1
FRANC3D Workshop/Training
Drs. Paul “Wash” Wawrzynek, Bruce Carter, Tony Ingraffea,
and Omar Ibrahim
Fracture Analysis Consultants, Inc.
Corning GlassMay 7, 2012
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• General introduction to FRANC3D: - capabilities and limitations
• Present theory and approaches to computational fracture mechanics built into the program.
• Hands-on sessions give participants a chance to try the code with tutors here to help.
• Opportunity for participants to ask questions.
Objectives
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• Introduction to FRANC3D
• Demo/Hands-on: build an uncracked model
• Overview of the crack insertion process
• Demo/Hands-on: insert initial crack and run analysis
• Stress Intensity Factor (SIF) computation - theory
• Demo/Hands-on: SIF computation - practice
• Crack growth - theory
• Demo/Hands-on: Crack growth - practice
• Demo/Hands-on: Student generated models
Agenda
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FRANC3D Product
• FRANC3D (FRacture ANalysis Code 3-D) uses finite element method to simulate crack growth analysis
• Adaptively remeshes a finite element model to simulate crack growth.
• Has several elements to be used for modeling the crack front
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FRANC3D Product• Designed to work in conjunction with a commercial
finite element solvers:– ANSYS– ABAQUS– NASTRAN
• The FRANC3D program has a programming interface that is an extension to the Python programming language.
• Written in the C++ programming language• Support the following operating systems:
– Windows– Linux
6
FRANC3D Development History
• 1988 to 1994– FRANC3D v1.0 BEM only
• 1994 to 2001– FRANC3D v2.0 BEM & Thin Shell FEM
• 2001 to 2005– FRANC3D v3.0 BEM & Thin Shell & Solid FEM (ANSYS)
• 2005 to 2009– FRANC3D v4.0 Solid FEM only (ANSYS, ABAQUS, NASTRAN)
– Completely new code written in C++
• 2009 to 2010– FRANC3D v5.0 – Additional enhancements
• 2010 to 2011– FRANC3D v6.0 – Fretting Fatigue, Fatigue Life, Post-processing & other enhancements
• 2012– FRANC3D v7.0 is under development
7
FRANC3D Development History
• Development of FRANC3D was funded by:
– USA Air Force
– USA Navy
– NASA
– Others
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• insert a flaw into an existing finite element mesh and remesh locally, using special crack-front elements.
• compute stress intensity factors (SIF’s) for all nodes along a crack front for isotropic and anisotropic materials.
• predict how a crack will grow (relative extension and angle) using engineering growth criteria, and will then extend the crack geometry and remesh locally.
What Does FRANC3D Do?
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• not a general finite element pre-processor or post-processor. External codes are required to build uncracked FE models and to visualize results (FRANC3D can display deformations).
• not a finite element analysis program. An external FE code is required (e.g., ANSYS or ABAQUS) to perform stress analysis.
• not a general purpose fatigue life prediction code, although some basic life prediction models are available. An external lifing code (e.g., AFGRO, NASGRO or DARWIN) can be used.
What FRANC3D is NOT
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FRANC3D Typical Work Flow
Full 3D FE Model
portion to be cracked
Stress Analysis
ANSYS/ABAQUS/NASTRAN
Define crack(s) geometry
FRANC3D
displacements, temperatures,
crack surface tractions
remainder of model
Insert crack(s) into portion of model
and remesh
Compute stress intensity factors
Extend crack(s) geometry
ANSYS/ABAQUS/NASTRAN
Combine portions
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“global” model
“sub-model”crack growth region
Global and Sub-models
FE package (e.g., ANSYS or ABAQUS) is used to define a global model and a sub-model. The sub-model should encompass the crack growth region with ‘space’ for remeshing.
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FRANC3D
FRANC3D Modifies the Sub-model
uncracked model after crack insertion
FRANC3D modifies the sub-model, inserting a crack and remeshing the model locally. It outputs an input file that combines the global and sub-model (ABAQUS) or it outputs the sub-model and a macro command file that will combine the models (ANSYS).
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mesh compatibility
FRANC3D Maintains Compatibility
FRANC3D can retain surface meshes on “cut” surfaces so that there is FE compatibility between the global and sub-model. This is the preferred approach. However, FRANC3D can also instruct the FE program to insert constraint equations.
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Combined (Full Model) Analysis
FRANC3D does not use a global/local approach. The FE analysis is performed with the full combined model. (However, a global/local approach can be used.)
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Crack Growth
after 21 steps of crack growth
Crack growth is simulated by FRANC3D repeatedly reading and modifying the initial sub-model. At each step, the global and modified sub-model are re-combined and the full model is analyzed.
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“free mesh” cut surfaces
Sub-models for “free” meshes
It is possible to cut out a FRANC3D sub-model from a “free” (unstructured) mesh. (However, surface facets of tetrahedral elements with poor aspect ratios can cause local meshing problems.)
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Agenda
• Introduction to FRANC3D
• Demo/Hands-on: build an uncracked model
• Overview of the crack insertion process
• Demo/Hands-on: insert initial crack and run analysis
• Stress Intensity Factor (SIF) computation - theory
• Demo/Hands-on: SIF computation - practice
• Crack growth - theory
• Demo/Hands-on: Crack growth - practice
• Demo/Hands-on: Student generated models
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FRANC3D Tutorials
Using ANSYS: Using ABAQUS:
extract sub-model
crack insertion & automated growth
crack face traction vsfar-field loading
crack face traction vsfar-field loading
through-crack
simple global model vs sub-model with global model
automated crack growth
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FRANC3D Tutorials
Step 1: Build the FE modelStep 2: Extract small portion from the full FE modelStep 2.1: Separate element components
• Separate the FE model into a small portion (local model) and the remaining of the FE model (global model)
• Local FE model will be used for fracture analysis
Local Model
Global Model
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FRANC3D Tutorials
Step 2.2: Create node component for cut-surface• Select the nodes on the cut surfaces of each component
and save a node component. For the 3x3x3 ‘local’ model, name this node component CUT_SURF.
Step 2.3: Save local and global• Archive each element component as a separate model
for the local and other for global• Global model, which consists of the exterior elements,
will include the boundary conditions and material properties
• Local model will include the CUT_SURF node component and FRANC3D will use this information to retain those mesh facets
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FRANC3D Tutorials
Step 3: Read the local FE model into FRANC3D
• Step 3.1: Reading Local FE Model
• Start with the FRANC3D graphical user interface
• Select File and Open• Switch File Filter in
the Open Model File dialog box to proper file extension name and select the file name for the local model
• Click Accept.
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FRANC3D Tutorials
Step 3.2: Selecting the Retained Items in the Local FE Model
• Material, mesh facet groups, contact/constraint & residual stress
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FRANC3D Tutorials
Step 3.3: Selecting Cut Surface Nodes• Lists the node components present in the local
FE model file
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FRANC3D Tutorials
Step 3.4: Importing and Displaying the Local FE Model• User can turn on the surface mesh and manipulate
the view
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Agenda
• Introduction to FRANC3D
• Demo/Hands-on: build an uncracked model
• Overview of the crack insertion process
• Demo/Hands-on: insert initial crack and run analysis
• Stress Intensity Factor (SIF) computation - theory
• Demo/Hands-on: SIF computation - practice
• Crack growth - theory
• Demo/Hands-on: Crack growth - practice
• Demo/Hands-on: Student generated models
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FRANC3D Wizardfor Defining the Crack Type and
Meshing Process for the Cracked Portion of the FE Model
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Current Crack Type Options in FRANC3D
• Elliptical Crack• Through-the-thickness
– One crack front– Two crack fronts
• Long-shallow surface crack shape
• Elliptical crack shape with two fronts
• User-defined crack
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Defining Crack Geometry
• Crack geometry and location can be prescribed either by:– Interactively using the Graphical User
Interface (GUI)– Using FRANC3D extensions to the Python
programming language
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Crack Insertion Wizard (Elliptical Flaw)
Fracture Analysis Consultants, Inc.
crack size/shape parameters
Define the crack surface geometry, position and orient
crackcrack-front template
parameters
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Crack Insertion Wizard – Flaw Library
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User Defined Crack Front Points
User-defined flaw allows an analyst to define an arbitrary (planar) shape by entering (or reading from a file) a series of points that define the vertices of a polygon.
Crack front vertices should be flagged.
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Surface Meshes after Crack Insertion
Fracture Analysis Consultants, Inc.
crack surface mesh
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Crack-Front Template Element Types
Fracture Analysis Consultants, Inc.
quarter-point singular wedge crack-front elements
two or more “rings” of brick elements
pyramids enforce compatibility between brick and tetrahedral
elements
tetrahedral elements are used for the bulk of the volume
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Crack Insertion: Input Sub-model Mesh
Fracture Analysis Consultants, Inc.
The first major input to the crack insertion procedure is a finite element mesh. Usually this is a sub-model, but a full model mesh is acceptable. In the case of a sub-model, the cut surfaces are flagged.
cut surface
This model has brick elements only. However, brick, wedge, pyramid, and tetrahedral elements of both first and second order are okay. Currently, FRANC3D can handle ANSYS, ABAQUS and NASTRAN models.
cutting planes
sub-model
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Crack Insertion: Approximate Surface Geometry
Fracture Analysis Consultants, Inc.
Curved surface geometry is approximated from the faceted surface of the input finite element mesh. Locally refined meshes near flaws will fall on the curved surface rather than on the faceted finite element input.
Step 1: compute weighted average normals at all nodes.Step 2: define 1 or 2 triangular Bezier patches for each FE facet.Step 3: identify “topological” edges and group together facets that form logical faces.
Bezier patches
Topological edges and logical faces
Note that FE facets on the cut surfaces are retained for
compatibility
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Crack Insertion: Flaw Definition
Fracture Analysis Consultants, Inc.
The second major input to the crack insertion procedure is a description of a flaw shape and location. FRANC3D has tools to define and place a flaw interactively. Flaws can be zero volume (cracks) or finite volume (voids).
The crack above appears to have a piecewise linear crack front, but that is a just a display artifact. Flaw surfaces are defined as Bezier patches and can have curved crack fronts. In theory, initial flaws can be non-planar, but there is currently no practical user-interface for such a capability.
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Crack Insertion: Crack-Front Templates
Fracture Analysis Consultants, Inc.
Crack-front templates are generated to emplace regular well-shaped elements near crack fronts. The template elements are a combination of brick and quarter-point wedge elements.
A typical template cross-section
Additional processing is required where templates intersect free surfaces. Locally template element topology and geometry must be modified to conform to the surface geometry.
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Crack Insertion: Intersections & Trimming
Fracture Analysis Consultants, Inc.
Surface/surface intersections are computed for all body and flaw patches. The body and flaw patches are trimmed and combined into one composite object.
Outside Inside
Trimmed patches are divided into triangular sub-patches to keep the model “water-tight”.
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Crack Insertion: Surface Meshing
Fracture Analysis Consultants, Inc.
Surface meshes are generated for all “logical” model surfaces. The surface meshes are constrained to conform to the meshes on cut surfaces.
retained cut surface meshes
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Crack Insertion: Pyramids & Volume Meshing
Fracture Analysis Consultants, Inc.
Pyramid elements are generated to enforce compatibility between quadrilateral facets on both the template and “cut” surfaces and triangular faces in the volume mesh.
An advancing front meshing algorithm* is used to generate a tetrahedral volume mesh (not shown). This algorithm respects the special case of distinct nodes on opposite sides of crack faces, which are geometrically coincident.
cut surfacestemplate surfaces
*Neto, J.B., Wawrzynek, P.A., Martha, L.F., and Ingraffea, A.R., “An algorithm for three-dimensional mesh generation for arbitrary regions with cracks,” Engng with Comp., vol. 17, 75-91 (2001)
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Volume Meshing
• After completing the surface, the volume mesh starts
• Options for performing volume meshing:– FRANC3D– ANSYS– ABAQUS CAE
• Final mesh smoothing are used to improve the elements quality
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A Sub-Volume Definition Issue
It can be difficult to mesh a thin section that is constrained with a large quadrilateral patch on one side.
There is not enough room for a well shaped pyramids and transition tetrahedral elements.
Retained cut-surface facet
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Workshop Agenda
• Introduction to FRANC3D
• Demo/Hands-on: build an uncracked model
• Overview of the crack insertion process
• Demo/Hands-on: insert initial crack and run analysis
• Stress Intensity Factor (SIF) computation - theory
• Demo/Hands-on: SIF computation - practice
• Crack growth - theory
• Demo/Hands-on: Crack growth - practice
• Demo/Hands-on: Student generated models
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FRANC3D Tutorials – Crack Insertion Steps
• Step 1: Selecting Cracks from FRANC3D Menu– From the FRANC3D menu, select Cracks and New Flaw Wizard.
The first panel of the wizard should appears. The default flaw type is Crack (zero volume flaw) and select Next.
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FRANC3D Tutorials – Crack Insertion Steps
• Step 2: Selecting Crack Type– The next panel allows the user to choose type of crack, hint
Next after the selection.
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FRANC3D Tutorials – Crack Insertion Steps
• Step 3: Specify the Crack Size– The next panel allows us to specify the size of the ellipse.
Select Next after the size definition.
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FRANC3D Tutorials – Crack Insertion Steps
• Step 4: Specify Crack Location and Orientation– The next panel allows us to specify location and orientation of the
flaw. After defining the location and orientation; select Next.
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FRANC3D Tutorials – Crack Insertion Steps
• Step 5: Specify Crack Front Template Parameters– The next panel allows us to specify the crack front template
parameters. After specifying the parameters; select Finish.
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FRANC3D Tutorials – Crack Insertion Steps
• Step 6: Surface and Volume Meshing of Local Model after the Crack Insertion – FRANC3D begins the process of inserting the flaw into the original
model and then meshes the resulting cracked model.– Operations is displayed on the screen– When meshing is completed, the newly meshed cracked model will be
displayed.
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FRANC3D Tutorials – Static analysis Steps
• Step 1: Select Static Crack Analysis– From the FRANC3D menu,
select Analysis and Static Crack Analysis. The first panel of the wizard should appear, specify the file name for the FRANC3D database first.
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FRANC3D Tutorials – Static analysis Steps
• Step 2: Select FE Solver– Next panel allows you to specify the solver
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FRANC3D Tutorials – Static analysis Steps
• Step 3: Select Analysis Options – Next panel allows you to
specify the solver output and analysis options
– Specify global models– Use all quadratic elements– Solver executable should
be defined
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FRANC3D Tutorials – Static analysis Steps
• Step 4: Merging Local/Global FE Models – Next panel allows for the
specification of whether the local and global models are combined by merging nodes or by defining constraints or contact conditions.
– Specify node component names in the local and global models for nodes that will be merged or you can let the programs (FRANC3D and Solver) do the work.
– Select Finish
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Workshop Agenda
• Introduction to FRANC3D
• Demo/Hands-on: build an uncracked model
• Overview of the crack insertion process
• Demo/Hands-on: insert initial crack and run analysis
• Stress Intensity Factor (SIF) computation - theory
• Demo/Hands-on: SIF computation - practice
• Crack growth - theory
• Demo/Hands-on: Crack growth - practice
• Demo/Hands-on: Student generated models
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Stress Intensity Factors
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Continuum Fracture Modes
Mode I Mode II Mode IIIBasic modes of crack loading. Positive sense shown for each:
Mode I = crack openingMode II = in-plane sliding
Mode III = anti-plane tearing EACH MODE HAS ITS OWN STRESS INTENSITY FACTOR
y,v
x,u
z,wz,w
x,u
y,v y,v
x,u
z,w
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Stress Intensity Factors
• FRANC3D Computes the stress intensity factors associated with all three “modes” of fracture for the mid-side nodal points along the crack front
• Under conditions of small-scale yielding, all crack front displacement fields (crack behavior) are controlled by the stress intensity factors– Stability – will the crack tip move?– Trajectory – in what direction?– Rate – how fast?
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• Relatively simple to understand and implement
• Relatively poor accuracy (~5% error for a reasonable mesh)
• Good sanity check but not for production work
Computing Stress Intensity Factors
• Somewhat involved formulation and implementation.
• In the literature, the M-Integral is sometimes known an "interaction integral”.
• Relatively good accuracy (<1% error for a reasonable mesh)
• Requires special additional terms for crack face tractions, residual stresses, FGM’s, etc.
FRANC3D has two methods to compute stress intensity factors (SIF’s):
Displacement Correlation:
M-Integral (Interaction Integral):
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Computing Stress Intensity Factors
M-Integral (Interaction Integral):• Numerically the M-Integral is similar to the J-Integral.• M-Integral is used to compute the strain energy release
energy rates (GI, GII, and GIII) and stress intensity factors (KI, KII, and KIII) associated with the three modes of fracture.– Mode II (KII) is needed to predict the crack kink angle to
determine the crack front direction• M-integral implementation in FRANC3D allows the
computation of the three modes of SIFs for isotropic and anisotropic materials.– FRANC3D is the only available code that will compute
stress intensity factors for generally anisotropic materials
• The method to use for production work
6060
Stress Intensity Factor Computations
SIF’s are computed with the M-integral for isotropic and generally anisotropic materials.
61
Fracture mechanics gives the theoretical asymptotic displacement fields.
2cos22
2sin
22
2/1 rK Iv
2sin21
2cos
22
2/1 rK Iu
2cos22
2sin
22
2/1 rK IIu
2sin21
2cos
22
2/1 rK IIv
Note: for plane stress, let = /(1+ )
, v
, u
Set r = ra-b, and = 180°
222
baI
ab
rKvv
22
2
baII
ab
rKuu
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Displacement Correlation Methods
ba
abIII
ba
abII
ba
abI
rK
rK
rK
2
22
2
22
2
ww
uu
vv
where is the shear modulus, is Poisson's ratio, r is the distance from the crack tip to the correlation point, and ui, vi, wi are the x, y, and z displacements at point i
The same expressions can be used for plane stress assumptions if is replaced with = / (1+).
For plane strain case:
ra-b
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Energy Release Rates
222
22 111
IIIIII KE
KE
KE
G
The crack-tip energy release rates can be determined from Irwin’s crack closure integral
3,2,1,),()0,(1
lim0 2
0
jrurG jj
Substituting crack-tip stress and displacement fields yields
2
u
r
64
dsx
uTWnJ i
ix
ijijW 21
The J-Integral
* Rice, J.R. (1968) A path independent integral and approximate analysis of strain concentrations by notches and cracks, Journal of Applied Mechanics, 35, 379-386
The J-Integral* measures the energy flux into the crack-tip region
Under conditions of small scale yielding the J-Integral is equal to the energy release rate
dsx
qW
x
uJ
jj
iij
11
The contour J-Integral can be recast as an equivalent area (volume in 3D) integral**, which is more accurate and stable in a finite element context
** Li, F.Z., Shih, C.F., and Needleman, A. (1985) A comparison of methods for calculating energy release rates, Engineering Fracture Mechanics, 21, 405-421
q is a function that is one at the crack tip and zero on the boundary of the integration domain. It can be interpreted as a virtual crack extension.
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The 3D J-Integral
In 3D, the J-Integral is evaluated within a cylindrical domain centered on a portion of the crack-front
qt
t
A
J
dssq
dssqsJJ
)(
)()(In 3D
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Formulating the M-Integral From the Stress and Displacement Fields
For linear analysis, we can add two valid solutions and the result is a valid solution
)2()1(ijijij )2()1(
ijijij )2()1(iii uuu
Substituting these into the expression for the J-integral
dsx
qWWW
x
u
x
u
x
u
x
uJ
jjjj
iij
iij
iij
iij
1)2,1(
1)2(
1)1(
1
)2()2(
1
)1()2(
1
)2()1(
1
)1()1(
)1()2()2()1()2,1(ijijijijW
where
take the (1) solution to be the FEM results
the (2) solution(s) are solutions we get to select
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Collecting terms
ds
x
qW
x
uds
x
qW
x
uJ
jj
iij
jj
iij 1
)2(
1
)2()2(
1)1(
1
)1()1(
)2,1()2()1( MJJJ or
Formulation of the M-Integral (cont.)
dsx
qW
x
u
x
u
jj
iij
iij
1)2,1(
1
)1()2(
1
)2()1(
)2(J
)2,1(M
)1(J
dsx
qW
x
u
x
uM
jj
iij
iij
1)2,1(
1
)1()2(
1
)2()1()2,1( with
A definition of M in terms of the crack tip field variables we can get from an FEM analysis (solution 1) or form the theoretical expressions if we know KI, KII, and KIII (solution 2)
68
Formulating the M-Integral From the Definition of the Energy Release Rate
)2()1(III KKK )2()1(
IIIIII KKK )2()1(IIIIIIIII KKK
for small scale yielding
substituting into the expression for the energy release rate
)2()1()2()1(2
)2()1(2
2)2(2)2(22)2(
2
2)1(2)1(22)1(
2
)2,1()2()1(
111
111
111
IIIIIIIIIIII
IIIIII
IIIIII
KKE
KKE
KKE
KE
KE
KE
KE
KE
KE
MJJJ
222
22 111
IIIIII KE
KE
KE
JG
69
Formulation of the M-Integral (cont.)
)2()1()2()1(2
)2()1(2
)2,1( 111IIIIIIIIIIII KK
EKK
EKK
EM
equating the two definitions for the M-Integral
)2()1()2()1(2
)2()1(2 111
IIIIIIIIIIII KKE
KKE
KKE
qj
ji
iji
ij Adsxq
Wx
u
x
u1
)2,1(
1
)1()2(
1
)2()1(
A definition of M in terms of K’s and material properties.
70
KI KII KIII
a 1.0 0.0 0.0
b 0.0 1.0 0.0
c 0.0 0.0 1.0
Formulation of the M-Integral (cont.)
We select three simple auxiliary solutions (2a), (2b), and (2c)
From the analytical expressions for the crack-front fields, we obtain
)2()2()2( ,, cba )2()2()2( ,, cba )2()2()2( ,, cba uuu
Substitution gives three equations for the unknown K(1)’s
We use the FEM results for the (1) solution
qc
qb
qa
III
II
I
AM
AM
AM
K
K
K
E
E
E
)2,1(
)2,1(
)2,1(
)1(
)1(
)1(2
2
1200
012
0
0012
71
Independent FRANC3D Mode I SIF Verification
Fracture Analysis Consultants, Inc.
2w
2a2h
t
S
S
1
2
3
w
a2h
t
S
S
1
2
3
2w
2a2h
t
S
S
1
2
3
2w
2a2h
t
S
S
1
2
3
1
2
3
w
a2h
t
S
S
1
2
3
w
a2h
t
S
S
1
2
3
1
2
3
CCT SENAnalyses performed by
Dawn Phillips of the NASA Langley Research Center
72
Independent FRANC3D Mode I & II SIF Verification
Fracture Analysis Consultants, Inc.
Analyses performed by Dawn Phillips of the
NASA Langley Research Center
2w
a
2h
t
S
S
R
c
1
2
3
2w
a
2h
t
S
S
R
c
1
2
3
1
2
3
Mode I
Mode II
Slant edge crack starting from a circular hole
73
Typical Isotropic M-Integral Verification
Fracture Analysis Consultants, Inc.
Stress intensity factors are computed at all nodes along the crack front
Surface crack, a = c = 0.8, remote unit traction
The oscillations arise because different virtual crack extension are used for element corner and mid-side nodes.
virtual crack extensions
corner node mid-side node
crack front
1.05
1.1
1.15
1.2
1.25
1.3
0 0.2 0.4 0.6 0.8 1
normalized distance along crack front
str
es
s in
ten
sit
y f
ac
tor
(ps
i*in
^.5
)
Raju-Newman
f3dngFRANC3D
74
2 Banks-Sills, L., Wawrzynek, P.A., Carter, B., Ingraffea, T.R., and Hershkovitz, I., “Methods for computing stress intensity factors in anisotropic geometries: Part II – arbitrary geometry,” Engng. Fracture Mech., in review
1 Wawrzynek, P.A., Carter, B., and Banks-Sills, L. “The M-integral for computing stress intensity factors in generally anisotropic materials,” NASA/CR-2005-214006
Anisotropic Stress Intensity Factors
• FRANC3D includes an M-Integral implementation for general anisotropic materials.1,2
75
Workshop Agenda
• Introduction to FRANC3D
• Demo/Hands-on: build an uncracked model
• Overview of the crack insertion process
• Demo/Hands-on: insert initial crack and run analysis
• Stress Intensity Factor (SIF) computation - theory
• Demo/Hands-on: SIF computation - practice
• Crack growth - theory
• Demo/Hands-on: Crack growth - practice
• Demo/Hands-on: Student generated models
76
FRANC3D Tutorials – SIF Computation Steps
• Step 1: Re-Open FRANC3D restart file– From the FRANC3D menu, select File and
Open. – Choose the *.fdb file and select OK. – FRANC3D will automatically read the FE
solver results
77
FRANC3D Tutorials – SIF Computation Steps
• Step 2: Select Compute SIFs– From the FRANC3D menu, select Cracks and Compute SIFs. The
Stress Intensity Factor wizard is displayed– Use the M-Integral– User can select thermal or crack face traction terms if they are
used. – Select Finish, the SIFs Plot dialog is displayed
78
FRANC3D Tutorials – SIF Computation Steps
• Step 2 (cont’d): Select Compute SIFs– View the three stress intensity factor (SIF) modes and export
the data
79
Workshop Agenda
• Introduction to FRANC3D
• Demo/Hands-on: build an uncracked model
• Overview of the crack insertion process
• Demo/Hands-on: insert initial crack and run analysis
• Stress Intensity Factor (SIF) computation - theory
• Demo/Hands-on: SIF computation - practice
• Crack growth - theory
• Demo/Hands-on: Crack growth - practice
• Demo/Hands-on: Student generated models
80
Crack Growth
81
Crack Growth
Stress Intensity Factors are used to predict the direction and relative extent of crack growth
local kink angle
local extensionsmoothed front (red)
predicted front (blue)
original front
local kink angle
local extensionsmoothed front (red)
predicted front (blue)
original front
82
Crack Growth Prediction within FRANC3D
• Computing crack front growth is a three-step process:– Kink angle for each node (direction)
• Based on the crack-front stresses in polar coordinates• Five options for computing kink angle
– Relative amount of local crack extension for each node• Computed using a fatigue growth model (using one node
extension with a median SIF or using a specify number of load cycles)
• Simplest model is Paris growth model
– Smooth the crack front• Polynomial curves are used to fit the crack front• User can specify the order of the polynomial or FRANC3D find
the polynomial order that will give the best fit
83Confidential
Crack Growth
after 21 steps of automatic crack growth
83
84
85
Crack Extension
Fracture Analysis Consultants, Inc.
Cracks are “extended” by “reinserting” an extended crack definition. This approach to extension: 1) simplifies the code, 2) reduces the amount of information stored between steps, and 3) allows the sub-volume to be changed between crack growth steps.
initial crack
crack extension
meshed extended crack
non-planar crack growth
86
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88
Kink Angle: Max Stress Criterion (orthotropy)
Fracture Analysis Consultants, Inc.
The orthotropic max stress criterion says that the crack will kink in the direction where the ratio of the hoop stress to the effective toughness is maximum.
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91
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92
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93
Kink Angle: Max Stress Criterion (isotropy)
Fracture Analysis Consultants, Inc.
The max stress criterion says that the crack will kink in the direction of a maximum value of a stress component.
-30
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94
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95
under development, ignore for now
96
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97
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98
NASGRO Equation Dialog
99
User Equation Dialog
Can read AFGRO formatted files and excel CSV or text files.
100
no smoothing
polynomial fit
no crack front fitting
Program selected polynomial order
user specified polynomial order
101
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100
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All crack increments are specified
103
value21 NN
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All cycle increments are specified
104
Workshop Agenda
• Introduction to FRANC3D
• Demo/Hands-on: build an uncracked model
• Overview of the crack insertion process
• Demo/Hands-on: insert initial crack and run analysis
• Stress Intensity Factor (SIF) computation - theory
• Demo/Hands-on: SIF computation - practice
• Crack growth - theory
• Demo/Hands-on: Crack growth - practice
• Demo/Hands-on: Student generated models
105
FRANC3D Tutorials – Manual Crack Growth Steps
• Step 1: Select Grow Crack– From the FRANC3D menu,
select Cracks and Grow Crack
– Crack Growth wizard is displayed
– Choose Quasi-Static or Fatigue growth type
– Select Next
106
FRANC3D Tutorials – Manual Crack Growth Steps
• Step 2: Specify Growth Rate– Second panel of the Crack
Growth allows you to specify the growth rate model data
– Use the Paris model and set C to 1e-10 and leave n at 2
– Select Next.
107
FRANC3D Tutorials – Manual Crack Growth Steps
• Step 7.3: Specify Extension or Cycles– Third panel of the Crack
Growth allows you to specify whether you will grow the crack based on a median extension or a number of cycles
– Use a median extension– Select Next.
108
FRANC3D Tutorials – Manual Crack Growth Steps
• Step 7.4: Specify Fitting and Extrapolation– Fourth panel of the Crack
Growth allows you to specify a value for median extension as well as the fitting and extrapolation parameters
– Specify a median extension of 0.1 and use a fixed 3rd order polynomial with 3% extrapolation on both ends to ensure the fitted end points fall outside the model
– Select Next
109
FRANC3D Tutorials – Manual Crack Growth Steps
• Step 7.5: Specify Crack Front Template– Final panel allows you to
specify the crack front mesh template parameters
– Set the template radius to 0.06
– Select Next to proceed with growing the crack and remeshing
– Once the remeshing is completed, another Static Crack Analysis can be performed
110
FRANC3D Tutorials – Automatic Crack Growth Steps
• Assuming the crack insertion and static analysis was completed
• Step 1: Re-Open FRANC3D restart file– From the FRANC3D menu, select File and Open. – Choose the *.fdb file and select OK. – FRANC3D will automatically read the FE model and solver results
111
FRANC3D Tutorials – Automatic Crack Growth Steps
• Step 2: Select Crack Growth Analysis– From the FRANC3D menu, select Analysis and Crack Growth
Analysis– First panel of the wizard allows you to choose the method for
computing SIFs– Use all the default values. – Select Next
112
FRANC3D Tutorials – Automatic Crack Growth Steps
• Step 3: Specify Growth Parameters– Second panel appears– Select Quasi-Static for simplicity– All other values are left as defaults– Select Next.
113
FRANC3D Tutorials – Automatic Crack Growth Steps
• Step 4: Specify Growth Model Data– Third panel appears– Set the value of n to 2 for the power-law crack growth model– Select Next
114
FRANC3D Tutorials – Automatic Crack Growth Steps
• Step 5: Specify Fitting and Template Parameters– Fourth panel appears– Set the value for the template
radius to 0.06. The extrapolation could be increased from 3 to 5%, but 3% should suffice for the first 5 steps
– Select Next.
115
FRANC3D Tutorials – Automatic Crack Growth Steps
• Step 6: Specify Extension or Cycle Data– Fifth panel appears– Grow the crack for 5 steps using
a Constant Median Crack Growth Increment of 0.1
– Select Next.
116
FRANC3D Tutorials – Automatic Crack Growth Steps
• Step 7: Specify Analysis Code– Sixth panel appears– Use ANSYS and the Current crack growth step is 1 as if you
are starting from the initial crack
117
FRANC3D Tutorials – Automatic Crack Growth Steps
• Step 8: Specify Analysis Options– Seventh panel appears– Select your FE Solver– Select global model– FRANC3D transfers all
the boundary conditions from the global model to the combined model, so leave the Transfer all retained bc’s checked.
– Click Next
118
FRANC3D Tutorials – Automatic Crack Growth Steps
• Step 9: Specify Local/Global Model Connection– Final panel allows you to
choose how the local and global models will be connected
– Click Finish to start the automatic crack
119
The Python Programming Interface
• The FRANC3D program has a programming interface that is an extension to the Python programming language.
• Python is an open source, object oriented, scripting language, which is popular in engineering and scientific computing community (e.g., it is used to drive the ABAQUS GUI).
• The Python interface allows one to automate repetitive and possibly error prone tasks.
• It also provides a possible strategy for coupling FRANC3D with other computational applications.
120
A simple PyF3D Program
Fracture Analysis Consultants, Inc.
import PyF3D
# file names for the models
uncracked_fname = "minidisk_submodel.cdb“fname_base = "minidisk_crack" # lists of crack size parameters to a_sizes = [0.0160, 0.0320, 0.0480, 0.0640, 0.0787, 0.2362, 0.3937]b_sizes = [0.0160, 0.0787, 0.2362, 0.3937] app = PyF3D.F3DApp() # loop through the crack size matrix for a in a_sizes: for b in b_sizes: # skip cases with really #bad aspect ratios if b > 0.2 and a < 0.065: continue
# create a flaw object
flaw = PyF3D.Flaw("Ellipse",[a,b]) flaw.Translate([0.499,4.179,-.374]) flaw.Rotate(1,"Y",90.0) flaw.Rotate(2,"Z",-53.61) # open an uncrack model, insert the flaw app.OpenModel(uncracked_fname) app.InsertFlaw(flaw) # generate a new file name like: # minidisk_crack_160_320.fdb fname = "%s_%d_%d.fdb" % \ (fname_base,int(a*1000),int(b*1000)) # save the file app.SaveModel(fname)
121
Some FRANC3D Known Bugs
If any of the original body patches fall completely inside the template (no intersections) the crack insertion will not be successful.
122
Some FRANC3D Known Bugs
If the none of the crack mouth or template edges intersect any of the edges of any of the original boundary patches the crack will not be inserted successfully.
123
Some FRANC3D Known Bugs
FRANC3D can have difficulties meshing in situations where the crack-front template (the singular crack-front element and the two surrounding rings of brick elements) intersects one of the corner of the models.
124
Some FRANC3D Known Bugs
The code is currently able to detect that the template intersects a corner and in many cases does a reasonably good job making the external mesh compatible with both the template and the geometry of the body.
However, reasonable pyramid elements cannot be added on the outside of the template. The “Simple Template Intersections Only” option may work around this issue.
125
• Use the “Advanced -> Flaw to File Wizard” option to create a .crk file that describes the flaw you are trying to insert.
• Send the .crk file along with the mesh file (.inp or .cdb) to us.
What to do when something goes wrong
• Check to make sure that no part of the flaw or crack-front template is in the retained (cut surface) portion of the sub-model.
• Look for a file called “debug.tst” in your working directory and send it to us.
If the program crashes before you see the “Flaw Insertion Status” window:
If the program crashes during flaw insertion or the program reports that it cannot insert the flaw:
126
Workshop Agenda
• Introduction to FRANC3D
• Demo/Hands-on: build an uncracked model
• Overview of the crack insertion process
• Demo/Hands-on: insert initial crack and run analysis
• Stress Intensity Factor (SIF) computation - theory
• Demo/Hands-on: SIF computation - practice
• Crack growth - theory
• Demo/Hands-on: Crack growth - practice
• Demo/Hands-on: Student generated models