FF 29 03 2012s550682939.onlinehome.fr/Fatigue/fichier/gt7/Fretting Fatigue - S... · Q* 100 N/mm CN = 10 6 cycles S. Fouvry et al., LTDS, SF2M, 29/03/2012 . 10 Application of the

1

Fretting Fatigue

“Etude & prédiction de la durée de vie”

S. Fouvry, K. Kubiak, H. Proudhon

LTDS, CNRS, Ecole Centrale de Lyon, Ecully , France

contact : [email protected]

SF2M – Commission Fatigue 29 mars 2012, PARIS“Prise en compte des phénomènes aggravants dans la conception en fatigue”

Context and challenges

microdisplacements

[< ± 100 µm]

contact

pressure

blade / disk contacts in turbine engine

electrical connectors

bridge cables

[Bosh]

[M. Park et al.]S. Fouvry et al., LTDS, SF2M, 29/03/2012

2

Normal Force (P)

Cyclic tangential

displacement δδδδ(t)

Damage induced by plain fretting loading

Cyclic tangentialforce Q(t)

Cracking

Small amplitude

Q (N)tangential force

displacementδ (µm)

Hertziancontact

stickzone

Partial Slip

Wear

Surface damages

Gross Slip

displacementδ (µm)

Q (N)tangential force

Large amplitude

S. Fouvry et al., LTDS, SF2M, 29/03/2012

Industrial application : Pressed fitted Wheels-Axles contact

Fretting-Fatigue Loading (Partial Slip)

Question : Are can be predicted the cracking risk ?

Fatigue(R=-1)

Pressure

Fretting(R=-1)

AxleAISI 1034

New Train Speed Record (April 2007)

Fretting-Fatigue Loading

Ultra severe

technological test

Cracking on

the axle

FRETTING


3

Part A : Prediction of the infinite Fretting Fatigue endurance Conditions (No crack nucleation or Crack Arrest conditions)

Part B: Prediction of finite endurance life time under Fretting Fatigue stressing

Part C: Palliatives against Fretting Fatigue


Part A : Prediction of the infinite Fretting Fatigue endurance Conditions

⇒ Crack Nucleation Boundary

⇒ Crack Arrest Boundary


4

Number of fretting cycles (N)cra

ck length

(µm

)

No nucleation

Nucleation butcrack arrest

Failurepressure

cyclic tangential

force

+

Heterogeneousstress field

Fatigue Loading

)MPa( ±σ

Homogeneous stress field

Fretting Loading

Fretting Fatigue : Stress & Damage evolutions

)MPa( ±σ


Fretting Fatigue : Fretting – Fatigue Map Concept (Partial Slip)

Fre

ttin

g loadin

g

(Q*/

µP

, R

Q)

Fatigue loading

Failure

domainplain

Fretting

test

Plain fatiguetest

P

Q*

aσ

FrettingFatigue

Test

aσ

PQ

δδδδ

), ( σσ Ra

Crack arrest boundaryCrack nucleation boundarySafe crack

nucleation

domain

Safe crack

propagation

domain

GROSSSLIP CONTACT

d

a

σ

σ

P.µ

*Q

P : Normal force

Q* : Tangential force amplitude

σa : Fatigue stress amplitude

Fretting Loading

Q (N)

δ (µm)

Q* (N)


5

How can be formalized the Fretting Fatigue

Mapping Concept ?

(i.e. How can be predicted the different damage domains ?)


Topics of the presentation

Materials

Prediction of the Fretting-Fatigue crack nucleation boundary

Modelling (Contact stressing+ Crack Nucleation + Crack Propagation)

Conclusions

Experimental strategy (combined plain fretting & fretting fatigue tests)

Prediction of the Fretting-Fatigue crack propagation boundary


6

Ferrite - Perlite structure

Material : Low carbon steel (AISI 1034)

600Maximum stress, Rm

(MPa)

350Yield stress, Re 0.2 (MPa)

0.3Poisson coefficient, ν(ratio)

200Young modulus, E (GPa)

Low carbon steelMatériau

Mechanical properties

3.5m exponant (Paris law)

270 MPaFatigue limite (R=1)

2·10-12C coefficient (Paris law)

117

7

Crack propagation (long crack) & fatigue

SIF range threshold, ∆K0

maximum SIF, Kc ( )mMPa ⋅

( )mMPa ⋅

Gros V. , Ph.D Thesis, Ecole Centrale de Paris, France,1996.


P

σσσσext

δδδδ

Q*

σσσσext

δδδδ

σσσσext

δδδδ

σσσσext

δδδδ

σσσσext

δδδδ

σσσσext

δδδδ

Fretting Fatigue Test

δδδδδδδδ

P

P

δδδδ

δδδδ

P

δδδδ

Q*

Plain Fretting Test(fretting wear test)

Fretting Experiments : Coupling Between Plain Fretting & Fretting Fatigue tests

Acquisition systemdisplacement normal force

tangential force temperature

humidity

FRETING CYCLE(Partial Slip)


7

Fn

ext

δδδδ

Q*

ext

δδδδ

ext

δδδδ

ext

δδδδ

ext

δδδδ

σσσσext

δδδδ

fatigue loading(R=-1)

iso-fretting loading(R=-1)

δδδδ

P

δδδδ

Q*

- Friction behavior (Tribology)- Crack nucleation- Short crack propagation

(systematic crack arrest conditions)

- Crack propagation (short & long)- Crack arrest condition- Lifetime endurance

This combined Plain Fretting and Fretting Fatigue test allow us to dissociatethe impact of contact and bulk cyclic loading on the fretting fatigue damage

AISI 1034

P= 230 N/mm

R= 40 mm

p0H= 450 MPa , aH = 320 µm

52100

Similar contact condition

Fretting Experiments : Coupling Between Plain Fretting & Fretting Fatigue tests

Plain Fretting Test Fretting Fatigue Test


Plain Fretting Wear Test →→→→ Friction analysis

Coefficient of Friction (µt) = 0.85

cycles

Q[N]

δ[µm]

Fretting Cycles

Am

plitu

de v

alu

es

incremental method

0

0.2

0.4

0.6

0.8

1

0 5 10 15 20 25

0

0.2

0.4

0.6

0.8

displacement amplitude δ* (µm)

Energy discontinuity

*Q..4

EA

g

d

δ=P

*Q

Partial

Slip

GTµ

P

*Q≠µ

Gross Slip

en

erg

y r

atio A

,

tan

gential fo

rce r

atio,Q

*/P

tµ

coefficient of frictionat the sliding transition

Displacement

Gross

Slip Tangential forcePartial

Slip

Recorded cycle


8

Analytical description of Plain Fretting and Fretting Fatigue contacts

P

Q

X=x/a

Y=y/a

+1-1

)X(p

surfacepressure field

)X(q

Loadingshear stress

field (+Q*)

p0

slidingzones

-c/a c/astickingzone

Unloadingshear stress

field (-Q*)

)X(q

Plain Fretting Contact

Maximum loading locatedsymetrically at the contact

borders

Mindlin et al, 1949

-1 +1

a

e

-1 +10

+Q*

)(Xq

slidingzones

)(Xp

Trailing edge

Loading

Tangential

force

a

e0

-Q*

)(Xq

)(Xp

Unloading

Tangential

force

Compression

ac /2

ac /2

aσ−

aσ+

Tension

X=x/a

X=x/a

Fretting-Fatigue Contact

Maximum loading locatedat the trailling edges (at the

Loading state)

Nowell et al, 1989


Contact modeling: Stress field analysis

FEM ANALYSIS

Can include plasticity

Long and fastidious (inappropriate to developA mapping investigation !!)

X

p(X)

Analytical formulation: Green’s functionsSuperposition of piecewise-lineOverlapping triangular elements(K.L. Johnson, 1985)[Elastic Half Space Hypothesis]

Σ=Σ t)(M,

Very fast !!S. Fouvry et al., LTDS, SF2M, 29/03/2012

9

Crack Nucleation Analysis


Plain Fretting Wear Test →→→→ Friction Identification of the crack nucleation

2c 2a

A

A

2c 2a

A

A

Surface observation

stick zone sliding zone

b

Cross section observation: measure of thecrack length

Fretting Test : Q*=± 200 N/mm, 106 cycles

0

20

40

60

80

0 100 200 300 400

tangential force amplitude, Q* (N/mm)

cra

ck len

gth

, b (

µm

)

Crack

nucleation

threshold

*

CNQ

P=230N/mm, µ=0.85

(106 cycles, p0= 450 MPa)

mm/N100Q*CN =

106 cycles


10

Application of the Dang Van’s (multiaxial criteria)

determination of the loading path

computation of the

cracking risk (Dang Van)

Σ(M,t)0- c- a c a

ZX

PQ (t)

stick domain slidingdomain

M

Surface (X=x/a)

Subsurface (Y=y/a)

DVd

Cra

ckin

g r

isk

Plain Fretting

Cracking at the contact borders

3

3

d

ddC

σ

σ−τ=α

dσ

dτ: alternating bending fatigue limit

: alternating shear fatigue limit.

α−τ

τ

(t)p̂.

t),n( ˆ max=d

dnt,DV

r

r

if dDV>1 cracking

$ ( ) * ( )σ ρt t= +Σ

point M fixed

shakedown

( ) ( )α τ σ σ= −d d d2 3/

$ ( , )τrn t

shear$ ( )p tH

tension


Surface (X=x/a)

Subsurface (Y=y/a)

DVd

Cra

ckin

g r

isk

Application of the Dang Van (Quantitative Prediction)

0

20

40

60

80

0 100 200 300 400

tangential force amplitude, Q (N/mm)

crack

leng

th, b

(µ

m)

Crack

nucleation

threshold

*

CNQ

P=227N/mm, µ=0.85

(106 cycles, p0= 450 MPa)

mm/N100Q*CN =

Overestimation of the cracking risk !!

1dDV =


11

“Non local approach” to capture stress gradient effects


“Non local approach” to capture stress gradient effects

nucleation process

volume approach nucleation process

surface approach

Critical distance

method

)MPa(Σ

a

y

2D plane straincondition

(cylinder/plane)

contact steep

stress gradient( )y,xD3RΣ

D3l

( )xD2RΣ

D2l

Averagingover a constantsquare volume

Averagingover a line

( )xD1RΣ

D1l

Stress analysisAt a critical distancefrom the “Hot point”

Non local fatigue approaches

« Hot point »


12

Identification of representative length scales (Dang Van)

length scale parameter,

maxi

mum

Dang V

an v

alu

e : m

ax(

dC)

0.0

1.0

2.0

3.0

4.0

0 30 40 60 80 100 120

µm 60 D3 =l

)(d D3)Q(DV*CN

l

(µm) D3l

( )y,xD3RΣ??D3l

D3l( )*CNQΣ

)Q(DV *CN

d

1d)Q(DV *

CN=

untilReverse approach

µm 60 D3 =l µm 75 D2 =l µm 28 D1 =l

2 D1

2DD3

lll ≈≈

Consistent with notchdescription (Taylor and al)

3.44

1 - What is the stability of the different “averaging approaches” regarding Fretting – Fatigue stressing ?

2 - Is the length scale parameters defined from Plain Fretting configuration can be extrapolated to predict crack nucleation under Fretting Fatigue ?

Questions ?


13

Fretting – Fatigue Experiments : Identification of the crack nucleation Fretting Fatigue map

NO CRACK78120

CRACK91120

NO CRACK62100

NO CRACK80100

CRACK100100

CRACK110100

CRACK115100

NO CRACK8250

CRACK9250

Cross section

Examination

Tangential

force

amplitude

Q* [N/mm]

(R=-1)

Fatigue

stress

amplitude :

σa [MPa]

(R=-1)

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1norm

aliz

ed f

rettin

g loadin

g: Q

*/µ

P, (R

=-1

)

normalized fatigue loading: σa/σd, (R=-1)

safe cracknucleation

failure

crack

no crack

PF threshold

106 cycles

Low influence of fatigue stress amplitude in the low fatigue stress range !(Conventional idea : crack nucleation is controlled by fretting)


0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

crack

no crack

PF threshold


failure

norm

aliz

ed f

rettin

g load

ing: Q

*/µ

P, (R

=-1

)


1dDV =Theoretical prediction of the

Fretting Fatigue crack

nucleation boundary

µm 60 D3 =l

Similar tendencies !!

µm 28 D1 =l

Pessimistic (i.e. secure) prediction of the safe crack nucleation domain from Plain Fretting identification !

Correlation Experiments // Modelling (Dang Van)

µm 75 D2 =l


14

Comparison between Multiaxial Criteria (Crossland)

Deviatoric

Plane

)t(Σ

)t(S

'Φ

Φgeneral

stress pathduring fatigue

loading

Deviatorictensor

D

2

D

2

1a =ζ

Deviatoric

Plane

)t(Σ

)t(S

'Φ

Φgeneral

stress pathduring fatigue

loading

Deviatorictensor

D

2

D

2

1a =ζ

dmaxhCa P τ<⋅α+ξ

Crossland Criterion

Σ=

∈))t((trace

3

1maxP

Ttmaxh

Hydrostatic pressure

−−=ξ

∈∈

21

00TtTt

a ))t(S)t(S(:))t(S)t(S(2

1maxmax

2

1

0

)t(J2component

3

3

d

ddC

σ

σ−τ=α

maxhCd

aC

Pd

⋅α−τ

ξ=

- If is greater than or equal to 1, there is a risk of cracking;

- If remains less than 1, there is no risk of cracking.

Fatigue material component


norm

aliz

ed f

rettin

g loadin

g: Q

*/µ

P, (R

=-1

)


0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1


failure

Comparison between Multiaxial Fatigue Criteria

crack

no crack

PF threshold

Crosslandµm 45 D3 =l

Dang Vanµm 60 D3 =l

( )y,xD3RΣ

D3l

Plain Fretting

No differences between multiaxial fatigue criteria

(Quasi uniaxial stress loading state at the contact border)

Selected “Non local Fatigue approach” => “Crossland +square averaging “S. Fouvry et al., LTDS, SF2M, 29/03/2012

15

How to prediction the Crack Arrest ?


SIF modeling at the fretting crack tip (decouple approach)

21

21 2( ) 1 * *

t tM t t m m

h h

− = + +

cylinder

hW

H

t

σ(t)

P

Q

∫ σ⋅π

= dt)t()t(M2

1K

∫ τ⋅π

= dt)t()t(M2

2K

τ(t)

SIF integration method by Weight Functions

1

2

2

2

yy

yx

K

r

K

r

σπ

σπ

=

=

x 21

21 2( ) 1 * *

t tM t t m m

h h

− = + +

cylinder

hW

H

t

σ(t)

P

Q

∫ σ⋅π

= dt)t()t(M2

1K

∫ τ⋅π

= dt)t()t(M2

2K

τ(t)

SIF integration method by Weight Functions

1

2

2

2

yy

yx

K

r

K

r

σπ

σπ

=

=

x 0

1

2

3

4

5

6

7

8

0 20 40 60 80 100 120 140 160 180 200

K1, M

pa.v

m

K1max_P540_Q283

a0=170µm

Weight Functionsstraight crack (0º)

Short crack domain (a<a0)

crack length, µm

Evolution of SIF (mode I)

0

1

2

3

4

5

6

7

8

0 20 40 60 80 100 120 140 160 180 200

K1, M

pa.v

m

K1max_P540_Q283

a0=170µm

Weight Functionsstraight crack (0º)

Short crack domain (a<a0)

crack length, µm

Evolution of SIF (mode I)

Q*= 125 N/mm

P= 230 N/mmFretting Wear

condition

surface

" the crack length increase

but the contact stress field

is decreasing very fast"

Stress field extraction (FEM) +

Weigth Functions (WF)

Other approaches : Distributed Dislocations

Dubourg et al. Nowell et al;

(Bueckner H.F.)


16

Comparison : Couple (FEM: contact+crack) // Decouple FEM(contact) + WF

Couple approach (FEM: contact+crack)

"Crack box"- Automatic remeshing

Crack length

Couple approach

(FEM: Contact+Crack)

0 50 100 150 200 250 300 350 400 450 500 550 600

Uncouple approach

(FEM+WF)

KImax

0 50 100 150 200 250 300 350 400 450 500 550 600

Crack length

Couple approach

(FEM: Contact+Crack)

0 50 100 150 200 250 300 350 400 450 500 550 600

Uncouple approach

(FEM+WF)

KImax

0 50 100 150 200 250 300 350 400 450 500 550 600

Selected “SIF computation” => “ FEM + Weigth Functions “S. Fouvry et al., LTDS, SF2M, 29/03/2012

0

2

4

6

8

0 40 80 120 160 200

KIm

ax,

MP

a√m

crack length, b(µm)

the crack length increase

but the contact stress field

is decreasing very fast

Q*= 125 N/mm

P= 230 N/mm

Plain Frettingcondition

Evolution of the SIF below the contact: Non monotonic evolution !

Increase of the crack

length

Decrease of the contact

Stress field

The crack stops ! (situation of plain fretting condition)

Plain Fretting

The crack stops !


17

Determination of the effective SIF (combining mode I and II)

2IIeff

2Ieffeff KKK ∆+∆=∆General formulation

I_effK∆ )1µc(mixed_effK =∆ )0µc(mixed_effK =∆< <

Mode I Mode II

Mixed Mode A (Crack edge with high friction)2

axImI

2

axIm)µc(mixed_eff KKK +=∆ 0K inImI =0c >>µ

Mixed Mode B (Crack edge friction free)

2inImIaxImI

2

axIm)0µc(mixed_eff )KK(KK −+=∆ = inImIK

0c =µ

Pure mode I (Usual hypothesis)

axImI_eff KK =∆ Because R=-1 (closure effect)0K inIm =


Identification of the crack arrest approach : KT’s formulation

Q*= 125 N/mm P= 230 N/mm

Crack arrest approach

based on the Kitagawa-Takahashi

diagram

Specific behavior of the crack arrest condition for the small crack !!!

0

2

4

6

8

10

0 50 100 150 200 250 300

Propagationarea

8

10

0 50 100 150 200 250 300

crack length b, µm

crack arrestboundary

short crack

long crack

2

f

00

H

K1b

⋅σ

∆

π=

if short crack (b<b0)0

0thb

bKK ⋅∆=∆

if long crack (b>b0) 0th KK ∆=∆

b0 = 170µm

Araujo J.A., Nowell D., Int. J. of. Fatigue, 1999, 21

∆K

eff

_m

ixe

d(µ

c=

0), M

Pa√m

non propagation

area0b

MPa 120max =σ

Stop!

MPa 150max =σ

propagation

0K∆

0

0thb

bKK ⋅∆=∆


18

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

crack arrest

failure

norm

aliz

ed f

rettin

g load

ing: Q

*/µ

P, (R

=-1

)normalized fatigue loading: σa/σd, (R=-1)

broken125160FF18

broken125150FF17

broken125140FF16

broken100130FF15

broken125130FF14

broken145130FF13

59100120FF12

290125120FF11

344145120FF10

Maximum

crack

length

expertised :

b (µm)

Tangential

force

amplitude

Q*

[N/mm]

(R=-1)

Fatigue

stress

amplitude

:

σa [MPa]

(R=-1)

Fretting

Fatigue

Test

(107

cycles)

107 cycles

Fretting – Fatigue Experiments : Identification of thecrack arrest Fretting Fatigue map

failure

non failure

Low influence of fretting stressing on the crack arrest boundary !(Conventional idea : crack propagation is controlled by fatigue)


0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

crack arrest

failure

norm

aliz

ed f

rettin

g load

ing: Q

*/µ

P, (R

=-1

)


Comparison between experiments & Model (KT’s hypothesis of Crack arrest process)

I_effK∆

Pure mode I

)0µc(mixed_effK =∆

Mixed mode(Crack edge without friction)

Not predicted !

Provide too much optimistic prediction of the crack arrest boundary (non conservative)

Mixed mode(Crack edge with friction)

)µc(mixed_effK∆


19


based on the El Haddad et al approach


0

1

2

3

4

5

6

7

8

9

10

0 50 100 150 200 250 300

propag

ation

area

crack arrest

boundary

propagation

0

0thbb

bKK

+⋅∆=∆

Crack Boundary

0

0thbb

bKK

+⋅∆=∆

non propagationarea

El Haddad approach

crack length b, µm

∆K

eff

_m

ixe

d(µ

c=

0), M

Pa√m

Continuous evolution of the crack arrest boundary (more conservative)

Alternative crack arrest approach : El Haddad et al. formulation

0K∆


0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

crack arrest

failure

norm

aliz

ed f

rettin

g load

ing: Q

*/µ

P, (R

=-1

)


CAFFM: Comparison between experiments & Modelling(EH et al. hypothesis of Crack arrest process)

I_effK∆

Pure mode I

Mixed mode(Crack edge with friction)

)µc(mixed_effK∆

failure

non failure


Mixed mode

(Crack edge without friction) +El Haddad’s Short crack

Arrest

Most representative &

conservative prediction

of the Crack arrest boundary

Mixed mode(Crack edge without friction)



20

0

2

4

6

8

10

0 100 200 300 400 500 600

Crack lenght, µm

Fretting Fatigue (107 cycles)

Plain Fretting (106 cycles)

El Haddad et al. formulation provides a more conservative predictionof maximum crack length relate to crack arrest

crack arrest formulation KT

KT

∆K

eff

_m

ixe

d(µ

c=

0), M

Pa√m

Comparison of the crack arrest condition based on the crack length prediction

crack arrest formulation EH

EH


crack arrest boundary

(El Haddad approximation)

)0µ(mixed_eff CK =∆

dDV=1 µm 60 D3C =l

crack nucleation boundary

(Dang Van)

no crack crack

cross section expertise (106 cycles)

failure no failure

very long test (107 cycles)

crack nucleation threshold identified

from plain fretting condition

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1


norm

aliz

ed f

rettin

g load

ing: Q

*/µ

P, (R

=-1

)

failure domain

safe crack nucleationdomain

crackarrest

domain

CAtha _σ

FFM: Synthetic Fretting Fatigue Map


21

Conclusions

- A Fretting-Fatigue Mapping is introduced to formalize the cracking damages(Relative impacts of contact fretting & fatigue loadings are quantified)

- The crack nucleation boundary can be predicted combining a Multiaxialfatigue approach (Dang Van , Crossland, etc ….) but taking into account stress gradient effects(Length scale identification from plain fretting test is validated : safe predictionof the crack nucleation boundary)

- The crack arrest boundary can be predicted combining mixed modecrack edge friction free estimation of the effective SIF range and a El Haddaddescription of the short crack arrest description.


Part B : Prediction of the Finite

Endurance Behaviour


22

0

50

100

150

200

250

300

0 2.E+06 4.E+06 6.E+06 8.E+06 1.E+07

number of cycles

fatig

ue s

tress a

mplit

ud

e (

R=

-1),

MP

a

Fatigue Limit σd = 270 MPa

Fretting Fatigue LimitσFF=120 MPa

Identification of the Fretting Fatigue Wohler curve for a constantfretting loading : "Iso fretting fretting-fatigue analysis"

Modelling of the Endurance curve ?

2 - Infinite endurancereduction?

Fretting loading

P = 230 N/mm

Q* = 125 N/mm

R (cylinder) = 40 mm


2 - Short crack propagationNS- Fretting cycles in short crack

propagation (a<a0)Dowling N.E. et al. ASTM-STP- 637Vormwald M. IJF, 28

3 - Long crack propagation

NL- number of cycles in long

crack propagation regime (a>a0) Loi de Paris

CylinderP

Q

Fatigue Load

(homegeneous)

1- Nucleation

NN : Fretting Cycle Related

to the crack nucleation

aS

aL

Kmax > Kc

rupture

a0= 170 µm

short crack domain

long crack domain

aN=10µm

W

Fretting Load

(heterogeneous)

( )∫ ∆=

a

a 'mFC0 J'C

daN

Finite endurance formulation

( )∫ ∆⋅=

a

a mFL0 KeffC

daN

Paris Law

NTotal=NN+NS+NL

Fretting FatigueEndurance

Modeling strategy

2

f

00

H

K1a

⋅σ

∆

π=

shortcrack

transitionS. Fouvry et al., LTDS, SF2M, 29/03/2012

23

Identification of the finite endurance behavior (reverse identification of plain fretting tests)

Plain Fretting Experiments

Q*15kC0

10

20

30

40

50

60

70

80

80 100 120 140 160 180 200

N=15000

N=25000

N=35000

N=50000

N=75000

N=100000

Fretting Cycles

tangential force amplitude, Q* (N/mm)

maxim

um

cra

ck len

gth

, l (N

/mm

)

0

20

40

60

80

100

120

140

160

180

200

0 25000 50000 75000 100000 125000

tangentialfo

rce a

mplit

ude, Q

* (N

/mm

)

crack nucleation fretting cycles NN (l=10 µm)

mN *)Q.(KN =

K=6.1013

m=-4.2

P= 230 N/mm

R= 40 mm

p0H= 450 MPa , aH = 320 µm

δδδδ

P

δδδδ

Q*


mN *)Q.(KN =

K=6.10-13, m=-4.2

Plain Fretting Test condition

P= 230 N/mm

R= 40 mm

p0H= 450 MPa , aH = 320 µm

Identification of the finite endurance behavior (NN computation)

0

50

100

150

200

250

300

350

0 25000 50000 75000 100000 125000

crack nucleation fretting cycles NN (l=10 µm)

( )nC_eqN .HN σ=

H= 7.6710-16

n= -5.13

Crack nucleation master curve

Identified fromPlain fretting tests

)( D3Crossland_eq lσ

Fretting Fatigue

)Fatigue Fretting(NN

)( D3Crossland_eq lσ

µm45D3 =l

maxhCaCrossland_eq P⋅α+ξ=σ

Plain Fretting


24

Identification the short crack kinetics (a < a0)

0

20

40

60

80

100

0 0.5 1.0 1.5 2.00

fretting cycles (x106)

maxim

um

cra

ck l

en

gth

(µ

m)

crack arrest

Q*= 125 N/mm P= 230 N/mm

Plain Fretting Experiments

reverse indentification of the

Vormwald law integration !!!

(da/dN=c’∆Jm’ )

1E-12

1E-11

1E-10

1E-06 1E-04 1E-02 1E+00

log

(da/d

N)

(m/c

yc

les

)

1E-08

917.0)J(7e3.2

dN

da∆⋅−=

log(∆J)

Short crack propagationunder fretting

1E-12

1E-11

1E-10

1E-06 1E-04 1E-02 1E+00

log

(da/d

N)

(m/c

yc

les

)

1E-08

917.0)J(7e3.2

dN

da∆⋅−=

log(∆J)

Short crack propagationunder fretting


Identification of the crack arrest approach


Araujo J.A., Nowell D., Int. J. of. Fatigue, 1999, 21


based on the El Haddad et al approach

0

1

2

3

4

5

6

7

8

9

10

0 50 100 150 200 250 300

propag

ation

area

crack arrest

boundary

propagation

0

0thbb

bKK

+⋅∆=∆

Crack Boundary

0

0thbb

bKK

+⋅∆=∆

non propagationarea

crack length b, µm

∆K

eff

_m

ixe

d(µ

c=

0), M

Pa√m

Continuous evolution of the crack arrest boundary (more conservative)

0K∆


25

EnduranceNT

Algorithm to identify the fretting fatigue endurance

a+∆a < a0

∆KI & ∆KII extraction at the crack tip

Paris law integration (da/dN=C.∆Keff m)

short crack

propagation ∆∆∆∆NS

NT = NT+∆∆∆∆NS

long crack propagation ∆NL

NT = NT+ ∆∆∆∆NL

Vormwald law integration (da/dN=c’∆Jm’ )

a+∆a

∆KI < ∆Kth YesCrackarrest !

a+∆a > a0

Keff> Kc Yes failure

a+∆a < a0

∆KI & ∆KII extraction at the crack tip

Paris law integration (da/dN=C.∆Keff m)

short crack

propagation ∆∆∆∆NS

NT = NT+∆∆∆∆NS

long crack propagation ∆NL

NT = NT+ ∆∆∆∆NL

Vormwald law integration (da/dN=c’∆Jm’ )

a+∆a

YesCrackarrest !

a+∆a > a0

Yes failure

Nucleation Initial imput

nD3Crossland_eqN ))(.(HN lσ=

Ntotal= NNucleation+ N Propgation (Short Crack) +N Propagation (Long Crack)

theff KK ∆<∆

ICaxIm KK >

Propagation Stage


Fatigue Limit σd=270 MPa

0

50

100

150

200

250

300

0 5.E+06 1.E+07 2.E+07

number of cycles

fati

gu

e lo

ad

am

pli

tud

e,M

Pa

Fretting Fatigue LimitσFF=120 MPa

Experimental points

modelised curve

Overrun tests

%55)N(

)N()N((%)K

dF

dFFdF)N(FF =

σ

σ−σ=

Material limit reduction factor under

fretting fatigue loading

RESULTS : Prediction of the endurance and infinite life

Crack Arrest !


26

Conclusions

- Combined Fretting Wear and Fretting Fatigue analysis appears aspertinent approach to quantify the different stages of the fretting fatigue damages

- It is shown that applying a reverse analysis of Fretting Wear crack length data it is possible to determine the short crack propagation kinetics but the fretting fatigue cycles to crack nucleation

- By summing successively the cycles related to the crack nucleation, short crack propagation and long crack propagation, a good approximation of the total fretting-fatigue endurance is achieved


Part C : Materials and Palliative Strategies


27

Impact of material properties : ratio ∆∆∆∆K0/σσσσd

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

failure

domain

safe crack

nucleation

domain

crack arrest

domain

CAtha _σ

normalized fatigue loading: σa/σd(AISI 1034) (R=-1)

norm

aliz

ed fre

ttin

g loadin

g: Q

*/µ

P, (R

=-1

)

TA6V : ∆K0= 5 MPa√m, σd=450 MPa

Very limited crack arrest domain:A designing based on a crack

nucleation prediction is unstable.A damage tolerance approach appearsmore conservative than a crackNucleation strategy !!!

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

CAtha _σ

failure

domain

safe crack

nucleation

domain

crack

arrest

domain

normalized fatigue loading: σa/σd(AISI 1034) (R=-1)

norm

aliz

ed fre

ttin

g loadin

g: Q

*/µ

P, (R

=-1

)AISI 1034 : ∆K0= 7 MPa√m, σd=270 MPa

A designing based on a cracknucleation prediction is securedby the presence of an extendedCrack arrest domain

Crack nucleation

boundary

Crack arrest boundary


0 10

1

normalized fatigue loading,

σa/σd(AISI 1034) (R=-1)

norm

aliz

ed f

rettin

g load

ing,

Q*/

µP

, (R

=-1

)

crack

arest

domain

safe crack

nucleation

domain

CAth_aσ

failure

domain

Increase of the Safe Crack Nucleation domain

Pb. : Wear of Coating ?

-Hard coating inducing very high andStable compressive stresses on top surface

(ex. TiN, etc ..)

- Soft coating : capacity to accommodateThe deformation by plasticity (Thick CuNiIn, Aluminum, Bronze, etc … )

Coatings !

No crackwith WC-Co

Surf. & Coat. Technology, 201, 2006

Plain Fretting experiments

Plain steel

Shot peening

WC-Co


28

0 10

1


σa/σd(AISI 1034) (R=-1)

norm

aliz

ed f

rettin

g load

ing,

Q*/

µP

, (R

=-1

)

crack

arest

domain

safe crack

nucleation

domain

failure

domain

CAth_aσ

Increase of the Crack Arrest Domain

Pb. : Relaxation of residual stresses ?

Surf. & Coat. Technology, 201, 2006

Don’t modifythe crackNucleation!

… but reduceThe crack extension !

Plain Fretting experiments

Plain steel

Shot peening

WC-Co

Solution: Shot peening, laser Peening !

Introduction of compressive residualStresses which block the crackPropagation…


0 10

1


σa/σd(AISI 1034) (R=-1)

norm

aliz

ed f

rettin

g load

ing,

Q*/

µP

, (R

=-1

)

crack

arest

domain

safe crack

nucleation

domain

failure

domain

CAth_aσ

Combined approach : crack nucleation & crack Arrest domains extension

Ex. : Shot peening + WC-Co (HVOF) !

Suf. & Coat. Technology, 201, 2006

Fretting Fatigue experimentsPlain steel

Shot peening

Shot peening +WC-Co

Fretting Fatigue Experiments


29

CONCLUSIONS

Different strategies are now effectives to

predict the finite endurance

induced by fretting fatigue loadings

0

50

100

150

200

250

300

0 5.E+06 1.E+07 2.E+07

number of cycles

fati

gu

e lo

ad

am

plitu

de,

MP

a

But also to identified the Fretting – Fatigue

loading region where no crack can be nucleated

Or at least are supposed to stop !

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

σa/σd, (R=-1)

Q*/

µP

, (R

=-1

) failure domain

safe crack nucleationdomain

crackarrest

domain

CAtha _σ

Adequate strategies can be developed to select

Pertinent palliatives

0 10

1

σa/σd(AISI 1034) (R=-1)

Q*/

µP

, (R

=-1

)

crackarest

domain


domain

failuredomain

CAth_aσ

Fretting Fatigue

- Non local fatigue approach

- Short Crack Arrest pproach



30

References (LTDS => Send a Email for copy : [email protected])

S. Fouvry, Ph. Kapsa, L. Vincent, K. Dang Van, "Theoretical analysis of fatigue cracking under dry friction forfretting loading conditions", WEAR, 195, (1996), p.21-34

S. Fouvry, Ph. Kapsa, F. Sidoroff, L. Vincent, "Identification of the characteristic length scale for fatigue crackingin fretting contacts”, J. Phys. IV France 8 (1998), Pr8-159-166.

S. Fouvry, Ph. Kapsa, L. Vincent, “A Multiaxial Fatigue Analysis of Fretting Contact Taking into Account the Size Effect”, Fretting Fatigue 1998,ASTM STP 1367, 2000, p.167-182.

H. Proudhon, S. Fouvry, and G.R. Yantio "Determination and prediction of the fretting crack initiation:introduction of the (P, Q, N) representation and definition of a variable process volume", International Journal of Fatigue, Volume 28, Issue 7, 2006, Pages 707-713.

S. Muñoz, H. Proudhon, J. Domínguez and S. Fouvry "Prediction of the crack extension under fretting wear loading conditions" International Journal of Fatigue, Volume 28, Issue 12, December 2006, Pages 1769-1779.

Kubiak K., S. Fouvry S., Marechal A.M., Vernet J.M, " Behaviour of shot peening combined with WC–Co HVOF coating under complex fretting wear and fretting fatigue loading conditions ", Surface & Coatings Technology 201 (2006) p. 4323-4328.

Proudhon H., Buffière J-Y. and Fouvry S., Three-dimensional study of a fretting crack using synchrotron X-ray micro-tomography, Engineering Fracture Mechanics, Volume 74, Issue 5, March 2007, Pages 782-793.

S. Fouvry, D. Nowell, K. Kubiak and D.A. Hills, Prediction of fretting crack propagation based on a short crack methodology, Engineering Fracture Mechanics, Volume 75, Issue 6, April 2008, Pages 1605-1622.

S. Fouvry, K. Kubiak, Introduction of a fretting-fatigue mapping concept: Development of a dual crack nucleation– crack propagation approach to formalize fretting-fatigue damage, International Journal of Fatigue (2009), 31, 250-262.

S. Fouvry, K. Kubiak, Development of a fretting–fatigue mapping concept: The effect of material properties and surface treatments, Wear (2009), 267, 2186–2199


JP2012 : Fretting Fatigue & Fatigue de ContactParis 23 – 24 mai 2012

www.sf2m.asso.fr/JP2012/JP2012.htm

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FF 29 03 2012s550682939.onlinehome.fr/Fatigue/fichier/gt7/Fretting Fatigue - S... · Q* 100 N/mm CN = 10 6 cycles S. Fouvry et al., LTDS, SF2M, 29/03/2012 . 10 Application of the