ASTM E1049-85(2023)
(Practice)Standard Practices for Cycle Counting in Fatigue Analysis
Standard Practices for Cycle Counting in Fatigue Analysis
SIGNIFICANCE AND USE
4.1 Cycle counting is used to summarize (often lengthy) irregular load-versus-time histories by providing the number of times cycles of various sizes occur. The definition of a cycle varies with the method of cycle counting. These practices cover the procedures used to obtain cycle counts by various methods, including level-crossing counting, peak counting, simple-range counting, range-pair counting, and rainflow counting. Cycle counts can be made for time histories of force, stress, strain, torque, acceleration, deflection, or other loading parameters of interest.
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, health, and environmental practices and determine the applicability of regulatory limitations prior to use.
1.3 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
General Information
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Standards Content (Sample)
This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
Designation: E1049 − 85 (Reapproved 2023)
Standard Practices for
Cycle Counting in Fatigue Analysis
This standard is issued under the fixed designation E1049; 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 (´) indicates an editorial change since the last revision or reapproval.
1. Scope 3.1.3 mean crossings—in fatigue loading, the number of
times that the load-time history crosses the mean-load level
1.1 These practices are a compilation of acceptable proce-
with a positive slope (or a negative slope, or both, as specified)
dures for cycle-counting methods employed in fatigue analysis.
during a given length of the history (see Fig. 1).
This standard does not intend to recommend a particular
3.1.3.1 Discussion—For purposes related to cycle counting,
method.
a mean crossing may be defined as a crossing of the reference
1.2 This standard does not purport to address all of the
load level.
safety concerns, if any, associated with its use. It is the
3.1.4 mean load, P —in fatigue loading, the algebraic
responsibility of the user of this standard to establish appro- m
average of the maximum and minimum loads in constant
priate safety, health, and environmental practices and deter-
amplitude loading, or of individual cycles in spectrum loading,
mine the applicability of regulatory limitations prior to use.
1.3 This international standard was developed in accor-
P 5 P 1P /2 (1)
~ !
m max min
dance with internationally recognized principles on standard-
or the integral average of the instantaneous load values or
ization established in the Decision on Principles for the
the algebraic average of the peak and valley loads of a spec-
Development of International Standards, Guides and Recom-
trum loading history.
mendations issued by the World Trade Organization Technical
Barriers to Trade (TBT) Committee. 3.1.5 peak—in fatigue loading, the point at which the first
derivative of the load-time history changes from a positive to
2. Referenced Documents
a negative sign; the point of maximum load in constant
amplitude loading (see Fig. 1).
2.1 ASTM Standards:
E912 Definitions of Terms Relating to Fatigue Loading;
3.1.6 range—in fatigue loading, the algebraic difference
Replaced by E 1150 (Withdrawn 1988)
between successive valley and peak loads (positive range or
increasing load range), or between successive peak and valley
3. Terminology
loads (negative range or decreasing load range); see Fig. 1.
3.1 Definitions:
NOTE 2—In spectrum loading, range may have a different definition,
3.1.1 constant amplitude loading—in fatigue loading, a
depending on the counting method used; for example, “overall range” is
loading in which all of the peak loads are equal and all of the
defined by the algebraic difference between the largest peak and the
valley loads are equal.
smallest valley of a given load-time history.
3.1.2 cycle—in fatigue loading, under constant amplitude
3.1.6.1 Discussion—In cycle counting by various methods,
loading, the load variation from the minimum to the maximum
it is common to employ ranges between valley and peak loads,
and then to the minimum load.
or between peak and valley loads, which are not necessarily
successive events. In these practices, the definition of the word
NOTE 1—In spectrum loading, definition of cycle varies with the
counting method used.
“range” is broadened so that events of this type are also
included.
These practices are under the jurisdiction of ASTM Committee E08 on Fatigue
3.1.7 reversal—in fatigue loading, the point at which the
and Fracture and are the direct responsibility of Subcommittee E08.04 on Structural
first derivative of the load-time history changes sign (see Fig.
Applications.
1).
Current edition approved Nov. 1, 2023. Published December 2023. Originally
approved in 1985. Last previous edition approved in 2017 as E1049–85(2017). DOI:
NOTE 3—In constant amplitude loading, a cycle is equal to two
10.1520/E1049-85R23.
reversals.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
3.1.8 spectrum loading—in fatigue loading, a loading in
Standards volume information, refer to the standard’s Document Summary page on
which all of the peak loads are not equal or all of the valley
the ASTM website.
loads are not equal, or both. (Also known as variable amplitude
The last approved version of this historical standard is referenced on
www.astm.org. loading or irregular loading.)
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E1049 − 85 (2023)
FIG. 1 Basic Fatigue Loading Parameters
3.1.9 valley—in fatigue loading, the point at which the first 5.1.2 In practice, restrictions on the level-crossing counts
derivative of the load-time history changes from a negative to are often specified to eliminate small amplitude variations
a positive sign (also known as trough); the point of minimum which can give rise to a large number of counts. This may be
load in constant amplitude loading (see Fig. 1). accomplished by filtering small load excursions prior to cycle
counting. A second method is to make no counts at the
3.2 Definitions of Terms Specific to This Standard:
reference load and to specify that only one count be made
3.2.1 load—used in these practices to denote force, stress,
between successive crossings of a secondary lower level
strain, torque, acceleration, deflection, or other parameters of
associated with each level above the reference load, or a
interest.
secondary higher level associated with each level below the
3.2.2 reference load—for spectrum loading, used in these
reference load. Fig. 2(b) illustrates this second method. A
practices to denote the loading level that represents a steady-
variation of the second method is to use the same secondary
state condition upon which load variations are superimposed.
level for all counting levels above the reference load, and
The reference load may be identical to the mean load of the
another for all levels below the reference load. In this case the
history, but this is not required.
levels are generally not evenly spaced.
3.3 For other definitions of terms used in these practices
5.1.3 The most damaging cycle count for fatigue analysis is
refer to Definitions E912.
derived from the level-crossing count by first constructing the
largest possible cycle, followed by the second largest, etc.,
4. Significance and Use
until all level crossings are used. Reversal points are assumed
to occur halfway between levels. This process is illustrated by
4.1 Cycle counting is used to summarize (often lengthy)
Fig. 2(c). Note that once this most damaging cycle count is
irregular load-versus-time histories by providing the number of
obtained, the cycles could be applied in any desired order, and
times cycles of various sizes occur. The definition of a cycle
this order could have a secondary effect on the amount of
varies with the method of cycle counting. These practices cover
damage. Other methods of deriving a cycle count from the
the procedures used to obtain cycle counts by various methods,
level-crossings count could be used.
including level-crossing counting, peak counting, simple-range
counting, range-pair counting, and rainflow counting. Cycle
5.2 Peak Counting:
counts can be made for time histories of force, stress, strain,
5.2.1 Peak counting identifies the occurrence of a relative
torque, acceleration, deflection, or other loading parameters of
maximum or minimum load value. Peaks above the reference
interest.
load level are counted, and valleys below the reference load
level are counted, as shown in Fig. 3(a). Results for peaks and
5. Procedures for Cycle Counting
valleys are usually reported separately. A variation of this
method is to count all peaks and valleys without regard to the
5.1 Level-Crossing Counting:
reference load.
5.1.1 Results of a level-crossing count are shown in Fig.
5.2.2 To eliminate small amplitude loadings, mean-crossing
2(a). One count is recorded each time the positive sloped
peak counting is often used. Instead of counting all peaks and
portion of the load exceeds a preset level above the reference
valleys, only the largest peak or valley between two successive
load, and each time the negative sloped portion of the load
mean crossings is counted as shown in Fig. 3(b).
exceeds a preset level below the reference load. Reference load
crossings are counted on the positive sloped portion of the 5.2.3 The most damaging cycle count for fatigue analysis is
loading history. It makes no difference whether positive or derived from the peak count by first constructing the largest
negative slope crossings are counted. The distinction is made possible cycle, using the highest peak and lowest valley,
only to reduce the total number of events by a factor of two. followed by the second largest cycle, etc., until all peak counts
E1049 − 85 (2023)
(a)—Level Crossing Counting
(b)—Restricted Level Crossing Counting
FIG. 2 Level-Crossing Counting Example
are used. This process is illustrated by Fig. 3(c). Note that once counted, then each is counted as one cycle. If both positive and
this most damaging cycle count is obtained, the cycles could be negative ranges are counted, then each is counted as one-half
applied in any desired order, and this order could have a
cycle. Ranges smaller than a chosen value are usually elimi-
secondary effect on the amount of damage. Alternate methods
nated before counting.
of deriving a cycle count, such as randomly selecting pairs of
5.3.2 When the mean value of each range is also counted,
peaks and valleys, are sometimes used.
the method is called simple range-mean counting. For the
5.3 Simple-Range Counting:
example of Fig. 4, the result of a simple range-mean count is
5.3.1 For this method, a range is defined as the difference
given in Table X1.1 in the form of a range-mean matrix.
between two successive reversals, the range being positive
5.4 Rainflow Counting and Related Methods:
when a valley is followed by a peak and negative when a peak
5.4.1 A number of different terms have been employed in
is followed by a valley. The method is illustrated in Fig. 4.
the literature to designate cycle-counting methods which are
Positive ranges, negative ranges, or both, may be counted with
this method. If only positive or only negative ranges are similar to the rainflow method. These include range-pair
E1049 − 85 (2023)
(a)—Peak Counting
(b)—Mean Crossing Peak Counting
(c)—Cycles Derived from Peak Count of (a)
FIG. 3 Peak Counting Example
counting (1, 2), the Hayes method (3), the original rainflow 5.4.2 The various methods similar to the rainflow method
method (4-6), range-pair-range counting (7), ordered overall may be used to obtain cycles and the mean value of each cycle;
range counting (8), racetrack counting (9), and hysteresis loop they are referred to as two-parameter methods. When the mean
counting (10). If the load history begins and ends with its value is ignored, they are one-parameter methods, as are
maximum peak, or with its minimum valley, all of these give simple-range counting, peak counting, etc.
identical counts. In other cases, the counts are similar, but not
5.4.3 Range-Pair Counting—The range-paired method
generally identical. Three methods in this class are defined
counts a range as a cycle if it can be paired with a subsequent
here: range-pair counting, rainflow counting, and a simplified
loading in the opposite direction. Rules for this method are as
method for repeating histories.
follows:
5.4.3.1 Let X denote range under consideration; and Y,
previous range adjacent to X.
The boldface numbers in parentheses refer to the list of references appended to
these practices. (1) Read next peak or valley. If out of data, go to Step 5.
E1049 − 85 (2023)
FIG. 4 Simple Range Counting Example—Both Positive and Negative Ranges Counted
(2) If there are less than three points, go to Step 1. Form (8) End of counting. See the table in Fig. 5 for a summary
ranges X and Y using the three most recent peaks and valleys of the cycles counted in this example, and see Table X1.2 for
that have not been discarded. this cycle count in the form of a range-mean matrix.
(3) Compare the absolute values of ranges X and Y. 5.4.4 Rainflow Counting:
(a) If X < Y, go to Step 1. 5.4.4.1 Rules for this method are as follows: let X denote
(b) If X ≥ Y, go to Step 4. range under consideration; Y, previous range adjacent to X; and
(4) Count range Y as one cycle and discard the peak and S, starting point in the history.
valley of Y; go to Step 2. (1) Read next peak or valley. If out of data, go to Step 6.
(5) The remaining cycles, if any, are counted by starting at (2) If there are less than three points, go to Step 1. Form
the end of the sequence and counting backwards. If a single ranges X and Y using the three most recent peaks and valleys
range remains, it may be counted as a half or full cycle. that have not been discarded.
5.4.3.2 The load history in Fig. 4 is replotted as Fig. 5(a) (3) Compare the absolute values of ranges X and Y.
and is used to illustrate the process. Details of the cycle (a) If X < Y, go to Step 1.
counting are as follows: (b) If X ≥ Y, go to Step 4.
(1) Y = |A-B |; X = |B-C|; and X > Y. Count |A-B| as one (4) If range Y contains the starting point S, go to Step 5;
cycle and discard points A and B. (See Fig. 5(b). Note that a otherwise, count range Y as one cycle; discard the peak and
cycle is formed by pairing range A-B and a portion of range valley of Y; and go to Step 2.
B-C.) (5) Count range Y as one-half cycle; discard the first point
(2) Y = |C-D|; X = |D-E|; and X < Y. (peak or valley) in range Y; move the starting point to the
(3) Y = |D-E|; X = |E-F|; and X < Y. second point in range Y; and go to Step 2.
(4) Y = |E-F|; X = |F-G|; and X > Y. Count |E-F| as one (6) Count each range that has not been previously counted
cycle and discard points E and F. (See Fig. 5(c).) as one-half cycle.
(5) Y = |C-D|; X = |D-G|; and X > Y. Count |C-D| as one 5.4.4.2 The load history of Fig. 4 is replotted as Fig. 6(a)
cycle and discard points C and D. (See Fig. 5(d).) and is used to illustrate the process. Details of the cycle
(6) Y = |G-H|; X = |H-I|
...
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