1 FRANC3D Workshop/Training Drs. Paul “Wash” Wawrzynek, Bruce Carter, Tony Ingraffea, and Omar Ibrahim Corning Glass May 7, 2012

1

FRANC3D Workshop/Training

Drs. Paul “Wash” Wawrzynek, Bruce Carter, Tony Ingraffea,

and Omar Ibrahim

Fracture Analysis Consultants, Inc.

Corning GlassMay 7, 2012

2

• 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

3

• 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

4

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

5

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

8

• 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?

9

• 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

10

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

11

“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.

12

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).

13

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.

14

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.)

15

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.

16

“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.)

17

Agenda










18

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

19

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

20

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

21

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.

22

FRANC3D Tutorials

Step 3.2: Selecting the Retained Items in the Local FE Model

• Material, mesh facet groups, contact/constraint & residual stress

23

FRANC3D Tutorials

Step 3.3: Selecting Cut Surface Nodes• Lists the node components present in the local

FE model file

24

FRANC3D Tutorials

Step 3.4: Importing and Displaying the Local FE Model• User can turn on the surface mesh and manipulate

the view

25

Agenda










26

FRANC3D Wizardfor Defining the Crack Type and

Meshing Process for the Cracked Portion of the FE Model

27

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

28

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

29

Crack Insertion Wizard (Elliptical Flaw)


crack size/shape parameters

Define the crack surface geometry, position and orient

crackcrack-front template

parameters

30

Crack Insertion Wizard – Flaw Library

31

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.

32

Surface Meshes after Crack Insertion


crack surface mesh

33

Crack-Front Template Element Types


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

34

Crack Insertion: Input Sub-model Mesh


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

35

Crack Insertion: Approximate Surface Geometry


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

36

Crack Insertion: Flaw Definition


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.

37

Crack Insertion: Crack-Front Templates


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.

38

Crack Insertion: Intersections & Trimming


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”.

39

Crack Insertion: Surface Meshing


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

40

Crack Insertion: Pyramids & Volume Meshing


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)

41

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

42

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

43

Workshop Agenda










44

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.

45


• Step 2: Selecting Crack Type– The next panel allows the user to choose type of crack, hint

Next after the selection.

46


• Step 3: Specify the Crack Size– The next panel allows us to specify the size of the ellipse.

Select Next after the size definition.

47


• 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.

48


• 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.

49


• 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.

50

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.

51


• Step 2: Select FE Solver– Next panel allows you to specify the solver

52


• 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

53


• 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

54

Workshop Agenda










55

Stress Intensity Factors

56

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

57

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?

58

• 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):

59

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

62

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

63

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.

65

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

66

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

67

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


)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


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


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


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


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










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


• 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


• Step 2 (cont’d): Select Compute SIFs– View the three stress intensity factor (SIF) modes and export

the data

79

Workshop Agenda










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


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

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

ba

abIII

ba

abII

ba

abI

rK

rK

rK

2

22

2

22

2

ww

uu

vv

87

max

thatsuch

p

c k

llll

ppk

n

k

n

k

nkk

21

23

23

22

22

21

21,

an

n

n

ik

k

n

ij

jii

K

a

K

aak

21

2

2

2

221

a

)0( pk

)90( pk

)(pk

n = . 3n = . 3

n = . 5n = . 5

n = 1n = 1

n = 2n = 2

n = n =

88

Kink Angle: Max Stress Criterion (orthotropy)


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.

2232

21312

3

232

12123232

2

222

31322122

1

21

111aKaK

a

naKaK

a

naKaK

a

nKeff

na,maxfor

effkink K

a

n

na,effK

x

y

predicted direction ofcrack propagation

Where Keff is a function of six principal toughnesses and crack orientation relative to the material

89time

maxK

minK

SIF (K) K

max

min

K

KR minmax KKK

analysis

analysis

PRKK

PKK

min

max

RPRKK

RPKK

KK

analysis

analysis

analysis

1

1

min

max

90

bcaseloadb

acaseloada

KPK

KPK

__min

__max

time

maxK

minK

SIF (K) K

max

min

K

KR minmax KKK

load case a

load case b

91

bcaseloadbacaseloada

bcaseloadbacaseloada

KPKPK

KPKPK

____min

____max

time

maxK

minK

KacaseloadK __

bcaseloadK __

92

0kink

22

22

max )()(,)(MAX

thatsuch

zIIIc

Icr

IIc

Ic

kink

K

K

K

K

max)(thatsuch kink

max

22

22

2 )()()(

thatsuch

zIIIc

Icr

IIc

Ic

kink

K

K

K

K

93

Kink Angle: Max Stress Criterion (isotropy)


The max stress criterion says that the crack will kink in the direction of a maximum value of a stress component.

-30

-20

-10

0

10

20

30

40

50

60

70

80

0 10 20 30 40 50 60 70 80 90

LEFM Max stressAmstutz (1995) 2024-T3, L-TAmstutz (1995) 2024-T3, T-LHallback & Nilsson (1994) 7075-T6Maccagno & Knott (1989), PMMAMaccagno & Knott (1991), HY130 @ -196C

Mode I

Transition7075-T6

Transition2024-T3

Mode II

c

III KK1tan,mixityMode

r

x

y

Some materials show a transition from Mode I to Mode II crack growth for stable tearing.

maxforkink

rkink max,maxmaxfor

Mode I only:

Mode I or Mode II:

94

max323121231312 ,,,,,,,,thatsuch

nlKKKKKKK pkink

max),,(thatsuch IIIkink KK

max),,,(thatsuch IIIIIIkink KKK

95

under development, ignore for now

96

point with the median K value

current crack front

predicted new crack front

am specified extension

ai computed extension

point i

n

m

imi K

Kaa

,...,

,...,

RKf

RKfaa

mNASGRO

iNASGROmi

,...,

,...,

RKf

RKfaa

muser

iusermi

97

current crack front

predicted new crack front

ai computed extension

point i

nii KNCa

,..., RKNfa iNASGROi

,..., RKNfa iuseri

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

ia

tr

100

value

100

value

value

min

it

t

t

ar

ar

r

102

value21 aa

miaai 11

All crack increments are specified

103

value21 NN

miNNi 11

All cycle increments are specified

104

Workshop Agenda










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


• 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


• 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


• 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


• 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


• 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


• Step 3: Specify Growth Parameters– Second panel appears– Select Quasi-Static for simplicity– All other values are left as defaults– Select Next.

113


• 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


• 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


• 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


• 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


• 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


• 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


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


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


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


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










Documents

1 FRANC3D Workshop/Training Drs. Paul “Wash” Wawrzynek, Bruce Carter, Tony Ingraffea, and Omar Ibrahim Corning Glass May 7, 2012