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FRETTING FATIGUE MODELING AND LIFE PREDICTION IN AN ADVANCED

SIMULATION FRAMEWORK

Adarsh Pun (NextGen Aeronautics Inc)Tom Curtin (Computational Mechanics Inc)

Kenneth Barlow (NAVAIR)

PSAR Conference

Myrtle Beach, SC

March 2008

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Acknowledgments

• Ken Barlow, TPOC

– SBIR Contract N68335-07-C0018

– Naval Air Warfare Center

• Tom Curtin, Computational Mechanics Inc

• SimLab Corporation

– Developers of the Advanced SimLabTM

Simulation Framework

• Safe Technology

– Developers of FE-Safe®

• Solver Support – CAEFEM, NEi/Nastran

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Program Objective

• Utilize advanced simulation and modeling techniques to accurately characterize stresses in aircraft engine system components under fretting to:

• Predict crack initiation and crack growth

• Predict component failure event

• Determine useful remaining service life

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Program Status

• Completed Phase I & Phase I Option• Phase I feasibility Study Demonstrated

• Efficient modeling of contact surfaces and stresses in ourAdvanced Simulation framework

• Demonstrated usage of the Dang Van Criterion for predicting initiation under complex high cycle multiaxial loading

• Predicted initiation sites and 3D non-planar crack growth under contact stresses

• Performed Extensive literature Survey • Summary of tests already performed in journal papers that can be used in the validation process

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Literature Survey

• Major Fretting Variables• Coefficient of Friction• Contact Pressure• Slip Amplitude - Fretting occurs for small slip amplitude

• Crack Initiation and Propagation• Fretting causes shear crack initiation and propagation depends on stress field• Propagation dominates lifetime (75-80% of life)

• Test Data of various sample shapes and materials available

• “Dove tail” – (AFRL)• “Dog bone”

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Approach

• Automatically Identify Contact

Surfaces

• Extract Surface Stresses And

Through The Thickness Stress

Gradients

• Modify Dang Van HCF Multiaxial

Model To Account For Through

The Thickness Stress Gradients

• Identify Initiation Sites And

Demonstrate The Effectiveness Of

A Boundary Element Contact

Algorithm As A Method To Solve

Edge Of Contact Type Problems

• Perform Mixed Mode Crack

Growth Analysis

• Correlate With Existing Test Data

(P&W, Navair)

• Imbed Developed Software Into

Simlab Fatigue & Fracture

Workbenches

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Process

Assembly Modeling

Mesh & Contact

CAD Geometry, Meshing, Contact FE Run in < 20 Minutes

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Contact Results

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Process

Results Post-processing – Animation And Stress Contours To Extract Critical Zones For Fatigue Analysis

Stresses Imported Into FE-Safe

Dang Van Analysis At The Critical Location(s)

Crack Growth Analysis with BEASY

Load-Time History

Materials – Specify or Create

Stress/Strain Import

Load/Stress AssociateSolution Control

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Identifying Initiation Sites

• Used The Dang Van Criterion*

• Applicable For High Cycle Fatigue Under Multiaxial Loading

• ‘Micro-structural’ Method

– Based on the separation of microscopic stresses (on a scale of individual grains)

from the macroscopic stresses derived by classical engineering computations

– Accounts for local plasticity at the granular level even though on a macroscopic

scale the stress may be elastic

• Fatigue phenomena are local and usually occur in grains which have undergone local plastic deformation in characteristic slip bands

– Defines a safe region where all combinations of stresses are permissible (Dang

Van Diagram)

• Simplest sense – initiation will occur if – Where shear on slip bands causes cracks and the Hydrostatic Component

accelerates damage accumulation

* Dang Van, K., Cailletaud, G., Flavenot, J.F., le Douaron, A., Lieurade, H.P. (1989) Criterion for High Cycle Fatigue Failure Under Multiaxial Loading, Biaxial and Multiaxial Fatigue, EGF 3, Mechanical Engineering Publications, London, pp. 459-478.

f(σ(t)) > 0

βατσ −−= )()())(( tpttf h

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)()()()( ttStAt ijklijklij ρσ +=

Dang Van Method

• Relationship between Microscopic and Macroscopic Stresses S (from FE

Analysis)

• Beyond time t in the spectrum, a time-independent stable residual stress field ρ* exists such as

.)()()(∗+= ijklijklij tStAt ρσ

• Fatigue criterion (safety domain) is expressed in terms of microscopic stress σ as linear combination of principal shear stress τ and principal hydrostatic

stress ph

• τ calculated using Tresca Shear Theory and ρij* is calculated through an

iterative procedure where the yield surface translates and grows through

kinematic and isotropic hardening

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Dang Van Method

The constants α and β in the equation of the Dang Van failure line are obtained from two materials tests (Pure Shear and Pure Axial at R = -1; or two different tests with different fatigue stress ratios R1 and R2).

Safety Zones

Remains within two bounding failure lines signifying infinite life. Any excursion outside the damage line indicates failure.

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Dang Van Analysis

Results

Inputs

Output

Dang Van Plot

Hydrostatic Stress Time History

Mesoscopic Shear Stress Time History

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Development of Prototype Fretting

Fatigue Crack Growth Software

Goal: Quick assessment of simple fretting

fatigue type problems. Provide insight into how the various fretting variables impact crack growth behavior. Incorporate validated process in 3D Fretting Fatigue Crack Growth software.

• Develop 2D Non Conforming Frictional Contact Capability

in BEASY

• Couple BEASY’s Automatic Crack Growth Algorithm with Non Conforming Contact Solver

• Prototype Software Assumes- Uniform friction coefficient along contact interface

- Load cases involving crack closure and sliding are not evaluated

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Boundary Element Contact Solution

• Boundary Integral Equation Method• Surface-Only Discretization for each Contacting Body• Equations Coupled in Area of Contact• Direct Solution of Stress and Displacement on Contact

Surface• Iterative-Incremental Contact Solver

– Suitable for friction problems which are nonlinear and load path dependent

– Friction modeled using Coulomb’s Law• Contact Constraint Technique

– Displacement Compatibility– Traction Equilibrium

ADVANTAGES OF SOLUTION PROCEDURE

Model Progressive Nature of DeformationEnsure Accurate Load and Contact History Method Accounts for Partial Slip

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Cylindrical Fretting Pad(Benchmark Case)

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BEASY Model

2D Plane Strain Boundary

Element Model (915 elements)

Contact Solver Controls

MAXIMUM NUMBER OF CONTACT ITERATIONS : 25

MAXIMUM NUMBER OF CONTACT LOAD STEPS : 10

NORMAL CONTACT TOLERANCE : 0.005

TANG CONTACT TOLERANCE : 0.0075

Solution times ranged from 1-2 minutes per

load case on a single processor PC

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Comparison of Normal and Shear Traction(P = 1335 N/mm Q = 570 N/mm)

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Comparison of σxx Stress(P = 1335 N/mm Q = 570 N/mm)

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Comparison of Shear Traction(P = 1335 N/mm Q = 570 N/mm σb = 410 MPa)

bulk stress σb applied to specimen

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BEASY Fracture

Workbench

NEW MODELING TOOLS TO

FACILITATE CRACK INSERTION

AND CRACK GROWTH

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3

Wide Range of Crack Growth Controls

1

2

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Crack Growth Near Edge of Contact

10 micron crack located normal to surface at peak σx locationCrack growth increment = 5 micronsCrack growth angle calculated using strain energy density method

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Crack Growth Path for Different

Friction Coefficients

Examples of fretting cracks

(SEM images) for cylindrical

fretting pads

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100.00

200.00

300.00

400.00

500.00

600.00

0.000 0.100 0.200 0.300 0.400 0.500 0.600

Crack Length (mm)

Str

es

s I

nte

ns

ity

Fa

cto

r (M

Pa

mm

0.5

)

SIF1 (u =0.5) SIF 1 (u=0.95) SIF1 (u =1.2)

Mechanically Short CracksMicrostructurally

Short Cracks

Effect of Friction Coefficient on K1

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Key Issues Requiring Further Investigation

• Non Uniform Friction Coefficient (µ) Model

– Literature review suggests µ is related to the relative slip.

– Difficult problem requiring trial & error solution to determine the length of the stick-slip region.

– Models using linear varying µ in the slip region have been

investigated by others (Wang, R.H., Jain, V.K. Mall, S., Wear, No.262, 2007, pp. 607-616)

• Modeling Crack Closure and Sliding

– Fractures problems that involve contact and friction on the crack

surface are difficult to solve

– Partially closed cracks may have complex interfacial boundary conditions

from Wang J. and Crouch S., “An iterative algorithm

for modeling crack closure and sliding”., Eng. Fract.

Mech. V 75 2008 p 128-135

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Key Issues Requiring Further Investigation

• The Need to Treat Short Cracks Differently– Mechanical short cracks tend to grow faster at same ∆K (particularly near

∆Kth) than long cracks

• Two Stage Micromechanics Model for Short Fatigue Cracks*

n = a/c

κ = 1- ν for edge dislocation* De Los Rios, E.R. and Navarro, A.

“A two-stage micromechanics model

for short fatigue cracks”, Eng. Fract.

Mech., V 44, No.3, 1993, pp 425-436

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Future Work

• Account for through the thickness

stress gradients

• Dang Van Analysis with multiple friction coefficients

• Develop 3D fretting fatigue crack growth software

• Imbed Algorithms and Developed Software Into Simlab® Fatigue And Fracture Workbenches Utilizing FE-Safe & BEASY Analysis Engines

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Conclusions

• Dang Van Method is a viable approach for predicting initiation under fretting conditions

• 2D boundary element contact solution provides accurate edge of contact stress and is numerically efficient.

• Prototype 2D Fretting Fatigue Crack Growth software shows promise in predicting mixed mode SIFs and crack growth path for coupled contact and crack growth type analyses.

• Demonstration of Technology in SimLab – Advanced Assembly Modeling and Contact Simulation for Engine Applications