Crack propagation in Ansys

© 2011 CAE Associates

Fatigue Crack Propagation

Analysis 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 not explicitly 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 life

prediction, 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 is based 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 find

the 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 of elasticity.

— 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.

=

+

=

−

=

23sin

2sin

2cos

2

23sin

2sin1

2cos

2

23sin

2sin1

2cos

2

θθθπ

σ

θθθπ

σ

θθθπ

σ

rK

rK

rK

Ixy

Iyy

Ixx

6


K is based on the crack geometry and applied cyclic loading:

),2/(:/12.1

σπσ

cafQwhereQaKI

=

=

Through thickness crack Edge crack Surface (thumbnail) crack

a

c2

Dependence of flaw shape parameter Q on the ratio of depth to width 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, KII and KIII can be calculated in ANSYS, but it is typical to assume that KI is the dominant parameter.

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When KI reaches some critical value, the part will fail.

Critical value of KI, called the fracture toughness or KIC, is obtained from a controlled 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 a linear 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 I22 1 ν−

==

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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 KI of 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, KI for a compact specimen is given as:

−

+

−

+

−

+=

=

432

23 60.572.1432.1364.4886.0

1

2

Wa

Wa

Wa

Wa

Wa

Wa

Waf

PWBK

Waf 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 with

quarter-point nodes. — Half specimen modeled using symmetry boundary conditions.

Crack tip Crack 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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Numerical Methods

Demonstration problem: ANSYS J-integral method. — CINT commands used to define crack tip node and request number of

contours to use (10). — Same model as before, but special crack tip elements are not required. — Paths are created automatically around the crack tip, using the next available

row of elements.

Path 7 of 10

Crack tip Crack face

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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

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Numerical Methods

Demonstration problem: ANSYS J-integral method. — Relating J and KI for plane strain, assuming no plasticity:

( )E

KJ I22 1 ν−

=

KI = 225.3 psi-in1/2 J = 0.00154 lb/in

E = 30 x 106 psi

ν = 0.3

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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 is

repeated.

( )nKCdNda

∆=

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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: ( )nKC

dNda

∆=

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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.

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nCode crack growth analysis steps:

Spectrum loading defined using a CSV file, or from files containing more general load data.

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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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nCode crack growth analysis demonstration problem.:

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Crack propagation in Ansys