Advances I n Crack Growth Modelling Of 3D Aircraft Structures - - PowerPoint PPT Presentation

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Advances I n Crack Growth Modelling Of 3D Aircraft Structures

Sharon Mellings, John Baynham, Bob Adey C M BEASY Ltd

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Contents

Introduction Overview of methodology Model creation Crack growth examples Fatigue loading with mixed mode growth Contact on crack faces Conclusions

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I ntroduction

Effective fracture analysis and crack growth prediction can be invaluable in airframe structural design

Critical crack sizes can be determined Inspection intervals can be computed Failure modes can be simulated

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Crack growth analytical methods used

A variety of techniques can be used to predict the rate and in some cases the paths for crack growth in structures including

Reference solution methods (“Cook Book” Solutions) Finite element analysis Boundary element analysis

Each of these has their own advantages and disadvantages.

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Boundary elements analysis

This analysis is ideal for crack growth analysis as it deals purely with the boundary of the model.

However boundary element models of the part generally do not exist and it would be necessary to create the BEM model as well as defining the loads and restraints.

This methodology will be used in this paper overcomes these difficulties, with a tool that automatically creates a BEM model using existing FE models.

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Crack growth process

Create model Add initial crack Solve to compute stress intensity factors Determine where the crack is growing to and how far Grow the crack Add the grown crack to the un-cracked model

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Example Model

The analysis process will be demonstrated using a number of models. All of the examples in this presentation demonstrate crack growth within a curved, machined, stiffened panel.

The initial model is a finite element representation of part of a stiffened panel. The part is modelled in ABAQUS using tetrahedral elements.

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Finite element model of a panel (ABAQUS)

Detailed crack growth to be studied in this area.

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Crack growth process

Create loaded model Add initial crack Solve to compute stress intensity factors Determine where the crack is growing to and how far Grow the crack Add the grown crack to the un-cracked model

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Model creation

The ABAQUS FE model will be used to create a boundary element sub-model.

A group of FE elements is selected from the full ABAQUS model The external surfaces of the group are used to create boundary elements Loading is created on the boundary element model to give the same load condition as in the finite element model.

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Section of ABAQUS model selected for analysis

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Boundary element mesh of the selected sub-model

Triangular boundary elements created from the tetrahedral finite elements.

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Crack growth process

Create loaded model Add initial crack Solve to compute stress intensity factors Determine where the crack is growing to and how far Grow the crack Add the grown crack to the un-cracked model

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Crack growth process

Using the sub-model a number of different crack growth studies will be performed. This will look at how crack front shapes change through the thickness transitions in the model. In the initial examples, a uniaxial tension loading is applied to the model. Subsequent studies will look at crack turning and compressive loads, resulting from multi-axial loading.

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Examples of crack growth studies in the model

Example 2 Example 1 Example 3

Cracks are initiated at three different locations in the model

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Adding the crack

In the analysis process the user is simply required to select the type of crack and then add it to the model. The cracks used are selected from a list of “library” cracks.

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Example 1

In the first example, a through crack will be placed at the top of the stiffener itself.

The changing shape of the crack front will be examined as the crack grows.

First we will look at the tools used to generate this crack growth model. Note that in this analysis, we will not be looking at the fatigue life, but just the shape of the grown crack.

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Selection of library crack

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Diagram of added crack

Through thickness Crack depth Crack Growth

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Specify crack size

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Fatigue properties

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Mesh after the initial crack is added

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Crack growth process

Create loaded model Add initial crack Solve to compute stress intensity factors Determine where the crack is growing to and how far Grow the crack Add the grown crack to the un-cracked model

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Adding the crack to the model

The stresses and displacements are computed using the Dual Boundary Element method. This model is then solved to give the stress intensity factors.

These are computed using the J-Integral

Ω ∂ ∂ + Ω ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ∂ ∂ ∂ ∂ − Γ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ∂ ∂ − =

∫ ∫ ∫

Ω Ω

d x d x u x d x u Wn J

ij ij i i C i ij 1 1 3 3 1 1 1

θ α δ σ σ σ

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Stress intensity factors along the crack front

0.0000E+00 1.0000E+00 2.0000E+00 3.0000E+00 4.0000E+00 5.0000E+00 6.0000E+00 0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000 xi SIF Mode 1 Mode 2 Mode 3

Note fully mixed mode Ki, Kii and Kiii are predicted

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Crack growth process

Create loaded model Add initial crack Solve to compute stress intensity factors Determine where the crack is growing to and how far Grow the crack Add the grown crack to the un-cracked model

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Crack growth rate

In this analysis, the crack growth is modelled using the Paris equation: For this equation we need a single dK value.

From the analysis we have 3 independent stress intensity factor values These are combined into a Keff value

( )

n

K C dN da Δ =

( )

( )

2 2

2

II III I eff

K K K K + + =

min max eff eff eff

K K dK − =

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Crack growth direction

The Paris equation determines how fast the crack is growing. The direction for the crack growth depends on the loading direction.

For this example, the crack growth direction is determined to be the direction in which the strain energy density is minimised.

This computation uses both the K1 and K2 values

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Predict the crack growth

In the simulation process the crack front is grown using δA values which vary along the front. The average δA is used to limit the growth.

This distance is pre-defined before the analysis is started.

The crack is grown, using successive recalculations of the da/dN crack growth rate until the required growth increment is reached.

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Predicted new crack front positions

Predict new crack

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Crack growth process

Create loaded model Add initial crack Solve to compute stress intensity factors Determine where the crack is growing to and how far Grow the crack Add the grown crack to the un-cracked model

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Grow the crack

The predicted crack growth positions are used to create a new crack surface This grown crack is added to the un- cracked model A new cracked model is produced and the new stress intensity factors are computed.

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Crack mesh after first growth step

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Crack growth through stiffener

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Crack surfaces after breakthrough.

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Example 2

In the previous example, the initial crack was a straight through-crack. However would the crack growth be different if the initial crack was a smaller, corner crack, for example? In this second example the initial crack is changed.

Note this just requires a change of the selected crack, not a completely new model.

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View of the crack added to the model

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Crack growing in the stiffener

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Comparison of growth between different cracks

The resultant crack shape is similar to the through crack growth performed earlier. However any computed life would not include the growth from the corner crack.

Growth from through crack Growth from corner crack

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Example 3

For the third example we now look at a crack that is growing in the main panel itself. In this example we are simulating a crack that is growing through the panel towards the stiffened section.

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Crack growth through base panel

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Fatigue analysis with multi- axial loading

In the previous examples the cracks have been grown with a uniaxial load applied to the panel In most practical applications, mixed mode loads are applied to structures. In addition load can be applied in different directions during the loading cycle (multi- axial loading).

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Multi-Axial Loading Example

Analysis performed using the through crack in a stiffener. Two further load cases were studied which give twisting in panel. Initially different combinations of the loading were investigated showing the twisting loads acting with or against each

• ther.

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Loads act “in phase” so that the loads cycle together

Loads in phase

• 1
• 0.8
• 0.6
• 0.4
• 0.2

0.2 0.4 0.6 0.8 1 90 180 270 360 Loading phase angle Load factor Load Case 1 Load Case 2

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Loads act in opposite directions to each other

180 Degrees Out of Phase

• 1
• 0.8
• 0.6
• 0.4
• 0.2

0.2 0.4 0.6 0.8 1 90 180 270 360 Loading phase angle Load factor Load Case 1 Load Case 2

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Load cases apply out of phase from each other

90 Degrees Out of Phase

• 1
• 0.8
• 0.6
• 0.4
• 0.2

0.2 0.4 0.6 0.8 1 90 180 270 360 Loading phase angle Load factor Load Case 1 Load Case 2

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Comparison of crack growth rates with different loading

0.00 5.00 10.00 15.00 20.00 25.00 10000 20000 30000 40000 50000 60000 70000 80000 90000 100000 Cycles Crack Size "In Phase" 90 Degrees out of phase 180 Degrees out of phase

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Comparison of crack growth from different fatigue

Loads in phase Loads 90 degrees

• ut of

phase Loads 180 degrees

• ut of

phase

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Contact on the crack faces

In the previous example, negative K values were generated.

Load reversal generates positive and negative K values Negative mode 1 SIF values means that the crack faces are closing and interfering. These are used in the analytical expressions to give crack closure.

However it is more accurate to compute full contact on the crack faces

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Contact Analysis

A new load case is generated in which there is a negative KI value and a high twisting load Using a standard analysis negative SIF values are computed. Contact conditions are applied to the crack faces.

New SIF values are then obtained.

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Comparison of “contact” and “no-contact” K1 results

• 2.0000E+02
• 1.5000E+02
• 1.0000E+02
• 5.0000E+01

0.0000E+00 0.0000 0.2000 0.4000 0.6000 0.8000 1.0000 Position along crack front Stress intensity factor K1 No Contact K1 Contact

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Example of crack growth with contact on faces

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Crack growth in box

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Conclusion

A methodology has been presented that can perform fracture analysis of structural components including realistic

Geometry Loading

This can be used as an “add-on” during normal airframe stress analysis, using models and results which already exist.

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Conclusion

Model generation can be automated and simplified by capturing geometry and loading from larger FE models Design changes can be studied in detail using accurate representation of components shape and loading

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Conclusion

The crack shape and behaviour is fully mixed mode and 3D

Complex stress fields can lead to detailed crack growth shapes without being constrained by handbook solutions

The improved information and understanding of the crack growth paths and rates give improved confidence in determining inspection intervals.