ASTM E1049-85(1997)
(Practice)Standard Practices for Cycle Counting in Fatigue Analysis
Standard Practices for Cycle Counting in Fatigue Analysis
SCOPE
1.1 These practices are a compilation of acceptable procedures for cycle-counting methods employed in fatigue analysis. This standard does not intend to recommend a particular method.
1.2 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.
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Designation: E 1049 – 85 (Reapproved 1997)
Standard Practices for
Cycle Counting in Fatigue Analysis
This standard is issued under the fixed designation E 1049; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (e) indicates an editorial change since the last revision or reapproval.
1. Scope ortheintegralaverageoftheinstantaneousloadvaluesorthe
algebraic average of the peak and valley loads of a spectrum
1.1 These practices are a compilation of acceptable proce-
loading history.
duresforcycle-countingmethodsemployedinfatigueanalysis.
3.1.5 peak—in fatigue loading, the point at which the first
This standard does not intend to recommend a particular
derivative of the load-time history changes from a positive to
method.
a negative sign; the point of maximum load in constant
1.2 This standard does not purport to address all of the
amplitude loading (see Fig. 1).
safety concerns, if any, associated with its use. It is the
3.1.6 range—in fatigue loading, the algebraic difference
responsibility of the user of this standard to establish appro-
between successive valley and peak loads (positive range or
priate safety and health practices and determine the applica-
increasing load range), or between successive peak and valley
bility of regulatory limitations prior to use.
loads (negative range or decreasing load range); see Fig. 1.
2. Referenced Documents
NOTE 2—In spectrum loading, range may have a different definition,
2.1 ASTM Standards:
depending on the counting method used; for example, “overall range” is
defined by the algebraic difference between the largest peak and the
E 912 Definitions of Terms Relating to Fatigue Loading
smallest valley of a given load-time history.
3. Terminology
3.1.6.1 Discussion—In cycle counting by various methods,
3.1 Definitions:
it is common to employ ranges between valley and peak loads,
3.1.1 constant amplitude loading—in fatigue loading,a
or between peak and valley loads, which are not necessarily
loading in which all of the peak loads are equal and all of the
successive events. In these practices, the definition of the word
valley loads are equal.
“range” is broadened so that events of this type are also
3.1.2 cycle—in fatigue loading, under constant amplitude
included.
loading, the load variation from the minimum to the maximum
3.1.7 reversal—in fatigue loading, the point at which the
and then to the minimum load.
first derivative of the load-time history changes sign (see Fig.
1).
NOTE 1—In spectrum loading, definition of cycle varies with the
counting method used.
NOTE 3—In constant amplitude loading, a cycle is equal to two
reversals.
3.1.3 mean crossings—in fatigue loading, the number of
times that the load-time history crosses the mean-load level
3.1.8 spectrum loading—in fatigue loading, a loading in
with a positive slope (or a negative slope, or both, as specified)
which all of the peak loads are not equal or all of the valley
during a given length of the history (see Fig. 1).
loadsarenotequal,orboth.(Alsoknownasvariableamplitude
3.1.3.1 Discussion—For purposes related to cycle counting,
loading or irregular loading.)
a mean crossing may be defined as a crossing of the reference
3.1.9 valley—in fatigue loading, the point at which the first
load level.
derivative of the load-time history changes from a negative to
3.1.4 mean load, P —in fatigue loading, the algebraic
m a positive sign (also known as trough); the point of minimum
average of the maximum and minimum loads in constant
load in constant amplitude loading (see Fig. 1).
amplitude loading, or of individual cycles in spectrum loading,
3.2 Definitions of Terms Specific to This Standard:
3.2.1 load—used in these practices to denote force, stress,
P 5 ~P 1 P !/2 (1)
m max min
strain, torque, acceleration, deflection, or other parameters of
interest.
3.2.2 reference load—for spectrum loading, used in these
These practices are under the jurisdiction ofASTM Committee E-8 on Fatigue
practices to denote the loading level that represents a steady-
and Fracture and are the direct responsibility of Subcommittee E08.04 on Structural
Applications. state condition upon which load variations are superimposed.
Current edition approved Feb. 22, 1985. Published June 1985.
Discontinued, see 1986 Annual Book of ASTM Standards, Vol 03.01.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
E 1049 – 85 (1997)
FIG. 1 Basic Fatigue Loading Parameters
The reference load may be identical to the mean load of the 5.1.3 The most damaging cycle count for fatigue analysis is
history, but this is not required. derived from the level-crossing count by first constructing the
3.3 For other definitions of terms used in these practices largest possible cycle, followed by the second largest, etc.,
refer to Definitions E 912. until all level crossings are used. Reversal points are assumed
to occur halfway between levels. This process is illustrated by
4. Significance and Use
Fig. 2(c). Note that once this most damaging cycle count is
obtained, the cycles could be applied in any desired order, and
4.1 Cycle counting is used to summarize (often lengthy)
this order could have a secondary effect on the amount of
irregular load-versus-time histories by providing the number of
damage. Other methods of deriving a cycle count from the
times cycles of various sizes occur. The definition of a cycle
level-crossings count could be used.
varieswiththemethodofcyclecounting.Thesepracticescover
the procedures used to obtain cycle counts by various methods,
5.2 Peak Counting:
including level-crossing counting, peak counting, simple-range
5.2.1 Peak counting identifies the occurrence of a relative
counting, range-pair counting, and rainflow counting. Cycle
maximum or minimum load value. Peaks above the reference
counts can be made for time histories of force, stress, strain,
load level are counted, and valleys below the reference load
torque, acceleration, deflection, or other loading parameters of
level are counted, as shown in Fig. 3(a). Results for peaks and
interest.
valleys are usually reported separately. A variation of this
method is to count all peaks and valleys without regard to the
5. Procedures for Cycle Counting
reference load.
5.1 Level-Crossing Counting:
5.2.2 To eliminate small amplitude loadings, mean-crossing
5.1.1 Results of a level-crossing count are shown in Fig.
peak counting is often used. Instead of counting all peaks and
2(a). One count is recorded each time the positive sloped
valleys, only the largest peak or valley between two successive
portion of the load exceeds a preset level above the reference
mean crossings is counted as shown in Fig. 3(b).
load, and each time the negative sloped portion of the load
5.2.3 The most damaging cycle count for fatigue analysis is
exceeds a preset level below the reference load. Reference load
derived from the peak count by first constructing the largest
crossings are counted on the positive sloped portion of the
possible cycle, using the highest peak and lowest valley,
loading history. It makes no difference whether positive or
followed by the second largest cycle, etc., until all peak counts
negative slope crossings are counted. The distinction is made
are used.This process is illustrated by Fig. 3(c). Note that once
only to reduce the total number of events by a factor of two.
thismostdamagingcyclecountisobtained,thecyclescouldbe
5.1.2 In practice, restrictions on the level-crossing counts
applied in any desired order, and this order could have a
are often specified to eliminate small amplitude variations
secondary effect on the amount of damage. Alternate methods
which can give rise to a large number of counts. This may be
of deriving a cycle count, such as randomly selecting pairs of
accomplished by filtering small load excursions prior to cycle
peaks and valleys, are sometimes used.
counting. A second method is to make no counts at the
5.3 Simple-Range Counting:
reference load and to specify that only one count be made
5.3.1 For this method, a range is defined as the difference
between successive crossings of a secondary lower level
associated with each level above the reference load, or a between two successive reversals, the range being positive
secondary higher level associated with each level below the when a valley is followed by a peak and negative when a peak
reference load. Fig. 2(b) illustrates this second method. A is followed by a valley. The method is illustrated in Fig. 4.
variation of the second method is to use the same secondary Positive ranges, negative ranges, or both, may be counted with
level for all counting levels above the reference load, and this method. If only positive or only negative ranges are
another for all levels below the reference load. In this case the counted, then each is counted as one cycle. If both positive and
levels are generally not evenly spaced. negative ranges are counted, then each is counted as one-half
E 1049 – 85 (1997)
(a)—Level Crossing Counting
(b)—Restricted Level Crossing Counting
FIG. 2 Level-Crossing Counting Example
cycle. Ranges smaller than a chosen value are usually elimi- counting (1, 2), the Hayes method (3), the original rainflow
nated before counting.
method (4-6), range-pair-range counting (7), ordered overall
5.3.2 When the mean value of each range is also counted, range counting (8), racetrack counting (9), and hysteresis loop
the method is called simple range-mean counting. For the
counting (10). If the load history begins and ends with its
example of Fig. 4, the result of a simple range-mean count is
maximum peak, or with its minimum valley, all of these give
given in X1.1 in the form of a range-mean matrix.
identical counts. In other cases, the counts are similar, but not
5.4 Rainflow Counting and Related Methods:
generally identical. Three methods in this class are defined
5.4.1 A number of different terms have been employed in
here: range-pair counting, rainflow counting, and a simplified
the literature to designate cycle-counting methods which are
method for repeating histories.
similar to the rainflow method. These include range-pair
The boldface numbers in parentheses refer to the list of references appended to
these practices.
E 1049 – 85 (1997)
(a)—Peak Counting
(b)—Mean Crossing Peak Counting
(c)—Cycles Derived from Peak Count of (a)
FIG. 3 Peak Counting Example
5.4.2 The various methods similar to the rainflow method (3) Compare the absolute values of ranges X and Y.
may be used to obtain cycles and the mean value of each cycle; (a)If X < Y, go to Step 1.
they are referred to as two-parameter methods.When the mean (b)If X$ Y, go to Step 4.
value is ignored, they are one-parameter methods, as are (4) Count range Y as one cycle and discard the peak and
simple-range counting, peak counting, etc. valley of Y; go to Step 2.
5.4.3 Range-Pair Counting—The range-paired method (5) The remaining cycles, if any, are counted by starting at
counts a range as a cycle if it can be paired with a subsequent the end of the sequence and counting backwards. If a single
loading in the opposite direction. Rules for this method are as range remains, it may be counted as a half or full cycle.
follows: 5.4.3.2 The load history in Fig. 4 is replotted as Fig. 5(a)
5.4.3.1 Let X denote range under consideration; and Y, and is used to illustrate the process. Details of the cycle
previous range adjacent to X. counting are as follows:
(1) Read next peak or valley. If out of data, go to Step 5. (1) Y =|A-B|; X =|B-C|; andX>Y. Count |A-B|asone
(2) If there are less than three points, go to Step 1. Form cycle and discard points A and B. (See Fig. 5(b). Note that a
ranges X and Y using the three most recent peaks and valleys cycle is formed by pairing range A-B and a portion of range
that have not been discarded. B-C.)
E 1049 – 85 (1997)
FIG. 4 Simple Range Counting Example—Both Positive and Negative Ranges Counted
(2) Y = |C-D|; X = |D-E|; andX
(3) Y = |D-E|; X = |E-F|; andX
second point in range Y; and go to Step 2.
(4) Y = |E-F|; X = |F-G|; andX>Y. Count |E-F|asone
cycle and discard points E and F. (See Fig. 5(c).) (6) Count each range that has not been previously counted
(5) Y = |C-D|; X = |D-G|; andX>Y. Count |C-D| as one as one-half cycle.
cycle and discard points C and D. (See Fig. 5(d).)
5.4.4.2 The load history of Fig. 4 is replotted as Fig. 6(a)
(6) Y = |G-H|; X = |H-I|; andX
and is used to illustrate the process. Details of the cycle
count backwards.
counting are as follows:
(7) Y = |H-I|; X = |G-H|; andX>Y. Count |H-I|asone
(1) S = A; Y = |A-B|; X = |B-C|;X>Y.Y contains S, that is,
cycle and discard points H and I. (See Fig. 5(e).)
point A. Count |A-B| as one-half cycle and discard point A;
(8) End of counting. See the table in Fig. 5 for a summary
S=B. (See Fig. 6(b).)
of the cycles counted in this example, and see Appendix X1.2
(2) Y = |B-C|; X = |C-D|;X>Y.Y contains S, that is, point
for this cycle count in the form of a range-mean matrix.
B. Count| B-C| as one-half cycle and discard point B; S=C.
5.4.4 Rainflow Counting:
(See Fig. 6(c).)
5.4.4.1 Rules for this method are as follows: let X denote
(3) Y = |C-D|; X = |D-E|;X
range under consideration; Y, previous range adjacent to X; and
(4) Y = |D-E|; X = |E-F|;X
S, starting point in the history.
(5) Y = |E-F|; X = |F-G|;X>Y. Count |E-F| as one cycle
(1) Read next peak or valley. If out of data, go to Step 6.
and discard points E and F. (See Fig. 6(d). Note that a cycle is
(2) If there are less than three points, go to Step 1. Form
formed by pairing range E-F and a portion of range F-G.)
ranges X and Y using the three most recent peaks and valleys
(6) Y = |C-D|; X = |D-G|;X>Y; Y contains S, that is, point
that have not been discarded.
C. Count |C-D| as one-half cycle and discard point C.S=D.
(3) Compare the absolute values of ranges X and Y.
(See Fig. 6(e).)
(a)IfX
(7) Y = |D-G|; X = |G-H|;X
(b)If X$ Y, go to Step 4.
(8) Y = |G-H|; X = |H-I|;X
(4) If range Y contains the starting point S, go to Step 5;
otherwise, count range Y as one cycle; discard the peak and (9) Count |D-G| as one-half cycle, |G-H| as one-half cycle,
valley of Y; and go to Step 2. and| H-I| as one-half cycle. (See Fig. 6(f).)
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