a methodology for on line fatigue life monitoring
TRANSCRIPT
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
11 Collation t
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20 Personal author (s) i
21 p., 10 figs.
N.K. Mukhopadhyayj B.K. DuttaiH.S. Kushwaha
21 Affiliation of author <s) : Reactor Engineering Division,Bhabha Atomic Research Centre, Bombay
22 Corporate author<s> i Bhabha Atomic Research Centre,Bombay - 400 0B5
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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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