pro-EMFATIC E ngineering M aterial FATI gue C alculator Users Guide V2.5 <Preliminary English version 2010.03.16> Copyright © 2009 Pro-Lambda Solutions
Oct 14, 2014
pro-EMFATIC
Engineering Material FATIgue Calculator
Users Guide
V2.5
<Preliminary English version 2010.03.16>
Copyright © 2009 Pro-Lambda Solutions
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Table of Contents
1. How to set up pro-EMFATIC ............................................................................................. 3
2. System Requirements ......................................................................................................... 4
3. Overview ............................................................................................................................. 5
4. pro-EMFATIC GUI (Graphical User Interface) ................................................................. 7
5. pro-EMFATIC Material Data System ............................................................................... 12
6. pro-EMFATIC for User Input Values ............................................................................... 15
7. pro-EMFATIC for User Input Time History ..................................................................... 19
8. pro-EMFATIC for Femap ................................................................................................. 29
9. pro-EMFATIC for RecurDyn ............................................................................................ 42
10. Common Knowledge about Material Fatigue .................................................................. 43
10.1 Definition of Material Fatigue .................................................................................. 43 10.2 The Progression of Material Fatigue....................................................................... 43 10.3 High-Cycle and Low-Cycle Fatigue ........................................................................ 44 10.4 Experimental and Analytical Fatigue Assessments ................................................ 44 10.5 Fatigue Evaluations ................................................................................................ 45 10.6 S-N Curves ............................................................................................................. 45 10.7 Loading Amplitude and Mean ................................................................................. 46 10.8 Palmgren-Miner’s Rule for Damage Accumulation ................................................. 47 10.9 Rainflow Counting .................................................................................................. 48 10.10 Fatigue Concentration/Correction Factors .............................................................. 48
11. Selecting Life Criteria for Fatigue Evaluation ................................................................. 50
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1. How to set up pro-EMFATIC
Double Click on the file pro-EMFATIC_v2.5_setup.exe to install the pro-EMFATIC
software. During the installation process, first select the installation directory, then continue
clicking on the “Next” button until finish.
In addition to the software installation, a license file (*.lic) is needed to run pro-EMFATIC.
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2. System Requirements
Hardware:
• Intel /AMD 2.0 GHZ or above
• Memory 512M or above
Operating System:
• Window XP (sp2 or Above)
Software: (included in the installation folder)
• Microsoft .Net Framework 2.0
• Microsoft Visual C++ 2005 Redistributable
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3. Overview
pro-EMFATIC is a software product that predicts material life, fatigue damage, and
safety factors of mechanical components in various products, based on “crack-initiation”
fatigue calculations.. pro-EMFATIC provides more than a dozen life criteria for fatigue
evaluations, covering most of the common methods used in the industry for fatigue predictions,
and comes with a fatigue material library of more than 180 common materials.
pro-EMFATIC can be used as a standalone calculator by simply inputting stress or strain
values or time histories. It can also be used in FEMAP and RecurDyn as an integrated module
to predict fatigue life and damage using the results from FEA (finite element analysis) and
MBD (multi-body dynamics) solutions, respectively. Depending on the license type, the user
can choose one or more of the following for fatigue evaluations.
pro-EMFATIC can be used to calculate uniaxial and multiaxial fatigue, the user can
choose the corresponding criterion according to the loading type.
User Input Values
When this option is chosen, one can define a loading cycle by keying in either min/max
stress (or strain) or mean/amplitude of stress (or strain). Based on the stress/strain cycle
keyed in by the user, the software calculates life, damage, and/or safety factors.
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This option is available to licensees of pro-EMFATIC Basic, pro-EMFATIC Advanced,
pro-EMFATIC for Femap, and pro-EMFATIC for RecurDyn.
User Input Time History
When this option is chosen, one can define a loading cycle by importing stress (or strain)
time history. Based on the stress/strain cycle defined by the time history, the software
calculates life, damage, and/or safety factors.
User can calculate multiple elements of damage or life at the same time by selecting
multiple columns of CSV file.
This option is available to licensees of pro-EMFATIC Advanced, pro-EMFATIC for Femap,
and pro-EMFATIC for RecurDyn.
Select From Femap
When this option is chosen, one can define a loading cycle using FEA stress (or strain)
results in Femap. Based on the stress/strain cycle defined by the time history, the software
calculates and displays (by contour plots) life, damage, and/or safety factors for the groups of
elements selected by the user in Femap.
This option is only available to licensees of pro-EMFATIC for Femap.
Select From RecurDyn
When this option is chosen, one can define a loading cycle using FEA stress (or strain)
results in RecurDyn. Based on the stress/strain cycle defined by the time history, the software
calculates and displays (by contour plots) life, damage, and/or safety factors for the groups of
elements selected by the user in RecurDyn.
This option is only available to licensees of pro-EMFATIC for RecurDyn.
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4. pro-EMFATIC GUI (Graphical User Interface)
pro-EMFATIC GUI contains four sections: menu-bar, input entries, preference setting, and
evaluations.
Menu Bar
On the menu bar, the user will find the “File”, “Options”,and “Help” buttons.
Under “File”, the user can choose to “Exit” and shut down pro-EMFATIC at any time.
Under “Options”, the user can choose the source of the stress/strain cycles from User
Input Values, User Input Time History, Select from FEMAP, and Select from RecurDyn. The
user can also define a preferred evaluation setting by clicking on “Preferences…” and filling
menu-bar
input entries
preference setting
evaluations
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out the “Preference setting” form. “Reset All to Defaults” will reset all evaluation preferences. If
“Biaxial mode” is selected, the GUI will change accordingly.
Under “Help”, the user can access the online User Manual (“User Manual”), import the
license file (“Import License…”), and check current license (“About…”).
Input Entries
In the section of input entries, the user selects the material and life criterion for evaluation.
Stress/strain data can also be entered in this section if the “User Input Values” mode has been
selected. Or, if the “User Input Time History” mode is selected, the user can import
stress/strain histories in this section. In the “pro-EMFATIC for Femap” mode, the user can
define a loading or duty cycle using stress/strain results from Femap, and control how fatigue
results are displayed and stored in Femap.
Evaluations
To calculate fatigue results and display them in the “evaluations” section, click the
“Evaluate” button. Then, using the right mouse button, the user can either save the results into
a text file, or clear the results display window.
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Preference Setting
There are two ways to access the “preference setting” section: 1) by clicking on the
“Settings” button right above the “evaluations” section, or 2) by clicking on “Preferences…”
under Options from the menu bar.
There are six setting pages to help the user set up preferences for evaluations and/or
displays: General, Factors, Time History, FEMAP, Iteration, and RainFlow.
A. General
Under “General”, the user can set the “Working Directory”, “Material Library” and “User
define S-N curve Library”, select the display unit system (of the material library), and choose
the input method (for “User Input Values” option).
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B. Factors
Under “Factors”, the user can define various fatigue concentration factors that are used to
adjust the s-n curves for fatigue calculations. These factors include:
the notch factor (Kf, Kt), the surface factor (ms), the size factor (md), the load factor (mt),
and other factors (mo).
“Overall Scale Factor” is used to scale the input stress/strain. The software will first
multiply the stress (or strain) or stress history (or strain history) by this factor before any fatigue
evaluations.
C. Time History
Under “Time History”, the user sets the mode of time-history input, including both Bi-Axial
and Uni-Axial methods.
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D. FEMAP
Under “FEMAP”, the user defines how fatigue results are displayed in Femap.
“Number of Most Damaged Elements” defines the number of tags to be displayed on the
Femap contour plot to show the highest fatigue damage and/or the shortest life in the finite
element model.
“Output Set” controls whether the fatigue results are to be added into a new results set in
FEMAP or to the “active” results set.
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“Tag Style” defines how the tags are displayed in the Femap contour plot.
Under “Iteration”, the user determines how Newton’s method is used to solve the
nonlinear equations of different life equations.
E. Iteration
F. Rainflow
The User uses a “Peak-Valley” value to define the tolerance used to eliminate insignificant
cycles. When the value is set to “0”, all peak-valleys are retained for Rainflow counting. When
the value is set to “1”, only the largest peak-to-valley cycle is kept. Generally, a value between
0 and 1 is recommended.
“Number of Ranges” determines the number of ranges for cycle counting (i.e. the ranges
for amplitude and mean values). Generally, a value between 10 and 20 is recommended.
5. pro-EMFATIC Material Data System
An XML-based material data system is used to create, edit, evaluate, select, and manage
material properties for fatigue predictions. Users can use a text editor to open and/or create an
XML file that contains the materials and their fatigue properties, or use the “Material Manager”
GUI form to create, edit, and manage their own fatigue material libraries.
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The user can enter the “Material Manager” GUI by clicking on the “…” icon on the main
dialog box of pro-EMFATIC. On the “Material Manager” dialog form, first select or create a
material library, which is an XML file of fatigue material properties. The software comes with an
SAEJ1099.xml, which contains more than 180 sets of fatigue properties.
Once an XML library is selected or created, all available materials in that library are
displayed in the form. For each material, it lists a set of properties including material name,
modulus of elasticity, Poisson ratio, yield stress, ultimate stress, and a variety of cyclic
stress-strain conversion coefficients and properties of S-N formulations.
If the user enters pro-EMFATIC from Femap, the unit system used for the “Material
Manager” is consistent with the one used for Femap.
The user can use the RMB (Right Mouse Button) to select (i.e. “Make Active”), edit (i.e.
“Edit”), create (i.e. “New Material…”), copy (i.e. “Copy”), paste (“Paste”), and delete (i.e.
“Delete”) materials. The S-N curve (i.e. “S-N Curve”) can also be displayed using the current
life criterion defined in the main dialog box.
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6. pro-EMFATIC for User Input Values
The dialog box for the “User Input Values” option is shown below.
Preference Settings
Under “Options” on the menu bar, clicking on “Preferences…” will open the “Preferences”
GUI dialog box.
On the “General” page, choose the unit system for this pro-EMFATIC evaluation session.
Also select either Min/Max or Mean/Amplitude for inputting stress or strain cycles in this
session.
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Select Life Criterion
Depending on your applications and the stress/strain amplitudes of the loading cycles,
choose an appropriate method from four categories of fatigue life or safety evaluations (for
further details, please refer to the section “Selecting Life Criteria for Fatigue Evaluations” of
this document):
• Stress life
• Strain life
• BWI stress life for welds
• Fatigue safety factors
If one of the stress and strain life criteria is selected for evaluations, a stress correction
method can be chosen for the correction of the S-N curve.。
If “BWI Stress Life” is selected for evaluation, a set of BWI weld classes (e.g. B, C, and
etc.) are available for selection. The user will also have to provide the Number of Standard
Deviations for BWI evaluations.
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Choose Fatigue Material Properties
Please refer to the section “pro-EMFATIC Material Data System” in this document.
Define Fatigue Concentration Factor
In the “Preference” dialog box, choose and define various fatigue concentration factors as
needed.
Key in loading cycles
According to the loading type, fatigue factors, and scaling factors defined in the
“Preferences” dialog box, the user can input either min-max or mean-amplitude of stress or
strain cycles.
Calculate and log the results
Fatigue calculations begin when the “Calculate” button is clicked,. The evaluation results
will be displayed in the “evaluation” section of the main dialog, and the displayed results can
be saved into a text file by clicking the RMB (Right Mouse Button) and choosing “Save As”.
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7. pro-EMFATIC for User Input Time History
Under “Options” on the menu bar, choose “User Input Time History” to enter the main
dialog box for “User Input Time History”. By checking “Bi-Axial Mode”, the user can find the
Bi-axial interface, which is different from the uniaxial one.
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Time history interface
a. Uniaxial mode:
There are 3 time history input modes under uniaxial fatigue; the different interfaces are as
follows:
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(1)One cyclic stress/strain(in terms of values or histories):
In this mode, at least 1 time history CSV file is necessary for fatigue evaluation, and at
least 1 column of time history data is needed for the calculation. More columns of data may be
used to evaluate more results.
(2)stress/strain tensors (Z-axis is normal to the evaluation plane) and loading direction
(on the plane):
In this mode, at least 1 time history CSV file and an angle are necessary for fatigue
evaluation. There must be at least 3 columns of data in the CSV file, and the angle (degrees) is
decided by the user to identify the direction of damage.
The user can also output the time history data file of the given angle from X-axis to
another CSV file by checking the “stress/strain tensor history1(output)” .
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(3)stress/strain tensors (Z-axis is normal to the evaluation plane) and loading direction
(on the plane)will be determined by the software:
In this mode, at least 1 time history CSV file, an angle range, and a searching increment
are necessary for fatigue evaluation. There must be at least 3 columns of data in the CSV file,
and the angle range in degrees is defined by a basic angle, and an angle spread range to
identify the areas to search. The searching increment is used to determine the searching
frequency.
The user can also output the time history data file of the given angle from X-axis to
another CSV file by checking the “stress/strain tensor history1(output)” .
b. Biaxial mode:
It is similar to the uniaxial time history mode, There are also 3 time history input modes
about biaxial fatigue; the different interfaces are as follows:
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(1)two cyclic stress/strain(in terms of values or histories):
In this mode, at least 2 time history CSV files are necessary for fatigue evaluation, and at
least 1 column of time history data is needed for calculation. More columns of data could be
used to evaluate more results.
(2)stress/strain tensors (Z-axis is normal to the evaluation plane) and loading direction
(on the plane):
In this mode, at least 1 time history tensor CSV file and an angle are necessary for fatigue
evaluation. There must be at least 3 columns of data in the CSV file, and the angle (in degrees)
is defined by the user to decide the direction of damage.
The user can also output the 2 time history data file related to the given angle from X-axis
to another 2 CSV file by checking the “stress/strain tensor history1(output)” and
“stress/strain tensor history2(output)”.
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(3)stress/strain tensors (Z-axis is normal to the evaluation plane) and loading direction
(on the plane)will be determined by the software:
In this mode, at least 1 time history tensor CSV file , an angle range, and a searching
increment are necessary for fatigue evaluation. At least 3 columns of data are needed in the
CSV file, and the angle range is defined by a basic angle (in degrees) and an angle spread
range to define the areas to search. The searching increment is used to determine the
searching frequency.
The user can also output the time history data file related to the given angle from X-axis to
another 2 CSV file by checking the “stress/strain tensor history1(output)” and “stress/strain
tensor history2(output)”.
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c. Biaxial mode for Brown-Miller:
According to the 3 different time history input modes under biaxial mode, there are 3
different interfaces for the Brown-Miller criterion.
(1)two cyclic stress/strain(in terms of values or histories):
At least 2 time history CSV files are necessary for Brown-Miller fatigue evaluation, and at
least 1 column time history data is needed for calculation. More columns of data could be used
to evaluate more results.
(2)stress/strain tensors (Z-axis is normal to the evaluation plane) and loading direction
(on the plane):
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In this mode, 1 time history tensor CSV file and an angle are necessary for fatigue
evaluation. At least 6 columns of data are needed in the CSV file, and the angle (in degrees) is
decided by the user to define the critical plane. In addition, the user must select the shear
plane angle between 45 and 90 degrees.
The user can also output the 2 time history data file related to the given angle from X-axis to
another 2 CSV file by checking the “stress/strain tensor history1(output)” and “stress/strain
tensor history2(output)”.
(3)stress/strain tensors (Z-axis is normal to the evaluation plane) and loading direction
(on the plane)will be determined by the software:
In this mode, 1 time history tensor CSV file, an angle range, and a searching increment
are necessary for fatigue evaluation. At least 6 columns of data are needed in the CSV file,
and the angle range is defined by a basic angle (in degrees) and an angle spread range to
define the areas to search. The searching increment is used to determine the searching
frequency. In addition, the user must select the shear plane angle between 45 and 90 degrees.
The user can also output the time history data file related to the given angle from X-axis to
another 2 CSV file by checking the “stress/strain tensor history1(output)” and “stress/strain
tensor history2(output)”.
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Select Life Criterion
Based on the user’s applications and the stress/strain amplitudes of the loading cycles,
choose an appropriate method from four categories of fatigue life or safety evaluations (for
further details, please refer to the section “Selecting Life Criteria for Fatigue Evaluations” of
this document):
• Stress life
• Strain life
• BWI stress life for welds
• Fatigue safety factors
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If one of the stress and strain life criteria is selected for evaluations, a stress correction
method can be chosen for the correction of the S-N curve.。
If “BWI Stress Life” is selected for evaluation, a set of BWI weld classes (e.g. B, C, and
etc.) are available for selection. The user will also have to provide the Number of Standard
Deviations for BWI evaluations.
Choose Fatigue Material Properties
Please refer to the section “pro-EMFATIC Material Data System” in this document.
Define Fatigue Concentration Factor
From the “Preferences” dialog box, choose and define various fatigue concentration
factors as needed.
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Import loading path (time history)
Please refer to “Time history interface” of this section.
Perform evaluation
Clicking the “Evaluate” button in the main dialog box instructs the software to perform
calculations automatically, as shown in the following.
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8. pro-EMFATIC for Femap
Femap versions
1. pro-EMFATIC v2.0 supports the following Femap version(s)
• Femap v9.3.1
Set up for pro-EMFATIC for Femap
Once the compatible versions of Femap and pro-EMFATIC are both installed,
pro-EMFATIC will appear as a tool set on the Femap toolbar, as shown below.
Initiate pro-EMFATIC in Femap
While Femap is running, click on “pro-EMFATIC” on Femap’s toolbar to initiate a
pro-EMFATIC evaluation session.
Even though the pro-EMFATIC session is initiated from within FEMAP, users can still
perform fatigue evaluations by inputting Values or Time History. In order for the software to
automatically take FEMAP stress/strain results for fatigue evaluations, please choose “Select
from Femap” under “Options” on the menu bar of the pro-EMFATIC main GUI dialog box as
shown above.
Prepare finite elements results in Femap
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By either performing the finite element solutions using FEMAP with NX Nastran or
importing FE results, you can create FE results data sets in Femap. Make sure that stress
and/or strain results are available for fatigue evaluations.
Define how fatigue results are displayed in Femap
In pro-EMFATIC main dialog, click “Settings” to enter the “Preferences” dialog box. On the
“FEMAP” page of “Preferences”, the user can choose to display one or more of the most
damaged elements on Femap’s contour plots. The user can also choose to store the fatigue
results in a new Femap data set or add them to the “active” set in Femap.
Select Life Criterion
Based on the applications and the stress/strain amplitudes of the loading cycles, choose
an appropriate method from four categories of fatigue life or safety evaluations (for further
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details, please refer to the section “Selecting Life Criteria for Fatigue Evaluations” of this
document):
• Stress life
• Strain life
• BWI stress life for welds
• Fatigue safety factors
If either stress or strain life is selected for evaluations, a stress correction method can be
chosen for the correction of the S-N curve.。
If “BWI Stress Life” is selected for evaluation, a set of BWI weld classes (e.g. B, C, and
etc.) are available for selection. The user also has to provide the Number of Standard
Deviations for BWI evaluations.
Choose Fatigue Material Properties
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Please refer to the section “pro-EMFATIC Material Data System” in this document.
Define Fatigue Concentration Factor
From the “Preferences” dialog box, choose and define various fatigue concentration
factors as needed.
Define results setting
From pro-EMFATIC main dialog box, the user can choose the followings:
• “List Results in History Windows”, i.e. the fatigue evaluation results are logged
in the “evaluation” section of the dialog box.
• “Append Results to Femap”, i.e. the fatigue evaluation results are stored in
Femap as a data set.
• “Display Contour”, i.e. the fatigue evaluation results are automatically
displayed in Femap as contour plots.
• “Place Tags on Most Damaged Elements”, i.e. the fatigue results of the most
damaged elements are highlighted in Femap contour plots.
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Setting up results type for evaluation
From ”Data Component for Evaluation" in the main menu, select one Femap results type
for fatigue calculation. This results type serves as a filter to help the user select stress or strain
results from Femap for evaluation.
In general, maximum principal stress is recommended for the calculation of Stress-Life
and safety factor, and maximum principal strain is recommended for Strain-Life and
Smith-Topper-Watson calculations. Ramberg-Osgood equation is used for the conversion
between stress and strain amplitudes when needed.
Setting up loading type for evaluation
From the main menu ”FEMAP Results Sets Table", click the drop-down box on the far
right of the toolbar and select ”Duty Cycle" or ”Load History” as the loading type for evaluation.
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A. Duty Cycle
A duty cycle is composed of a set of simple loading cycles. For each “simple loading
cycle”, the minimum load of the cycle is zero and the maximum load of the cycle is depicted by
a single stress and/or strain result from a linear or nonlinear finite element solution. The user
selects one stress or strain results set to define a simple loading cycle.
Once “Duty Cycle” is selected as the loading type, the user can use the “Add Results Set”
icon to select the Femap results available to define the simple stress/strain cycles.
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After this selection, the user can move the cursor onto the selected results sets, and use
the right mouse button to “Copy”, “Delete”, “Edit”, “Insert”, and “Paste”.
A “Clear All” icon is also available at the top of the table.
B. Loading Path
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A “Loading Path” is depicted by stress or strain results sets calculated by dynamic
response or nonlinear FE solutions. You can put the stress/strain results in their loading
sequence for pro-EMFATIC to calculate fatigue results.
Once “Loading History” is selected as the loading type, the user can click the “Add Results
Sets” icon to select the Femap results available for defining the stress/strain path due to
complex loading history.
After this selection, the user can move the cursor onto the selected results sets and use
the right mouse button to “Copy”, “Delete”, “Edit”, “Insert”, and “Paste”.
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To re-sequence the stress/strain path, use the “Move Up” and “Move down” icons.
A “Clear All” icon is also available at the top of the table.
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Fatigue Evaluations
Once the “Duty Cycle” or the “Loading Path” is defined in the table, the user can click the
“Evaluate” icon for fatigue evaluations. For fatigue safety calculation, the software will
evaluate the safety factors and store them as a results set in Femap. For other
evaluations, the software will calculate both “damage” and “life” results sets and store
them in Femap. Please note that “life” means the “number of duty cycles” or the “number
of loading paths” it takes to failure.
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When the “Evaluate” button is clicked, the “Entity Selection-Enter Element(s) to Select”
dialog box will appear in FEMAP. The user then can use it to select the elements from Femap
for evaluations.
Rainflow Counting
“Counting Cycles” and “Counting Damage” are available for “Loading Path” evaluations.
The user may click either one of these buttons, then select one element in Femap, and the
software will perform Rainflow counting for the stress or strain history at the centroid of the
selected element and display the results in an Excel spreadsheet.
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Review fatigue results
Based on the setting in the main dialog box of pro-EMFATIC, fatigue results can be
displayed in Femap’s graphical windows, stored in Femap as a data set, or listed in the
pro-EMFATIC’ dialog box (for both review and storage).
Review Rainflow cycle counting results
Raiflow counting results can be displayed as bar charts and tables for “damage” or
“number of cycles” versus range and mean bins.
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9. pro-EMFATIC for RecurDyn
TBD.
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10. Common Knowledge about Material Fatigue
In addition to overloading, buckling, resonance, and rotating instability, fatigue is also a
common cause of material failure that CAE engineers aim to predict and, thus, avoid at the
product design phase using numerical techniques. Today, about 90% of fractures in
mechanical parts are, either directly or indirectly, results of material fatigue.
Fatigue failure is generally the cumulative result of a long process of operations at low
stress levels, which makes physical prototyping more difficult and numerical predictions more
meaningful. In order for CAE analysts to more precisely predict fatigue damage and life, some
common knowledge about material fatigue is imperative.
10.1 Definition of Material Fatigue
After many operational loading cycles, cracks may start to appear on the surface of the
material; they then grow wider and deeper with more operations (loading cycles) until
complete fracture occurs. This process is generally referred to as material fatigue failure.
According to the definition of American Society of Testing and Materials, material fatigue is
defined as follows:
“The process of progressive localized permanent structural change occurring in a material
subjected to conditions which produce fluctuating stresses and strains at some point or points
and which may culminate in cracks or complete fracture after a sufficient number of
fluctuations.” - ASTM E206-72 (1979)
10.2 The Progression of Material Fatigue
Material fatigue usually occurs over a period of time in localized areas. The material
generally undergoes 3 phases before complete fracture: “material softening/hardening”, “crack
initiation”, and “crack growth”. The process from “crack growth” to complete fracture may be
sudden and the result catastrophic. Therefore, engineers generally prefer to predict when the
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crack initiates and make it the life of the part, hence part replacement. Only in the rare cases of
very expensive parts are engineers inclined to simulate the complete fracture process for more
precise life predictions. pro-EMFATIC provides a variety of life criteria for “crack-initiation”
fatigue evaluations.
10.3 High-Cycle and Low-Cycle Fatigue
A. High-Cycle Fatigue
High-cycle fatigue refers to the type of fatigue in which cracks initiate after a relatively
large number of loading cycles (generally 105-107 cycles). Normally, for high-cycle fatigue,
material behavior is localized in the elastic region, the stress-strain relations are linear,
and the alternating stresses are less than 1/3 of the yield stress. Stress cycles are
normally used to calculate the damage and predict the life for high-cycle fatigue.
High-cycle fatigue commonly exists in various mechanical systems.
B. Low-Cycle Fatigue
Low-cycle fatigue refers to the type of fatigue in which cracks initiate after a relatively small
number of loading cycles (generally 104-105 cycles). For low-cycle fatigue, the material
behavior is normally localized in the elastic-plastic region, the stress-strain relations are
normally nonlinear, and the alternating stresses could be close to or even exceed the yield
stress. Normally, strain cycles are used to calculate the damage and predict the life for
low-cycle fatigue.
10.4 Experimental and Analytical Fatigue Assessments
In the real world, durability experiments of parts and products generally take a very long
time and can be very expensive. In order to make durability assessments more efficient,
material fatigue properties obtained from standard specimens in a controlled laboratory
environment are commonly used to predict fatigue damage and life, using the strain histories
measured by strain gauges mounted on critical areas of a structure. However, there is no good
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way to identify all possible fatigue concentration areas for the strain gauges to be mounted,
and it may not be technically possible to mount a strain gauge on every critical location.
Due to modern computer technology, the stress and strain variations under various
loading conditions can be timely and accurately calculated on digital models. The cost (in
terms of both money and time) of analytical fatigue analyses is generally a lot lower than the
cost of durability tests. Besides, using analytical approaches, fatigue assessments can be
performed everywhere on the structure; there are no mounting limitations as in physical
testing.
10.5 Fatigue Evaluations
Analytical fatigue assessments for “crack initiations” normally follow four major steps:
Step 1: Describing the material fatigue behavior (e.g. number of cycles to failure under
different stress cycles) mathematically;
Step 2: Calculating stress (or strain) histories due to cyclical loading by numerical methods
(e.g. finite element methods or multibody dynamics);
Step 3: Identifying loading cycles from the time histories of stress (or strain);
Step 4: Calculating life (i.e. number of cycles to failure), damage (i.e. the reciprocal of life), and
safety factor (i.e. the rate of safety for the most damaged cycle by comparing against the
alternating stress at the design life of the product) using the mathematical expression of the
fatigue behavior as stated in Step 1.
The following sections may be useful to help understand how pro-EMFATIC performs the four
steps of fatigue evaluations.
10.6 S-N Curves
The S-N curve describes the fatigue behavior of the material, defined by a set of fatigue
material properties that are obtained from test data using curve-fitting approaches. The S-N
curve is defined on log-log scales; its Y-axis is either alternating stress (or alternating strain) or
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stress range (or strain range); and its X-axis is either number of cycles to failure or number of
reversals to failure.
10.7 Loading Amplitude and Mean
There are two common ways to describe a fatigue loading cycle; one is using the cycle
amplitude (i.e. stress amplitude σa or strain amplitude εa), the other is using the cycle range (i.e.
stress range △σ or strain range Δε). Taking the stress cycle as an example, the relation
between cycle amplitude and cycle range are defined as follows:
In which σmax and σmin represent the maximum and minimum stresses respectively in the
loading cycle.
The stress amplitude σa defines the alternating stress of the cyclic loading. In addition to
the alternating stress, there may be stress offset due to the existence of a static load in the
Endurance Limit
S-N Curve indicates stress level vs. number of cycles required to initiate a crack
[1]
Fatigue limit
Design Criterion
Design life Cyclic testing ends here
Life Prediction
Fatigue Safety Assessment
2σσ
=σ minmaxa
aσσσσ 2=−=∆ minmax
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cyclic loading. When both stress offset and alternating stress exist, the stress cycles are
shown as below.
symmetric cyclic loading asymmetric cyclic loading
Stress offset in the cyclic loading is commonly referred to as the mean stress of the cycle,
represented by σm; it’s defined by the following equation.
10.8 Palmgren-Miner’s Rule for Damage Accumulation
Many different theories and approaches can be used to combine the fatigue damage
resulted from different loading cycles into one damage value called the cumulative damage.
Among them, the Palmgren-Miner method, a simple and easy approach, is well accepted and
commonly used for crack-initiation fatigue predictions. The Palmgren-Miner theory assumes
that the fatigue damage of different cyclic loading cycles can be linearly combined into one
damage value. The damage of one cycle is determined by the mean stress and amplitude of
the loading cycle, and it is not affected by the previous cycles and existing damage. By
checking the S-N Curves, the life (in terms of the number of cycles) of each identified cyclic
loading is determined and can be used to calculate damages as in the following.
For each cyclic loading cycle:Damage1 = 1/Life
For n times of repeated cycles: Damagen = n/Life
2minmax
mσσσ +
=
0
t
σ
σm
ax
σm
in
△σ
σa
t
σm
σm
ax
σm
in σ
a σ 0
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After experiencing multiple cyclic loading cycles of(σnm, sn
a)for n times, (σpm, sp
a)for p
times, etc....the cumulative damage value is calculated by
DamageTotal = n/Lifen + p/Lifep + ...
10.9 Rainflow Counting
Different methods can be used to identify and count fatigue cycles from time histories of
stress or strains. Among them, the Rainflow counting method is the most well accepted and
commonly used counting method. Using Rainflow counting, a time history is re-sequenced into
various numbers of fatigue loading cycles of stress (or strain) amplitudes with mean stresses.
Once the loading cycles are identified and the number of cycles counted, the fatigue damage
of each cycle can be calculated and then linearly combined into a cumulative damage for the
whole loading history.
10.10 Fatigue Concentration/Correction Factors
Fatigue material properties are obtained experimentally. In a well-managed environment
and under ideal conditions, the smoothly polished specimens are uni-axially loaded in the
laboratory for data gathering. These test measurements are then converted into a set of
fatigue properties using statistical methods and curve-fitting approaches.
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When these test-based properties are used on real parts or products for fatigue
assessments, real-world conditions such as surface treatments and corrosions, notches and
stress concentrations, geometric shapes and dimensions, multi-axial loading and so on, must
be taken into account as well. A set of coefficients (e.g. kf as the notch factor) are normally
used for correction purposes.
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11. Selecting Life Criteria for Fatigue Evaluation
In pro-EMFATIC, the user can select one of the following life criteria for fatigue
evaluations.
i. Stress-based life criteria for fatigue damage assessment and life prediction
• Manson-Coffin
• Morrow
• Basquin
• ASME boilers and pressure vessels
ii. Strain-based life criteria for fatigue damage assessment and life prediction
• Manson-Coffin
• Morrow
• Smith-Watson-Topper
• Maximum Shear Strain
• Brown-Miller
iii. Weld life criteria for fatigue damage assessment and life prediction
• BWI (BS7608)
iv. Stress-based fatigue safety factor calculations
• Goodman safety factor
• Gerber safety factor
• Dang Van safety factor
When selecting a life criterion for fatigue evaluations, please consider the following
guidelines as they may be helpful.
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Stress-based life criteria are generally used for “high-cycle fatigue” applications.
Strain-based life criteria are generally used for “low-cycle fatigue” applications.
Brown-Miller life criterion is commonly used for bi-axial fatigue evaluations.
Whenever possible, request stress or strain results directly from FEA (Finite Element
Analysis) for corresponding stress-based or strain-based fatigue assessment.
In pro-EMFATIC, Ramberg-Osgood cyclical stress-strain relation is automatically used
by the software to convert strain cycles (in terms of mean and amplitude) into stress
cycles, and stress cycles into strain cycles, as needed.
Using Ramberg-Osgood to convert stress cycles into strain cycles for strain-based
low-cycle fatigue evaluations is generally NOT recommended, particularly when the
stress amplitude is greater than 30% of the material yield or ultimate stress.
For loading sequences that are predominantly tensile in nature, the
Smith-Topper-Watson approach is more conservative and is therefore recommended.
For loading sequences that are predominantly compressive in nature, particularly for
wholly compressive cycles, the Morrow strain life generally provides more realistic life
estimates and is thus recommended.
ASME stress life criterion is the standard formulation that follows ASME (American
Society of Mechanical Engineers) Boiler and Pressure Vessel Code, and is thus
commonly used for boilers and pressure vessels.
BWI weld life criterion uses British Weld Institute’s formulations (BWI welds) to predict
fatigue damage and life for various classes of butt welds.
Basquin stress life is an approximation approach that is commonly used when material
fatigue properties are unknown or missing.
In pro-EMFATIC, four correction methods (i.e. Goodman, Gerber, Soderberg, and
Morrow) are available for users to use the mean stress effect in fatigue evaluations.
Among the four methods, both Goodman and Gerber are commonly used in
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engineering applications. The Goodman correction method, being very simple and
conservative, is the most frequently used.