hence, the problem is a single site thermal loading problem.

The fluid temperature is recorded by gas thermometer. Nearly

twenty seven days fluid temperature data is collected. The

fluid temperature variation is shown in Fig.6.

A finite element discretisation has been done.

Axisymmetric four noded elements are chosen. 69 elements are

taken. Total number of nodes is 96. Each node has two

displacement degrees of freedom. This is shown in Fig.7.

The corner node A is found to be the critical location.

The stress Green's functions are derived at the node A using

the developed code GREFIN. This stress Green's functions are

shown in Fig.8.

The stress response at A is found out using the stress

Green's functions and fluid tenperature history using the

developed code SREGRE. These stress responses are compared and

the peak and valley stresses are found out. These peaks and

valleys are shown in Fig.9.

Using the developed code FRAIN the accumulated fatigue

usage factor for the reducer is computed. The fatigue data is

taken from [2]. The stress range and mean stress of the cycles

experienced by the component is found out by rainflow cycle

counting method. For each cycle the fatigue usage factor is

computed from material fatigue data and they are added to

compute the accumulated fatigue usage factor for all counted

cycles. The accumulated fatigue usage factor is found out to be

low. The counted cycles as derived by rainflow cycle method are

grouped into several bands of stress ranges and this output is

shown in Fig.10.

FUTURE WORK

The following course of future work is suggested.

(i) To have some predictable information about

accumulation of fatigue damage, the data are to be analysed for

a longer period of time.

(ii) A graphix code is to be developed and to be

interfaced with the earlier developed codes to make the whole

methodolgy menu driven.

(iii) All the developed codes are to be commissioned in

P.C.

(iv) This methodology is to be experimentally conducted in

small test apparatus in Hall No. 7.

8

ACKNOWLEDGEMENT

The authors are thankful to Shri H.K.Sadhukhan,Director

Chemical Engineering Group,Shri T.G. Varadarajan, Head Heavy

Water Division andShri K.Bhar.ja, Scientific OfficerHeavy Water

Division for the kind help and cooperation for providing all

the data needed for the case study.

REFERENCES

[1] N.K.Mukhopadhyay, B.K.Dutta and H.S.Kushwaha, A

methodology for on line fatigue life monitoring of Indian

nuclear power plant components, B.7V.R.C./ 1992/ E/ 019.

[2] ASNE Boiler and pressure vessel code, Division 1,

Appendices III, 1986.

[3] N.E.Dowling, Fatigue life predictions for complex load

versus time histories. Pressure vessels and piping: Design

technology- A decade of progress, S.Y.Zamrik and D.Dietrich

(eds), Section 7.4, p487-498, ASME 1982.

[4] D.F.Socie, Fatigue life prediction using local stress-

strain concepts, Experimental mechanics (17, no.2), p5O-56,

1977.

[5] I.Rychlik, A new definition of the rainflow cycle counting

method, Int.J.Fatigue (9, no.2), p119-121, 1987.

[6] S.D.Downing and D.F.Socie, Simple rainflow counting

algorithm, Int.J.Fatigue (4, no.1), p31-40, 1982.

[7] G.Glinka and J.C.P.Kam, Rainflow counting algorithm for

very long stress histories, Int.J.Fatigue (9, no.3), p223-228,

1987.

[8] D.F.Socie, G.Shifflet and H.Berns, A field recording

system with applications to fatigue analysis. Int.J.Fatigue (1,

no.2), p103-111, 1979.

[9] H.Anzai and T.Endo, On site indication of fatigue damage

under complex loading, Int.J.Fatigue (1, no.1), p49-57, 1979.

[10] S.Crocker, Piping handbook, 4-th ed, McGraw Hill.

IDENTIFICATIONOF COMPONENT)

FOR OLFM

EVALUATION OF GREEN'SFUNCTIONS BY FINITE

ELEMENT METHOD

DATA BASEFOR GREEN'S

FUNCTIONS

ON LINEPROCESS

.PARAMETER;DATA

APPLICATION OF GREEN'SFUNCTIONS TO COMPUTE

STRESS RESPONSE

ON LINEMATERIAL

DATA FROMASME

ATA OF PEAKSAND VALLEYSOF STRESS

UPDATING OFACCUMULATED

FATIGUE USAGEFACTOR

APPLICATION OF RAINFLOWALGORITHM FOR COMPUTINGFATIGUE CYCLES ANDFATIGUE USAGE FACTORS

FIG. 1 DIFFERENT STEPS IN ON-LINE FATIGUE LIFEMONITORING SCHEME

r

(a) IRREGULAR LOADING HISTORY

k-^-3-4AJLJ-TUI

AS14 J IS-8-J1-4 fcj

AS'( b) RAINFLOW CYCLE COUNTING

APPLIED TO HISTORY OF(a)

B P D B

~e

0 STRESS /STRAIN RESPONSE AND RAINFLOW CYCLE COUNTING

FIG. 2 RAINFLOW CYCLE COUNTING METHOD

HYSTERESISEXCEEDED

INDEXOVER FULL

SCALE COUNT

TEMPORARYPEAK

STORAGE

/CLOSED^\HYSTERESIS

\ L O O P CHECKS

•w YINDEX

HISTOGRAMCOUNT

,

RETRIEVTEMPOF

P E *

ELASTRARY

FIG. 3. FLOW DIAGRAM FOR RAINFLOW CYCLE COUNTING ALGORITHM

FIG. U SCHEMATIC OF PORTION STUDIED

25 -H-2.11

hi 1

i

CM

856 2.11

E * 19.03 X W* N/m2

V x 0.3t = 8.027 x 10' Kg/hi1

k = 16.265 *M-kCp = 502.403 J/Kg-K• F 17.»2 X /Khi F 96.57

FIG. 5 GEOMETRICAL DETAILS.MATERIAL PROPERTIES AND BOUNDARY CONDITIONS FOR THECASE STUDY

[\

6-00 12.00 18.00 24.00 30-00T I M E ( d a y )

FIG.6. FLUID TEMPERATURE HISTORY

'**..„ ̂ j

FI3.7. FINITE: ELEMENT MESH OF REDUCER

oo

oo

Q_.It

0.00 10.00 20.00 30-00 40-00 50-00

F I G . 8 .T I M E ( s e c )

STRESS GREEN'S FUNCTION OF REDUCER

6.00 12-00 18-00T I M E ( d a y )

24.00 30.00

FIG.9. STRESS RESPONSE OF REDUCER FOLLOWINGFLUID TEMPERATURE FLUCTUATION

134

UJ

60

U lCD5

JZZA0.5X10* 0.5X10' 0.5X10*

STRESS RANGE (KPa)-

FIG.10 VARIATION OF RAINFLOW CYCLES WITH STRESS RANGE ASEXPERIENCED BY REDUCER FOLLOWING FLUID TEMPERATUREVARIATION

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