Quantifying Fretting Damage Using a Contact-Evolution ......10001886:1999-12-20 3 2nd Workshop on Joints Modelling, Dartington Hall, Totnes, Devon, UK 26-29 April 2009 Contact-evolution

10001886:1999-12-20

12nd Workshop on Joints Modelling, Dartington Hall,

Totnes, Devon, UK 26-29 April 2009

Quantifying Fretting Damage Using a Contact-Evolution Based Modelling Approach

Jian (Kenny) Ding, Sean Leen, Phil Shipway, Tom Hyde

School of Mechanical, Materials and Manufacturing Engineering, University Technology Centre in Gas Turbine Transmission Systems

University of Nottingham, UK

10001886:1999-12-20



Nottingham UTC in Gas Turbine Transmission Systems

Study of Spline Couplings

• Experimentally characterise the fretting behaviour of

splines using scaled-down spline and/or representative

specimens

• Develop lifing methodologies for spline against fretting

Spline Joints

• Improved lifing methods

• Fretting fatigue & wear modelling

• Assessment of coatings & alternative materials

Support structures

• Super plastic forming

• Robotic plasma arc welding

• Weld distortion

RFW Process Modelling

• Dual-alloy shafts

• Other components

Shaft Plain Section

• Buckling

• Damage tolerant design

• TiMMC technology

Spline Joints

• Improved lifing methods

• Fretting fatigue & wear modelling

• Assessment of coatings & alternative materials

Support structures

• Super plastic forming

• Robotic plasma arc welding

• Weld distortion

RFW Process Modelling

• Dual-alloy shafts

• Other components

Shaft Plain Section

• Buckling

• Damage tolerant design

• TiMMC technology

Spline fretting failure

10001886:1999-12-20



Contact-evolution based lifing methodology

• An approach that considers transient interaction between wear and fatigue under fretting, especially the effect of wear on fatigue life.

• Contact-evolution based lifing approach comprises: o A finite element wear simulation tool to determine the evolution of

contact geometry. o Damage Accumulation approach for crack nucleation.

• Ongoing EPSEC project in collaboration with Oxford (total grant ~0.6 Millions)

cracking

(partial slip)

Displacement amplitude, μm

wear

(gross sliding)

cracking+ wear

Norm

al forc

e, N

(mixed regime)

Fretting Map *

cracking

(partial slip)


wear

(gross sliding)

cracking+ wear

Norm

al forc

e, N

(mixed regime)

Fretting Map *


wear

(gross sliding)

cracking+ wear

Norm

al forc

e, N

(mixed regime)

Fretting Map *

wear

(gross sliding)

cracking+ wear

Norm

al forc

e, N

(mixed regime)

Fretting Map *

Gross slidingPartial SlipStick Reciproc.sliding

Slip amplitude ( m)�

We

ar

rate

(m/N

m)

3

Fa

tig

ue

life

(cy

cle

s)

107

106

105

10-16

10-15

10-14

1 3 10 30 100 300 1000

Fatigue

life

(cyc

les)

Wea

r ra

te (

m3/N

m)

Gross slidingPartial SlipStick Reciproc.sliding

Slip amplitude ( m)�

We

ar

rate

(m/N

m)

3

Fa

tig

ue

life

(cy

cle

s)

107

106

105

10-16

10-15

10-14

1 3 10 30 100 300 1000

Fatigue

life

(cyc

les)

Wea

r ra

te (

m3/N

m)

10001886:1999-12-20



Modelling Framework

The approach integrates a number of ‘tools’.

o Fretting wear tool is central, which predicts the extent of wear damage and the concomitant change of contact geometry

o For each wear step n, accumulated fatigue damage is calculated by fatigue parameter Smith-Woston-Topper; thus, total accumulated damage is given by

All cycles completed ?

Calculate wear depth increment by modified Archard’s equation

NO

Yes

Output results

FE analysis of fretting contact

Calculate cumulative fatigue damage of the load step

Update contact geometry

Initial parameters• Contact geometry• Applied loads• Wear coefficient & friction coefficient

∑Δ

=

=

Δ=

NN

n

n fnc

T

NND

1∑Δ

=

=

=NN

n

n ni

T

N1 ,

1ϖ

Archard’s Wear equation:

),(),(),( txdstxpktxdh ii ××=

10001886:1999-12-20



Normal load -120 N/mm Stoke - 20 μm

Gross slip case

Worn surface profile (after 5000 cycles)

Original surface profile

Partial slip case


Contact width increase markedly from Hertz

prediction

Fretting Wear Modelling

(Ding et al, Int J of Fatigue, 2004)

Little change of contact size, wear occurring at slip zone

10001886:1999-12-20



0200400600800

100012001400

-0.15 -0.1 -0.05 0 0.05 0.1 0.15

Hoizontal position (mm)C

onta

ct p

ress

ure

(MPa

)

0 cycle

1000 cycles

5000 cycles

0100200300400500600700800900

-0.4 -0.2 0 0.2 0.4

Hoizontal position (mm)

Con

tact

pre

ssur

e (M

Pa)

0 cycle

1000 cycle

5000 cycle


Partial slip case

Normal load -120 N/mmStoke - 5 μm

Fretting Wear Modelling

Evolution of contact pressure

Gross slip case

10001886:1999-12-20



Contact-evolution based prediction of crack nucleation (I) gross sliding

-25

-20

-15

-10

-5

0

5-800 -600 -400 -200 0 200 400 600 800

surface height (μm)

Horizontal position (μm)

Predicted profileMeasured profile

0

0.5

1

1.5

2

2.5

-6 -4 -2 0 2 4 6x/a

SWT (MPa)0 cycle

10000 cycle20000 cycle80000 cycle

0

0.5

1

1.5

2

2.5

0 20000 40000 60000 80000Number of fretting cycles

SWT (MPa)

x/a=0.90

x/a=1.24

x/a=1.75

SWT snapshots

Sample SWT evolutions

Ti-6Al-4V

10001886:1999-12-20



Contact-evolution based prediction of crack nucleation (II) partial slip

-0.005-0.004-0.003

-0.002-0.001

0-2 -1 0 1 2

x/a

Wear depth (mm)

25, 000 cycle150,000 cycle300,000 cycle

0

2

4

6

8

10

0 100000 200000 300000Number of cycles

SWT (MPa)x/a = 1x/a = 0.7 x/a = 0.8 x/a = 0.4

Sample SWT evolutionsWear scar evolution

50μm

Slip Stick Slip

Slip Stick Slip

Ti-6Al-4V

10001886:1999-12-20



Contact-evolution based prediction of crack nucleation (II) partial slip

0

200

400

600

800

1000

1200

1400

1600

-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2

Horizontal position (mm)

Contact pressure (MPa)

50 μm50 μm50 μm50 μm

300000th cycle150000th cycle75000th cycle30000th cycle0th cycle

Complex pressure evolution predicted due to plasticity effects

Multiple cracking locationso x ≈ ± 0.11 mm (light blue)o x ≈ ± 0.04 mm (red)o x ≈ ± 0.13 mm (yellow)

x ≈ ± 0.13 mmo Initial Hertzian contact edgeo early cycles, low COF: gross sliding (N < 3k)

x ≈ ± 0.04 mmo ~ initial stick-slip boundarieso late cycles (N ≈ 150k-300k)

x ≈ ± 0.11 mmo intermediate cycles (3k < N < 150k)o due to flat indenter type pressure peaks

10001886:1999-12-20



Prediction vs. tests (Madge et al, 2007)

Effect of slip amplitude on fretting fatigue is captured by taking into account how wear affects fatigue damage parameter.

Effect of slip amplitude on fretting fatigue

10001886:1999-12-20



Cyclic Plasticity in Fretting

Prager linear kinematic hardeningMaterial: Ti-6Al-4V (α + β)Coefficient of friction – 0.9

EE

σ

ε

EE

σ

ε

EE

σ

EE

σ

εε

EE

σratchetting strain,

rεΔ

σ2

σ1

EE

σ2

ε2|x|

Initial yield locus Subsequent

translated yield locus

σ2

σ1

EE

σ2

ε2|x|

Initial yield locus Subsequent

translated yield locus

0100200300400500600700800900

1000

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018

Strain

Stre

ss (M

Pa)

E = 115 GPa

c = 7317 MPa

0100200300400500600700800900

1000

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018

Strain

Stre

ss (M

Pa)

0100200300400500600700800900

1000

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018

Strain

Stre

ss (M

Pa)

E = 115 GPa

c = 7317 MPa

Plastic shakedownsteady reversed cyclic

plastic strains

Ratchettingplastic strain magnitude

increases continually with load cycling

10001886:1999-12-20



-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0 50000 100000 150000 200000 250000 300000

Fretting cycles

Plas

tic s

trai

n

p22ε

p11ε

p12ε

p

c

N

ir

r

εε∑ =Δ

Cyclic Plasticity in Partial Slip

Nominal Hertzian geometry elastic Wear simulation with plasticity ratchetting phenomenon Possibility of damage/cracking due to ductility exhaustion

rij

rijr εεε ΔΔ=Δ 3

2

Predicted wear-induced evolution of plastic strains at final stick-slip interface

10001886:1999-12-20



0.000

0.001

0.002

0.003

0.004

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

x (mm)

p

3000th cycle75000th cycle150000th cycle300000th cycle

• Gross sliding: shear-dominant plasticity

• g.s. plasticity take a W-shape

• Wearing away of plasticity reduction in equivalent plastic strain

FE-predicted plastic strain in surface layer

Cyclic Plasticity in Gross Sliding

10001886:1999-12-20



Conclusions and Future Challenges

• Contact-evolution based fretting lifing methodology provides

o an integrated solution for fretting wear and fatigue prediction.

o a convincing explanation about the effects of slip amplitude on fretting fatigue

• Future challenges:o Incorporate near-surface effects into fretting fatigue

prediction, such as asperity, oxidation, plasticity and debris accumulation. How important are they for fretting crack nucleation?

o Fretting contact mechanics under micro or nano scales.

10001886:1999-12-20



Contact-evolution based prediction of crack nucleation (I) gross sliding

∑==

=

NNn

n ni

T

NNΔ Δϖ

1 ,

cbniff

bni

fnia )N'('εσ)N(E

')(σεσ ++= ,

2,

2

,max 22)( Δ

Crack nucleation defined to occur at material point i when accumulated damage ω reaches value of 1, where ω is defined as :

Each Ni,n is calculated based on a critical-plane fatigue damage parameter Smith-Watson-Topper (SWT). -25

-20

-15

-10

-5

0

5-800 -600 -400 -200 0 200 400 600 800

surface height (μm)

Horizontal position (μm)

Predicted profileMeasured profile

0

0.5

1

1.5

2

2.5

-6 -4 -2 0 2 4 6x/a

SWT (MPa)0 cycle

10000 cycle20000 cycle80000 cycle

0

0.5

1

1.5

2

2.5

0 20000 40000 60000 80000Number of fretting cycles

SWT (MPa)

x/a=0.90

x/a=1.24

x/a=1.75

SWT snapshots

Sample SWT evolutions

Ti-6Al-4V

Quantifying Fretting Damage Using a Contact-Evolution Based Modelling ApproachNottingham UTC in Gas Turbine Transmission SystemsContact-evolution based lifing methodologyModelling FrameworkContact-evolution based prediction of crack nucleation �(I) gross slidingContact-evolution based prediction of crack nucleation �(II) partial slipContact-evolution based prediction of crack nucleation �(II) partial slipConclusions and Future ChallengesContact-evolution based prediction of crack nucleation �(I) gross sliding

Quantifying Fretting Damage Using a Contact-Evolution ......10001886:1999-12-20 3 2nd Workshop on Joints Modelling, Dartington Hall, Totnes, Devon, UK 26-29 April 2009 Contact-evolution

Documents