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TRANSCRIPT
Reference
Manual
Version 7
Fracture Analysis Consultants, Inc
www.fracanalysis.com
Revised: January 2016
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Table of Contents:
Table of Contents: ........................................................................................................................... 1 1. Introduction ................................................................................................................................ 6 2. General and 3D View Manipulation .......................................................................................... 6
2.1 View Controls ...................................................................................................................... 8
3. Menus ....................................................................................................................................... 12 3.1 Help .................................................................................................................................... 12
3.1.1 License Status ............................................................................................................. 13 3.1.2 About Dialog ............................................................................................................... 14
3.2 File ..................................................................................................................................... 14
3.3 Edit ..................................................................................................................................... 15
3.4 Cracks ................................................................................................................................ 16
3.5 Loads .................................................................................................................................. 17 3.6 Analysis.............................................................................................................................. 17 3.7 Fatigue................................................................................................................................ 18 3.8 Fretting ............................................................................................................................... 18
3.9 Advanced ........................................................................................................................... 19 4. File Menu Wizards and Dialog Boxes ..................................................................................... 19
4.1 Open…Ctrl-O .................................................................................................................... 19 4.1.1 FRANC3D Restart (.fdb) Files ................................................................................... 20
4.2 Set Work Directory ............................................................................................................ 22
4.3 Close .................................................................................................................................. 23 4.4 Save As… .......................................................................................................................... 23
4.5 Import… ............................................................................................................................. 24
4.5.1 Import a Complete Model ........................................................................................... 24
4.5.2 Import and Divide Model............................................................................................ 26 4.5.2.1 Cropping Selection Options ................................................................................. 27 4.5.2.2 Relative to a principal plane ................................................................................ 28
4.5.2.3 Plane normal and offset ....................................................................................... 29 4.5.2.4 Plane from three points ........................................................................................ 30
4.5.2.5 Rubberband box ................................................................................................... 31 4.5.2.6 Element by element.............................................................................................. 31 4.5.2.7 By material ........................................................................................................... 32
4.5.2.8 By element group ................................................................................................. 33 4.5.2.9 Retained from file ................................................................................................ 33 4.5.2.10 Crop, Undo and Redo ........................................................................................ 34
4.5.2.11 Show Elems ....................................................................................................... 35
4.5.3 Import Already Divided Model .................................................................................. 35 4.6 Export… ............................................................................................................................. 36 4.7 Read Results....................................................................................................................... 37 4.8 Playback…. ........................................................................................................................ 38 4.9 Quit - Ctrl-Q ....................................................................................................................... 39
5. Edit Menu Wizards and Dialog Boxes..................................................................................... 39 5.1 Undo - Ctrl-Z ..................................................................................................................... 39
5.2 Redo ................................................................................................................................... 39
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5.3 Set Units… ......................................................................................................................... 40 5.4 Preferences… ..................................................................................................................... 40
5.4.1 Folders Tab ................................................................................................................. 41 5.4.2 Window Tab................................................................................................................ 41
5.4.3 3D View Tab ............................................................................................................... 43 5.4.4 Display Tab ................................................................................................................. 43 5.4.5 ANSYS Tab ................................................................................................................ 44 5.4.6 ABAQUS Tab ............................................................................................................. 45 5.4.7 NASTRAN Tab .......................................................................................................... 46
5.4.8 Meshing Tab ............................................................................................................... 47 5.4.9 Advanced Meshing Tab .............................................................................................. 48
6. Cracks Menu Wizards and Dialog Boxes ................................................................................ 49 6.1 New Flaw Wizard .............................................................................................................. 49
6.1.1 Flaw type panel ........................................................................................................... 50 6.1.2 Crack type panel ......................................................................................................... 51
6.1.3 Elliptical crack panel ................................................................................................... 51 6.1.4 Single-front Through-the-thickness crack panel ......................................................... 52
6.1.5 Two-front Through-the-thickness crack panel ............................................................ 53 6.1.6 Long shallow surface crack panel ............................................................................... 53 6.1.7 Two-front Elliptical crack panel ................................................................................. 54
6.1.8 User-defined crack panel ............................................................................................ 55 6.1.9 Long shallow interior crack panel ............................................................................... 57
6.1.10 Advanced Geometry button ...................................................................................... 57 6.1.10.1 Refine ................................................................................................................. 58 6.1.10.2 Reset ................................................................................................................... 58
6.1.10.3 Edit ..................................................................................................................... 59
6.1.11 Ellipsoidal void panel ............................................................................................... 60 6.1.12 Flaw translation and rotation panel ........................................................................... 61
6.1.12.1 Orient with Vectors ............................................................................................ 62
6.1.13 Crack Front Mesh Template Panel ........................................................................... 62 6.1.13.1 Meshing Parameters Dialog ............................................................................... 64
6.1.13.2 Advanced Template Options Dialog .................................................................. 65 6.1.14 Flaw Insertion ............................................................................................................ 66
6.2 Flaw from Files ................................................................................................................. 66 6.3 Multiple Flaw Insert ........................................................................................................... 68 6.4 Compute SIFs..................................................................................................................... 69
6.4.1 M-integral or Displacement Correlation Panel ........................................................... 69 6.4.1.1 SIF Plot Panel ...................................................................................................... 70
6.5 Grow Crack ........................................................................................................................ 72 6.5.1 Growth Model and Parameters .................................................................................... 72
6.5.1.1 Crack Extension Model......................................................................................... 73 6.5.1.2 Kink Angle Model ................................................................................................ 74
6.5.2 Crack Growth Display ................................................................................................. 75 6.5.2.1 Crack Extension and Fitting.................................................................................. 75 6.5.2.2 Crack Front Mesh Template ................................................................................. 81
6.6 Read Crack Growth Wizard ............................................................................................... 82
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6.7 Grow/Merge Cracks Wizard .............................................................................................. 83 6.8 SIFs Along a Path .............................................................................................................. 85
6.8.1 Define Path Tab .......................................................................................................... 85 6.8.1.1 Constant Normalized Distance ............................................................................ 86
6.8.1.2 Nearest Point on Next Front ................................................................................ 87 6.8.1.3 Intersection of Fronts with a Plane ...................................................................... 87 6.8.1.4 Path Constraints ................................................................................................... 88 6.8.1.5 Path Curve Fitting ................................................................................................ 88 6.8.1.6 Crack Starting Information .................................................................................. 89
6.8.2 Export Tab .................................................................................................................. 89 6.9 SIFs For All Fronts ............................................................................................................ 89
7. Wizards and Dialog Boxes for Loads Menu ............................................................................ 91 7.1 Map Current State .............................................................................................................. 91
7.2 Crack Face Pressure/Traction ............................................................................................ 91 7.2.1 Constant Crack Face Pressure Panel ........................................................................... 92
7.2.2 1-D Radial Residual Stress Distribution Panel ........................................................... 93 7.2.3 2-D Radial Residual Stress Distribution Panel ........................................................... 95
7.2.4 Surface Treatment Residual Stress Distribution Panel ............................................... 96 7.2.5 Mesh-Based Stress Distribution Panel ........................................................................ 98
8. Wizards and Dialog Boxes for Analysis Menu ........................................................................ 99
8.1 Static Crack Analysis ......................................................................................................... 99 8.1.1 Fdb File Name Panel ................................................................................................... 99
8.1.2 Analysis Code Panel ................................................................................................. 100 8.1.3 ANSYS Options Panel .............................................................................................. 101 8.1.4 ANSYS local/global model connection Panel .......................................................... 102
8.1.5 ANSYS Command Line Panel.................................................................................. 103
8.1.6 ABAQUS Options Panel........................................................................................... 103 8.1.7 ABAQUS local/global model connection Panel ....................................................... 104 8.1.8 ABAQUS Command Line Panel .............................................................................. 105
8.1.9 NASTRAN Options Panel ........................................................................................ 106 8.1.10 NASTRAN local/global model connection Panel .................................................. 107
8.1.11 NASTRAN Command Line Panel .......................................................................... 108 8.2 Crack Growth Analysis .................................................................................................... 109
8.2.1 Crack Front Smoothing Panel ................................................................................... 109 8.2.2 Crack Growth Increments Panel ............................................................................... 110 8.2.3 Analysis Code Panel ................................................................................................. 110 8.2.4 ANSYS Analysis ...................................................................................................... 111 8.2.5 ABAQUS Analysis ................................................................................................... 111
8.2.6 NASTRAN Analysis ................................................................................................. 111 9. Fatigue Menu Wizards and Dialog Boxes ............................................................................. 111
9.1 Fatigue Life Predictions ................................................................................................... 111 9.1.1 Read SIF Data ........................................................................................................... 112 9.1.2 Set Parameters ........................................................................................................... 113 9.1.3 Read Parameters........................................................................................................ 113 9.1.4 Save Parameters ........................................................................................................ 114 9.1.5 Plot Cycles ................................................................................................................ 115
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9.1.6 Plot SIFs .................................................................................................................... 116 9.1.7 Plot SIF Sequence ..................................................................................................... 117 9.1.8 Data Table ................................................................................................................. 118
10. Fretting Menu Wizards and Dialog Boxes........................................................................... 118
10.1 Read Model and Results ............................................................................................. 118 10.2 Import Nucleation Data............................................................................................... 121 10.3 Fretting Crack Nucleation ........................................................................................... 125 10.4 Turn Off Region Color................................................................................................ 132
11. Advanced Menu Wizards and Dialog Boxes ....................................................................... 133
11.1 Edges Wizard ................................................................................................................. 133 11.2 No Crack Regions .......................................................................................................... 134 11.3 Write COD Data ............................................................................................................ 136 11.4 Write Template Data ...................................................................................................... 137
11.5 View Response............................................................................................................... 138 11.6 Create Growth History ................................................................................................... 139
11.7 Crack Growth Sequence ................................................................................................ 141 11.8 Export Crack Data.......................................................................................................... 142
12. FRANC3D Crack Growth Models....................................................................................... 143 12.1 Crack Extension Model................................................................................................... 144
12.1.1 Fatigue, Constant Amplitude ................................................................................... 144
12.1.2 Fatigue, Variable Amplitude .................................................................................... 145 12.1.3 Quasi-Static .............................................................................................................. 145
12.2 Kink Angle Model .......................................................................................................... 145 12.2.1 Maximum Tensile Stress.......................................................................................... 145 12.2.2 Maximum Shear Stress ............................................................................................ 146
12.2.3 Maximum Generalized Stress .................................................................................. 147
12.2.4 Maximum Strain Energy Release Rate .................................................................... 147 12.2.5 Planar ....................................................................................................................... 148
12.3 Fatigue Crack Growth Model Parameters....................................................................... 148
12.3.1 Crack Extension Type .............................................................................................. 149 12.3.2 FEM Model Units .................................................................................................... 150
12.3.3 Crack Growth Rate Model ....................................................................................... 150 12.3.4 Temperature ............................................................................................................. 150
12.3.5 Crack Growth Resistance ......................................................................................... 151 12.3.6 Mixed-mode equivalent K ....................................................................................... 151 12.3.7 Effective Delta K ..................................................................................................... 152 12.3.8 Integration Algorithm .............................................................................................. 153
12.4 Quasi-Static ..................................................................................................................... 153
12.4.1 Power Law ............................................................................................................... 153 12.4.1.1 Power Law Growth Parameter .......................................................................... 154
12.4.1.2 Crack Growth Resistance .................................................................................. 154 12.4.1.3 Mixed Mode Equivalent K................................................................................ 155 12.4.1.4 Load Cases Contributing to Total K ................................................................. 155
12.4.2 Maximum Fracture Energy ...................................................................................... 155 12.4.2.1 Crack Growth Resistance .................................................................................. 156 12.4.2.2 Mixed Mode Equivalent K................................................................................ 156
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12.4.2.3 Load Cases Contributing to Total K ................................................................. 156 12.5 New Fatigue Crack Growth Rate Model ........................................................................ 156
12.5.1 Model Label, Description and Units ........................................................................ 157 12.5.2 Model Selection ....................................................................................................... 158
12.5.3 Model Temperature Dependence ............................................................................. 159 12.5.4 Stress Ratio Models ................................................................................................. 159
12.5.4.1 No Stress Ratio Model ...................................................................................... 159 12.5.4.2 Walker Equation ............................................................................................... 160 12.5.4.3 Newman Closure ............................................................................................... 160
12.5.4.4 Tabular Stress Ratio Mode................................................................................ 161 12.5.5 Paris Model Parameters ........................................................................................... 161 12.5.6 Bilinear Paris Model Parameters ............................................................................. 164 12.5.7 Sigmoidal Model Parameters ................................................................................... 164
12.5.8 Hyperbolic Sine Model Parameters ......................................................................... 165 12.5.9 Table Lookup Values ............................................................................................... 166
12.5.10 NASGRO Version 4 equation ................................................................................ 171 12.5.11 NASGRO Version 3 equation ................................................................................ 173
12.6 Constant Amplitude Load Case Selection ...................................................................... 175 12.7 Variable Amplitude Load Case Selection ....................................................................... 175
12.7.1 Sequence Load Option ............................................................................................. 176
12.7.2 Spectrum Load Option ............................................................................................. 176 12.7.3 Transient Load Option ............................................................................................. 181
12.8 Temperature Dependent Growth Rate ............................................................................ 182 12.9 Orthotropic Toughness.................................................................................................... 187
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1. Introduction
FRANC3D is a program that inserts and extends cracks and/or voids in pre-existing finite
element meshes. This manual describes the components of the graphical user interface of the
program, specifically for Version 7. It also includes some underlying theory and concepts where
appropriate, but the FRANC3D Theory Reference provides more of these details. A separate
FRANC3D Command Language & Python Extensions reference provides a listing of all the
commands and the corresponding Python functions.
There are three separate FRANC3D Tutorial documents that describe the program usage when
combined with the three supported commercial FE codes: ANSYS, ABAQUS and NASTRAN.
In addition, there is a FRANC3D Benchmark document that describes a number of crack
configurations for which there are analytical or handbook solutions for stress intensity factors
(SIFs), and the FRANC3D SIFs are compared to these values.
To get started using FRANC3D, one can choose one of the tutorials and follow the steps. One
can consult this reference document for more details at any of the FRANC3D modeling steps in
the tutorials. One should also try to reproduce some of the Benchmark examples, or choose your
own models for validation.
In this document, menu buttons, dialog or wizard panel titles, and buttons on these panels are
indicated by bold text. Fields, labels and selectable options inside the dialog or wizard panels
are indicated by underlined text. Model and file names will be indicated by italic text. This
formatting should be consistent with the tutorials.
2. General and 3D View Manipulation
An image of the main FRANC3D window is shown in Figure 2.0.1. Most of the screen is used
by a 3D graphics window that displays the current model.
When a model is first displayed, the 3D view is set such that the viewer is looking toward the
center of the model from a position in the positive z direction. The distance from the viewer to
the model is set so that the full model is visible.
For most operations, one will likely want to change the view to see a different side of the model
and/or to view details more closely. As with many other programs, the view is changed by
moving the mouse in the 3D graphics window with the appropriate combination of mouse
buttons and keyboard keys depressed. There are five basic functions for view manipulation. A
unique combination of mouse buttons and keyboard keys is defined for each of the functions.
The button and key assignments can be changed using the 3D View tab in the Preferences
dialog box (described in Section 5.4).
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Menu Bar
3D Model View Window
View Controls
Camera Positions
Status Bar
Orientation Axes
Figure 2.0.1 FRANC3D main window.
The view functions are (using FRANC3D default mouse and keyboard key assignments):
Rotate (left mouse button, no keyboard keys): Mouse motion rotates the model on the screen.
The mouse can be moved in any direction. The axis of rotation is defined to be perpendicular to
the mouse motion and passes through the current center of rotation. The center of rotation is
defined as the horizontal and vertical center of the graphics window at a location midway
between the front and back clipping planes (described below).
Pan (center mouse button or wheel, no keyboard keys): Mouse motion pans or drags the model
around the screen. The mouse can be moved in any direction, and the model moves in such a
way as if it were following the mouse.
Zoom/Spin (right mouse button, no keyboard keys): These are actually two different types of
updates activated by the same mouse key. If the mouse is moved up or down it will appear as if
the viewer is getting closer or farther, respectively, from the model. If the mouse is moved left
or right, the model rotates about an axis that is perpendicular to the plane of the screen and
passes through the horizontal and vertical centers of the window.
8
Front Clip (center mouse button or wheel plus shift key): A cutting or clipping plane can be
moved parallel to the screen from the viewer toward the model. This can be used, for example,
to clip away the front of a model to see internal features such as cracks. Moving the mouse
upward "pushes" the clipping plane away from the viewer toward the model, cutting away the
portion of the model closest to the viewer. Moving the mouse downward "pulls" the plane away
from the model and toward the viewer.
Back Clip (right mouse button or wheel plus shift key): A cutting or clipping plane can be
moved parallel to the screen from behind the model toward the viewer. This can be used, for
example, to clip away parts of the model that may be making the view confusing (this is
especially useful when the model is displayed in "wireframe" mode without polygons). Moving
the mouse upward "pushes" the clipping plane away from the viewer. Moving the mouse
downward "pulls" the clipping plane toward the viewer, which will cut away the back portion of
the model.
Figure 2.0.2 Recenter View dialog.
2.1 View Controls
The View Controls box along the right hand side of the FRANC3D main window provides
additional options for manipulating the view of the model, Figure 2.1.1.
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Graphical Element Toggles
Gain Controls
Axes Display Toggle
Front/Back Surface Coloring Toggle
Named Camera Positions
Preset Camera Positions
Surface Mesh Display Toggle
Clipping Plane Dialog
Recenter View Dialog
Cutting Plane Dialog
Box Zoom Option
Figure 2.1.1 View control panel.
Graphical Element Toggles: Graphics in 3D display windows consist of a combination of
markers, vectors, polygons, and text. The toggles in this box will turn these items on or off
independently.
Gain Controls: The Set Speed button will display the dialog shown in Figure 2.1.2. The sliders
allow one to control the rotation, translation and zoom speeds independently.
Figure 2.1.2 Set Speed dialog.
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Axes Toggle: This turns the Cartesian axes display on or off.
F/B Colors Toggle: This turns the front/back coloring on or off. By default, the front and back
side of a surface are shaded differently. This toggle is useful when looking at the crack surface,
where the two surfaces are coincident.
Named camera positions: The list of named camera positions is displayed in the list box. There
should always be a reset view provided as the default (d) view. A crack view will be saved
automatically after a crack is inserted. Other camera positions can be Saved to a file or Read
from a file.
Preset Controls: These icons provide quick access to preset views that place the viewer along
one of the Cartesian axes. The two icons on the right switch the view from perspective (the
default) to orthographic.
Clipping: This button displays the Clipping View dialog, Figure 2.1.3. The front and back
clipping planes can be moved by dragging the red boxes left or right. This is an alternative to the
mouse-keyboard combinations described previously.
Figure 2.1.3 Clipping view dialog.
Recenter: This button displays the Recenter View dialog, Figure 2.1.4. The center of rotation
can be set by dragging the red boxes left or right and up or down. The new center of rotation is
the intersection of the 3 lines that have the red-box-handles.
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Figure 2.1.4 Recenter view dialog.
Cut Planes: This button displays the Cut Planes dialog, Figure 2.1.5. Cutting planes normal to
the global Cartesian axes can be set; these will cut away a portion of the model. These are
independent from the front and back clipping planes.
Figure 2.1.5 View cutting plane manager dialog.
Box Zoom: This allows one to zoom-in on a portion of the model by dragging a box, Figure
2.1.6. Press the Box Zoom button and then, using the left mouse button, click, hold and drag the
mouse to create the box.
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Zoom box
Figure 2.1.6 Box zoom used to zoom-in on a portion of the model.
Mesh Toggle: This toggles the surface mesh on and off.
3. Menus
A brief summary of the menus, from the menu bar shown in Figure 2.0.1, is provided here. In
general, selecting a menu item leads to a wizard or dialog. The Help menu is described here,
while all other menu options are described in more detail in Sections 4 through 12.
3.1 Help
The Help menu, Figure 3.1.1, is on the far-right side of the menu bar and has options for
accessing the FRANC3D documentation either locally, if installed, or on-line from FAC’s web
site (http:\\www.fracanalysis.com/software.html). If the user selects the Reference, Tutorial
for…, or Benchmark menu options, the appropriate documentation will be displayed in a web
browser window if the files have been installed locally and the file paths set. If the file paths
have not been set, the user is presented with the dialog box shown in Figure 3.1.2 and can select
the appropriate PDF file. Alternatively, if the Online Documentation menu option is selected,
FAC’s web site is accessed and the appropriate documentation can be selected there.
13
Figure 3.1.1 Help Menu.
Figure 3.1.2 FRANC3D documentation file location dialog.
3.1.1 License Status
The second last menu item displays the License Status dialog, Figure 3.1.3, which shows when
the current license will expire.
14
Figure 3.1.3 License status dialog box.
3.1.2 About Dialog
The last menu item displays the About dialog, which contains the version number, the build
number and date, acknowledgements, and a list of supporting agencies, Figure 3.1.4. We also
appreciate the help and support of our many users and their contributions.
Figure 3.1.3 FRANC3D About dialog box.
3.2 File
The File menu is shown in Figure 3.2.1. Each of the menu items is listed below.
15
Figure 3.2.1 File Menu.
Open ... - Displays an Open File dialog box that allows a user to read a FRANC3D restart file;
see Section 4.1.
Set Work Directory ... - Displays a dialog box that allows a user to set the working directory; see
Section 4.2.
Close - Closes the current model so that a new model can be read or imported; see Section 4.3.
SaveAs ... - Displays a Save File As dialog box, which allows a user to save the current model to
a FRANC3D restart file; see Section 4.4.
Import ... – Allows a user to import an uncracked FE model file. A number of different types of
files can be read, including: .cdb, .inp, .bdf. The .cdb files are ANSYS database files in ASCII
format. The .inp files are ABAQUS input files. The .bdf (or .nas) files are NASTRAN database
files; see Section 4.5.
Export ... – Allows a user to export a FE model file. ANSYS .cdb, ABAQUS .inp and
NASTRAN .bdf file formats can be written; see Section 4.6.
Read Results ... - Invokes the Read Results File dialog; see Section 4.7.
Playback ... - Invokes the Playback Session File dialog, which allows a user to read in a session
log file and reproduce the commands in that file; see Section 4.8.
Quit - Closes the model and exits the program; see Section 4.9.
3.3 Edit
The Edit menu is shown in Figure 3.3.1. Each of the menu items is listed below.
16
Figure 3.3.1 Edit Menu.
Undo - Undo the last executed command. This feature is not completed yet.
Redo - Redo the last command that was undone. This feature is not completed yet.
Implementation note: the mechanism is in place to support Undo and Redo, but the details have
not yet been implemented.
Set Units... - Invokes the Model Units dialog box; see Section 5.3.
Preferences... - Invokes the Preferences dialog box; see Section 5.4.
3.4 Cracks
The Cracks menu is shown in Figure 3.4.1. Each of the menu items is listed below.
Figure 3.4.1 Cracks Menu.
New Flaw Wizard ... - Invokes the New Flaw wizard; see Section 6.1.
Flaw From Files ... - Invokes the Locate Flaw File dialog, described in Section 6.2, followed by
a subset of the New Flaw wizard. This option allows a user to select a flaw description from a
17
file, or from multiple files, and insert it into the current model. Note that one cannot insert a
crack into an already-cracked model.
Multiple Flaw Insert ... Invokes the Multiple Flaw wizard; see Section 6.3.
Compute SIF's ... - Invokes the Compute SIF's wizard; see Section 6.4. Note that
displacements from a completed analysis must be available for this option to be enabled.
Grow Crack ... - Invokes the Crack Growth wizard; see Section 6.5. Note that displacements
from a completed analysis must be available for this option to be enabled.
Read Crack Growth ... - Invokes the Read Crack Growth wizard; see Section 6.6.
Grow/Merge Cracks ... - Invokes the Crack Growth/Merge wizard; see Section 6.7. This
feature is not completed yet.
SIFs Along a Path ... - Invokes the SIFs Along a Path dialog; see Section 6.8.
SIFs For All Fronts... - Invokes the SIFs For All Fronts dialog; ; see Section 6.9.
3.5 Loads
The Loads menu is shown in Figure 3.5.1. Each of the menu items is listed below.
Figure 3.5.1 Loads Menu.
Map Current State ... - Invokes the Map Current State dialog; see Section 7.1. Note that a
previous model and previous results must be available for this option to be enabled. This option
is not completed yet and the menu option is inactive.
Crack Face Pressure/Traction ... - Invokes the Crack-Face Tractions dialog; see Section 7.2.
3.6 Analysis
The Analysis menu is shown in Figure 3.6.1. Each of the menu items is listed below.
18
Figure 3.6.1 Analysis Menu.
Static Crack Analysis ... - Invokes the Static Crack Analysis wizard; see Section 8.1.
Crack Growth Analysis ... – Invokes the Crack Growth Analysis wizard; see Section 8.2.
3.7 Fatigue
The Fatigue menu is shown in Figure 3.7.1. There is a single menu item listed below.
Figure 3.7.1 Fatigue Menu.
Fatigue Life Predictions ... - Invokes the Fatigue Life dialog; see Section 9.1.
3.8 Fretting
The Fretting menu is shown in Figure 3.8.1. Each of the menu items is listed below.
Figure 3.8.1 Fretting Menu.
Read Model and Results ... - Invokes the Fretting Model Import wizard; see Section 10.1.
Import Nucleation Data ... - Invokes the Fretting Data Import/Analysis wizard; see Section
10.2.
Fretting Crack Nucleation ... - Invokes the Fretting Crack Nucleation wizard; see Section
10.3.
19
Turn Off Region Color ... - Invokes the Region Color dialog; see Section 10.4.
3.9 Advanced
The Advanced menu is shown in Figure 3.9.1. Each of the menu items is listed below.
Figure 3.9.1 Advanced Menu.
Edges Wizard ... - Invokes the Edge Extraction wizard; see Section 11.1.
No Crack Regions ... - Invokes the No Crack Regions dialog; see Section 11.2.
Write COD Data ... - Invokes the Write COD Data wizard; see Section 11.3.
Write Template Data ... - Invokes the Write Template Data dialog; see Section 11.4.
View Response ... - Invokes the View Response dialog; see Section 11.5.
Create Growth History ... - Invokes the Create Growth History dialog; see Section 11.6.
Crack Growth Sequence ... - Invokes the Crack Growth Sequence dialog; see Section 11.7.
Export Crack Data ... - Invokes the Export Crack Data dialog; see Section 11.8.
4. File Menu Wizards and Dialog Boxes
The wizards and dialog boxes for the File menu options are described in this section.
4.1 Open…Ctrl-O
The File Open menu option allows the user to read a FRANC3D restart file, with .fdb extension.
The Restart File dialog allows one to select a .fdb file, Figure 4.1.1.
20
Figure 4.1.1 Model File dialog box.
4.1.1 FRANC3D Restart (.fdb) Files
FRANC3D reads the contents of the .fdb file along with reading any files that are referenced
inside it. The .fdb file is organized in blocks, with each block having a title and a version
number. The blocks and their content are summarized here:
F3D_V7.0 (
Uncracked finite element file name, type, and retained data.
)
HISTORY_SUMMARY (
Summary of the crack step file names.
)
STATICMETA (
Analysis type, input and results file names.
)
FLAWSURF (
Description of crack geometry: surface patches, crack front vertices, and template parameters.
)
CRACKFRONTIDS (
List of crack front identifiers.
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)
TEMPLATENODES {
List of crack front mesh template node ids.
}
TEMPLATENODECOORDS {
List of crack front mesh template node coordinates.
}
SIF_COMP_PARAMS (
Stress intensity factor computation parameters.
)
GROWTH_PARAMS (
Crack growth model paremeters.
)
TEMPLATE_PARAMS (
Crack front mesh template parameters.
)
CRACKFACENODES {
List of crack face nodes with the local normal to the crack surface.
}
EDGE_EXTRACT_PARAMS (
Edge extraction parameters.
)
MESH_PARAMS (
Meshing parameters.
)
CRACK_GROWTH_DATA (
Crack growth history data.
)
UNITS (
Model units for length, stress and temperature.
)
SUBMODEL_NODE_MAP (
Node id mapping between .fdb and FE model input.
)
SUBMODEL_ELEM_MAP (
Element id mapping between .fdb and FE model input.
)
RETAINED_NODES (
List of retained surface mesh nodes.
)
SAVED_VIEWS {
List of saved camera positions.
}
FRANC3D attempts to read all the files referenced in the .fdb file. If a file is missing, the user is
prompted to locate that file, Figure 4.1.2. Note that you need the original uncracked finite
element model file to perform crack growth simulations.
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Figure 4.1.2 Locate File dialog box for finding missing files.
4.2 Set Work Directory
The File Set Work Directory menu item allows the user to set a current working directory to
save subsequent analysis files. The Set Working Directory dialog, Figure 4.2.1, is displayed.
Select the folder and then press Accept.
Figure 4.2.1 Set Working Directoy dialog box for setting the current directory.
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4.3 Close
The File Close menu item closes the current model without quitting FRANC3D. If a model is
open and has not been saved, the Save Model Warning dialog, Figure 4.3.1, is displayed. If the
user wishes to save the model, the Cancel button can be selected. Selecting the OK button will
close the model without saving.
Figure 4.3.1 Save Model Warning dialog.
4.4 Save As…
The File Save As menu item can be used to save the FRANC3D restart (fdb) file of a cracked
model if the user does not want to perform an immediate analysis of the model. In addition to
the .fdb file, a FE analysis file will be saved; the FE file type will be the same as the original
input file type. The user is prompted to enter the .fdb file name, Figure 4.4.1, and press Accept.
Figure 4.4.1 Save File As dialog.
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4.5 Import…
The File Import menu item is used to import initial uncracked FE models into FRANC3D. The
dialog shown in Figure 4.5.1 is presented. The user can choose: 1) import a complete model into
FRANC3D, 2) import and divide so that FRANC3D works on a local submodel, or 3) import an
already divided model. Depending on the radio button that is chosen, different dialogs will be
displayed next.
Figure 4.5.1 Select Model Import Type dialog.
4.5.1 Import a Complete Model
The dialog shown in Figure 4.5.1.1 is displayed. The user chooses the FE model type: ANSYS,
ABAQUS or NASTRAN using the radio button at the top. If ANSYS is chosen, the user can
also check the Extra load files box if ANSYS load step files (.s##) are to be imported as well.
If the ANSYS Extra load files box is checked, the dialog shown in Figure 4.5.1.2 is displayed.
The user can select one or more .s## files. Use the shift or ctrl key to select multiple file names.
25
Figure 4.5.1.1 Select Model to Import dialog.
Figure 4.5.1.2 Select ANSYS Extra load step files dialog.
Once the FE model file has been selected, the Select Retained BC Surfaces dialog is displayed,
Figure 4.5.1.3. Any surface that has boundary conditions will be highlighted in blue. These
26
surfaces can be selected using the Select All button, and the blue surfaces will be colored red.
Node sets and surfaces can also be displayed using the Show Node Sets and Show Surfaces
buttons; these buttons allow surfaces without boundary conditons to be retained.
Note that cracks cannot be inserted into or propagated into a surface mesh that has been retained.
If a surface has boundary condtions and a crack must be inserted into this surface, do not retain
the mesh facets on this surface; the boundary conditions will be transferred to the remeshed
surface. If a crack will not be inserted into a surface with boundary conditions, it is more
efficient and accurate to retain the mesh so that boundary conditions are transferred directly.
Figure 4.5.1.3 Select Retained BC Surfaces dialog.
4.5.2 Import and Divide Model
If the user chooses to import and divide, the first dialog that is presented is the same as that
shown in Figure 4.5.1.1. Once the model file has been selected, the Submodel tool is displayed,
Figure 4.5.2.1. There are a number of options for selecting a portion or portions of the model
and these are described in the subsections below. Once a sub-model has defined and cropped,
press Next and this will lead to the Select Retained BC Surfaces dialog (see Figure 4.5.1.3) if
the sub-model has boundary conditions or node sets or surfaces.
27
Figure 4.5.2.1 Define Submodel dialog.
4.5.2.1 Cropping Selection Options
The first settings in the Cropping Options allow one to specify which ‘side’ of the selection plane
or box is selected. The top radio button in Figure 4.5.2.2 lets one choose the ‘left’ or ‘right’ side
(Figure 4.5.2.3); this is straightforward to describe when using the planar options below, but it
also applies to the other options. For instance, when using the Rubberband Box, the selection
will be either inside or outside of the rubberband box depending on which radio button is
selected.
The second radio button allows one to select elements with either one or all nodes of the element
collected. Figure 4.5.2.4 shows a case where the cutting plane is half-way through the elements;
choosing the first option includes these cut-elements, while choosing the second option discards
the elements that are cut.
Note that selected elements are colored red.
Figure 4.5.2.2 Cropping Options selection options dialog.
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Figure 4.5.2.3 Selection based on ‘left’ and ‘right’ selections.
Figure 4.5.2.4 Selection based on ‘left’ and ‘right’ selections.
4.5.2.2 Relative to a principal plane
The first cropping option allows one to choose a plane that is aligned with the Cartesian axes,
Figure 4.5.2.5. The plane can be offset from the origin, and the elements on either the ‘left’ or
‘right’ side of the plane are selected. In this case and in all cases below, the radio buttons at the
top (see Section 4.5.2.1) will be the defaults, which means left-side selection and one-node-in,
Figure 4.5.2.6.
Figure 4.5.2.5 Relative to principal plane cropping option.
29
Figure 4.5.2.6 Selection based on principal plane and left-side selection.
4.5.2.3 Plane normal and offset
The second cropping option allows one to define a plane that is normal to the unit vector defined
by the x, y and z coordiantes, Figure 4.5.2.7. The plane can be offset from the origin. Figure
4.5.2.8 shows a plane that is normal to the vector (1,0,0), which is the same as the YZ principal
plane in Section 4.5.2.2.
Figure 4.5.2.7 Plane normal and offset cropping option.
Figure 4.5.2.8 Selection based on a plane and offset.
30
4.5.2.4 Plane from three points
The third cropping option allows one to define a plane based on the selection of three points,
Figure 4.5.2.9. The user presses the Select button for each point, and then uses the (cross) cursor
to pick the point; three points of a triangle define the plane. Figure 4.5.2.10 shows the second
(green) point that was selected here. Figure 4.5.2.11 shows the resulting plane that was created
by picking 3 points at x=5 coordinates; this is the same as the YZ principal plane in Section
4.5.2.2.
Figure 4.5.2.9 Plane from three points cropping option.
Figure 4.5.2.10 Second (green) selected point used to define a plane.
Figure 4.5.2.11 Selection based on a plane from three points.
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4.5.2.5 Rubberband box
The fourth cropping option allows one to define a box, Figure 4.5.2.12. The user presses the
Define button and then uses the left-mouse button to drag the outline of a box on the screen,
Figure 4.5.2.13. The right-side image in Figure 4.5.2.13 shows the resulting box that was
created. Note that the box is displayed using the default perspective view.
Figure 4.5.2.12 Rubberband box cropping option.
Figure 4.5.2.13 Selection based on a rubberband box.
4.5.2.6 Element by element
The fourth cropping option allows one to select (or unselect) individual elements, Figure
4.5.2.14. The user presses the Select button and then uses the left-mouse button to select
elements one at a time, Figure 4.5.2.15. The default is to have all elements pre-selected and the
Select button actually turns off the selection, while the Unselect button re-selects the element.
Figure 4.5.2.14 Element-by-element cropping option.
32
Figure 4.5.2.15 Selection based on element-by-element selection.
4.5.2.7 By material
The fifth cropping option allows one to select elements based on the material id, Figure 4.5.2.16.
The user enters the material id # and then presses the Select button, Figure 4.5.2.17. Note that
this will be enhanced to provide a list of available id #s. The model in Figure 4.5.2.17 has two
materials with ids or 1 and 2.
Figure 4.5.2.16 By material id cropping option.
Figure 4.5.2.17 Selection based on material id #. The left-side image shows material #1 and the
right –side image shows material #2.
33
4.5.2.8 By element group
The sixth cropping option allows one to select elements based on an element group name, Figure
4.5.2.18. The user enters the label and then presses the Select button, Figure 4.5.2.19. Note that
this will be enhanced to provide a list of available element group labels. For ANSYS, this will
be ‘CMBL’ data in the .cdb file, and for ABAQUS, this will be a ‘ELSET’ data in the .inp file.
Figure 4.5.2.18 By element group label cropping option.
Figure 4.5.2.19 Selection based on element group label.
4.5.2.9 Retained from file
The final cropping option allows one to select element id’s from a file, Figure 4.5.2.20. The user
presses the Browse button to display the file selection dialog, Figure 4.5.2.21. This option is
useful for re-selecting elements that were selected during a previous import. The .txt file is
ASCII and simply contains a list of element ids; a range of ids is specified using a dash. Figure
4.5.2.22 shows the selected elements that were identified in the .txt file.
Figure 4.5.2.20 Retained from file cropping option.
34
Figure 4.5.2.21 Retained element id file selection dialog.
Figure 4.5.2.22 Selection based on element ids provided in a ASCII .txt file.
4.5.2.10 Crop, Undo and Redo
The three buttons at the bottom on the left side perform the actual cropping operation. Once the
selection has been made using one of the options above, the selected elements are cropped by
pressing the Crop button, Figure 4.5.2.23. The un-selected elements are removed. The user can
Undo or Redo the cropping operation. Multiple selections and crops can be performed in
sequence.
35
Figure 4.5.2.23 Crop button pressed to remove the un-selected elements.
4.5.2.11 Show Elems
The Show Elems option at the bottom turns on or off the display of element edges, Figure
4.5.2.24. For some models, with many elements or with very refined meshes, the element edges
can obscure the element selection. Un-checking this box turns off the black element edge
coloring, which can make the red-colored elements more visible.
Figure 4.5.2.24 Crop button pressed to remove the un-selected elements.
4.5.3 Import Already Divided Model
If the user has model files that have already been subdivided, the dialog shown in Figure 4.5.3.1
is displayed, which allows the user to select their global and local model files. These can be files
created by FRANC3D in Section 4.5.2, or can be files created by the user from the FE analysis
software.
36
Figure 4.5.3.1 Select Global and Local files dialog.
4.6 Export…
The File Export menu item can be used to save the FE model data without saving the
FRANC3D .fdb file. The dialog shown in Figure 4.6.1 is presented; the user selects the analysis
FE model type and enters the file name. This option can be used to convert FE model files from
one type to another.
Figure 4.6.1 Export Model File dialog.
37
4.7 Read Results
The File Read Results menu item invokes the dialog shown in Figure 4.7.1, which allows the
user to choose the analysis results file to be read.
For ANSYS, the results file will either be a .dtp file that is created using the FRANC3D
generated ANSYS macros or a simple ANSYS nodal listing of displacements saved to a .dsp file.
The .dtp file will contain displacements, temperatures if those are not equal to the reference
temperature, and contact pressures on crack surfaces if such exist.
For ABAQUS, the results file will either be a .dtp file that is created using the FRANC3D
generated ABAQUS Python script, the ABAQUS generated .fil file, or the ABAQUS CAE
Report file format. The .dtp file will contain displacements, temperatures if those are not equal
to the reference temperature, and contact pressures on crack surfaces if such exist.
For NASTRAN, all results will be contained in a NASTRAN generated .pch file, which will
include displacements, temperatures if those are not equal to the reference temperature, and
contact pressures on crack surfaces if such exist.
Figure 4.7.1 Read results file dialog.
38
4.8 Playback….
The File Playback menu item allows playback of recorded session (log) files. Each time the
FRANC3D program is executed, a session##.log file is saved. This file records the commands
that the user executes using the menus and dialogs. A sample .log file might look like this:
OpenMeshModel (
model_type=ANSYS,
file_name='C:\cube\cube.cdb',
retained_nodes_file=`cube_RETAINED.txt'
)
InsertFileFlaw (
file_name='C:\cube\cube_05.crk')
RunAnsysAnalysis (
file_name='C:\cube\cracked_cube',
flags=[QUADRATIC],
executable='C:\ANSYS Inc\v121\ansys\bin\WINX64\ANSYS150.exe',
command='"C:\ANSYS Inc\v121\ansys\bin\WINX64\ANSYS150.exe" -b -p
struct -i "C:\cube\cracked_cube.macro" -o "C:\cube\cracked_cube.out"',
license=struct)
ComputeSif (
do_press_terms=true)
A complete description of the FRANC3D command language is provided in the FRANC3D
Version 7 Command Language & Python Extensions document.
Selecting the Playback menu item invokes the Playback Session File selection dialog, Figure
4.8.1. The user selects the desired session file and then presses Accept. FRANC3D will read
and execute the commands from the session file.
39
Figure 4.8.1 Playback session file selection dialog.
4.9 Quit - Ctrl-Q
The File Quit menu item exits FRANC3D. The Save Model Warning dialog (see Figure 4.3.1)
will be displayed if the model has not been saved.
5. Edit Menu Wizards and Dialog Boxes
The wizards and dialog boxes for the Edit menu options are described in this section. Note that
the first two options, Undo and Redo, are inactive in Version 7.
5.1 Undo - Ctrl-Z
The Edit Undo menu item is intended to undo user actions. It is not active in Version 7.
5.2 Redo
The Edit Redo menu item is intended to redo actions that have been undone. It is not active in
Version 7.
40
5.3 Set Units…
Selecting the Edit Set Units menu item invokes the Model Units dialog, which allows one to set
the FE model units for length, stress and temperature, Figure 5.3.1. The units are used to label
plots, and they are important when defining the crack growth model where additional material
data is entered that is not typically part of the FE model. Units should be self-consistent;
FRANC3D can do some unit conversions when matching the crack growth material data with the
FE model results to compute crack growth.
Figure 5.3.1 Model Units dialog.
5.4 Preferences…
Selecting the Edit Preferences menu item invokes the Preferences dialog, which allows one to
set program-wide configurations, Figure 5.4.1. These preferences are stored in a database that is
read when FRANC3D is started. Some settings might not take effect until the program is
restarted. The Preferences dialog has nine tabs, described next.
41
Figure 5.4.1 Preferences dialog with Folders tab displayed.
5.4.1 Folders Tab
In the Folders tab, one can set the default working directory and the help file directory, Figure
5.4.1. The working directory is the folder where the model files will be read from and written to
by default; it also can be set under File and Set Work Directory.
The Help File directory is the top level directory for the documentation as described in Section
3.1. Documentation is accessed from the Help menu.
The Default FE Input radio button sets the user’s default FE model type for importing a new
model (see Section 4.5).
5.4.2 Window Tab
In the Window tab, one can set the font and colors used in the graphical user interface windows,
Figure 5.4.2.1. The GUI font Select button will pop up a dialog box that will allow one to select
from the available fonts, Figure 5.4.2.2. Clicking any of the color swatches (colored rectangles)
will pop up a dialog box, Figure 5.4.2.3, which allows one to select a new color.
The Defaults button restores all values to default settings.
42
Figure 5.4.2.1 Window tab of Preferences dialog.
Figure 5.4.2.2 Font selection dialog.
Figure 5.4.2.3 Color selection dialog.
43
5.4.3 3D View Tab
The 3D View tab is used to set the combinations of mouse buttons and keyboard keys that are
used to invoke the view and select functions, Figure 5.4.3.1. One should ensure that each
function has a unique set of buttons and keys. The view manipulations are described in Section 2.
The Defaults button restores all values to default settings. Rotate, pan, zoom and the front and
back clipping options were described in Section 2.1. The Select option is used by the Flaw
Editor (see Section 6.1.10).
Figure 5.4.3.1 3D View tab of Preferences dialog.
5.4.4 Display Tab
The Display tab allows the user to set the colors used for the 3D model view, Figure 5.4.4.1.
Clicking any of the color swatches will pop up a dialog box (see Figure 5.4.2.3), which allows
one to select a new color. The line width can be set also; the default is 1, but this value can be
increased for thicker lines. The program can be restarted or the model reread for this setting to
take effect.
The Defaults button restores all values to default settings.
44
Figure 5.4.4.1 Display tab of Preferences dialog.
5.4.5 ANSYS Tab
The ANSYS tab allows the user to set default ANSYS analysis parameters, Figure 5.4.5.1.
Configuration details that do not change frequently, such as the path to the ANSYS executable
and the license type can be set here. These values will then appear as default values for every
ANSYS analysis.
Ansys Executable stores the path to the ANSYS executable program. The Browse button will
pop up a file browser that can be used to locate the program.
License Type stores the ANSYS license type.
Solver allows one to specify the ANSYS equation solver.
Total and Database Memory options allow one to set the amount of memory that will be
requested on the ANSYS command line (see ANSYS documentation for details).
Number of Processors is self-explanatory.
Element series switches between older (92/95) and newer (185/187) solid element types.
Include full path in file names adds the path to any file name for the ANSYS analysis files
written by FRANC3D.
Delete unnecessary analysis files allows FRANC3D to delete ANSYS analysis files that are not
needed by FRANC3D. The ANSYS .db and .rst file are not deleted so that a user can use
45
ANSYS to visualize the model and results. Note that these two files can be regenerated from the
files that FRANC3D creates.
Figure 5.4.5.1 ANSYS tab of Preferences dialog.
5.4.6 ABAQUS Tab
The ABAQUS tab allows the user to set default ABAQUS analysis parameters, Figure 5.4.6.1.
Abaqus Executable stores the path to the ABAQUS executable program. The Browse button
will pop up a file browser that can be used to locate the program. For MSWindows, choose the
abaqus.bat file from the ABAQUS Commands folder.
Number of Processors is self-explanatory.
Include full path in file names adds the path to any file name for the ABAQUS files written by
FRANC3D.
Delete unnecessary analysis files allows FRANC3D to delete ABAQUS analysis files that are
not needed by FRANC3D. The ABAQUS .odb file is not deleted so that a user can use
ABAQUS CAE to visualize the model and results. Note that this file can be regenerated by re-
running the analysis.
Ask: ‘Old job files exist. Overwrie? (y/n)’ disables the ABAQUS prompt.
46
Figure 5.4.6.1 ABAQUS tab of Preferences dialog.
5.4.7 NASTRAN Tab
The NASTRAN tab allows the user to set default NASTRAN analysis parameters, Figure 5.4.7.1.
NASTRAN Executable stores the path to the NASTRAN executable program. The Browse
button will pop up a file browser that can be used to locate the program.
Pyramid elements allows one to use pyramid elements or splits them into two tetrahedra. MSC
NASTRAN does not support pyramid elements, so all pyramid elements in FRANC3D must be
split into two tetrahedral elements. NX NASTRAN supports pyramid elements, and these are
preferred.
Split-pyramid added node tells NASTRAN to retain or omit the extra mid-side node of a split-
pyramid element.
Crack front elements allows one to choose quarter-point or mid-side node locations for the crack
front wedge elements.
Include full path in file names adds the path to any file name for the NASTRAN files written by
FRANC3D.
47
Delete unnecessary analysis files allows FRANC3D to delete NASTRAN analysis files that are
not needed by FRANC3D.
Figure 5.4.7.1 NASTRAN tab of Preferences dialog.
5.4.8 Meshing Tab
The Meshing tab allows the user to set default meshing parameters, Figure 5.4.8.1. The options
are listed here.
Max volume elements sets a limit on the number of volume elements FRANC3D can generate.
Max backtrack restarts sets a limit on the number of FRANC3D volume meshing attempts. If
the volume meshing gets stuck, the program will backtrack and restarts.
Coarsen crack mouth turns on/off the mesh coarsening along the crack mouth. For shallow
cracks or for cases where the user wishes to have a higher mesh density, this box can be
unchecked. The higher surface mesh density will result in a higher volume mesh density.
Local surface refinement turns on/off the local surface mesh refinement. If a crack front is close
to a model surface that is not retained and not intersected by the crack, that model surface mesh
will be refined if this box is checked.
48
Volume mesh using allows the user to choose between FRANC3D, ANSYS and ABAQUS
volume meshing.
ANSYS or ABAQUS volume meshing: write files only allows the user to write the surface mesh
and the commands to generate the volume mesh from the surface mesh to files without actually
running ANSYS or ABAQUS. This gives the user the option of sending the files to a different
computer or modifying the commands. During the meshing phase of crack insertion, FRANC3D
will prompt the user to save the surface mesh files, and then will wait for the volume mesh file to
be selected.
Figure 5.4.8.1 Meshing tab of Preferences dialog.
5.4.9 Advanced Meshing Tab
The Advanced Meshing tab allows the user to set default advanced meshing parameters, Figure
5.4.9.1. The options are listed here. The advanced meshing options are described more fully in
the FRANC3D Theory reference. In general, a smaller number will lead to a more refined mesh.
Surface Refinement Factor controls how quickly the surface mesh transitions.
Surface Boundary Factor controls how quickly the surface mesh transitions.
Volume Optimal Sphere Factor controls how quickly the volume mesh transitions.
Volume Optimal Size Factor controls how quickly the volume mesh transitions.
49
Volume Octree Refinement Factor controls how quickly the volume mesh transitions.
Figure 5.4.9.1 Advanced Meshing tab of Preferences dialog.
6. Cracks Menu Wizards and Dialog Boxes
The wizards and dialog boxes for the Cracks menu options are described in this section.
6.1 New Flaw Wizard
The New Flaw wizard leads the user through the process of creating and orienting a
parametrically defined flaw. This wizard contains a number of different panels; however,
normally one will not see all panels. Choices in some of the panels determine which panels are
shown next. The overall flow is illustrated in Figure 6.1.1. Note that the elliptical and through
crack boxes house a couple of crack shapes.
The individual wizard panels are described below.
50
Figure 6.1.1 New Flaw wizard flow diagram.
6.1.1 Flaw type panel
The first panel determines the flaw type, Figure 6.1.1.1. This panel allows one to specify that
either a crack (zero volume flaw) or a void (finite volume flaw) should be inserted.
It also allows one to save the flaw description to a file. The default is to add the flaw to the
model without saving to a (.crk) file. The second radio button (Save to file and add flaw) allows
the user to save the flaw to a file and add it to the model. The third option (Save to file only)
saves the flaw to a file without adding it to the model.
Figure 6.1.1.1 New Flaw wizard first panel selects flaw type.
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6.1.2 Crack type panel
The current crack types include: 1) an elliptical crack with one crack front – top left icon in
Figure 6.1.2.1, 2) a through-the-thickness crack with one front – bottom left, 3) a through-the-
thickness crack with two fronts – top second from the left, 4) a long-shallow surface crack shape
to be used instead of long thin ellipses – bottom middle, 5) an elliptical crack shape with two
fronts – top second from the right, 6) a user-defined crack – bottom right, or 7) a long-shallow
interior crack shape – top right. The crack fronts are indicated by the thicker lines. Selecting the
crack shape icon specifies the crack type that will be shown in the next panel.
Figure 6.1.2.1 New Flaw Wizard crack (zero volume flaw) types.
6.1.3 Elliptical crack panel
Single front elliptical cracks are defined by entering the semi-axes lengths (a and b). Once
values have been specified for the length of the axes, the ellipse is displayed in the 3D view
window, Figure 6.1.3.1. The ellipse is displayed in its local orientation, which is in the x-y plane
and centered at the global Cartesian origin.
The Advanced Geometry button is common to all predefined crack shapes and will be described
in Section 6.1.10.
52
Figure 6.1.3.1 New Flaw Wizard elliptical crack parameters panel.
6.1.4 Single-front Through-the-thickness crack panel
Single-front through-the-thickness cracks are specified using three lengths (a – c) and the width
(d), Figure 6.1.4.1. If set appropriately, the three lengths can be used to define a straight or a
quadratic shape crack front. The crack is displayed in its local orientation, which is in the x-y
plane with one corner at the global Cartesian origin.
Figure 6.1.4.1 New Flaw Wizard single-front through-crack parameters panel.
53
6.1.5 Two-front Through-the-thickness crack panel
Two-front through-the-thickness center cracks are specified using six crack lengths (a – f) and
the crack width (g), Figure 6.1.5.1. If set appropriately, the six lengths can be used to define
either straight or a quadratic shape crack fronts. The crack is displayed in its local orientation,
which is in the x-y plane with one mid-side at the global Cartesian origin.
Figure 6.1.5.1 New Flaw Wizard two-front through-crack parameters panel.
6.1.6 Long shallow surface crack panel
Long-shallow-surface cracks are specified using the crack length (a), the crack width (b), and a
corner radius (c), Figure 6.1.6.1. This crack shape can be used in place of high-aspect ratio
elliptical surface cracks. The crack is displayed in its local orientation, which is in the x-y plane
with the global Cartesian origin as shown in Figure 6.1.6.1.
54
Figure 6.1.6.1 New Flaw Wizard long shallow surface crack parameters panel.
6.1.7 Two-front Elliptical crack panel
Two-front elliptical (ring) cracks are defined by entering the outer semi-axes lengths (a and b)
and the inner semi-axes lengths (c and d). The user also has the option of turning off the crack
front for either the outer or inner front; this allows one to define a circumferential crack in the
outer or inner wall of a pipe.
Once values have been specified for the length of the axes, the ellipses are displayed in the 3D
view window, Figure 6.1.7.1. The ellipses are displayed in the local orientation, which is in the
x-y plane and centered at the Cartesian origin. Both outer axes must be larger than the inner axes
to create a valid crack.
55
Figure 6.1.7.1 New Flaw Wizard two-front elliptical crack parameters panel.
6.1.8 User-defined crack panel
The user-defined crack requires a set of points that completely defines the crack boundary
geometry, including the crack front. Click on Define Points, Figure 6.1.8.1, to display a dialog
that allows one to enter the geometry points, Figure 6.1.8.2. The front pts field in Figure 6.1.8.2
allows one to define points as crack front points using a value of 1; non-front points should have
this field set to 0. Note that unless one is defining an embedded crack, there typically should be
at least one point on the crack boundary that is not a crack front point. The front points are
displayed in blue (Figure 6.1.8.1) and numbered corresponding to the listing shown in Figure
6.1.8.2. Points must be consecutive around the boundary.
One can read the points from a file using the File Open menu in the dialog shown in Figure
6.1.8.2. The file should be a simple ASCII .txt file with the format:
x y z flag
x y z flag
x y z flag
…
The Smooth Front Points option in Figure 6.1.8.1 allows the user to smooth and re-parameterize
the crack front points. This allows for more uniform crack surface geometry as the boundary
points are used with a surface triangulation routine to produce the interior crack surface
geometry. A sufficient number of non-front points should be defined to produce a reasonable
triangulation of the interior region. Some non-planarity is possible; however interior points are
not defined by the user therefore this crack works best for planar or near-planar cracks.
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Figure 6.1.8.1 User-defined crack panel.
Figure 6.1.8.2 User-defined crack points dialog.
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6.1.9 Long shallow interior crack panel
Long-shallow-interior cracks are specified using the crack length (a) and an end radius (r),
Figure 6.1.9.1. This crack shape can be used in place of high-aspect ratio elliptical cracks. The
crack is displayed in its local orientation, which is in the x-y plane with the global Cartesian
origin as shown in Figure 6.1.9.1.
Figure 6.1.9.1 New Flaw Wizard long shallow surface crack parameters panel.
6.1.10 Advanced Geometry button
Selecting the Advanced Geometry button on any of the predefined crack shapes leads to the
dialog shown in Figure 6.1.10.1. The crack shape shown here corresponds to the single front
ellipse with equal major and minor axes. Note that the triangular facets represent the geometry,
not a finite element surface mesh.
There are three buttons on the top menu bar: Refine, Reset and Edit. The crack geometry is
shown in the window. The menu options are described below.
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Figure 6.1.10.1 Crack Advanced Geometry dialog.
6.1.10.1 Refine
The Refine button alters the discretization of the crack surface geometry. Although cracks
notionally have an analytical geometry (e.g. elliptical or quadratic), they are actually defined
geometrically by triangular cubic-Bezier patches. These patches only approximate the analytical
form. As the number of geometry patches is increased, the approximation improves, but at the
cost of additional processing time required to insert the crack. The Refine button performs a
uniform refinement of the patches, where each patch is divided into four smaller patches. This is
illustrated in the images in Figure 6.1.10.2. The Refine process can be repeated any number of
times.
Refinement might be required for higher-aspect ratio elliptical cracks, specifically for the ends of
the major axis.
6.1.10.2 Reset
The Reset button sets the crack geometry back to the original default configuration.
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Figure 6.1.10.2 Example of a Refined crack geometry. The left panel shows one level of
refinement from Figure 6.1.10.1, and the right panel shows a second level of refinement.
6.1.10.3 Edit
The Edit button invokes the Flaw Editor, Figure 6.1.10.3. This dialog allows the user to redefine
the default shape of the flaw. The vertices (black circles in Figure 6.1.10.3) can be selected by
holding down the Shift key and selecting the black circle with the left-mouse button. The
vertices turn red when they are selected (see right panel of Figure 6.1.10.3). The red circle can
be moved by holding down the Shift key and dragging the item to the new location using the left
mouse button. The x and y coordinates of the vertex are shown in the fields near the top of the
dialog.
Unselect the vertex by holding the Shift key down and picking a point that is not close to any
vertex. The undo and redo icons (to the left of the coordinate fields) allow the user to undo (or
redo) any movement of the vertices that is not desired.
Select Accept and the revised flaw shape will be shown in the initial Advanced Geometry
window (see Figure 6.1.10.1).
Select Accept in the Advanced Geometry window (see Figure 6.1.10.1) to return to the regular
flaw insertion wizard panel. The user can then proceed to locate and orient the edited flaw in the
model.
Note that the flaw editor must be used before rotating and translating the flaw.
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Figure 6.1.10.3 Flaw Editor dialog. Left panel shows the initial geometry and right panel shows
edited geometry.
6.1.11 Ellipsoidal void panel
Ellipsoidal voids are the only void shapes currently available. They are defined by entering the
three semi-axes lengths (a, b and c), Figure 6.1.11.1. The void is displayed in the local
orientation and centered at the Cartesian origin.
Figure 6.1.11.1 New Flaw Wizard ellipsoidal void parameters panel.
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6.1.12 Flaw translation and rotation panel
Once a flaw (crack or void) is defined, it must be inserted (translated and rotated) into the proper
location relative to the unflawed body. The flaw orientation panel displays the flaw and the
model in a 3D graphics window, along with controls to translate and rotate the flaw, Figure
6.1.12.1.
The translations move the local origin of the flaw to a location in the Cartesian space of the
body. It is usually simpler to specify the translations first and then "zoom in" on the display of
the flaw before specifying the rotations.
The Anchor at Node button allows the user to specify a node number where the crack center (or
anchor) should be located. The user is prompted to enter a node id, Figure 6.1.12.2, and select
OK.
Up to three rotations about the local (rotated) Cartesian axes can be specified. These are
essentially Euler angles, but the order of the rotation axes can be specified. The rotations follow
a "right-hand-rule" where the thumb points in the positive direction along the axis and the fingers
curl in the positive rotation direction.
There is an Orient with Vectors button at the bottom of the flaw rotations panel. This button is
described in the next sub-section.
Figure 6.1.12.1 New Flaw Wizard orientation panel.
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Figure 6.1.12.2 Center on Node dialog.
6.1.12.1 Orient with Vectors
The Orient with Vectors button provides another way to specify the flaw orientation, Figure
6.1.12.3. This button invokes a dialog box that allows one to specify the local x- and y-axes of
the flaw oriented relative to the Cartesian coordinates of the body. Note that these are unit
vectors.
Figure 6.1.12.3 New Flaw Wizard orientation vectors dialog.
6.1.13 Crack Front Mesh Template Panel
For accurate stress-intensity factor computations, a pattern or "template" of elements with
controlled sizes and shapes is placed about all crack fronts. The template takes the form of
generalized cylindrical tubes of elements with the crack fronts serving as the axes of the
cylinders. Wedge shaped elements are placed immediately adjacent to the crack fronts. These
are surrounded by rings of brick elements.
Figure 6.1.13.1 shows the Crack Front Mesh Template wizard panel with an elliptical surface
crack being inserted into a cube. The user can turn off the crack front template elements with the
use crack-front template toggle. In some cases, a crack front template mesh cannot be added to
the model; a crack front that touches or crosses a material boundary currently is one such case.
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The overall radius of the template can be adjusted with the Template Radius field. The default
value of the radius is based on a notion of the crack size, but it can be inappropriate in some
cases. In addition, the template radius can be decreased if a user wishes to do a mesh
refinement/convergence study.
The template elements are displayed in the 3D graphics window superimposed on the flaw and
model geometry. By default only one half of the template elements are shown. This allows one
to view the progression of element sizes as the elements transition from the crack front to the
outer boundary of the template. One can view the full template by turning on the Display Full
Template toggle.
The Simple Template Intersections Only toggle allows the user to terminate the template inside
the model surfaces. For cases where the template will intersect the model surface at shallow
angles or at corners, this option allows a crack to be inserted with template elements along the
bulk of the crack front. FRANC3D attempts to recognize instances where the template will
intersect model surfaces at poor angles and automatically triggers this option as needed.
The Meshing Parameters button at the bottom left is used to specify surface and volume
meshing parameters as well as choosing the volume mesher; this is described in Section 6.1.13.1.
The Advanced Options button allows the user to adjust the template elements and is described
in Section 6.1.13.2.
Figure 6.1.13.1 Crack front mesh template panel.
Note that this panel is displayed even if the flaw does not have any crack fronts (e.g. an elliptical
void). In this case, simply ignore this panel and select finish.
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6.1.13.1 Meshing Parameters Dialog
The Meshing Parameters dialog, Figure 6.1.13.2, is very similar to the Preferences meshing
tab described in Section 5.4.8. The user can control some aspects of the surface and volume
meshing.
The first parameter, Maximum Generated Elements, limits the total number of volume elements
that FRANC3D will create during volume meshing. The second parameter, Maximum Volume
Mesh Restarts, limits the number of volume meshing restarts. These two options only work
when FRANC3D is used for volume mesh. FRANC3D uses an advancing front volume meshing
algorithm; this algorithm can get stuck sometimes and the algorithm is designed to backtrack
(i.e., remove elements) and restart the meshing. If the program fails to create a volume mesh
after several restarts, then one can try volume meshing with ANSYS or ABAQUS.
The next two options allow the user to control surface mesh refinement: on the crack surface,
using the Do Coarsen Crack Mouth Mesh option, and on the model surface in areas where
adjacent region boundaries are near, using Do Local Surface Refinement.
FRANC3D, by default, is used to mesh the volume, but ANSYS and ABAQUS can also be used
by selecting the appropriate radio button for Volume mesh using. Note that the user must have a
licensed working copy of these programs to use their meshing algorithms. The user can select
the ANSYS and ABAQUS executables, using the Browse button, if not already set in the
Preferences (see Section 5.4).
For ANSYS or ABAQUS: write files only allows the user to write the surface mesh and the
commands to generate the volume mesh from the surface mesh to files without actually running
ANSYS or ABAQUS. This gives the user the option of sending the files to a different computer
or modifying the commands.
Figure 6.1.13.2 Meshing parameters dialog.
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6.1.13.2 Advanced Template Options Dialog
The Advanced Template Options dialog allows the user to adjust some of the default crack
front mesh template parameters, Figure 6.1.13.3. The parameters are described below and
illustrated in Figure 6.1.13.4, which shows a typical cross-section of a crack-front template.
Progression Ratio sets the relative width of the element (in the direction perpendicular to the
crack front) going from the crack front to the outer surface of the template. For example, a ratio
of 1 means that all the rings of elements will have the same width. For a ratio of 1.5, the width
of the elements in a ring will be 50% greater than the width of the elements in the next ring as we
approach the crack front.
Num Rings sets the number of rings of elements in the template.
Num Circumferential Elem sets the number of elements in the circumferential direction around
the crack front.
Max Aspect Ratio controls the aspect ratio of the quadrilateral faces on the outer surface of the
template that will trigger 1:2 or 1:3 transitions in the outer ring of elements.
Figure 6.1.13.3 Advanced template options dialog.
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first ring
second ring
third ring
first ring
second ring
third ring
template radiusnum rings = 3
num circumferential elems = 8
progression ration = /
Figure 6.1.13.4 Crack front template cross-section.
6.1.14 Flaw Insertion
After one selects Finish on the crack front mesh template panel (see Figure 6.1.13.1), the flaw is
inserted into the body and the model is remeshed. An information box is displayed to give a
sense of the current status of these operations, Figure 6.1.14.1. The crack geometry is inserted
into the model geometry first, represented by the Doing geometric intersections... status. Once
the crack geometry has been inserted, trimmed, and tied to the model geometry, the surface and
then volume meshing occurs. If using the FRANC3D volume meshing, the final volume mesh is
smoothed to improve the element quality.
Figure 6.1.14.1 Flaw Insertion Status dialog.
6.2 Flaw from Files
The user has the option of saving the flaw to a .crk file when defining a new flaw (see Figure
6.1.1.1). The Flaw from Files menu option allows the user to read one or more .crk files and
insert theses crack(s) into the model. The Locate .crk flaw file dialog, Figure 6.2.1, is
displayed, which allows the user to select one or multiple .crk files. Use the shift-key to select
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multiple files. After selecting Accept, the flaw is displayed with the model, Figure 6.2.2. A flaw
can be translated, but rotation is not allowed here. The crack front mesh template panel is the
same as in Section 6.1.13.
Figure 6.2.1 Locate .crk flaw file dialog.
Figure 6.2.2 Orient a flaw-from-file dialog; only translation allowed.
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6.3 Multiple Flaw Insert
The Multiple Flaw Insertion wizard allows the user to add multiple cracks to a model, Figure
6.3.1. The user defines each crack using the Flaw Insertion wizard panels described in Section
6.1. When all cracks have been defined, they can be added to the model and/or saved to a file.
The user starts by selecting the Add button in the dialog shown in Figure 6.3.1. This leads to the
flaw insertion wizard panels described in Section 6.1. Either voids or zero-volume cracks can be
added.
Once a crack has been added to the list, it can be edited or deleted by selecting the flaw name
and then selecting the Edit or Delete button. All of the added flaws can be displayed in the
model, Figure 6.3.2, to ensure that cracks do not overlap or intersect.
The set of radio buttons at the bottom of the dialog in Figure 6.3.1 allow one to: 1) add the flaws
to the model without saving to a file, 2) add the flaws to the model after prompting for a file
name to save a .crk file, or 3) save the flaws to a file without adding them to the model. Select
Accept to close the dialog and begin the process of crack insertion and re-meshing. The flaw
insertion status window as described in Section 6.1.14 is displayed.
Figure 6.3.1 Multiple flaw insertion - top level dialog.
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Figure 6.3.2 Multiple flaw insertion – flaw display window.
6.4 Compute SIFs
The user can compute and plot the stress intensity factors (SIFs) after performing an analysis of
the cracked model; the Analysis menu is described in Section 8. SIFs are computed at mid-side
nodes along the crack front.
6.4.1 M-integral or Displacement Correlation Panel
The Compute SIFs menu option brings up the SIF Computation dialog box, Figure 6.4.1.
Either the M-integral or Displacement Correlation method can be chosen to compute the SIFs.
The Virtual Crack Closure option computes and plots G (energy release rate) values. The
displacement correlation option generally is used only for checking the M-integral values and is
valid for isotropic materials only. For models where a crack front template cannot be added,
displacement correlation currently is the only option.
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Figure 6.4.1 Compute SIFs panel allows one to choose either M-integral or displacement
correlation computations.
Include Thermal Terms: The thermal terms can be included in the M-integral computation. The
nodal temperatures must exist in the results database and the user should supply the reference
temperature if not already given with the initial input file.
Include Applied Crack Traction: Any applied crack face traction/pressure terms should be
included in the M-integral.
Include Contact Crack Pressure: Any induced crack face contact pressure should be included in
the M-integral.
Note that it is possible to have both applied pressure and contact pressure on a crack surface and
these terms will be summed.
Plot Stress Intensity Factors: Turn on/off the display of the SIF plot dialog, which is described in
Section 6.4.1.1.
6.4.1.1 SIF Plot Panel
Stress-intensity factor distributions are displayed in this dialog, Figure 6.4.1.1. The left side of
the dialog is a 3D graphics window that displays the model. The right side of the dialog is a tab
box that shows graphs of the computed stress-intensity factor (SIF) distributions along the crack
front. The mode I, II, and III SIFs are represented by the KI, KII and KIII tabs, respectively.
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Figure 6.4.1.1 SIF plot panel.
The J-integral tab displays a plot of the total (elastic) J-integral distribution (total energy release
rate not segregated into modal components). The T-Str tab displays a plot the T-stress. The
Table tab shows a table of the SIF values along with the parametric location along the crack front
(N Coord). The crack front length is normalized from 0 to 1, going from A to B.
The Export tab allows one to export the SIF data, Figure 6.4.1.2. The user can specify the type
of delimiters to use, the grouping of the data, and order of the data. The program initially assigns
one end of the crack front as A and the other end as B. The data is plotted along the crack front,
normalized from 0 to 1.0 by the crack front length, starting from point A. Select the Create File
button to select the file name and save the data.
Figure 6.4.1.2 SIF table tab (left panel) and export tab (right panel).
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The dialog shown in Figure 6.4.1.1 includes options to display SIF data for a model with
multiple load steps, multiple crack fronts, and/or multiple growth steps. The drop-down boxes at
the top on the left side above the tabs provides this option, Figure 6.4.1.3.
Figure 6.4.1.3 SIF display drop-down selections for load step, crack front and crack growth step.
6.5 Grow Crack
When the Grow Crack menu option is selected, the Compute SIF's wizard is presented (see
Section 6.4), if the SIFs have not already been computed.
The first panel of the Crack Growth wizard is presented next. This wizard allows the user to
specify algorithms and parameters to determine the local direction and relative extension of
crack growth. The crack growth model is common to both crack growth and fatigue life
computations, and it is fully described in Section 12. We show only the first panel in this
section.
6.5.1 Growth Model and Parameters
The first panel in the wizard presents options for crack extension model and kink angle model,
Figure 6.5.1. Depending on the chosen models, different wizard panels will be displayed next
(see Section 12). The user must choose one crack extension model and one kink angle model.
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Figure 6.5.1. Growth parameters panel.
6.5.1.1 Crack Extension Model
The amount of crack propagation is determined by the extension model and the computed results
for the current crack front. Figure 6.5.2 shows an illustration of the current or original front and
the predicted crack front extension represented by the blue line. At each (mid-side) node along
the original crack front, SIFs are computed, and these SIFs are incorporated into an extension
model to compute the local extension at each node.
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local kink angle
local extensionsmoothed front (red)
predicted front (blue)
original front
local kink angle
local extensionsmoothed front (red)
predicted front (blue)
original front
Figure 6.5.2 Schematic illustration of the definition of the kink angle.
There are four crack extension models to choose from: 1) Fatigue, Constant Amplitude, 2)
Fatigue, Variable Amplitude, 3) Quasi-Static, and 4) User Defined Model. The last option is not
active in V7.0.
6.5.1.2 Kink Angle Model
The local direction of crack propagation is determined by the "kink" angle, which is defined by
the amount that the crack will deviate from the self-similar direction measured in a plane
perpendicular to the crack front. The kink angle is the angle illustrated in Figure 6.5.3.
Figure 6.5.3 Schematic illustration of the definition of the kink angle.
FRANC3D provides six options for determining the kink angle: 1) Maximum Tensile Stress
(MTS), 2) Maximum Shear Stress (MSS), 3) maximum Generalized Stress, 4) maximum Strain
Energy Release Rate, 5) Planar, and 6) User Defined Model. The last option is not active in
V7.0.
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6.5.2 Crack Growth Display
The Crack Growth Display wizard allows one to specify the amount of extension and the fitting
and crack front template mesh parameters. There are two panels, both of which display the
model and allow the user to view the new crack front as the parameters are adjusted. These two
wizard panels will be displayed once SIFs have been computed and the crack growth model and
parameters are set (see Section 12).
6.5.2.1 Crack Extension and Fitting
The crack growth display panel, Figure 6.5.2.1 allows one to adjust the median extension or
number of cycles and to set the fitting and extrapolation parameters to provide the best fit
function through the computed new crack front points. The model is displayed in the upper 3D
model view window and the user can select a camera position that shows the computed new
crack front points.
When there are multiple crack fronts in a model, an extra Grow crack fronts pane (see Figure
6.5.2.2) allows one to grow specific crack fronts using the grow check-boxes. In addition, the
extension for a selected crack front can be scaled up or down by adjusting the associated factor.
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Figure 6.5.2.1 Crack growth display panel – extension and fitting options.
Figure 6.5.2.2 Crack growth extension and fitting options for multiple crack fronts.
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The Front fitting options pane includes options for curve fitting, fields for extrapolating the ends
of the fitted curves, and the option to discard crack front points at either end. The curve-fit
options are: 1) kink angle/extension poly, 2) fixed order poly, 3) Hermitian, 4) cubic spline, 5)
moving poly, 6) partial smoothing, and 7) no smoothing. There are described in more detail
below.
The polynomial order for any of the poly-fitting options can be set in the fixed poly order field.
The default order is 3.
The ends of the fitted curves can be extrapolated to ensure that the curves intersect the model
surface. It is required that the crack surface geometry intersect the model surface. New crack
surface geometry is created between the current and new crack fronts. FRANC3D tries to ensure
that the curves are extrapolated far enough, but the user also can visually determine whether the
extrapolation is sufficient (or too much).
A set of points at either end of the crack front can be ignored. If the end points cause problems
in fitting or extrapolating, the user can ignore some of these end points.
The Save .frt and .crk files option allows the user to save the new front points and the new crack
geometry to a file before inserting it into the model. The .frt file can be read using the Read
Crack Growth wizard, which is described in Section 6.6. The .crk file can be read using the
Flaw From Files option, see Section 6.2.
The Kink Angles and Extension buttons bring up plots of the computed kink angle, Figure
6.5.2.3 – left panel, and crack front extension, Figure 6.5.2.3 – right panel, along the crack front,
respectively.
Figure 6.5.2.3 Plots of kink angle and crack front extension along the crack front.
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Kink Angle/Extension Poly Fit
Using the kink angle and extension data, a best fit polynomial is fit through the data, using
polynomial orders up the value entered in the fixed poly order field. The curve-fits can be
extrapolated and then new extrapolated crack front points are defined based on these and also on
the existing crack front geometry.
As an example, consider a penny-surface crack with the kink angle and extension shown in
Figure 6.5.2.3. Figure 6.5.2.4 shows the initial crack boundary edges, the actual crack surface,
which is shaded grey, the new front points as green dots, and the curve fit shown as a blue line.
The black dots on the original crack front correspond to the fitted front points, where the
extension and kink angle are applied to produce the new fitted points. The kink angle and
extension curves are extrapolated to compute these new end points that fall outside the model.
Figure 6.5.2.4 New front fit based on kink angle and extension curve-fits.
Fixed order poly through points
The fixed order polynomial option is the simplest and most commonly used fitting option. A
polynomial is fit through the new front points in Cartesian space based on a least-squares fit.
The order of the polynomial is provided in the fixed poly order field. This polynomial can be
extrapolated a small distance to make sure the new front intersects the model surface. Best
results are obtained with low order polynomials and limited extrapolation; if the crack front does
not suit a simple polynomial, one of the other fitting options should be chosen.
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Hermitian closed poly
The Hermitian polynomial is used for fitting closed crack fronts such as interior cracks. It is not
active if all of the cracks are open-ended surface cracks. The Hermitian fit is performed using
four equal segments, thus it works best for circular or elliptical shapes.
Cubic spline
A cubic spline fit can be used for crack fronts that do not allow for a simple low order
polynomial fit. A cubic spline will follow arbitrary curves. The ends of the crack front are
extrapolated using a linear segment through the end points for open-ended surface cracks.
Moving polynomial
A moving polynomial fit uses the polynomial order given in the fixed poly order field. A subset
of the crack front points is used for successive curve fits, moving along the full crack front in
increments from one end to the other. Like the cubic spline fit, this option is good for arbitrary
curves. The ends of the crack front are extrapolated using a linear segment through the end
points for open-ended surface cracks.
As an example of crack fronts that do not work well with a simple polynomial fit, consider the
crack fronts in Figure 6.5.2.5. Figure 6.5.2.6 shows these same crack fronts using a moving
polynomial fit; similar results can obtained for cubic spline fits. In the first example in Figure
6.5.2.5, am 8th
order polynomial fits the data, but extrapolating a high order polynomial does not
work well; in this case the extrapolated curve does not intersect the model surface. A low order
polynomial does not provide a good fit through the data. In the second example, a 12th
order
polynomial cannot capture the curve. As shown in Figure 6.5.2.6, a moving polynomial (or
spline fit) follows the data and provides good extrapolated end points.
Figure 6.5.2.5 New front fit based on a simple polynomial fit.
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Figure 6.5.2.6 New front fit based on a moving polynomial fit.
Partial smooting/extrapolation
Partial smoothing is designed for crack fronts where part of the crack front does not advance.
An example of this is a through crack in a plate subject to bending where half of the crack is
open and half is closed.
Figure 6.5.2.7 New front fit based on a partial smoothing fit.
No smoothing or extrapolation
The final option removes all smoothing and extrapolation. This option will generally only be
used when reading crack growth from a file where the front points have been defined by the user
and no fitting or extrapolation is desired.
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6.5.2.2 Crack Front Mesh Template
The second crack growth display wizard panel, Figure 6.5.2.8 allows one to set the crack front
mesh template parameters. The model is displayed in the upper 3D model view window and the
user can select a camera position that shows the template. The lower third of the window
contains one pane for the template parameters. The template parameters and buttons are
identical to those for inserting a new crack, see Section 6.1.13.
Figure 6.5.2.8 Crack front mesh template options.
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6.6 Read Crack Growth Wizard
The Read Crack Growth wizard consists of two panels. The first, Figure 6.6.1, allows the user to
specify the file name containing the new crack front points.
Figure 6.6.1 Read new crack front - file import dialog.
The format for this file is simply: "x y z" ; one set of coordinates per line.
The second panel, Figure 6.6.2, displays the new front points within the model and allows the
user to specify the fitting, extrapolation and template parameters. The front fitting options and
flaw template panes are similar to what was described in Section 6.5.2.
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Figure 6.6.2 Read new crack front - display panel.
6.7 Grow/Merge Cracks Wizard
The Grow/Merge Cracks wizard is not activated yet. The current implementation allows co-
planar cracks whose advancing crack fronts intersect, Figure 6.7.1, to be merged to create a
single crack, Figure 6.7.2. The implementation requires manual selection of the front points that
will be merged. These front points are written to a text file that can be read using the new flaw
user-defined crack algorithm that was described in Section 6.1.8. This capability will be
enhanced before it is finally activated.
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Figure 6.7.1 Grow/Merge Cracks – two co-planar cracks whose advancing fronts intersect.
Figure 6.7.2 Grow/Merge Cracks – two co-planar cracks merged.
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6.8 SIFs Along a Path
The SIFs along a Path dialog, Figure 6.8.1, allows the user to display SIF history data. The crack
front lines are displayed in the left-side model window, and the SIF history and path options are
displayed on the right-side of the dialog.
Figure 6.8.1 SIFs along a path dialog.
6.8.1 Define Path Tab
Traditional fatigue lifing methodologies require a SIF history that consists of a single valued
stress intensity factor (K) and a single valued crack size (a) for each crack increment.
Developing such a "K-history" is straightforward for a 2-D analysis, but is considerably more
complicated for 3D analyses. In 3D, one has a distribution of K values along a crack front, and
there might not be an obvious crack dimension that uniquely characterizes the crack “length”.
Three different algorithms are available in the Define Path tab of the dialog, Figure 6.8.2. The
results for the three algorithms are illustrated below using three different crack growth
simulations. It should be noted that while the crack growth might appear nearly planar in these
three examples, the algorithms work for non-planar growth.
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Figure 6.8.2 Define path tab.
6.8.1.1 Constant Normalized Distance
The first algorithm uses a constant, user-specified, normalized distance along the crack fronts.
Figure 6.8.3 shows the computed paths for 50% normalized distance. The figure shows that this
approach works very well for the first crack and reasonably well for the third crack. For the
middle crack, however, the path is somewhat sinuous; this can be even more pronounced for
crack fronts that transition from corner- to through-cracks.
Figure 6.8.1.1 Computed K paths for a constant normalized distance of 50%.
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6.8.1.2 Nearest Point on Next Front
The second algorithm is a modification of the first approach. The analyst selects a point on the
initial crack front. The algorithm then searches for the nearest point on the next crack front and
makes this the next point in the history. The process is repeated for all remaining crack fronts.
The K's in the history are the interpolated values at the "nearest points", and the crack length is
the distance from the crack "origin" to the initial crack front point plus the (straight line)
distances between successive "nearest points".
This algorithm is illustrated in Figure 6.8.1.2. For all three cracks, the path was started at
locations of 10%, 20%, ... 90% along the initial crack front. The algorithm performs very well
for the first crack. For the middle crack, some of the paths converge into one path at 10% of the
distance along the crack front. This is because of the path constraints, which are described in
Section 6.8.1.2. For the third crack, most of the paths merge together due to these path
constraints.
Figure 6.8.1.2 Computed K paths using nearest next point. Paths are at 10% increments with a
10% and 90% minimum and maximum threshold.
6.8.1.3 Intersection of Fronts with a Plane
The third algorithm defines a plane nominally perpendicular to the crack surface and gives the
path as the points where the crack fronts intersect the plane. This algorithm is illustrated for the
first of the three cracks above in Figure 6.8.1.3.
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Figure 6.8.1.3 Computed plane intersection points for the slot crack.
6.8.1.4 Path Constraints
There is a user-settable threshold that prevents the computed paths from getting too close to the
free surfaces where the accuracy of the computed stress intensity factors is questionable. The
user can set both the minimum and maximum thresholds in the dialog.
6.8.1.5 Path Curve Fitting
A best fit, in a least-squares sense, through the path computed by one of the three algorithms.
Figure 6.8.1.5 shows the least-squares fit to the paths shown in Figure 6.8.1.1. A quadratic curve
was used for the first crack, and as expected, there is little improvement in the path for this case.
A cubic curve was used for middle crack, which yields a path that is aesthetically more pleasing.
A fifth order curve was used for the third crack and gives some improvement over the initial
computed path by smoothing the kinks.
Figure 6.8.1.5 Computed least-squares fits to the paths of Figure 10.1.3.
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6.8.1.6 Crack Starting Information
The crack starting information has two options: crack start point and initial crack length. Setting
either of these provides a starting point for computing the total crack path length.
6.8.2 Export Tab
The Export tab, Figure 6.8.3,n allows one to save the SIF data to a file. This includes an option
to save the DARWIN format .kva file.
Figure 6.8.3 SIF history dialog – Export tab.
6.9 SIFs For All Fronts
The SIFs for all Fronts dialog, Figure 6.9.1, allows the user to display SIF history data. The
crack front lines are displayed in the left-side model window, and the SIFs for all crack fronts are
displayed on the right-side of the dialog.
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Figure 6.9.1 SIFs along a path dialog.
The Export tab, Figure 6.9.2, allows one to save the SIF data to a file. This includes an option to
save the DARWIN format .kva file.
Figure 6.9.2 Export tab for SIFs along a path dialog.
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7. Wizards and Dialog Boxes for Loads Menu
The wizards and dialog boxes for the Loads menu options are described in this section.
7.1 Map Current State
The Map Current State option is intended to allow one to map initial conditions or current state
information, such as stress or strain, from the current model to the model after crack insertion or
growth. Mapping is done by interpolating data from the current mesh, based on element shape
functions, to points (nodes or gauss points) of the new mesh.
This menu item is currently disabled.
Mapping of temperature and other boundary condition data that must be transferred from one
model to the next occurs automatically.
7.2 Crack Face Pressure/Traction
The Crack Face Pressure/Traction option allows one to define crack face pressures or tractions.
This capability is often used to simulate residual stresses. It can also be used in a local/global
modeling approach where the local model containing the crack is analyzed using crack face
tractions based on the stresses from the uncracked global model.
The first panel of the wizard is shown in Figure 7.2.1. The user selects Add to create a new
entry in the list. Once an entry has been added, it can be edited or deleted by selecting the name
and then the Edit or Delete button.
The Crack Face Traction/Residual Stress Type panel is displayed next, Figure 7.2.2; it allows
one to choose the type of crack face loading. The choices are: 1) Constant crack face pressure,
2) 1-D Radial residual stress distribution, 3) 2-D Radial residual stress distribution, 4) Surface
treatment residual stress distribution, and 5) Residual stress defined on a mesh. These types will
be described in more detail below.
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Figure 7.2.1 Crack Face Tractions – top level dialog.
Figure 7.2.2 Crack Face Tractions – type dialog.
7.2.1 Constant Crack Face Pressure Panel
The constant crack face pressure panel allows one to specify a uniform pressure on the crack
face, Figure 7.2.3. A positive pressure value will tend to open the crack.
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Figure 7.2.3 Constant Crack Face Pressure panel.
7.2.2 1-D Radial Residual Stress Distribution Panel
The 1-D radial residual stress distribution panel allows one to specify a radial distribution of
stress that can be applied to the crack face, Figure 7.2.4. The stress varies along a radius from
some origin. The user can specify the distribution axis as well as the axis offset. The user can
select the Define Distribution button to interactively define the distribution, Figure 7.2.5.
Figure 7.2.4 1-D radial residual stress distribution panel.
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Figure 7.2.5 User defined 1-D radial residual stress distribution plot.
As an example, consider a corner crack in a brick, Figure 7.2.6 – left panel. The crack has a
radius of 2.0 and the corner is located at x=0, y=5, and z=5. A 1-D radial distribution is defined,
Figure 7.2.7 – right panel, with the distribution axis set to y and the axis offset defined as x=0
and z=5. The crack face traction distribution is shown in Figure 7.2.7 – left panel. To visualize
the pressure that is applied to the crack, the ANSYS color contours for the pressure values are
shown in Figure 7.2.7 – right panel. This image shows how the radial pattern of the pressures
with the origin at the crack corner.
Figure 7.2.6 A corner crack in a brick (left panel) with a 1-D radial residual stress (right panel).
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Figure 7.2.7 A 1-D radial residual stress distribution (left panel) applied to the corner crack and
shown as color contours in ANSYS (right panel).
7.2.3 2-D Radial Residual Stress Distribution Panel
The 2-D radial residual stress distribution panel allows one to specify a stress distribution that
varies in 2 directions (axial and radial) that can be applied to the crack face, Figure 7.2.8. The
stress varies with radius from some origin. The user can select the Define Distribution button to
interactively define the distribution, Figure 7.2.9.
Figure 8.2.8 2-D radial residual stress distribution panel.
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Figure 7.2.9 User defined 2-D radial residual stress distribution plot.
7.2.4 Surface Treatment Residual Stress Distribution Panel
The surface treatment residual stress distribution panel, Figure 7.2.10, allows one to specify a
stress distribution that varies in a direction that is normal to a surface that has been retained as a
“residual stress surface” when reading the finite element file. The stress varies with distance
from the surface. The user can select the Define Distribution button to interactively define the
distribution, Figure 7.2.11.
Figure 7.2.10 User defined surface treatment residual stress panel.
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Figure 7.2.11 User defined surface treatment residual stress panel.
As an example, a brick model is defined with the top surface (positive y-axis) defined as a
“treated_surface” node component, Figure 7.2.12 – left panel. When reading the model into
FRANC3D, this component is retained as a residual surface (see Section 4.1.10). The stress
distribution shown in Figure 7.2.10 is applied as the surface treatment crack face traction. The
distribution acts normal to the “treated_surface”, and distance will be measured in the -y
direction. The resulting crack face traction distribution on the crack shown in Figure 7.2.12 (left
panel) can be visualized using ANSYS, Figure 7.2.12 – right panel.
Figure 7.2.12 Example of a surface treatment residual stress crack face traction.
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There are a number of things that will be noted here. Consider the crack shown in the left panel
of Figure 78.2.13 and the residual stress distributions shown in the right panel of Figure 7.2.13.
First, if the nodes on the crack surface are at a depth that is greater than the residual stress, no
crack face tractions are computed. Using distribution ‘a’, the lower third of the crack will not
have crack face tractions. Second, if the mesh on the crack surface is coarse compared to the
residual stress distribution, the computed crack face traction will not adequately capture the
residual stress distribution. Based on the coarse mesh shown in the left panel of Figure 7.2.14,
the computed traction value at the node indicated by the red circle, using distribution ‘a’ from
Figure 7.2.13, would be close to zero. If a pseudo-refined mesh is defined, as in the middle and
right panels of Figure 7.2.14, then the ‘a’ distribution can be captured and appropriately
distributed onto the nodes of the actual coarse mesh. Ideally, one would use a suitably refined
mesh in the model to avoid this problem.
Figure 7.2.13 Surface treatment residual stress applied as crack face traction up to the defined
depth of the distribution.
Figure 7.2.14 Surface treatment residual stress applied as crack face traction with automatic
pseudo-mesh refinement to capture the distribution.
7.2.5 Mesh-Based Stress Distribution Panel
The mesh-based stress distribution panel allows one to specify a stress distribution based on a
finite element mesh and stress file, Figure 7.2.15. The user chooses the mesh and associated
stress file, normally an uncracked model. The program queries this data to compute tractions on
the crack face. The uncracked model element shape functions are used to interpolate the results
onto nodes of the remeshed cracked model.
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Figure 7.2.15 Mesh based stress distribution panel.
8. Wizards and Dialog Boxes for Analysis Menu
The wizards and dialog boxes for the Analysis menu options are described in this section.
8.1 Static Crack Analysis
This Static Crack Analysis menu item allows one to set up and run a static (single step, no crack
growth) deformation analysis. One would use this, for example, if one had inserted a crack into
a body and wanted to compute stress-intensity factors for this crack without performing any
crack growth. The ANSYS, ABAQUS and NASTRAN wizard panels are discussed below; most
of the wizard panels are the same for all of the analysis codes, but there are some differences as
will be noted below.
8.1.1 Fdb File Name Panel
The first panel, Figure 8.1.1, allows one to specify the name of the .fdb file, which stores the
mesh and flaw information for this model. This file name will be used for all the files created for
this static analysis, with different file extensions applied. The .fdb extension will be added if the
user does not type it into the File Name field.
Note that the uncracked file name must not be re-used here; the uncracked model is needed for
crack growth and should not be overwritten.
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Figure 8.1.1 Fdb file name dialog.
8.1.2 Analysis Code Panel
The user next must choose the analysis code, Figure 8.1.2. ANSYS, ABAQUS or NASTRAN
can be chosen, and subsequent panels will differ slightly.
Figure 8.1.2 Analysis code panel.
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8.1.3 ANSYS Options Panel
If the user chooses ANSYS in Figure 8.1.2, the next wizard panel, Figure 8.1.3, allows the user
to set options and analysis parameters for ANSYS.
The first pane contains the ANSYS executable file name and license string. These values should
be set in the Preferences (see Section 5.3.5) but can be modified or set here.
The third pane allows the user to select the global model to connect to the local cracked model.
If there is no global model, this option should be unchecked.
The fourth pane allows the user to specify extra boundary conditions. Input model boundary
conditions are transferred automatically. Crack face tractions, if defined (see Section 7.2) can be
applied. Crack face contact conditions can be applied also.
The final pane contains the button View/Edit Command, which will be described in Sections
8.1.5. The user also can choose to write the files only, without running ANSYS. This can be
used to verify the files before running, or if the files will be transferred to a different computer
before running.
Figure 8.1.3 ANSYS options and analysis parameters.
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8.1.4 ANSYS local/global model connection Panel
If the user checked Connect to global model in Figure 8.1.3, the global model file must be
selected, Figure 8.1.4. The Browse button can be used to find the file. The global model file
field should be filled automatically.
Figure 8.1.4 ANSYS connect to global model box.
If the user connects to a global model file, the Finish button in Figure 8.1.3, switches to a Next
button. The Local/global model connection panel, Figure 8.1.5, defines how the local and global
models will be combined. Note that the user cannot proceed to this panel if the Connect to
global box is checked and the Global model filename has not been entered.
Figure 8.1.5 ANSYS local/global model connection panel.
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The simplest method to connect a local crack model to a global model is through node-merging.
If the user retained surface mesh facets on the cut-surfaces for the local model, then these
surfaces can easily be glued together by merging nodes. Alternatively, constraint equations or
contact conditions can be defined between the cut-surfaces of the local and global models. The
ANSYS macro that FRANC3D generates will contain necessary commands to join the two .cdb
files together.
Extra local/global contact/constraint can be defined, lower box of Figure 9.5, for surfaces other
than the crack faces and cut-surfaces. The user chooses the master and slave surfaces from the
list of components. The material id, real properties id, and element type id can be set.
8.1.5 ANSYS Command Line Panel
If the user selects the View/Edit Command button in Figure 8.1.5, the ANSYS command is
displayed in a separate panel, Figure 8.1.6. The command line can be edited if desired.
Figure 8.1.6 ANSYS Command Line panel.
8.1.6 ABAQUS Options Panel
If the user chooses ABAQUS in Figure 8.1.2, the next wizard panel, Figure 8.1.7, allows the user
to set options and analysis parameters for ABAQUS.
The first pane contains the ABAQUS executable file name. This should be set in the Preferences
(see Section 5.4.6) but can be modified or set here. A Python script can be executed on the .inp
file prior to running ABAQUS.
The third pane allows the user to select the global model to connect to the local cracked model.
If there is no global model, this option should be unchecked as in Figure 9.8.
The fourth pane allows the user to specify the extra boundary conditions. Input model boundary
conditions transferred automatically. Crack face tractions, if defined (see Section 7.2) can be
applied. Crack face contact conditions can be applied also.
The final pane contains the button View/Edit Command, which will be described in Sections
8.1.8. The user also can choose to write the files only, without running ABAQUS. This can be
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used to verify the files before running, or if the files will be transferred to a different computer
before running.
Figure 8.1.7 ABAQUS options panel.
8.1.7 ABAQUS local/global model connection Panel
If the user checked Connect to global model in Figure 8.1.7, the global model file must be
selected, Figure 8.1.8. The Browse button can be used to find the file.
Figure 8.1.8 ABAQUS connect to global model box.
If the user connects to a global model file, the Finish button in Figure 8.1.7, switches to a Next
button. The Local/global model connection panel, Figure 8.1.9, defines how the local and global
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models will be combined. Note that the user cannot proceed to this panel if the Connect to
global box is checked and the Global model filename has not been entered.
Figure 8.1.9 ABAQUS local/global model connection panel.
The simplest method to connect a local crack model to a global model is through node-merging.
If the user retained surface mesh facets on the cut-surfaces for the local model, then these
surfaces can easily be glued together by merging nodes. Alternatively, constraint equations or
contact conditions can be defined between the cut-surfaces of the local and global models.
8.1.8 ABAQUS Command Line Panel
If the user selects the View/Edit Command button in Figure 8.1.9, the ABAQUS command is
displayed in a separate panel, Figure 8.1.10. The command line can be edited if desired.
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Figure 8.1.10 ABAQUS Command Line panel.
8.1.9 NASTRAN Options Panel
If the user chooses NASTRAN in Figure 8.1.2, the next wizard panel, Figure 8.1.11, allows the
user to set options and analysis parameters for ABAQUS.
The first pane contains the NASTRAN executable file name. This should be set in the
Preferences (see Section 5.3.7) but can be modified or set here.
The third pane allows the user to select the global model to connect to the local cracked model.
If there is no global model, this option should be unchecked as in Figure 9.13.
The fourth pane allows the user to specify extra boundary conditions. Input model boundary
conditions are transferred automatically. Crack face tractions, if defined (see Section 7.2) can be
applied. Crack face contact conditions can be applied also.
The final pane contains the button View/Edit Command, which will be described in Section
8.1.11. The user also can choose to write the files only, without running NASTRAN. This can
be used to verify the files before running, or if the files will be transferred to a different computer
before running.
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Figure 8.1.11 NASTRAN options panel.
8.1.10 NASTRAN local/global model connection Panel
If the user checked Connect to global model in Figure 8.1.11, the global model file must be
selected, Figure 8.1.12. The Browse button can be used to find the file.
Figure 8.1.12 NASTRAN connect to global model box.
If the user connects to a global model file, the Finish button in Figure 8.1.11, switches to a Next
button. The Local/global model connection panel, Figure 8.1.13, defines how the local and
global models will be combined. Note that the user cannot proceed to this panel if the Connect
to global box is checked and the Global model filename has not been entered.
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Figure 8.1.13 NASTRAN local/global model connection panel – with a .dat file.
The simplest method to connect a local crack model to a global model is through node-merging.
If the user retained surface mesh facets on the cut-surfaces for the local model, then these
surfaces can easily be glued together by merging nodes. Alternatively, constraint equations or
contact conditions can be defined between the cut-surfaces of the local and global models.
8.1.11 NASTRAN Command Line Panel
If the user selects the View/Edit Command button in Figure 8.1.13, the NASTRAN command is
displayed in a separate panel, Figure 8.1.14. The command line can be edited if desired.
Figure 8.1.14 NASTRAN Command Line panel.
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8.2 Crack Growth Analysis
This wizard allows one to set up and run a series of crack growth analyses. The first set of
wizard panels are the same as for the Grow Crack wizard described in Section 6.5 and Section
12. The SIF computation method along with the crack growth extension and kink angle models
must be defined.
The wizard panels that are displayed after defining the crack growth model are described next.
The analysis code panels are the same as those described in Section 8.1.
8.2.1 Crack Front Smoothing Panel
The crack front smoothing panel, Figure 8.2.1, provides crack front fitting and template options.
The options here are the same as the front fitting options described in Section 6.5.2, although
they are arranged differently. One should normally do one step of crack growth as described in
Section 6.5 before attempting automatic growth to determine the appropriate (best) fitting and
extension for the model.
Figure 8.2.1 Crack growth analysis wizard panel for fitting and template parameters.
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8.2.2 Crack Growth Increments Panel
The next panel, Figure 8.2.2, allows the user to specify the number of crack growth steps and the
median crack growth increment per step or the number of cycles per step depending on the
choice for extension type made in the previous panel. There are three possible choices for
entering the data per step: a constant value for all steps, a linear variation, and a user-defined set
of values. The user-defined set of values can be read from a .txt file; the data simply consists of
extension length or number of cycles for each step.
Figure 8.2.2 Crack growth analysis wizard panel for median crack growth increments.
8.2.3 Analysis Code Panel
The next panel, Figure 8.2.3, allows one to specify the analysis code: ANSYS, ABAQUS or
NASTRAN. The user should also enter the base file name. All crack growth steps will use this
as the base for the file name; a crack step number will be appended. Finally, the current crack
growth step number can be set; this number is used to create the file name (e.g.
base_name_STEP_002).
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Figure 8.2.3 Crack growth analysis wizard panel for analysis code and base file name.
8.2.4 ANSYS Analysis
If the user chose ANSYS in the previous panel, then the ANSYS analysis panels are displayed;
these are identical to those described for static crack analysis (see Sections 8.1.3 - 8.1.5).
8.2.5 ABAQUS Analysis
If the user chose ABAQUS in the previous panel, then the ABAQUS analysis panels are
displayed; these are identical to those described for static crack analysis (see Sections 8.1.6 -
8.1.8).
8.2.6 NASTRAN Analysis
If the user chose NASTRAN in the previous panel, then the NASTRAN analysis panels are
displayed; these are identical to those described for static crack analysis (see Sections 8.1.9 -
8.1.11).
9. Fatigue Menu Wizards and Dialog Boxes
The wizards and dialog boxes for the Fatigue menu option are described in this section. There is
only one menu item in V7.
9.1 Fatigue Life Predictions
The Fatigue Life wizard, Figure 9.1.1, allows the user to compute fatigue cycles. The dialog
shows the cracked model on the left. The right side will display plots of cycles, SIFs and other
data. The buttons and options in the middle pane are described here.
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Note that the Set Parameters button leads to the crack growth model selection described in
Section 12. The crack growth model that was used to grow the crack (see Section 6.5) can be re-
used here, or one can choose a different model to compute the life.
Figure 9.1.1 Crack growth analysis wizard panel for analysis code and base file name.
9.1.1 Read SIF Data
The Read Sif Data button allows one to read a .fcg file. The .fcg file is FRANC3D’s file format
for storing fatigue crack growth data, which includes all the SIF history data. The .fcg file can
be created using the Advanced menu option: Create Growth History, Section 11.6. The file
selector dialog, Figure 9.1.1.1, is displayed.
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Figure 9.1.1.1 File selector dialog for .fcg files.
9.1.2 Set Parameters
The Set Parameters button leads to the definition of the crack growth rate model, which is fully
described in Section 12.
9.1.3 Read Parameters
The Read Parameters button allows one to read a previously saved crack growth rate model from
a file. The file selector dialog, Figure 9.1.3.1, is displayed with the available .cgp files.
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Figure 9.1.3.1 File selector dialog for .cgp files.
9.1.4 Save Parameters
The Save Parameters button allows one to save the current crack growth model data to a file.
The file selector, Figure 9.1.4.1, is displayed; the user can enter a .cgp file name. This file can be
re-used as in Section 9.1.3.
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Figure 9.1.4.1 File selector dialog for .cgp files.
9.1.5 Plot Cycles
Plot Cycles has three options: Growth Step, Surface Length, and Path.
Growth step corresponds to the discrete steps of crack growth that the user defines for analysis.
The plot on the right shows computed cycles versus crack step #. The cycle count at each step is
the average cycle count computed for all mid-side nodes when growing the crack from one step
to the next.
The second option, Surface length, produces a plot of cycles versus surface-breaking crack
length. In Figure 9.1.5.1, the image on the left shows the red-line where the crack surface and
model surface intersect. The cycles are plotted versus this path length on the right side.
The third option, Path, allows the user to define a path. Pressing the Define button, invokes the
dialog shown in Figure 9.1.5.2. This dialog is the same as for the Path tab described in Section
6.8.1.
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Figure 9.1.5.1 Surface length versus cycles.
Figure 9.1.5.2 Define Path dialog for plotting fatigue cycles vs path.
9.1.6 Plot SIFs
The Plot SIFs option displays the SIFs on the right side, Figure 9.1.6.1. One can use the drop-
down selection boxes to choose the crack growth step and the crack front, if there are multiple
crack fronts. The effective K is plotted, see Section 12.3.7.
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Figure 9.1.6.1 Plot SIFs option.
9.1.7 Plot SIF Sequence
The Plot SIF Sequence option displays the SIF for a point on a crack front plotted against
pseudo-time, Figure 9.1.7.1.
Figure 9.1.7.1 Plot SIF sequence option.
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9.1.8 Data Table
The Data Table option displays whatever data is currently active in tabular form, Figure 9.1.8.1.
The dialog has an Export button that allows one to save this data to a file. Press the Export
button to invoke the file export dialog to save the data to a .txt file.
Figure 9.1.8.1 Data table dialog.
10. Fretting Menu Wizards and Dialog Boxes
The wizards and dialog boxes for the Fatigue menu option is described in this section.
10.1 Read Model and Results
FRANC3D is able to read ANSYS, ABAQUS and NASTRAN files for fretting analysis. The
finite element (FE) information is contained in .cdb, .inp and .bdf files, respectively, Figure
10.1.1. The FE information consists of nodes, elements and usually a definition of the contact
surfaces. Once the FE model is imported, analysis results must be imported. A typical fretting
test is conducted by applying a normal load (P) and then applying a maximum and minimum
tangential (shear) load (Qmax and Qmin). The dialog box shown in Figure 10.1.2 allows the user
to select one or more of these load cases. At minimum, the P+Qmax load is required. If the
P+Qmin load is not selected, FRANC3D assumes that the minimum stress state is at zero. The P
only loading is not required for most fretting nucleation models.
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Figure 10.1.1 Fretting dialog for importing FE model data.
Figure 10.1.2 Fretting dialog for importing FE results data.
Selecting the Browse button from the dialog in Figure 10.1.2 leads to the dialog shown in
Figure 10.1.3. The user can select the results files from ANSYS, ABAQUS or NASTRAN.
The ANSYS .str files are simply the nodal stress listings saved to a file. Corresponding
strain (.stn), displacement (.dsp) and contact status (.con) listings should also exist with the
same name prefix. ABAQUS results are read from .fil files. NASTRAN results are read
from .pch files. Note that strains are not required for some of the fretting nucleation models.
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Figure 10.1.3: Fretting dialog for locating results files.
Selecting the FINISH button from the dialog in Figure 10.1.3 leads to the Data Filter dialog
shown on the left side of Figure 10.1.4. The user can let FRANC3D select all material regions
and let FRANC3D automatically determine the contact surfaces from the FE model and results
data. Selecting Next on this dialog leads to the dialog on the right, which allows the user to
either go Back to change prior selections, Cancel the entire operation, or Finish. Selecting
Finish concludes the user interaction and FRANC3D then processes the user selections for the
FE model and results.
Figure 10.1.4 Fretting dialog for choosing all or selected material regions and auto or
selected contact surfaces.
If the user chose user select for both Materials and Contact surfaces on the dialog shown in left
panel of Figure 10.1.4, a sequence of dialog boxes is displayed to allow the user to select the
required data, Figure 10.1.5. The first dialog shown in the upper left panel of Figure 10.1.5
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displays the material identifiers and has a check box for coloring the regions. By default, if there
are multiple material regions, the regions will be given different colors when the model is
displayed in the FRANC3D window. If there is only one material region or if the user unchecks
the Color different materials box, then the model is displayed in the default model color (grey).
The next dialog shown in the upper right of Figure 10.1.5 displays the contact surfaces and
named sets or surfaces that are part of the FE model data. The user must first select the
surface(s) that is the contact (fretting pad) surface. The next dialog shown in the lower left of
Figure 11.1.5 allows the user to select the target (fretting specimen) surface and the final dialog
shown in the lower right of Figure 2.6 allows the user to specify the edge of contact nodes if
desired. Selecting Next on this dialog leads to the dialog on the right side of Figure 11.1.4,
which will conclude the user interaction for the Fretting Read Model and Results menu item.
FRANC3D might automatically switch the definition of the contact (or master) and target (or
slave) surfaces based on the analysis results, in particular the contact status and pressure.
Figure 10.1.5 Fretting dialog for selecting material regions and contact surfaces.
10.2 Import Nucleation Data
FRANC3D is able to import experimental fretting fatigue test data and perform curve fit
operations on this data. The first dialog box that is displayed after selecting the Import
Nucleation Data menu item is shown in Figure 10.2.1. The user should select the file
containing the raw experimental data. The format for this text file should be:
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sigma_axial cycles
---------------------------
675.3 2.23e4
655.7 2.63e4
533.8 4.45e4
Figure 10.2.1 Fretting dialog for importing experimental fretting nucleation data.
Selecting the Browse button in the dialog shown in Figure 11.2.1 leads to the file selection
dialog shown in Figure 11.2.2. The user can select the appropriate .txt file.
Once the data file is selected, the user selects Next to arrive at the dialog shown in Figure
10.2.3. The fretting data is shown in tabular form. Selecting the Plot/Edit button leads to
the dialog shown in Figure 10.2.4.
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Figure 10.2.2 Fretting dialog for selecting the fretting nucleation data file.
Figure 10.2.3 Fretting dialog shows fretting nucleation data in tabular form.
The dialog shown in Figure 10.2.4 displays the fretting nucleation data in tabular and graph
form. The user can edit the data in the table by selecting the Edit menu item and switching
from the default Read Only mode. The user can also perform curve fitting operations on the
data using the Fit menu. The usual fretting nucleation model uses a power law relationship
with four coefficients to relate the fretting nucleation cycles on the horizontal axis with the
fretting parameter on the vertical axis. This power law is highlighted in Figure 10.2.5, which
also shows the fit through the data. The goodness-of-fit is displayed on the top of the plot
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with the equation. The coefficients can be output along with the fitted data by selecting the
Save to File button on the dialog in Figure 10.2.3. This text file is formatted as:
y=a(x^b)+c(x^d)
parameters: a=364.771 b=-0.0532003 c=442836 d=-0.681027
fitted data:
22300 698.23168
63777 439.16081
105254 365.42131
146731 327.89836
Figure 10.2.4 Fretting dialog for plotting fretting nucleation data.
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Figure 10.2.5 Fretting dialog for plotting fretting nucleation data with power law curve fit
through the data.
10.3 Fretting Crack Nucleation
FRANC3D computes fretting fatigue crack nucleation cycles and initial crack location (and
possibly orientation) based on one or more of the fretting nucleation models that have been
implemented. These include: the equivalent stres, the critical plane shear stress amplitude, the
critical plane Smith-Watson-Topper, a crack-analog, and the Ruiz-Chen model. The model
equations and parameters are briefly summarized here. For more details, refer to: Three-
dimensional Simulation of Fretting Crack Nucleation and Growth, B.J. Carter, E.C. Schenck,
P.A. Wawrzynek, A.R. Ingraffea, and K.W. Barlow, EFM, 96 (2012), p.447-460.
The equivalent stress model is defined by:
eq = 0.5 (psu)w (max)
1-w (1)
where psu and max are functions of the nodal stress components and w is a material dependent
fitting parameter. Based on curve fitting of experimental data, the equation, in the form of the
power law shown in Figure 2.11:
eq = aNib + cNi
d (2)
relates eq to Ni, where coefficients a – d are material dependent fitting parameters. For
example, for Ti-6Al-4V, a = 52476, b = -0.6471, c = 450.85 and d = -0.03582.
126
The critical plane shear stress amplitude model is defined by:
crit =max/G (1-R)m (3)
wheremax is the maximum shear stress on the critical plane, Ris the shear stress ratio, G is the
shear modulus and m is a material dependent fitting parameter. Substituting crit for eq in
equation (3), one can compute Ni given the appropriate values for the coefficients a – d. For Ti-
6Al-4V, a = 6.46, b = -0.686, c = 4.65x10-3 and d = 1.22x10-2.
The critical plane Smith-Watson-Topper model is defined by:
crit = max (f2 / E) (2Ni)
2b + f2Ni)
b+c (4)
where max is the maximum principal stress and represents the normal strain amplitude on the
critical plane; this equation is already in the form of equation (3). E is the elastic modulus, f
and f are material strength parameters, and b and c are fitting parameters. For Ti-6Al-4V, f =
376.6 MPa, b = 1.78x10-4, c = -0.767 and f = 32.4.
The crack analog model is quite different from the above three models. First, the fretting
parameter (Q) is only computed at the nodes along the EOC. Second, the FE analysis must be
conducted with bonded contact conditions rather than the standard contact (that allows for slip
and requires a coefficient of friction). Q can be related to JII from linear elastic fracture
mechanics:
Q = (JII E/(1-))
1/2 (6)
where is Poisson’s ratio. Ni is computed from:
log Ni = ( – Q ) / (7)
where and are material dependent fitting parameters. Q = Qmax - Qmin, is determined from
the maximum and minimum load cycles.
The last model is the Ruiz-Chen model. The fretting parameter, F2, is equal to the product of the
shear stress (), relative slip (), and bulk normal stress ():
F2 = (8)
The number of cycles is computed by replacing eq in equation (2) with F2. The parameters a, b,
c and d will be material dependent.
The first dialog box that is displayed after selecting the Fretting Crack Nucleation menu item is
shown in Figure 11.3.1. The user can select one of the four fretting nucleation models.
Selecting Next leads to the dialog shown in Figure 10.3.2, which lets the user define the
127
Equivalent Stress fretting model parameters. Note that the user can select the fitting coefficients
from the previous section based on a curve fit through the experimental data. If these
coefficients are not available, this option for curve fit values is disabled. The other three models
have similar dialog boxes as shown in Figures 10.3.2 - 10.3.5.
Figure 10.3.1 FRANC3D Fretting dialog to select fretting nucleation model.
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Figure 10.3.2 Fretting dialog to set equivalent stress fretting model parameters.
Figure 10.3.3 Fretting dialog to set critical shear stress model parameters.
129
Figure 10.3.4 Fretting dialog to set Smith-Watson-Topper model parameters.
Figure 10.3.5 Fretting dialog to set RAI Q model parameters.
130
The dialog boxes shown in Figures 10.3.2 - 10.3.4 have a check box for Volume Averaging.
Rather than computing the fretting parameters based on node-point stress (and strain) values, the
user can choose to do volume averaging. If this box is checked, the next dialog box that will be
displayed is shown in Figure 10.3.6. The user can adjust the size of the displayed sphere by
changing the Average over length value. Note that stress values are not averaged across material
region boundaries. Typical length values used in the literature are based on the material grain
size.
Figure 10.3.6 Fretting dialog for volume averaging of stress (and strain).
Selecting Next on the dialog shown in Figure 10.3.6 leads to the dialog shown in Figure 10.3.7.
This dialog shows the model and allows the user to view the contact surfaces, the edge of
contact, the fretting nucleation cycles and the fretting parameter values. The latter two items can
be displayed as text or using color contours.
131
Figure 10.3.7 Fretting dialog for displaying fretting nucleation cycles and parameter values
and contours.
Selecting the Save to File button on the dialog shown in Figure 10.3.7 leads to the file save
dialog shown in Figure 10.3.8. The fretting nucleation data is saved to a text file with the
following format:
master surface
node x y z parameter cycles
19222 0.49648972 0.91291108 0.15 25 19283
20917 0.52414545 0.94056681 0.12 29 18453
20881 0.51283174 0.92925310 0.12 24 19898
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Figure 10.3.8 Fretting dialog for selecting file to save fretting nucleation predictions.
The user can go Back and choose a different fretting nucleation model to compare predictions.
Selecting Finish on the dialog shown in Figure 2.18 closes the dialog.
10.4 Turn Off Region Color
FRANC3D will display material regions with different colors. The Turn Off Region Color
menu item allows the user to select the material regions to be colored using the dialog shown in
Figure 11.5.1. The regions that are checked are drawn in solid colors while the unchecked
regions are drawn as wireframes. Selecting Accept will draw colored regions while selecting
Cancel will convert all regions to the default (grey) model color. This option is purely for
display purposes so that interior regions can be viewed in complex multi-region models.
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Figure 11.5.1 Fretting dialog for turning off/on colored regions.
11. Advanced Menu Wizards and Dialog Boxes
The wizards and dialog boxes for the Advanced menu options are described in this section.
11.1 Edges Wizard
The Edge Extraction dialog, Figure 11.1.1, allows the user to control the geometry that is
extracted from the finite element facets. The angle threshold can be adjusted to increase or
decrease the number of surfaces by blending facets together.
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Figure 11.1.1 Edge extraction dialog.
For cylindrical surfaces such as a hole in a plate, the user should add edges to break the surface
into at least two surfaces. By selecting the Add button for Edge Lines in Figure 11.1.1, the
dialog in Figure 11.1.2 is displayed to allow the user to define edges.
Figure 11.1.2 Add edge dialog.
11.2 No Crack Regions
The no crack regions dialog box, Figure 11.2.1, allows the user to insert a crack into a single
region in a multi-region model. Each of the regions can be displayed using the Displayed
Region selection; the selected region is colored while the other regions are shown as wireframes.
The user selects the region that will not be cracked by checking the appropriate region id in the
No Crack Regions pane.
135
When a crack is inserted that crosses the material boundary, Figure 11.2.2, the crack geometry is
trimmed so that the final meshed crack model does not have any crack surface in the selected
region, Figure 11.2.3.
Figure 11.2.1 No crack regions dialog.
Figure 11.2.2 Inserting a crack into a two-region model where the second region is designated as
a no-crack region.
136
Figure 11.2.3 Crack inserted into one region of a two-region model.
11.3 Write COD Data
The Write COD Data menu item allows the user to save crack displacement data to a file. The
first dialog that is displayed, Figure 11.3.1, prompts the user to enter a distance back from the
crack front where crack displacements will be computed. The default is to compute the values at
the entered distance from crack front nodes. If the user turns this option off, values are
computed at geometric points along the crack front.
Figure 11.4.1 Write crack front data - Save File As dialog.
Select Accept on the dialog in Figure 11.3.1, and the dialog shown in Figure 11.3.2 is displayed.
This dialog allows the user to choose which data will be written to the file. The file is saved by
selecting the Create File button, which invokes the usual Save As File dialog. The file is an
ASCII text file.
137
Figure 11.3.2 Write COD data – create file dialog.
11.4 Write Template Data
The Save File As dialog, Figure 11.4.1, is presented so that template data can be saved to a file.
The data is saved to an ASCII text file with .std extension.
Figure 11.4.1 Write template data - Save File As dialog.
The file format for this file is briefly described here.
STD_TEMPLATE_DATA
138
{ VERSION: 1 NUM_FRONTS: 1 CRACK_FRONT: 0 49 25 OPEN CORNER_SET: 0 # corner node ids of template element ring 11978 12907 11421 12440 11888 6756 7686 7222 8147 5762 6227 10350 10816 973 1436 4673 5142 8373 8835 …. SIDE_SET: 0 # side node ids 6938 3386 6470 14975 6003 2013 616 1081 3384 2479 2916 6383 2450 7784 6385 6854 9277 8246 8815 4877 8353 3061 1198 1662 7643 3527 7180 13551 6713 14015 14362 6338 13898 4288 ….. NODE_COORDS: 1781 # list of all node ids and coordinates 7321 -0.52397588 -0.01178516 9.9308077 11252 -0.47625961 1.0479856e-014 9.7249057 …. NODE_DISP: 1781 # list of all node ids and displacements 7321 2.34113830186791e-005 0.000939063262674639 -0.000290174323814175 11252 2.24602369565477e-005 0.000940419013229567 -0.0002799458448084 …. }
11.5 View Response
The View Response menu item allows one to view the deformed shape of the current model.
Analysis results are required to activate this menu item. The dialog shown in Figure 11.5.1 is
displayed. The Display Mesh Overlay can be turned off to remove the surface mesh facets from
the model view. The deformed shape can be displayed by turning the Display on Deformed
Geometry option and entering a non-zero magnification factor, Figure 11.5.2.
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Figure 11.5.1 View Response dialog showing undeformed mesh.
Figure 11.5.2 View Response dialog showing the deformed shaded solid and the original
wireframe outline.
11.6 Create Growth History
The Create Growth History dialog, Figure 11.6.1, allows a user to create and edit the SIF
history data. A list of the crack growth steps is provided, and then for each step the crack front
data for each crack front is given. The dialog has three menu items: File, Edit and Plot. The
140
File menu has four options, Figure 11.6.2. The Open History menu item invokes the usual File
Open dialog with the .fcg file filter. The Add Step menu item invokes the usual File Open
dialog with the .sif file filter. The Add List menu item invokes the usual File Open dialog with
the .txt file filter; the .txt file should contain a list of .sif files. The last menu item, Save History
invokes the usual File Save As dialog for saving the data to a new .fcg file.
Figure 11.6.1 Create Growth History dialog.
Figure 11.6.2 File menu for Create Growth History dialog.
The Edit menu option has one item: Set Start Condition, which invokes the dialog shown in
Figure 11.6.3. This dialog allows the user to set the start condition for the SIF history be either
setting a location or providing an initial length. This initial length should be the initial crack
length, but this length is somewhat ill-defined for a general 3D crack.
141
Figure 11.6.3 Crack Start Condition dialog from Growth History dialog.
The Plot menu option has one item: Plot Crack Fronts, which invokes the dialog shown in
Figure 11.6.4. This dialog allows the user to view the crack front boundaries for all of the crack
fronts for all of the crack growth steps.
Figure 11.6.4 Plot crack fronts dialog from Growth History dialog.
11.7 Crack Growth Sequence
The Crack Growth Sequence menu item invokes the dialog boxes shown in Figure 11.7.1 and
11.7.2. The first dialog shows the model using the camera position for the current model in
FRANC3D. The second dialog allows the user to cycle through the crack steps using the Next,
142
Prev, First, and Last buttons. The user can snap images from this window to create a crack
growth sequence or animation or movie clip of the crack advance. Select Close when done.
Figure 11.7.1 Crack Growth Sequence dialog showing the ‘first’ crack step.
Figure 11.7.2 Crack growth sequence dialog lets the user cycle through the crack steps shown in
Figure 11.7.1.
11.8 Export Crack Data
The Export Crack Data menu item invokes the Compute SIFs dialog first if the SIFs have not
been computed (see Section 6.4). The export Crack Data File dialog shown in Figure 11.8.1 is
then displayed. The user should enter the .fcg file name to be saved.
143
Figure 11.8.1 Crack growth sequence dialog lets the user cycle through the crack steps
12. FRANC3D Crack Growth Models
Fatigue Crack Growth Rate Models (FCGRM) are used within FRANC3D to determine relative
amounts of extension for crack front points during crack growth (if fatigue growth is specified)
and to estimate the number of load cycles required to grow from one crack step to the next. The
library of models available within FRANC3D is based on the library in the DARWIN® program.
The dialog boxes and options described in this Section are the same for both crack growth
(Section 6.5) and for fatigue life computations (Section 9.1).
The first panel of the crack growth wizard presents options for the crack extension model and for
the kink angle model, Figure 12.0.1. Depending on the chosen models, different wizard panels
are displayed next.
144
Figure 12.0.1. Growth parameters panel.
12.1 Crack Extension Model
There are four crack extension models to choose from: 1) Fatigue, Constant Amplitude, 2)
Fatigue, Variable Amplitude, 3) Quasi-Static, and 4) User Defined Model. The last option is not
active in V7.0. A brief summary of the extension models and options is given here, along with
references to the appropriate sections below where each model is described more fully.
12.1.1 Fatigue, Constant Amplitude
There are two options for Fatigue, Constant Amplitude: 1) Given Stress Ratio (R), and 2)
Computed Stress Ratio (R). For the first case, crack growth computations are all done with a
user-supplied constant R value. For the second, the R value is computed from the FE analysis
results; R might vary along the front and from step to step.
Selecting this option first leads to the Growth Parameters dialog, described in Section 12.3. A
crack growth rate model must be defined, see Section 12.5; this is followed by dialogs for setting
the R value and selecting load cases, described in Section 12.6.
145
12.1.2 Fatigue, Variable Amplitude
There are three options for Fatigue, Variable Amplitude: 1) Sequenced Loads, and 2) Spectrum
Loads, and 3) Transient Loads.
Selecting this option first leads to the Growth Parameters dialog, described in Section 12.3. A
crack growth rate model must be defined, see Section 12.5; this is followed by dialogs for
selecting the spectrum and/or load cases, described in Section 12.7.
12.1.3 Quasi-Static
There are two options for Quasi-Static growth: 1) Power Law and 2) Maximum Fracture Energy.
Selecting this option leads to the quasi-static Growth Parameters dialog, described in Section
12.4.
12.2 Kink Angle Model
The local direction of crack propagation is determined by the "kink" angle, which is defined as
the amount that the crack will deviate from the self-similar direction measured in a plane
perpendicular to the crack front. The kink angle is the angle illustrated in Figure 12.2.1.
Figure 12.2.1 Schematic illustration of the definition of the kink angle.
FRANC3D provides six options for determining the kink angle: 1) Maximum Tensile Stress
(MTS), 2) Maximum Shear Stress (MSS), 3) maximum Generalized Stress, 4) maximum Strain
Energy Release Rate, 5) Planar, and 6) User Defined Model. The last option is not active in
V7.0. The kink angle models are described in more detail next.
12.2.1 Maximum Tensile Stress
The MTS theory predicts that a crack will propagate in the direction where the "hoop" stress,
, is maximum. For materials with isotropic stiffness properties, the hoop stress is related to
the resolved Mode I stress intensity factor,
K Ir , by the relation:
146
KIr() 2r cos
2KI cos
2
23
2KII sin
(12.2.1)
The expression for materials with anisotropic stiffness properties is considerably more complex
(see for example Banks-Sills, Wawrzynek, Carter, Ingraffea, and Hershkovitz, Methods for
computing stress intensity factors in anisotropic geometries: Part II – arbitrary geometry, EFM
74 (2007), p. 1293-1307). It can be expressed symbolically as:
KIr() 2r f I KI ,KII ,KIII ,, (12.2.2)
where
characterizes the angle cosines between the material property axes and the local crack-
front coordinate system.
If an isotropic material toughness is specified (default behavior), a numerical algorithm is used to
find the angle that maximizes
K Ir (and
) in equation 12.2.1 or 12.2.2. If anisotropic
toughness properties are specified, the kink angle is defined as the angle that maximizes the ratio
KIr() Kp(), where
Kp () is a measure of the materials directionally dependent resistance to
crack growth (see Section 12.9)
12.2.2 Maximum Shear Stress
Some materials exhibit crack growth in the direction of high shear stress, especially for
conditions of high shear loading at the crack front. The MSS theory predicts that a crack will
propagate in the direction where the resolved shear stress,
s r2 z
2 , is maximum. For
materials with isotropic stiffness properties, the components of the shear stress are related to the
resolved Mode II and III stress intensity factors by the relations:
KIIr () r 2r
1
2cos
2KI sin KII (3cos 1)
KIIIr () z 2r KIII cos
2
(12.2.3)
Symbolic expression for materials with anisotropic stiffness properties are:
KIIr () r 2r f II KI ,KII ,KIII ,,
KIIIr () z 2r f III KI ,KII ,KIII ,,
(12.2.4)
where
characterizes the angle cosines between the material property axes and the local crack-
front coordinate system.
If an isotropic material toughness is specified (default behavior), a numerical algorithm is used to
find the angle that maximizes the expression:
147
Ksr() IIKII
r () 2
IIIKIIIr ()
2
(12.2.5)
where
II and
III are user supplied parameters that can be used to tailor predicted shear crack
growth direction to match assumed or predicted behavior. Note that MSS driven crack growth is
not currently fully understood and there is no general agreement on how to select the beta
factors.
If anisotropic toughness properties are specified, the kink angle is defined as the angle that
maximizes the ratio
Ksr() Kp().
The mixed mode beta factors,
II and
III are used to tune the maximum shear stress and
maximum strain energy density kink angle criteria for specific assumed or observed crack
growth behavior. The values are also used if the mixed-mode option is selected for defining an
equivalent stress intensity factors.
12.2.3 Maximum Generalized Stress
The generalized stress criterion predicts that the crack will grow in the direction that corresponds
with the greater resolved stress intensity factor (
K Ir or
Ksr ) from the MTS or MSS criteria. The
beta factors can be set to tune the point of transition from tensile to shear fracture, which will
vary for different materials.
As a practical matter, if one portion of a crack front is determined to be in tensile fracture while
another part is in shear fracture, there will likely be an abrupt discontinuity in the predicted kink
angles. Such a crack will probably not grow or mesh successfully and if it does the crack
geometry probably will not be realistic. In such a case, the user should select either the MTS or
MSS criteria explicitly.
12.2.4 Maximum Strain Energy Release Rate
The maximum strain energy release rate criterion predicts that the crack will grow in the
direction that maximizes the rate of change of potential energy in the system due to crack
growth. For materials with isotropic toughness, this angle is determined by numerically
maximizing the expression:
G() KIr()
2
IIKIIr ()
2
IIIKIIIr ()
2
(12.2.6)
For materials with anisotropic toughness, the expression:
G() KIr()
K p ()
2
IIKII
r ()
K p ()
2
IIIKIII
r ()
K p ()
2
(12.2.7)
148
is maximized. The beta factors can be used to tune the behavior for assumed or observed
material behavior.
12.2.5 Planar
The planar crack growth option forces the crack to grow with a zero kink angle (self-similar
growth). It is recommended that this option be selected if the crack is expected to grow in a
plane. This will avoid small undulations that might develop in the predicted crack surface due to
numerical "noise" that can arise when computing the kink angles using one of the other criteria.
12.3 Fatigue Crack Growth Model Parameters
The fatigue crack Growth Parameters dialog is shown in Figure 12.3.1. This dialog is used for
both the Constant and Variable Amplitude options, see Section 12.1.1 and 12.1.2. There are 8
panes in this dialog, which are described below.
Figure 12.3.1. Growth parameters panel.
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12.3.1 Crack Extension Type
Either specified median crack front extension or specified number of applied cycles can be
chosen. For specified median extension, the crack extension at crack front point i is computed
from the expression
ai amedian
da
dN i
(K i,Ri,...)
da
dN median
(Kmedian,Rmedian,...)
(12.3.1)
where
amedian is the crack extension specified for the point with the median stress intensity
factor range (Figure 12.3.2),
da dNi is the crack growth rate computed at point i using the
specified growth rate model, and
da dNmedian
is the crack growth rate computed at the crack front
point with the median stress intensity value. The crack growth rates at crack front points will be
functions of the corresponding
K , R, and other model dependent parameters.
point with the
median K value
current
crack front
predicted new
crack front
am specified
extension
ai computed
extension
point i
Figure 12.3.2. Specified median extension.
Note that the selection of the reference
K value to use in equation 12.3.1 is somewhat arbitrary.
The maximum, minimum, and average
K are reasonable values to consider. The median value
is used in FRANC3D because experience shows that the maximum and minimum values
frequently occur where a crack front meets a free surface where the accuracy of the computed
stress intensity factors are known to be least accurate. In some cases, the inaccuracy of these
maximum and minimum values can lead to a very unintuitive relationship between the reference
specified amount of crack extension and the actual predicted crack front. In extreme cases,
inaccurate maximum and minimum values can have a significant impact on the average value
leading to an unintuitive behavior for this measure also.
The expression for crack extension at crack front point i using the specified cycles option is
150
ai N da
dN i
(Ki,Ri,...) (12.3.2)
where N is the specified number of cycles and
da dNi is the crack growth rate computed at point
i using the specified growth rate model.
The Specified number of applied cycles approach seems more intuitive than the Specified
median crack front extension approach for many analysts. However, the fatigue crack growth
models are highly nonlinear functions so trial-and-error might be required when using the
specified cycles approach to find a number of cycles that will not give exceedingly large or
exceedingly small predicted crack extensions. Exceedingly large values might give inaccurate
results, while exceedingly small crack extensions might require many crack growth steps or, in
some cases, might cause meshing problems.
WARNING, if the Specified number of applied cycles is used to grow the crack, it is strongly
suggested that one does not use the sum of the specified cycles for a series of crack growth steps
as an accurate prediction of the fatigue life. Crack extensions computed using this approach are
made assuming that the stress intensity factor range will remain constant over the step. In the
vast majority of crack growth analyses the stress intensity factors increase over each step. This
means that the sum of the cycles specified for all the steps will be a lower bound
(unconservative) estimate of the fatigue life. It is suggested that the FRANC3D Fatigue Life
wizard (Section 9) or an external fatigue life prediction program be used to calculate life (e.g.,
NASGRO or AFGROW). These programs allow for a variation of the stress intensity factor over
a crack growth step.
12.3.2 FEM Model Units
There are four options for FEM Model Units: two US customary units (stresses in psi, lengths in
inches, and stresses in ksi, lengths in inches) and two metric units (stresses in MPa, lengths in m,
and stresses in MPa, lengths in mm). This tells the program how to interpret the dimensions and
boundary conditions in the FEM model. It is not a units conversion feature. The unit
information is used primarily for labeling plots. They are also used to select the appropriate
parameter values if the NASGRO v3.0 crack growth rate model is specified and the material is
selected from the built-in material database.
If you use different units from these options, you will have to create your own plot labels.
12.3.3 Crack Growth Rate Model
This pane has buttons for defining a new or reading a saved model from a file. The New Model
dialog boxes are described in Section 12.5.
12.3.4 Temperature
The options for temperature include: 1) room temperature, 2) from FEM data, and 3) constant.
Selecting room temperature applies a default constant room temperature to all crack growth
151
computations. The FE material property data is assumed to be constant with respect to this
temperature also. From FEM data uses the temperature dependent material data and nodal
temperature boundary condition (or result) data. The temperature at each node is determined
from the applied nodal temperature boundary conditions, and if the material properties are
temperature dependent, the values at the given nodal temperature are used. The constant option
allows the user to enter a constant temperature value. This temperature is then used throughout
the crack growth computations similar to the default room temperature option.
Temperature dependent crack growth rate data can be entered with a new model; the dialogs for
entering this data are described in Section 12.8.
12.3.5 Crack Growth Resistance
This option allows one to specify the nature of a material’s resistance to crack growth. The
default setting is that a material is isotropic in toughness. In this case, the direction of crack
growth will be predicted based on the near crack-tip stress fields only. If an anisotropic
resistance to crack growth is specified, then the kink angle will be the angle that maximizes the
expression
Kr () Kp() , where
K r is the appropriate resolved stress intensity factor and
K p is
the resistance to crack growth, described in Section 12.9.
12.3.6 Mixed-mode equivalent K
There are two options for defining the Kequiv
. The simplest is the default, which is to set Kequiv
equal to the Mode I SIF. The second option includes Modes II and III SIFs.
Within FRANC3D, crack growth rates are computed as:
da
dN f Keffective
equivalent,Reffectiveequivalent
, ... , (12.3.3)
where the equivalent values account for mixed mode behavior and the effective values account
for the possibility that the crack might be closed for a portion of the cycle.
FRANC3D computes separate stress intensity factors for all three modes of fracture (
KI ,
KII ,
and
KIII ). However, conventional crack growth rate models consider only one stress intensity
factor range. By default, FRANC3D uses the Mode I stress intensity factors when computing the
maximum and minimum effective stress intensity factors:
Kmaxequivalent KI ,max
Kminequivalent
KI ,min
. (12.3.4)
FRANC3D also provides the option to use an equivalent stress intensity factors that is a function
of all three modes of fracture:
152
2
min,
2
min,
2
min,min
2
max,
2
max,
2
max,max
)(
)(
IIIIIIIIIII
equivalent
IIIIIIIIIII
equivalent
KKKK
KKKK
(12.3.5)
where II and III are user defined modal weighting parameters.
In both cases, the equivalent stress intensity factor range and R value are computed as:
Kequivalent Kmaxequivalent Kmin
equivalent
Requivalent Kminequivalent
Kmaxequivalent
. (12.3.6)
12.3.7 Effective Delta K
Effective values of the stress intensity factor range and R account for the situation where the
crack is actually closed during a portion of or all of a load cycle. The default behavior in
FRANC3D is to check for a closed crack for the complete cycle and to set the stress intensity
factor range and R to zero:
Keffectiveequivalent
0 Kmax
equivalent 0
Kequivalent Kmaxequivalent 0
(12.3.7)
and
Reffectiveequivalent
0 Kmax
equivalent 0
Requivalent Kmaxequivalent 0
. (12.3.8)
This default behavior allows for negative R values.
FRANC3D allows the option to truncate the stress intensity factor range to eliminate the negative
(closed) portion of the cycle. In this case, the expressions are:
Keffectiveequivalent
0 Kmaxequivalent 0
Kequivalent Kminequivalent
0
Kmaxequivalent Kmin
equivalent 0
(12.3.9)
Reffectiveequivalent
0 Kmaxequivalent 0
Requivalent Kminequivalent
0
0 Kminequivalent
0
(12.3.10)
153
Note that there are a number of mechanisms that have been identified as being able to keep the
crack closed even when the current "remote" loading is positive. The most significant is
plasticity-induced crack closure. This is one proposed explanation for the observed dependency
of crack growth rates on the R. The effective values computed here do not explicitly take this
into account (plasticity-induced closure is handled implicitly by some of the available crack
growth rate models), they only consider "global" closure where the currently applied "remote"
load is negative.
12.3.8 Integration Algorithm
The user can choose between Runge-Kutta (RK) and Cycle-by-cycle (CxC) integration to
compute life or cycles. A 2nd
order RK approach is implemented, Figure 12.3.3.
Figure 12.3.3. Second order Runge-Kutta integration.
12.4 Quasi-Static
The Quasi-Static growth option is much simpler than the Constant or Variable Fatigue options.
The dialog boxes for quasi-static growth are fully described here. There are two options for
Quasi-Static growth: 1) Power Law and 2) Maximum Fracture Energy.
12.4.1 Power Law
The Growth Parameters dialog for Power Law is shown in Figure 12.4.1.
154
Figure 12.4.1. Power Law growth parameters panel.
12.4.1.1 Power Law Growth Parameter
The crack extension for any crack front point i is computed as
ai amedianK i
Kmedian
n
(12.4.1)
where
amedian is the specified crack extension for the crack-front point with the median K value,
Kmedian is the median K value, and
K i is the stress intensity factor at crack front point i, and n is a
user supplied parameter that can be set on the panel.
There is no real theoretical basis for selecting an n value. In practice, values in the range of 2 to
3 seem to match observed crack shapes reasonably well.
12.4.1.2 Crack Growth Resistance
See Section 12.3.5.
155
12.4.1.3 Mixed Mode Equivalent K
See Section 12.3.6.
12.4.1.4 Load Cases Contributing to Total K
If there are multiple load cases, these will be listed, Figure 12.4.2. The user has the option of
settting the number of load cases that will be used as well as choosing which load case will be
used. If one double-clicks on the entry for FEM Load Step, a drop-down list of all load cases is
displayed, Figure 12.4.3. The load cases will be summed when computing crack growth. A load
multiplier as well as temperature multiplier and offset can be applied also.
Figure 12.4.2. Growth parameters panel.
Figure 12.4.3. Growth parameters panel.
12.4.2 Maximum Fracture Energy
The Growth Parameters dialog for Maximum Fracture Energy is shown in Figure 12.4.4.
156
Figure 12.4.4. Maximum Fracture Energy growth parameters panel.
12.4.2.1 Crack Growth Resistance
See Section 12.3.5.
12.4.2.2 Mixed Mode Equivalent K
See Section 12.3.6.
12.4.2.3 Load Cases Contributing to Total K
See Section 12.4.1.4.
12.5 New Fatigue Crack Growth Rate Model
Section 12.3 shows the Growth Parameters dialog that is displayed if a user chooses the Constant
or Variable Amplitude fatigue option, see Section 12.1.
When growing a crack based on fatigue, the pane shown in Figure 12.5.1 will be part of the
crack Growth Parameters dialog. The File and Label fields will be filled when the user defines
a new model or reads one from a file. If a model has not been defined and saved to a file
previously, one must define a New Model.
157
Figure 12.5.1. Crack Growth Rate definition.
Once the New Model button is selected, there are a number of growth models and corresponding
options to choose from in the dialogs described below. Once a model has been defined, it can be
Viewed/Edited and/or Saved to a File using the (currently inactive) buttons, in Figure 12.5.1
12.5.1 Model Label, Description and Units
The first panel of the new fatigue crack growth rate model wizard is shown in Figure 12.5.2.
This panel allows one to enter a single-line model label plus a more detailed description that can
span multiple lines. Both the label and the description are optional. The appropriate units for the
growth rate parameters should be selected. These units correspond to the growth rate model
parameters that will be input on subsequent panels. The units for these parameters can be
different than the units used in a finite element analysis where crack growth was simulated.
FRANC3D will perform any necessary unit conversions automatically. Select Next to choose the
model type.
Figure 12.5.2. New growth rate model – label, description and units.
158
12.5.2 Model Selection
The second panel of the growth rate model wizard is shown in Figure 12.5.3. There are two
groups of models: Paired and NASGRO. For the paired models, the base options are: Paris,
Bilinear Paris, Sigmoidal, Hyperbolic Sine, or Table Lookup. The applied stress ratio, R, model
is specified as either: None, Walker, Newman Closure, or Table Lookup. The NASGRO option
uses one of the equations used in version 3, or version 4 (and subsequent releases) of the
NASGRO program.
The stress ratio models account for the observed strong dependence of crack growth rates on R,
which is defined as:
maxmin SSR (12.5.1)
where maxS and minS are the maximum and minimum applied remote loads, respectively.
These models provide an effective stress intensity factor range, effK , as a function of the
applied K and R. There are two stress ratio equations built into FRANC3D: Walker and
Newman Closure. In addition, stress ratio effects can be ignored, or specified in a tabular
manner.
Once the model has been selected, press Next to specify whether the model is temperature
dependent or independent.
Figure 12.5.3. New growth rate model selection.
159
12.5.3 Model Temperature Dependence
The growth model can be made temperature dependent by specifying model parameters for
various temperatures and selecting a strategy for interpolating among these, Figure 12.5.4.
Temperature values can be added or subtracted from the table by changing the Number of
temperatures value.
A full description of the temperature dependent model data, dialogs and interpolation options is
given in Section 12.8.
Figure 12.5.4. New growth rate model temperature dependence selection.
12.5.4 Stress Ratio Models
The stress ratio models from Figure 12.5.3 are summarized here. Each of these options can be
paired with each of the growth models, described in the following Sections (12.5.5 – 12.5.9).
12.5.4.1 No Stress Ratio Model
This option turns off stress ratio effects. That is
Keff K (12.5.2)
160
12.5.4.2 Walker Equation
The expression for the Walker equation is
Keff (1 R)m1K
m m R 0
m R 0
(12.5.3)
The parameters m and m must be specified.
NOTE: the Walker equation is defined relative to R = 0. That is, the parameters used for the
paired growth rate model (e.g. Paris parameters) should be those appropriate for the case of R =
0.
12.5.4.3 Newman Closure
The expression for Newman Closure is
Keff (1 f )
(1 R)K (12.5.4)
where f is a function that accounts for the crack front being open for only a portion of the load
cycle due to plasticity induced crack front closure. It is defined as
f Kopen
Kmaxmax(R,A0 A1R A2R
2 A3R3) R 0
A0 A1R 2 R 0
(12.5.5)
where the coefficients are given by:
12
1
0071.0415.0
0)071.0415.0(
2cos)05.034.0825.0(
103
3102
0
max
1
1
0
max20
AAA
AAAA
R
RS
A
SA
(12.5.6)
The values of and
Smax 0 must be specified, where
is a plane stress/strain constraint
factor and
Smax 0 is the ratio of the maximum applied stress to the flow stress.
161
NOTE: the Newman Closure equation is defined relative to closureRR . That is, the parameters
used for the paired growth rate model (e.g. Paris parameters) should be those appropriate for the
case of closureRR , where closureR is the stress ratio where crack closure effects are no longer
significant. This value is typically about 0.7 for most materials.
12.5.4.4 Tabular Stress Ratio Mode
For a tabular stress ratio model, parameters for the associated growth rate model are specified for
various R values. For example, the specified values for a Paris model with tabular stress ratio
model would be
33
22
11
),,,(,
),,,(,
),,,(,
criticalthreshold
criticalthreshold
criticalthreshold
KKnCR
KKnCR
KKnCR
Linear interpolation is performed to find the crack growth rate for any R value between two
specified values iR and 1iR . That is
iiii
i
i dN
da
dN
da
RR
RR
dN
da
dN
da
11
(12.5.7)
If R is smaller than the smallest R specified, the growth rate corresponding to the smallest
specified R is used. Likewise, if R is greater than the greatest R specified, the growth rate
corresponding to the largest specified R is used.
12.5.5 Paris Model Parameters
The Paris growth rate model is a power law model expressed as
da dN C(Keff )n
(12.5.8)
The parameters
C and
n must be specified along with values for
Kthreshold and
Kcritical . If
Keff Kthreshold ,
da dN is set to zero. If
Keff (1R)Kcritical , unstable crack growth is
assumed and
da dN is infinite.
Figure 12.5.5 shows the Paris model. Note the red background colors and that the "Next" button
is not enabled; the “red” values that must be changed before the "Next" button is enabled. Note
that the internal checks for red values are only for values to avoid computational errors (e.g.,
162
divide by zero, logarithm of a negative number, etc.) it is NOT a check to see if the specified
values are reasonable for most engineering materials.
Figure 12.5.5. New Paris growth rate model, with no stress ratio effect.
Figure 12.5.5 indicates that no stress ratio effect was selected. If the user selects Walker,
Newman Closure or Table Lookup, the dialog reflects that as shown in Figures 12.5.6 – 12.5.9.
In each of these figures, note that the model is temperature independent; temperature dependent
models will be described in Section 12.8. The stress ratio is paired in the same way for all of the
“paired” growth models.
Figure 12.5.6. New Paris growth rate model, with Walker stress ratio effect.
163
Figure 12.5.7. New Paris growth rate model, with Newman Closure stress ratio effect.
For the Table Lookup option, the user must specify the number of R values that will be entered,
Figure 12.5.8, before entering the Paris parameters, Figure 12.5.9. The user must enter Paris
parameters and corresponding R values for the number specified in Figure 12.5.8.
Figure 12.5.8. New Paris growth rate model, with Table Lookup stress ratio effect and
temperature independent.
Figure 12.5.9. New Paris growth rate model, with Table Lookup stress ratio effect.
164
12.5.6 Bilinear Paris Model Parameters
The Bilinear Paris model is an extension of the Paris model; it has two linear portions when
plotted on a log/log graph. The equation is:
da
dNC1(Keff )
n1 Keff K*
C2(Keff )n2 Keff K
*
(12.5.9)
The parameters
C1,
C2 ,
n1, and
n2 must be specified along with values for
Kthreshold and
Kcritical . If
Keff Kthreshold ,
da dN is set to zero. If
Keff (1R)Kcritical , unstable
crack growth is assumed and
da dN is infinite.
Figure 12.5.10 shows the Bilinear Paris model, with no stress ratio effect. The stress ratio effect
can be paired with Bilinear Paris as it was for Paris.
Figure 12.5.10. New Bilinear Paris growth rate model, with no stress ratio effect.
12.5.7 Sigmoidal Model Parameters
The expression for the sigmoidal model is:
165
da
dN eB
Keff
Kthreshold
P
lnKeff
Kthreshold
Q
lnKcritical
Keff
D
(12.5.10)
The parameters B, P, Q, D,
Kthreshold , and
Kc must be specified.
Figure 12.5.11 shows the Sigmoidal model, with no stress ratio effect. The stress ratio effect can
be paired with Sigmoidal as it was for Paris.
Figure 12.5.11. New Sigmoidal growth rate model, with no stress ratio effect.
12.5.8 Hyperbolic Sine Model Parameters
The expression for the hyperbolic sine model is:
log(da dN)C1sinh(C2[log(K)C3])C4 (12.5.11)
The parameters
C1,
C2 ,
C3 ,
C4 ,
Kthreshold , and
Kc must be specified. If
Keff Kthreshold ,
da dN is set to zero. If
Keff (1R)Kcritical , unstable crack growth is assumed and
da dN is
infinite.
Figure 12.5.12 shows the Hyperbolic Sine model, with no stress ratio effect. The stress ratio
effect can be paired with Hyperbolic Sine as it was for Paris.
166
Figure 12.5.12. New Hyperbolic Sine growth rate model, with no stress ratio effect.
12.5.9 Table Lookup Values
For a table lookup model, a list of
Keff and corresponding
da dN values are specified. Linear
interpolation performed among logs of the specified values. The following equation is used to
interpolate between values i and i+1:
log(da dN) log(da dNi)log(Keff Ki )
log(Ki1 Ki )log
da dNi1
da dNi
(12.5.12)
In addition to the
(Keff ,da dN) values, a value must be specified for
Kcritical . The smallest
specified
Keff is assumed to be
Kthreshold . For
Keff greater than the largest value specified
and
Keff (1R)Kcritical , the slope of the curve between the two highest specified points is
extrapolated. This is unrealistic for many cases so it is best to provide
(Keff ,da dN) data that
extend past the critical values.
The User Table option allows one to read table of crack growth rates. The program will
interpolate within this equation to find a crack growth rate for a given K and R. The table data
must be read from a file. The Browse button allows one to select a file. The required format for
the file is described at the end of this subsection. The model label is a user supplied text string.
167
The View Table button brings up a dialog box showing the prescribed growth rate data in a
graphical and tabular form (Figure 12.5.13).
Figure 12.5.13 The User Growth Model display dialog box.
Given query values
Kquery and
Rquery, crack growth rates are extracted from the table using the
following algorithm:
1.
Rl and
Ru values are found that bracket the query value,
Rl Rquery Ru.
2.
Kll ,
Klu,
Kul , and
Kuu are found where
Kll Kquery Klu and
Kul Kquery Kuu, with
Kll and
Klu values associated with
Rl and
Kul and
Kuu
values associated with
Ru .
3. Linear interpolation in log/log space is used to find intermediate growth rate data,
logda
dN l
log
da
dN(K ll ,Rl )
log
da
dN(K lu,Rl )
da
dN(K ll ,Rl )
log Kquery K ll log K lu /K ll
and
168
logda
dN u
log
da
dN(Kul,Ru)
log
da
dN(Kuu,Ru)
da
dN(Kul,Ru)
log Kquery Kul log Kuu /Kul
4. Finally, normal linear interpolation is used to find the final growth rate
da
dNda
dN l
da
dN u
da
dN l
(Rqueary Rl )
(Ru Rl )
If during the interpolation process a query value (
Rquery or
Kquery) is found to be larger or
smaller than the largest or smallest corresponding value in the table, the query value is replaced
with the largest or smallest, respectively, available value.
Not that, as with all interpolation procedures, the accuracy of the results is dependent on the
density of the data available for interpolation. Very sparse tables can lead to inaccurate and in
some cases unrealistic crack growth predictions.
User Table File Format
The user table file format consists of a table of da/dN versus dK1 for given R values. The R-
ratio is used to label the columns of dK1 data. The rows represent the da/dN vs dK1 data. The
file is an ASCII text file.
dadN/R -1 -0.6 0 0.6 1.0000e-12 2.0469 2.1150 2.3531 2.6193 4.5249e-11 2.6618 2.6828 2.8066 2.8113 3.0422e-10 3.3872 3.3906 3.4624 3.2371 2.0454e-09 4.6844 4.7119 4.8342 4.4684 9.2459e-08 10.0399 10.4677 11.6805 12.6507 6.2164e-07 13.9172 14.6618 16.6286 17.2132 7.8884e-06 18.9059 19.8545 21.9998 20.0972 5.3036e-05 21.7701 22.6584 24.4075 20.8054 1.0000e-04 22.5218 23.3648 24.9475 20.9193
If a table lookup growth model option is specified, the corresponding panel is shown in Figure
12.5.14 (in this case for a temperature independent model). By default the number of data pairs
is set to zero. Setting this to a positive number will create slots in the table where K and
corresponding dNda values can be entered.
Another option is to read data values from a text file. The "Read From File" button will bring up
a standard file selection dialog box and then the panel shown in Figure 12.5.15. This panel
shows the columns of data in the file. The columns can be separated either by commas or "white
space" (spaces and/or tabs). For this example file, the program has determined that the first line
is not numeric data (typically column labels) and should be ignored.
169
Figure 12.5.14. New Table Lookup growth rate model, with no stress ratio effect.
Figure 12.5.15 The first file data page.
Selecting "Next" brings up the panel shown in Figure 12.5.16. For this panel the column
definitions are initially set to "Ignore". By selecting the pull-down menu above each column,
170
one can identify which column contains K data and which contains dNda data. The "Finish"
button will not be enabled until both types of data columns are identified. It is possible to read
files with addition data columns. In this case the pull-down menu above the unneeded columns
should be left at "Ignore".
Figure 12.5.16 The file data definition page.
If a table lookup option is selected for the stress ratio model, the procedure for entering data is
slightly different. In this case, parameters for a number of different R values must be entered for
each temperature. Figure 12.5.17 shows the panel that will allow one to specify the number of R
values that will be entered for a specific temperature.
171
Figure 12.5.17 A panel to specify the number of R values for a given temperature.
12.5.10 NASGRO Version 4 equation
NASGRO is a fatigue life prediction program initially developed at the NASA Johnson Space
Flight Center and now supported and maintained by Southwest Research Institute. Built into the
NASGRO program is an analytical crack growth rate equation that incorporates a number of
features observed in real materials such as sensitivity to near-threshold and near-critical growth,
sensitivity to the R-ratio, and some small crack sensitivity. The cost for the flexibility in the
growth model is that there are sixteen fitting parameters. Some are common material properties
(e.g., yield stress), but most must be determined by performing regression on empirical data.
The NASGRO package includes a database of pre-computed parameters for a wide range of
materials and product forms. However, as of NASGRO version 4, this database is only
accessible to members of the NASGRO consortium. As a practical matter, this means that this
model will be most useful to users who have access to the NASGRO program and can access the
parameters for a material of interest (see NASGRO version 3 below).
The NASGRO version 4 crack growth rate equation is:
da
dNC
1 f
1 R
n 1K thK
p
1Kmax
Kc
q (12.5.13)
172
where C, n, p and q are empirical constants. C and n are similar to the constants in the Paris and
Walker equations. However, while C in the Paris model should be selected to correspond to the
R of interest, and C in the Walker equation should be for R = 0, in the NASGRO equation the C
should correspond to a high R where closure effects are no longer significant (usually an R of
about 0.7)
f is the function associated with Newman closure.
Kth is the threshold stress intensity factor
range below which there is no crack growth. It is approximated by the following empirical
equations:
K th
K1* 1 R
1 f
(1RC thp)
(1 A0)(1R )C th
p
R 0
K1* 1 R
1 f
(1RC thm )
(1 A0)(C th
pRC th
m )R 0
(12.5.14)
where
K1* K1
a
a a0
1 2
(12.5.15)
and
Cth is an empirical constant,
K1 is the observed threshold for a high R-ratio, and
a0 is a
small crack parameter (usually 0.0015in, 0.0381 mm).
Kc is the fracture toughness. In FRANC3D, one has the choice to use the plane strain fracture
toughness,
KIc , the part-through toughness,
KIe , or compute it from:
Kc KIc (1Bke(Ak t t0 )
2
) (12.5.16)
where
t0 2.5 KIc ys 2
(12.5.17)
Ak and
Bk are empirical constants, and t, the "thickness", is specified by the user (in many 3D
applications the notion of thickness is not well defined and engineering judgment must be used
to set this value).
More details about this model can be found in the NASGRO theory manual.
Figure 12.5.18 shows the dialog for entering the NASGRO model parameters.
173
Figure 12.5.18. New NASGRO version 4 growth rate model.
12.5.11 NASGRO Version 3 equation
NASGRO version 3 is an earlier version of the NASGRO crack growth rate equation. The
current version of the equation (version 4) does a better job of modeling observed crack growth
rates for some conditions. This earlier version is included in FRANC3D because version 3 of
NASGRO, the last public domain version, included a database of equation parameters for a wide
variety of materials and product forms. That database is accessible from within FRANC3D.
The NASGROv3 crack growth rate equation is similar to version 4 equation. The base equation
is the same:
da
dNC
1 f
1 R
n 1K thK
p
1Kmax
Kc
q (12.5.18)
The difference has to do with how threshold values are computed. In version 3, the expression is
RC
th
th
RA
f
aa
aKK
1
000
)1)(1(
1 (12.5.19)
174
where a is the crack length and 0a has a fixed value of 0.0015 in (0.0381 mm).
Figure 12.5.19 shows the dialog for entering the NASGRO model parameters. The NASGRO
version 3 material database contains data for a wide variety of materials, and this data is included
in FRANC3D and accessible by selecting the From Database button. The dialog boxes shown
in Figure 12.5.20, allow the analyst to automatically fill in the required NASGRO v3 parameter
fields from this database.
Figure 12.5.19. New NASGRO version 3 growth rate model.
175
Figure 12.5.20. NASGRO version 3 material database dialog boxes
12.6 Constant Amplitude Load Case Selection
12.7 Variable Amplitude Load Case Selection
176
12.7.1 Sequence Load Option
Figure 12.7.1
12.7.2 Spectrum Load Option
177
Figure 12.7.2
The Load spectrum section allows one to specify a load spectrum (variable amplitude load
schedule) that is used when computing crack growth rates. A spectrum is defined as a series of
load ranges. Associated with each load range is an optional repeat count (the default value is
one). One can also specify a multiplier and offset that will be applied to all values in the
spectrum (e.g., to support the use of a normalized spectrum).
If only one load case is used in the analysis, and load range i has specified values
Smax,iraw
and
Smin,iraw
the expressions used for computing the stress intensity factor ranges and R ratio crack for range i
are
Smax,i sSmax,iraw t ,
Smin,i sSmin,iraw t (12.7.1)
Kmax,i Smax,i Kcomp ,
Kmin,i Smin,i Kcomp (12.7.2)
Ki Kmax,i Kmin,i and
Ri Kmin,i Kmax,i (12.7.3)
where s is the spectrum multiplier and t is the spectrum offset. The
Ki and
Ri are used to
compute the crack growth rate for stress range i. If multiple load cases are being used there are
additional options for setting these values.
178
For variable amplitude loading, the crack growth rates used for computing the relative amounts
of crack growth for crack front points (eqns. 6.5.1.4.1 and 6.5.1.4.2) are the average crack
growth rates computed for one pass through the spectrum. That is
da
dN
da
dN i
(K i,Ri,...)i1
n
n (12.7.4)
where
da dN is the crack growth rate computed for any given crack front point n is the number
of load ranges in the spectrum.
The corresponding predicted kink angle is weighted average kink angle computed as
kink
da
dN i
(K i,Ri,...) kink,i(KI ,i,KII ,i,KIII ,i,...)i1
n
da
dN i
(K i,Ri,...)i1
n
(12.7.5)
where
kink,i is the kink angle determined (implicitly) for range i using one of the criteria
described in section 12.2.
In the Variable amplitude panel, the Spectrum File field gives the path and file name for the
currently specified spectrum file (it is not editable). The Spectrum Label is a user specified text
string that can be used to identify the spectrum data. The Spectrum multiplier and Spectrum
offset are the s and t values, respectively, used in equation 12.7.1.
The Groups in spectrum and Group units values allow the user to set how plots and reports are
labeled. Analysts often find it convenient to group spectrum ranges into larger units that
represent meaningful engineering concepts (e.g. hours, flights, blocks, etc.). The Groups in
spectrum value specifies how many such groups are in the spectrum. The Group units value is a
label that identifies the group type. These values are primarily useful in the Fatigue Life wizard
(Section 10.2) where, for example a fatigue life plot might show the crack length as a function of
the number of flights, hours, blocks, or in user specified units. The default value for the Groups
in spectrum is one, and the default value of Group units is "passes". The spectrum groups
information is not used during crack growth predictions, but the information can be specified in
this wizard because, if set, the load spectrum data will be transferred to the Fatigue Life wizard
automatically.
The Read Load Spectrum button brings up the load spectrum input wizard. Load spectrum data
is assumed to be stored as columns of data in a text file. The columns can be separated either by
white space (spaces and tabs) or commas. The delimiters need to be used consistently
throughout the whole file.
The first panel in the wizard is a standard file selection dialog. The second panel is shown in
Figure 12.7.2.2.
179
Figure 12.7.3 The second load spectrum wizard panel.
The first option specifies if the data in the file represents sets of maximum and minimum values
from an already "counted" spectrum or if the data represents load points that will be cleaned and
counted by the program using a range-pair algorithm. If the file contains only one column of
data, only the latter option will be available.
The second option allows column delimiter to be specified.
The Data preview section displays how the file data will be segregated into columns based on the
specified delimiter type. It also gives the option to ignore the first line in the file so that the first
line can be used for identifying information or column labels.
If the Read a paired spectrum option is selected, the third panel is that shown in Figure 12.7.2.3.
180
Figure 12.7.4 The third load spectrum wizard panel for a paired file.
The pull-down boxes over each column are initially all set to "ignore". These can set to identify
the columns that specify the maximum, minimum, and, optionally, the repeat count associated
with each load range.
If the clean and pair option is selected and there is more than one column in the file then the third
panel is that shown in Figure 6.5.1.5.4. A pull-down box can be used to identify the column that
contains the load point data.
Figure 12.7.5 The third load spectrum wizard panel for a unpaired file.
181
The Plot Load Spectrum button brings up the Load Spectrum Display dialog. This is shown
in Figure 6.5.1.5.5. The Scaled Cycles tab shows the spectrum values after they have been
scaled and offset (eqn. 6.5.1.5.1). The tab shows the values as they appear in the spectrum file.
The magnifying glass icons allow one to view a smaller or greater segment of the spectrum and
the arrow icons allow one move forward and backward through the spectrum.
Figure 12.7.6 The load spectrum display dialog box.
12.7.3 Transient Load Option
182
Figure 12.7.7
Figure 12.7.8 Sequence of SIFs from multiple load cases used to predict cumulative crack
growth direction (from Spievak et al., EFM, 68, 2001).
12.8 Temperature Dependent Growth Rate
Temperature dependent growth rate models are implemented in a tabular manner. Growth model
parameters are specified for a number of different temperatures and interpolation is performed
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among the computed dNda values. For example, the specified data for a temperature
dependent paired Paris/Walker growth model would be
33
22
11
),,,,,(,
),,,,,(,
),,,,,(,
mmKKnCeTemperatur
mmKKnCeTemperatur
mmKKnCeTemperatur
criticalthreshold
criticalthreshold
criticalthreshold
Three different interpolation options are available: closest, next highest, and linear interpolation.
For closest interpolation, dNda is determined for the tabular temperature closest to the input
value. For next highest interpolation, dNda is determined for the next tabular temperature
higher than the input value. The expression for linear interpolation between two tabular values i
and i+1 is
iiii
i
i dN
da
dN
da
eTemperatureTemperatur
eTemperatureTemperatur
dN
da
dN
da
11
(12.8.1)
If the input temperature is smaller than the smallest temperature specified, the growth rate
corresponding to the smallest specified temperature is used. Likewise, if the input temperature is
greater than the greatest temperature specified, the growth rate corresponding to the largest
specified temperature is used.
If temperature data is not available in the data for the current FEM model, room temperature
(70˚F, 20˚C) is assumed.
The dialog box that allows one to view and edit a fatigue crack growth rate model is shown in
Figure 12.8.1
184
Figure 12.8.1 The growth model view/edit dialog box.
The main portion of the dialog contains a table showing the temperatures and growth model
parameters. The actual columns in the table will change with the various available growth
models. If only one set of parameters is specified, these will be used regardless of the
temperature.
The dialog for a tabular growth model is shown in Figure 12.8.2. Double clicking on the "da/dN
vs. DK" text in the table will bring up a popup window showing tabular values.
Figure 12.8.2 A dialog for a tabular growth model showing a popup with the
table values.
The dialog for a NASGRO model is shown in Figure 12.8.3. Double clicking on the "NASGRO
v4" text in the table will bring up a popup window showing NASGRO parameters.
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Figure 12.8.3 A dialog for a NASGRO model showing a popup with the
NASGRO parameter values.
The dialog for a bilinear Paris model with a tabular stress ratio model is shown in Figure 12.8.4.
Double clicking on the "da/dN vs. R" text will bring up a popup window, shown in Figure
12.8.5, which contains the parameter values for various R ratios.
Figure 12.8.4 A dialog for a bilinear Paris model with a tabular stress ratio model.
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Figure 12.8.5 A popup window corresponding to Figure 12.8.3 showing the bilinear Paris model
parameters for various R values.
The "Material property units" specifies the units in which the growth model parameters are
defined. These units do not need to be the same as the units used in the finite element modeling.
That is, for example, one can use Paris model parameters obtained from the literature specified in
units of ksi, inches and degrees F and use these with stress intensity factor values obtained from
an FEM model defined in terms of MPa, mm and degrees C. FRANC3D will automatically
perform the necessary unit conversions to obtain the proper crack growth rates (mm/cycle in this
instance).
The PLOT button pops up a window showing a plot of the defined growth rate model. An
example is shown in Figure 12.8.6.
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Figure 12.8.6 The growth model popup plot dialog.
The left portion of the dialog shows the various plotting options. These include plotting curves
for a fixed R and temperature, for multiple R's at a fixed temperature, or for multiple
temperatures at a fixed R. The plots can be generated for any of the Plot units.
12.9 Orthotropic Toughness
If one selects Orthotropic, the Set Parameters button is active. Pressing this button displays the
dialog in Figure 12.9.1. The toughness values, described next, are entered here.
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Figure 12.9.1 Anisotropic toughness dialog.
Currently, FRANC3D supports one anisotropic crack growth resistance model. It is an
orthotropic model based on six principal material toughnesses. These toughnesses are illustrated
in Figure 12.9.2. In the figure, the e's are the material property axes, which, in general, will not
be aligned with the global Cartesian or the crack front coordinate systems. The first toughness
subscript identifies the material axis perpendicular to the crack plane and second subscript gives
the direction of propagation.
Figure 12.9.2 Orientations for the six principal material toughnesses.
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Figure 12.9.3 shows the crack-front orientation and defines the a and n vectors. x, y, and z are
local crack-front coordinate axes that, in general, are not aligned with the global Cartesian
coordinate axes.
is the local kink angle.
Figure 12.9.3 Definition of the crack-front a and n vectors.
The crack orientation and kink angle sensitive local resistance to crack growth
Kp() is given by
K p(n,a) n12
K12
l
n22
K22
l
n32
K32
l
1 2l
(12.9.1)
Ki (a) 1 ai2 a j
2
Kij2
n
ak2
Kik2
n
1 2n
(12.9.2)
where
Kij and
Kik are the principal toughnesses (no summation on repeated indices),
ai and
ni
are the Cartesian components of the a and n vectors, and l and n (no subscript) are shape
parameters. The n shape parameters control the shape of the toughness envelope in the principal
planes. For example, Figure 12.9.4 shows the variation in
K3 as function of
assuming that
crack front coordinates are aligned with the Cartesian coordinates. The l shape parameter has a
similar effect on the variation of the toughness between the principal planes.
190
Figure 12.9.4 The variation in
K3 as function of
assuming that crack front coordinates are
aligned with the Cartesian coordinates.