sk hwt 08 fretting ss08

Höhere Werkstofftechnik: Tribologie Fretting and Fretting Fatigue

1

Fretting and Fretting Fatigue1 www.uni-due.de/wt

Universität Duisburg-EssenLotharstr 1, 47057 Duisburg, Germany

WerkstofftechnikMaterials Science & Engineering

Fretting Wear andFretting Fatigue

We would expect all four major wear mechanisms!SF-TCR-AB-AD




Fretting Wear

from Sulzer Innotec, Switzerland

Apperance of Fretting on IN718 at 500°C and 100 Hz. Predominantly

severetribochemical

reactions

The dovetails of turbine blades are subjected to fretting;

predominantly by surface fatigue

Apperance of Fretting on a 12% Cr-Steel; predominantly

by surface fatigue

from MPA Stuttgart, Germany


2




from Hartmann, PhD Thesis TU Berlin 2005

shaft/hub coupling after fretting test

Area of Slip

shaft coupling fretting failurewashers/disc and bolts/discs

from Falk Corp.. Wilwaukee, WI, USA 2004




Fretting Fatiguecyclic normal force (bulk) +

cyclic tangential force (surface)

Frettingcyclic tangential force (surface)

from Venkatesh et al. 2001

from Alfredson et al. 2004


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Fretting Wear: The Elastic Hertz-Mindlin* Approach

*R.D.Mindlin et al. Trans. ASME Ser. E, J.Appl.Mech. 20 (1953) 327-344 compiled in M.Kalin; Fretting Wear Mechanisms in Contact of Steel and Silicon Nitride Ceramics. Ph.D.Thesis, University of Ljubljana, Slovenia, 1999

E2RF²)1(3a Nν−

=size of contact area: a

distribution of normal pressure: p(r)

²a²r

1²a2

F3)r(p

N−

π=

distribution of shear traction under smallcyclic tangential force FT leading to microslipcorona: τ(r)

²r²aa2F)r( T

−π=τ






Now

for

but μ for static friction

Thus for slip occursaar)r(p)r(

ar)r(

≤=μ≤τ

=∞→τ

3N

T

FF

1aaμ

−∗=


4






Surface traction within the slip corona or annulusfor a´≤ r ≤ a

Surface traction within the stick zone for r ≤ a´

²a²r1

²a2F3)r( N

−πμ

=τ

⎥⎦

⎤⎢⎣

⎡−−−

πμ

=τ´²a²r1

aa

²a²r1

²a2F3)r( N




Transition: Stick – Partial Slip

R.D.Mindlin et al. Trans. ASME Ser. E, J.Appl.Mech. 20 (1953) 327-344K.C.Johnson, Contact Mechanics (1992)

3N

T

FF1aaμ

−∗=

Stick: a´= a

if FT very smallor μFN very big

Partial slip:0 < a´< a

if 0 < FT < μFN

Influence of the applied tangential force FT

FN=const, FT increasing


5




Transition: Stick – Partial Slip – Gross Slip


3N

T

FF1aaμ

−∗=

Stick: a´= a

if FT very smallor μFN very big

Partial slip:0 < a´< a

if 0 < FT < μFN

Gross slip:a´= 0

if FT=μFN

Influence of the applied tangential force FT




Fretting Wear Displacement: The Elastic Hertz-Mindlin* Approach


The elastic deformation of ball and flat results in tangential displacement δ

with

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

μ−−

μ=δ 3

2

N

T32N

F

F11

R²E

F

2k3

( )( )( )

3²13

2221k

ν−ν−ν+

=


6




Displacement: Stick - Partial Slip - Gross Slip

*M.Ödfalk et al. Wear 157 (1992) 435-444

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

μ−−

μ=δ 3

2

N

T32N

PS F

F11

R²E

F

2k3

3N

TR²EF

kFGSPS =δ →mit FT=μFN




with

Displacement: Stick - Partial Slip - Gross Slip

*M.Ödfalk et al. Wear 157 (1992) 435-444K.L.Johnson, Contact Mechanics, Cambridge University Press (1985)

δe δS

Now δ = δe + δS

δe

δe = reversible partδS = irreversible part, slip

While

k

R²EFk

3N

e =

e

Te k

F=δ

( )1

F,F,F TTT max

±=α

⎟⎠⎞⎜

⎝⎛ Δαδ=δ


7




Partial Slip: reversibel and irreversible displacements vs. time

*M.Ödfalk et al. Wear 157 (1992) 435-444K.L.Johnson, Contact Mechanics, Cambridge University Press (1985)

δ, δe, and δS are not in-phase

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

⎪⎪⎭

⎪⎪⎬

⎫

⎪⎪⎩

⎪⎪⎨

⎧

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

μ−−

μ−⎟

⎟

⎠

⎞

⎜⎜

⎝

⎛

μ−−

μ=Δ

32

N

T

N

T35

N

T

e

2N

F

F11

F6

F5

F

F11

k

F²36E maxmaxmaxEnergy lost




Fretting Wear: Elastic-Plastic Hertz-Mindlin-Vingsbo Approach

*O.Vingsbo et al. Wear, 126 (1988) 131-147

If the plastic deformation of asperities is regarded, the contactzone has an yielding annulus withinwhich the asperities are deformedbut not fractured.

The stick as well as the slip zonestill follow the elastic Mindlinapproach.


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* M.Ödfalk et al. Wear 157 (1992) 435-444

Fretting Wear: Elastic-Plastic Hertz-Mindlin-Vingsbo Approach

Elastic stick

Elastic partial slip

plastic displacement

Full FT-δ cycle




Fretting Wear: Regimes and Problems

Dissipated Energy Ed is transformed into crack initiation and propagation(partial slip) and wear (gross slip); can be described by the accumulateddissipated energy

Wear follows the accumulateddissipated energy, while crackinitiation does not*Fouvry et al. Wear 255 (2003) 287-298


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Fretting Wear: Wear Rate vs. Displacement

Vingsbo et al. Wear 126 (1988) 131-147Fouvry et al. Wear 203-204 (1997) 393-403

crack initiation

wear loss

δ < a δ > a




Fretting Wear: Partial Slip – Gross Slip – Fretting Map

Fouvry et al. Wear 200 (1996) 186-205

FT-δ curves aresignificantlydifferent forboth regimes

FT

δ δ

FT


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Fretting Wear: Partial Slip – Gross Slip

Fouvry et al. Wear 200 (1996) 186-205

FT-δ curves are significantlydifferent for both regimes

but during cycles one maychange from one regime(gross slip) to another (partial slip)

e.g. because of crackinitiation under the contactzone




Fretting Wear Regimes

Fouvry et al. Wear 200 (1996) 186-205

Thus, betweenpartial slip and gross slip a mixedslip regime has to be introduced.

These regimes canbe distinguished as to certain systemdependant and system independantvariables


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Fretting Wear Regimes: Definitions

*Fouvry et al. Wear 200 (1996) 186-205

FT-δ curveEd = energy during one cycleEt = total energy during one cycle

Energy Ratio Criterion A

A = Ed/Et

if A < 0,2; then partial slip

Ed

Et





*Fouvry et al. Wear 200 (1996) 186-205

FT-δ curveδ = max. displacement amplitudeδ0 = displacement amplitude at FT = 0 („aperture“)

Aperture Ratio Criterion B

B = δ0/δ

if B < 0,26; then partial slip

2δ

2δ0


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*Fouvry et al. Wear 200 (1996) 186-205

FT-δ curveEd = energy during one cycleE0 = energy during one cyclecorresponding to the area of a parallelogram in which the loop islocated

System Free Ratio C

C = Ed/E0

if C < 0,77; then partial slip

Ed

E0





Alternatively the normal force FNt or the displacement δt at transition PS-GRS could be calculated according to

21

1

23

N ³Ek4R3F

t ⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠

⎞⎜⎝

⎛μδ

=31

13

2

Nt R3E4

kF ⎟⎠⎞

⎜⎝⎛μ=δ

*Fouvry et al. Wear 200 (1996) 186-205

2

22

1

21

E

1

E

1

E1 ν−

+ν−

=

μ = static friction, Ei = Youngs Moduli, Gi = shear moduli, νi = Poissons ratios

⎟⎟⎠

⎞⎜⎜⎝

⎛ ν−+

ν−=

2

2

1

11 G

2

G

2

163k


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Fretting Wear: Route to solve Problems

*Fouvry et al. Wear 200 (1996) 186-205




Fretting Wear: Gross Slip Regime Wear Mechanisms

*Fouvry et al. Wear 200 (1996) 186-205, Liskiewicz et al. Tribology Int 38 (2005) 69-79

∑∑ =N

dd iEE1

)(

accumulated dissipated energy Ed

energy friction coefficient µe

gN

de F

Eδ

μ4

= ∑=N

gN

de iiF

iEN 1 )()(4

)(1δ

μ


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Fretting Wear: Gross Slip Regime

Wear volume follows theaccumulated dissipatedenergy

∑≈ dGRS EW α

*Fouvry et al. Wear 200 (1996) 186-205, Varenberg et al. Wear 252 (2002) 902-910, Liskiewicz et al. Tribology Int 38 (2005) 69-79

+ contact area

dissipated energydensity Edh





dissipated energydensity governs thelife time

*Fouvry et al. Wear 200 (1996) 186-205, Liskiewicz et al. Tribology Int 38 (2005) 69-79


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Wear volume follows the accumulated dissipated energy

*Fouvry et al. Wear 200 (1996) 186-205

∑=∑=

N

1idd )i(EE

for large amplitudes

D4E

FµF dNsT ==

sliding tangential force

with D = δ0

∑=∑=

N

1iiTid )DF4(E





Wear volume follows theaccumulated dissipatedenergy

∑≈ dGRS EW α

*Fouvry et al. Wear 200 (1996) 186-205, Varenberg et al. Wear 252 (2002) 902-910, Liskiewicz et al. Tribology Int 38 (2005) 69-79

+ contact area

dissipated energydensity Edh

α is constant and known!


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Pressure and shear stress fieldfor a full sliding sphere

*Fouvry et al. Wear 200 (1996) 186-205

thus, any local dissipated energy analysishas to regard

1. local FT~(p(x,y) and FN~(q(x,y))2. transition to reciprocating sliding wear

dX²X²Y1aq)Y,X(EeX

eX0d ∫ −−=

+

−

aaDe 0δ==




Wear: Gross Slip Reciprocating Sliding

Surface distribution Ed(X,Y) for e=0.5

*Fouvry et al. Wear 200 (1996) 186-205

Surface distribution Ed (X,Y), e=1.5


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Distribution in axial X, Y=0 and lateral X=0, Y direction differs

*Fouvry et al. Wear 200 (1996) 186-205

dX²X²Y1aq)Y,X(EeX

eX0d ∫ −−=

+

−

dX)0Y,X(EE ddA ∫ ==∞+

∞−dX)Y,0X(EE ddL ∫ ==

∞+

∞−

Daq2eq²a2E 00dA π=π=

for e ≥ 13

q²a4E 0RS

dLπ

=independent of e

for e < 1 ³)ee3(3

q²a2E 0GRS

dL −π

=





*Fouvry et al. Wear 200 (1996) 186-205

dX²X²Y1aq)Y,X(EeX

eX0d ∫ −−=

+

−

Evolution of theprincipal energy variable for one alternated cycle


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*Fouvry et al. Wear 200 (1996) 186-205

Shape of wear scar Contour for q0 and p0

acumulation ofthird bodies




Fretting Wear: Partial Slip Regime

*Fouvry et al. Wear 200 (1996) 186-205

Application of Dang Van´s theory of multaxial fatigue to contactproblems

Estimation of a local cyclic failure criterion dc from local hydrostaticpressure p (x,y,z,t) [=σm or σh] and macroscopic rotating bending stress σD and shear stress τD endurance limits:

if d > 1 initiation of fatigue crack likely

)t,z,y,x(p)t,z,x,y()t(d

α−βτ

=

3

2D

DD

D

σ

σ−τ

=α

τ=β


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The maximum of d(x,y,z,t) has to beestimated according to Fouvry et al.

d is biggest at the edge of the contact zone withinthe surfacex=a, z=y=0

*Fouvry et al. Wear 200 (1996) 186-205, Wear 195 (1996) 21-34, Tribotest J 3-1 (1996) 23-44





1Fouvry et al. Wear 195 (1996) 12-34, ²Cattaneo Rendiconto dell´Áccademia dei lincei 6, 27 (1938) 343-348; 434-436; 474-478, ³Midlin et al. Trans ASME, J Appl Mech 20 (1953) 327-344, 4Dang Van ASTM Stp. 1191, ASTM Philadelphia, PA (1993) 120-130, 5Hamilton Proc Inst Mech Eng, 197C (1983) 53-59

Procedure1:- normal pressure from Hertzian theory- partial slip tangential stress loading byCattaneo² and Midlin³- μ is independant of x, y and t³- combined isotropic and kinematic hardening4

- computing according to Hamilton5


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Schematic Fretting Wear Map with Dang Van Criterion:

Fouvry et al. 195 (1996) 21-34

σEXT = external stress from fretting fatiguep0fl = limit fatigue Hertzian pressure

Flat: mild steelBall: 52100R=50 mm

μ=0.8 (106 cycles)σD=660 MPaτD=410 MPaRp=1050 MPa




Measured Fretting Wear Map with Dang Van Criterion:

Fouvry et al. 200 (1996) 186-205


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Proposed Pressure Crack Nucelation Map for Partial Slip Fretting Wear Regimes

Fouvry et al. Wear 200 (1996) 186-205

σY = Rpσe,max calculatedfrom measuredvalues duringfretting tests




Proposed Pressure Crack Nucelation Map for Partial Slip Fretting Wear Regimes

Fouvry et al. 200 (1996) 186-205

Flat: mild steelBall: 52100R=50 mm

μ=0.8 (106 cycles)σD=660 MPaτD=410 MPaRp=1050 MPa


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Notice:

1Chivers et al. Proc Inst Mech Eng 199 (1985) 283-301

- Tribosystems must be definded precisely as to Partial Slip – Gross Slip by ABC or other suitable criteria

- Gross Slip: Accumulated Dissipated Energy governs wear and, therefore, endurance

- Partial Slip: Stress distribution over coordinates and time together with gross bending and torsion fatigue properties govern crack nucleation and propagation and, therefore, endurance.

- In a first rough approximation Haigh diagrams and principal stress investigation according to Chivers et al.1 might work as well.




Fretting Fatigue

We would expect all four major wear mechanisms!SF-TCR-AB-AD


23




Fretting Fatigue:from Venkatesh et al. 2001 from Vallellano et al. 2004

from Alfredson et al. 2004

from Vallellano et al. 2004




Fretting FatigueFretting fatigue brings about very small strokes. This leadsto a fretting contact within the partial slip or even stick regime

distribution of internal loadsfatigue

distribution of external loadsfretting

from Kimura et al. 2003

Thus, the highest tensile stresses appear at the rimof the stick zone leading to crack initiation and propagation


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Fretting FatigueThe superposition of internal and external loads brings about a distinct lossof endurance

Notice: The endurance isnot limited by wear but byfatigue properties! Earliercrack initation!

~AISI 1055 (EN Ck53)+ pressure 12.5 MPa + pressure 25 MPa

-20%

-96%

from Neuner, PhD Thesis, TU Erlangen-Nuremberg, Germany 2005




Fretting FatigueFretting fatigue is treatedaccording to the crackanalogy methodology, because of the similaritiesof the stress fields withfracture mechanics

Notice: The loading situationdepends on adhesion!

from Naboulsi 2005

weak adhesion

strong adhesion

crack


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Fretting Fatigue:

under a given load Fmax the maximum contact radius between e.g. a cylinder and flat is given by

3 max,2

max 4)1(3

⎥⎥⎦

⎤

⎢⎢⎣

⎡ −= NF

EDa ν

for weak adhesion

32

max,max,2

max 233

23

4)1(3

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛⎟⎠⎞

⎜⎝⎛+++

−= ad

Nadad

NDwFDwDwF

EDa πππν

for strong adhesion

D = diameter of the cylinderwad = work of adhesion ~ 1 N/m

Ginnakopoulos et al. Acta Mater 46 1998

Barquins et al. J Mech Theor Appl 1 (1982)

Semenchenko, Addison-Wesley (1962)




Due to this similarity of stress fields a fretting contact can be described bymeans of LEFM

The normal load FN, wich is not constant but oscillatory and > 0, bringsabout a stress field described by ΔKIThe tangential load FT, wich is not constant but oscillatory and > 0, bringsabout a stress field described by ΔKII

Fretting Fatigue:

max

max,a

FK N

I π=

max

max,a

FK T

II π=


26




Fretting Fatigue:

For e.g. strong adhesion and weak adhesion one can calculate amax and amin from measured FNmax and FNmin as well as the R-values:

max,

min,

N

NNFF

R =max,

min,

T

TTFF

R =

minmax

maxminmax, )(aa

RaaFK

NN

I πππ −

=Δ

minmax

maxminmax, )(aa

RaaFK

TT

II πππ −

=Δ




Fretting Fatigue:

For the bulk material, which is loaded with the oscillatory fatigue stress amplitude σa in the tangential direction of the contact one gets:

)(2 dcEbdEc

rK abulk

II +=Δ

πσ with E = Youngs-Modulus

r = polar coordinat along contact area2b = thickness of substratec = width of contact bodyd = width of substrate

then BulkIIIII

total KKKK 222 Δ+Δ+Δ=Δ


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Fretting Fatigue: (from Naboulsi, Eng.Frac.Mech. 72 (2005))

ΔKtotal characterizes crack initiation of fretting fatigue. It depends on loading and geometry. If one does not consider the bulk fatigue stress one

can express ΔKtotal by a CAF-factor(crack-analogy-fretting) which is a measure for the damagetolerance of the system.

With increasing CAF the numberof cycles to failure Nf decrease.

Knowing CAF vs. Nf for oneconfiguration one can recalculatefor other configurations for thestrong adhesion case (= stick regime).

Notice: CAF isnormalized to CAF(Nf=106)

sk hwt 08 fretting ss08

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