Turbo 3 d Crack Propagation

© 2008 ANSYS, Inc. All rights reserved. 1 ANSYS, Inc. Proprietary

2008 International ANSYS Conference

3-D Crack Propagation Modeling and Analysis: Turbocharger components under TMF loading

Ragupathy Kannusamy, Shailendra BistHoneywell Turbo Technologies

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• Turbine Housing– Also called turbine scroll contains the radial turbine wheel and directs gas

into it.– Mostly made of cast iron alloys for turbocharger applications.– During operation these components experience severe thermo

mechanical (TM) load.– Severe TM loading can lead to cracks initiating and propagating with

accumulation of cycles. – Presence of a crack is not necessarily a failure unless it leads to loss of

functionality (gas leakage, wheel rub etc) or is externally visible.– Knowledge of how cracks grow (path) and how fast they grow (growth

rate) is important.– Methods/tools that can help predict path and growth rate of cracks:

• Help design products quantitatively as opposed to a ‘better than’ approach.

• Increase confidence during testing phase.• Lead to more reliable products.

Introduction



Introduction

No of Cycles.

Tem

p (%

of I

nlet

). Stress S1 (% of M

ax).

Inlet gas temp.

Metal temp.

Stress S1.

A typical accelerated test duty cycle.A typical free floating Turbine housing.

Typical housing failures via cracking.



Challenges

• Several LEFM based, Mode I (planar) crack growth modeling codes and methods are popular and commercially available.

• However, due to the nature of loading and complexity of geometry above assumptions are not applicable to our case

• Large scale and even cross sectional yielding can occur in certain locations.– Cracks have been observed to exhibit mixed mode growth behavior (turning and

kinking)– Thermal loads can only be accounted for via an indirect approach in the above case.

• A conventional displacement (K) based approach is also an implementation challenge in 3D

– To capture the singularity in strain at the crack tip a focused/collapsed mesh is needed.

– Creating such a mesh at the crack front at each crack increment is near impossible in an automated manner.

• Developing an automated 3-d mixed mode crack growth code capable of dealing with elastic-plastic condition is a technical challenge !



Background of J-integral Approach

• J-integral is a path independent fracture mechanics parameter which predicts energy release rate and intensity of deformation at crack front (CF) for linear and nonlinear material behavior.

• W is strain energy and it is a point function. It varies from point to point within body of the component [13]

• ANSYS calculates J values using volume integral in terms of rings of elements at the crack front.

• The highest energy release rate is calculated for virtual crack extension angle for all the CF nodes and new crack front is extended in the direction of max energy value.



Crack Growth Rate using Paris Law :

( ) ( )mm JCKCdNda

Δ=Δ=

....33

22

11

+⎟⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛=Δ N

dNdaN

dNdaN

dNdaa

Evaluation of Crack growth vs Cycles : Constant Amplitude Approach

- During fatigue crack growth under LEFM assumptions, the relation between incremental crack growth and load cycles can be represented by Paris law.

- C and m are material properties and need to be evaluated (ASTM D647) .- However, under large scale yielding condition, J-integral approach needs to be directly implemented. This also involves non standard testing for estimating fcg material properties.

Crack growth calculation based on block technique:

N is cycles per Block

EKE

Kv

2

22 )1( −

J = Plane Strain.

Plane Stress



Thermal & Stress analysis for the

given load spectrum

Identify initial crack

location and orientation.

Create a model with crack

surface and crack front information

(CAD)

Preprocessing, Solution and

Post processing(ANSYS)

Spectrum File

Calculate next crack increment

size (∆a)

Report Result

Global DB and RST files

Yes

No

Report new crack front

location and crack surface information.

Stopping criterion reached?

FCG methodology implementation

• Sub model creation, crack feature insertion handled by CAD.

• Meshing, preprocessing, analysis and path/growth prediction handled by ANSYS.

• Logic and links implemented via in-house scripts (APDL and CAD package).

• Process is fully automated after initial set-up.• Can handle both elastic or elastic-plastic

analysis.



• Cruciform specimen.– Uniaxial mechanical loading.– Fully elastic, R = 0.1

Validation runs: Qualitative

Expected crack path.

Predicted crack path (cruciform specimen under uniaxial loading).



Validation runs: Qualitative.

Predicted crack path (cruciform specimen under biaxial loading).

• Cruciform specimen.– Biaxial mechanical loading.– Fully elastic, R = 0.1

Expected crack path.

Gives more confidence to J integral approach implementation and mixed mode capability !



.

Fixed in all 3 directions

Applied LoadGeometry details:

Length = 200mmWidth = 100 mmThickness = 20 mmLoads:Max. Load = 250 MpaMin. Load = 62.5 MpaR = 0.25Material Properties:E = 72400 Mpaע = 0.33Paris law constants:M=3.7C=1.515e-14Cycles per block (CPB) = 5000First crack radius = 3 mm

Full Model with Crack

Sub model with Crack

Validation runs: Quantitative.



Crack Front Profile Plot

0

5

10

15

20

25

30

0 5 10 15 20 25 30Width of Plate (mm)

Dep

th o

f Pla

te (m

m)

Transition from surface crack to through crack automated using a c/s stress based criterion.




Crack Length vs. Cycles

0

5

10

15

20

25

0 5000 10000 15000 20000 25000 30000 35000

Cycles, Np

Cra

ck L

engt

h (m

m)

NASGROFE approach-Sub-modelFE approach-Full Model

∆a

∆c

Crack depth, mm

Cra

ck le

ngth

, mm

1. Differences in NASGRO and FE approaches are due to location of crack increment size.

2. NASGRO calculates next crack increment by considering only ∆a from free surface whereas ANSYS takes highest ∆a value from the crack front. This leads to more conservative results.




Crack path prediction : real geometry

• CFD to obtain thermal B.Cs in the components.

• Elastic material properties used.

• In-house thermal shock cycle simulated.

• Global stress results used for crack path prediction.

Real life crack geometry.

Turbine Housing.

Center/bearing Housing.

V Band Connection.

Mounting base.



Results : Sub-models after each iteration

Actual crack path after tests.Predicted crack path.

Qualitative agreement between real life and analysis!



Results : Real life design comparison.

-34 design is 50% better in terms of fcg life!



Productivity gain: C(t) Specimen

.

0.5 minute 1 minute 0.5 minute

FE model creation with crack front in ANSYS.

Model creation in

CAD.

Manual ProcessAutomated Process

20

40

60

80

30 minutes45 minutes

The developed methodology reduces the crack growth analysis time of test specimen by more than 90%

Results extraction and Crack growth Calculation for a

given load spectrum.

25 minutes

100 minutes

25 minutes45 minutes

2.5 minutes

Total cycle time for simulation of one crack increment

(excluding solution)

100



Next steps:

• Elevated temperature fcg testing being currently conducted using M(t) specimen.

• In-house custom fcg test being developed for validation purposes.• Algorithms being further refined for robustness, accuracy and speed.• Further validation work is ongoing using literature cases.• Ansys Collaboration :• Bugs with CINT fixed in V11.0 SP1.• Thermal effects included in J calculation in V12.0 preview version.

– Tested and validated by HTT.• Need Ansys to implement J calculation using tetrahedral elements.• Need option for J value decomposition. (JI, JII, JIII)



Conclusion:

• The J integral (energy) approach to fcg modeling was effectively used to develop a 3-d mixed mode capable process/methodology.

• J integral approach has several benefits over K based approach:– Ease of implementation as meshing requirments at cf are much

more relaxed.– Capable of dealing with large scale yielding problems.– Directly account for thermal loading.

• Automation via scripts make the process feasible in a production environment. ( ~ 500 designs analyzed/year)

• Some baseline validation runs show good promise for the methodology.• Qualitative validation using fcg material test data will pose its own

challenges. (non isothermal Vs isothermal, LEFM vs NLFM, closure effects etc)



References

1. H.A Richard, M Fulland and M sander, Theoretical Crack Path Prediction, Fatigue Fracture Engg. Mater Struct. 28, 3-12, 2005

2. Shih, C. F., B. Moran, and T. Nakamura, “Energy Release Rate Along a Three-Dimensional Crack Front in a Thermally Stressed Body,” International Journal of Fracture, vol. 30, pp. 79–102, 1986.

3. Daniel Bromberg, Guido Dhondt, Automatic crack-insertion for arbitrary crack growth, Engineering Fracture Mechanics, 9 January 2007 ( Publication is in Press)

4. A.F Liu, Structural Life Assessment Methods, ASM International5. L.P Pook, Crack Paths, WIT Press, 20026. L.P Pook, Metal Fatigue, What is , Why it matters, Springer,20077. H A. Richard, Computational simulation and experimental results on 3D crack growth

in a 3PB specimen with a inclined plane, Key Engineering Material, Vol 251-252 (2003) pp 85-90

8. ANSYS Manuals,9. NASGRO 5.1 Manuals10.J. H Kuang, Crack initiation direction for a crack under mixed mode loading, Inter.

Journal of Fracture, 73 33 -37, 199511.L. P Pook, H.A Richard, Crack paths, Engineering Fracture Mechanics, may, 200712.D.M Parks, Application of Domain Integral Methods using Tetrahedral elements to

determine SIF values, Engg. Fracture Mechanics, 66 (2000), 455-482.



Authors would like to thank:

- Dr. Grama Bhashyam & Dr. Guoyu Lin of Ansys Inc for enabling key capabilities in Ansys to support fcg methodology implementation.

Special mention :

Documents

Turbo 3 d Crack Propagation