Fatigue Crackprop in Ansys

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2011 CAE Associates

Fatigue Crack

PropagationAnalysis in ANSYS


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Fatigue Crack Growth

Fatigue crack formation analysis predicts cycles to failure based purely on

material data of fatigue specimens.

Even though the total fatigue life includes the growth of cracks, cracks are notexplicitly modeled.

Fatigue performance of structures is more accurately described as follows:

The presence of stress risers such as holes, manufacturing errors, corrosion

pits, and maintenance damage serve as nucleation sites for fatigue cracking. During service, sub-critical cracks nucleate from these sites and grow until

catastrophic failure, i.e. unstable crack growth, occurs.

From an economic point of view, a costly component cannot be retired from

service simply on detecting a fatigue crack.

Hence, reliable estimation of fatigue crack propagation and residual lifeprediction, combined with inspections, are essential so that the component can

be timely serviced or replaced.


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Fatigue crack growth is performed by combining linear elastic fracture

mechanics and fatigue.

In this approach, an initial crack size and location is considered, and life isbased on the growth of the crack until unstable crack growth occurs.


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Two main approaches for modeling crack growth:

Fatigue crack growth codes. Use stresses from un-cracked structure ANSYS analysis.

Perform crack growth calculations assuming a crack geometry (library of standard

stress intensity functions) and crack growth law.

Crack modeled directly in finite element analysis. Include a crack in the finite element model, and perform a series of solutions to findthe stress intensity factors as the crack grows through the model.

Then use this data and a fatigue crack growth law to predict cycles until failure.

Most difficult and time-consuming approach, since the path of the crack may not be

known ahead of time, changes to the mesh must be made, multiple analyses are

required, etc.

In either case, the stresses near the crack are used to calculate the stress

intensity factor, K.


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Linear Elastic Fracture Mechanics

Determining if a crack will propagate under given loading conditions is

answered using linear elastic fracture mechanics (LEFM).

The stresses near the tip of the crack tend to infinity based on the theory ofelasticity.

By deriving the forms of these infinite stresses, the strength and order of the

singularity are found.

The strength of the singularity, called the stress intensity factor K, is used to

determine the behavior of the crack.

=

+

=

=

2

3sin

2sin

2cos

2

2

3

sin2sin12cos2

2

3sin

2sin1

2cos

2

r

K

r

K

r

K

I

xy

I

yy

I

xx


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Kis based on the crack geometry and applied cyclic loading:

),2/(:

/12.1

cafQwhere

QaKI

=

=

Through thickness crack Edge crack Surface (thumbnail) crack

a

c2

Dependence of flawshape parameter Q onthe ratio of depth towidth of surface crack.


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There are three basic modes of

crack surface displacement:

Mode I: Opening Mode II: In-plane shear.

Mode III: Out-of-plane shear.

Solutions for K exist for all modes,

and KI, KIIand KIIIcan be calculatedin ANSYS, but it is typical to

assume that KIis the dominant

parameter.


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When KIreaches some critical value, the part will fail.

Critical value of KI, called the fracture toughness or KIC, is obtained from acontrolled test of specimens.

Fracture toughness, KIC:

Is an indication of the amount of stress required to propagate a pre-existing

flaw.

Is a measured material property.

Can vary as a function of:

Thickness

Temperature

Yield stress


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There are a number of calculated fracture mechanics parameters used to

describe or predict crack response:

All of these parameters can be related to one another, assuming a crack in alinear elastic isotropic single material.

KI Stress intensity parameter

COD Crack opening displacement

Measurement of crack opening some distance from the crack tip.

CTOD Crack tip opening displacement Crack tip measurement based on plastic zone and root radius of crack.

G Strain energy release rate The rate of transfer of energy from the elastic stress field of the cracked structure to

the inelastic process of crack extension.

J J integral Path-independent line integral used to solve crack problems in the presence of

plastic deformation.


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Fracture parameters can be determined:

Using derived expressions for idealized crack geometries, found by selecting

the crack geometry from a library within nCode. By including the crack in ANSYS model and using one of the available

methods:

Stress intensity factors directly via special crack tip elements (K).

J-integral (J).

Energy release rate (G).

Assuming linear elastic single material, plane strain formulation, these

parameters are related:

( )

E

KGJ I

22 1 ==


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Stress intensity factors directly via special crack tip elements (K).

Midside nodes moved to quarter point location to provide shape function with

correct order of singularity. Linear elastic materials only.

J-integral (J).

The nonlinear energy release rate, J, can be written as a path-independent line

integral. Calculated by defining paths around crack tip (path creation automated in

ANSYS).

J uniquely characterizes crack tip stress and strain in nonlinear materials.

Energy release rate (G). Measure of the energy available for an increment of crack extension.

Uses the virtual crack closure technique (VCCT).

Can use along interface between materials, i.e. delamination.

Automated crack growth procedure coming in version 14.


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Numerical Methods

Demonstration problem:

Prediction and comparison of KIof compact specimen using the following

methods: Hand calculation.

ANSYS special crack tip elements.

ANSYS J-integral method.


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Numerical Methods

Demonstration problem: Hand calculation.

From fracture mechanics text, KIfor a compact specimen is given as:

+

+

+=

=

432

2

3 60.572.1432.1364.4886.0

1

2

W

a

W

a

W

a

W

a

W

a

W

a

W

af

P

WBK

W

af I

1.25 W

B = 1 in

a = 1 in

W = 2 in

P = 33.3 lb

KI= 227.7 psi-in1/2


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Numerical Methods

Demonstration problem: ANSYS special crack tip elements.

2D plane strain mesh.

KSCON command used to automatically create local crack tip mesh withquarter-point nodes.

Half specimen modeled using symmetry boundary conditions.

Crack tipCrack face


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Numerical Methods

Demonstration problem: ANSYS special crack tip elements.

KCALC command used with quarter-point elements to determine KI.

KI= 225.6 psi-in1/2


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i l h d


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Numerical Methods

Demonstration problem: ANSYS J-integral method.

Printed J-integral values for 10 contours:

Plotted J-integral values for 10 contours:

J = 0.00154 lb/in

N i l M h d


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Numerical Methods

Demonstration problem: ANSYS J-integral method.

Relating J and KIfor plane strain, assuming no plasticity:

( )E

KJ I

221

=

KI= 225.3 psi-in1/2

J = 0.00154 lb/in

E = 30 x 106psi

= 0.3

Li El ti F t M h i


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The fatigue crack growth procedure:

Obtain K from crack geometry and cyclic loading definition.

Either using library or calculating directly in ANSYS. Calculate the change in the length of the crack per cycle using a crack growth

law.

The damage tolerant procedure:

Inspections to determine current crack sizes and locations.

Finite element analysis to determine stress and/or K.

Crack growth code to determine remaining cycles to failure.

Use life prediction to set inspection interval, at which time the procedure isrepeated.

( )nKCdN

da=

F ti C k G th


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There are many different crack growth laws currently used in industry.

No single universally-accepted method exists; each has its own capabilities

and limitations.All use a differential equation to describe the crack growth rate (da/dN) as a

function of the stress intensity factor range at the crack tip (K).

The first and most basic relationship is the Paris power law [1963], which

describes the linear region in the log-log plot below:

( )nKCdN

da=

F ti C k G th


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The crack growth module in nCode will accept the following laws:

BasicParis - Walker

Austen - InterpolatedRAE Forman - InterpolatedForman

NASGRO3 - MarshallsSentry

Built-in stress intensity factor library contains most common idealized

crack geometries, such as the single edge crack in tension. Or can supply K vs. crack length data directly from finite element analysis.

F ti C k G th


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nCode crack growth analysis steps:

Spectrum loading defined

using a CSV file, or from

files containing more

general load data.

F ti C k G th


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nCode crack growth analysis steps:

Select crack growth law,

crack geometry, and

material property.

NASGRO3 material library, obtained from AFGROW, is

available. Can create user-defined materials via

Material Manager or directly creating XML file.

Results shown

graphically or

in tabular form.


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Fatigue Crackprop in Ansys

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