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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 and Fretting Fatigue2 www.uni-due.de/wt
Universität Duisburg-EssenLotharstr 1, 47057 Duisburg, Germany
WerkstofftechnikMaterials Science & Engineering
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
Höhere Werkstofftechnik: Tribologie Fretting and Fretting Fatigue
2
Fretting and Fretting Fatigue3 www.uni-due.de/wt
Universität Duisburg-EssenLotharstr 1, 47057 Duisburg, Germany
WerkstofftechnikMaterials Science & Engineering
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 and Fretting Fatigue4 www.uni-due.de/wt
Universität Duisburg-EssenLotharstr 1, 47057 Duisburg, Germany
WerkstofftechnikMaterials Science & Engineering
Fretting Fatiguecyclic normal force (bulk) +
cyclic tangential force (surface)
Frettingcyclic tangential force (surface)
from Venkatesh et al. 2001
from Alfredson et al. 2004
Höhere Werkstofftechnik: Tribologie Fretting and Fretting Fatigue
3
Fretting and Fretting Fatigue5 www.uni-due.de/wt
Universität Duisburg-EssenLotharstr 1, 47057 Duisburg, Germany
WerkstofftechnikMaterials Science & Engineering
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
Fretting and Fretting Fatigue6 www.uni-due.de/wt
Universität Duisburg-EssenLotharstr 1, 47057 Duisburg, Germany
WerkstofftechnikMaterials Science & Engineering
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
Now
for
but μ for static friction
Thus for slip occursaar)r(p)r(
ar)r(
≤=μ≤τ
=∞→τ
3N
T
FF
1aaμ
−∗=
Höhere Werkstofftechnik: Tribologie Fretting and Fretting Fatigue
4
Fretting and Fretting Fatigue7 www.uni-due.de/wt
Universität Duisburg-EssenLotharstr 1, 47057 Duisburg, Germany
WerkstofftechnikMaterials Science & Engineering
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
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
Fretting and Fretting Fatigue8 www.uni-due.de/wt
Universität Duisburg-EssenLotharstr 1, 47057 Duisburg, Germany
WerkstofftechnikMaterials Science & Engineering
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
Höhere Werkstofftechnik: Tribologie Fretting and Fretting Fatigue
5
Fretting and Fretting Fatigue9 www.uni-due.de/wt
Universität Duisburg-EssenLotharstr 1, 47057 Duisburg, Germany
WerkstofftechnikMaterials Science & Engineering
Transition: Stick – Partial Slip – Gross Slip
*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
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 and Fretting Fatigue10 www.uni-due.de/wt
Universität Duisburg-EssenLotharstr 1, 47057 Duisburg, Germany
WerkstofftechnikMaterials Science & Engineering
Fretting Wear Displacement: 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
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+
=
Höhere Werkstofftechnik: Tribologie Fretting and Fretting Fatigue
6
Fretting and Fretting Fatigue11 www.uni-due.de/wt
Universität Duisburg-EssenLotharstr 1, 47057 Duisburg, Germany
WerkstofftechnikMaterials Science & Engineering
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
Fretting and Fretting Fatigue12 www.uni-due.de/wt
Universität Duisburg-EssenLotharstr 1, 47057 Duisburg, Germany
WerkstofftechnikMaterials Science & Engineering
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
Höhere Werkstofftechnik: Tribologie Fretting and Fretting Fatigue
7
Fretting and Fretting Fatigue13 www.uni-due.de/wt
Universität Duisburg-EssenLotharstr 1, 47057 Duisburg, Germany
WerkstofftechnikMaterials Science & Engineering
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 and Fretting Fatigue14 www.uni-due.de/wt
Universität Duisburg-EssenLotharstr 1, 47057 Duisburg, Germany
WerkstofftechnikMaterials Science & Engineering
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.
Höhere Werkstofftechnik: Tribologie Fretting and Fretting Fatigue
8
Fretting and Fretting Fatigue15 www.uni-due.de/wt
Universität Duisburg-EssenLotharstr 1, 47057 Duisburg, Germany
WerkstofftechnikMaterials Science & Engineering
* 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 and Fretting Fatigue16 www.uni-due.de/wt
Universität Duisburg-EssenLotharstr 1, 47057 Duisburg, Germany
WerkstofftechnikMaterials Science & Engineering
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
Höhere Werkstofftechnik: Tribologie Fretting and Fretting Fatigue
9
Fretting and Fretting Fatigue17 www.uni-due.de/wt
Universität Duisburg-EssenLotharstr 1, 47057 Duisburg, Germany
WerkstofftechnikMaterials Science & Engineering
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 and Fretting Fatigue18 www.uni-due.de/wt
Universität Duisburg-EssenLotharstr 1, 47057 Duisburg, Germany
WerkstofftechnikMaterials Science & Engineering
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
Höhere Werkstofftechnik: Tribologie Fretting and Fretting Fatigue
10
Fretting and Fretting Fatigue19 www.uni-due.de/wt
Universität Duisburg-EssenLotharstr 1, 47057 Duisburg, Germany
WerkstofftechnikMaterials Science & Engineering
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 and Fretting Fatigue20 www.uni-due.de/wt
Universität Duisburg-EssenLotharstr 1, 47057 Duisburg, Germany
WerkstofftechnikMaterials Science & Engineering
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
Höhere Werkstofftechnik: Tribologie Fretting and Fretting Fatigue
11
Fretting and Fretting Fatigue21 www.uni-due.de/wt
Universität Duisburg-EssenLotharstr 1, 47057 Duisburg, Germany
WerkstofftechnikMaterials Science & Engineering
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
Fretting and Fretting Fatigue22 www.uni-due.de/wt
Universität Duisburg-EssenLotharstr 1, 47057 Duisburg, Germany
WerkstofftechnikMaterials Science & Engineering
Fretting Wear Regimes: Definitions
*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
Höhere Werkstofftechnik: Tribologie Fretting and Fretting Fatigue
12
Fretting and Fretting Fatigue23 www.uni-due.de/wt
Universität Duisburg-EssenLotharstr 1, 47057 Duisburg, Germany
WerkstofftechnikMaterials Science & Engineering
Fretting Wear Regimes: Definitions
*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
Fretting and Fretting Fatigue24 www.uni-due.de/wt
Universität Duisburg-EssenLotharstr 1, 47057 Duisburg, Germany
WerkstofftechnikMaterials Science & Engineering
Fretting Wear Regimes: Definitions
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
Höhere Werkstofftechnik: Tribologie Fretting and Fretting Fatigue
13
Fretting and Fretting Fatigue25 www.uni-due.de/wt
Universität Duisburg-EssenLotharstr 1, 47057 Duisburg, Germany
WerkstofftechnikMaterials Science & Engineering
Fretting Wear: Route to solve Problems
*Fouvry et al. Wear 200 (1996) 186-205
Fretting and Fretting Fatigue26 www.uni-due.de/wt
Universität Duisburg-EssenLotharstr 1, 47057 Duisburg, Germany
WerkstofftechnikMaterials Science & Engineering
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
Höhere Werkstofftechnik: Tribologie Fretting and Fretting Fatigue
14
Fretting and Fretting Fatigue27 www.uni-due.de/wt
Universität Duisburg-EssenLotharstr 1, 47057 Duisburg, Germany
WerkstofftechnikMaterials Science & Engineering
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
Fretting and Fretting Fatigue28 www.uni-due.de/wt
Universität Duisburg-EssenLotharstr 1, 47057 Duisburg, Germany
WerkstofftechnikMaterials Science & Engineering
Fretting Wear: Gross Slip Regime
dissipated energydensity governs thelife time
*Fouvry et al. Wear 200 (1996) 186-205, Liskiewicz et al. Tribology Int 38 (2005) 69-79
Höhere Werkstofftechnik: Tribologie Fretting and Fretting Fatigue
15
Fretting and Fretting Fatigue29 www.uni-due.de/wt
Universität Duisburg-EssenLotharstr 1, 47057 Duisburg, Germany
WerkstofftechnikMaterials Science & Engineering
Fretting Wear: Gross Slip Regime
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
Fretting and Fretting Fatigue30 www.uni-due.de/wt
Universität Duisburg-EssenLotharstr 1, 47057 Duisburg, Germany
WerkstofftechnikMaterials Science & Engineering
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
α is constant and known!
Höhere Werkstofftechnik: Tribologie Fretting and Fretting Fatigue
16
Fretting and Fretting Fatigue31 www.uni-due.de/wt
Universität Duisburg-EssenLotharstr 1, 47057 Duisburg, Germany
WerkstofftechnikMaterials Science & Engineering
Fretting Wear: Gross Slip Regime
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==
Fretting and Fretting Fatigue32 www.uni-due.de/wt
Universität Duisburg-EssenLotharstr 1, 47057 Duisburg, Germany
WerkstofftechnikMaterials Science & Engineering
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
Höhere Werkstofftechnik: Tribologie Fretting and Fretting Fatigue
17
Fretting and Fretting Fatigue33 www.uni-due.de/wt
Universität Duisburg-EssenLotharstr 1, 47057 Duisburg, Germany
WerkstofftechnikMaterials Science & Engineering
Fretting Wear: Gross Slip Regime
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
=
Fretting and Fretting Fatigue34 www.uni-due.de/wt
Universität Duisburg-EssenLotharstr 1, 47057 Duisburg, Germany
WerkstofftechnikMaterials Science & Engineering
Fretting Wear: Gross Slip Regime
*Fouvry et al. Wear 200 (1996) 186-205
dX²X²Y1aq)Y,X(EeX
eX0d ∫ −−=
+
−
Evolution of theprincipal energy variable for one alternated cycle
Höhere Werkstofftechnik: Tribologie Fretting and Fretting Fatigue
18
Fretting and Fretting Fatigue35 www.uni-due.de/wt
Universität Duisburg-EssenLotharstr 1, 47057 Duisburg, Germany
WerkstofftechnikMaterials Science & Engineering
Fretting Wear: Gross Slip Regime
*Fouvry et al. Wear 200 (1996) 186-205
Shape of wear scar Contour for q0 and p0
acumulation ofthird bodies
Fretting and Fretting Fatigue36 www.uni-due.de/wt
Universität Duisburg-EssenLotharstr 1, 47057 Duisburg, Germany
WerkstofftechnikMaterials Science & Engineering
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
Höhere Werkstofftechnik: Tribologie Fretting and Fretting Fatigue
19
Fretting and Fretting Fatigue37 www.uni-due.de/wt
Universität Duisburg-EssenLotharstr 1, 47057 Duisburg, Germany
WerkstofftechnikMaterials Science & Engineering
Fretting Wear: Partial Slip Regime
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
Fretting and Fretting Fatigue38 www.uni-due.de/wt
Universität Duisburg-EssenLotharstr 1, 47057 Duisburg, Germany
WerkstofftechnikMaterials Science & Engineering
Fretting Wear: Partial Slip Regime
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
Höhere Werkstofftechnik: Tribologie Fretting and Fretting Fatigue
20
Fretting and Fretting Fatigue39 www.uni-due.de/wt
Universität Duisburg-EssenLotharstr 1, 47057 Duisburg, Germany
WerkstofftechnikMaterials Science & Engineering
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
Fretting and Fretting Fatigue40 www.uni-due.de/wt
Universität Duisburg-EssenLotharstr 1, 47057 Duisburg, Germany
WerkstofftechnikMaterials Science & Engineering
Measured Fretting Wear Map with Dang Van Criterion:
Fouvry et al. 200 (1996) 186-205
Höhere Werkstofftechnik: Tribologie Fretting and Fretting Fatigue
21
Fretting and Fretting Fatigue41 www.uni-due.de/wt
Universität Duisburg-EssenLotharstr 1, 47057 Duisburg, Germany
WerkstofftechnikMaterials Science & Engineering
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
Fretting and Fretting Fatigue42 www.uni-due.de/wt
Universität Duisburg-EssenLotharstr 1, 47057 Duisburg, Germany
WerkstofftechnikMaterials Science & Engineering
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
Höhere Werkstofftechnik: Tribologie Fretting and Fretting Fatigue
22
Fretting and Fretting Fatigue43 www.uni-due.de/wt
Universität Duisburg-EssenLotharstr 1, 47057 Duisburg, Germany
WerkstofftechnikMaterials Science & Engineering
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.
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Universität Duisburg-EssenLotharstr 1, 47057 Duisburg, Germany
WerkstofftechnikMaterials Science & Engineering
Fretting Fatigue
We would expect all four major wear mechanisms!SF-TCR-AB-AD
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Fretting and Fretting Fatigue45 www.uni-due.de/wt
Universität Duisburg-EssenLotharstr 1, 47057 Duisburg, Germany
WerkstofftechnikMaterials Science & Engineering
Fretting Fatigue:from Venkatesh et al. 2001 from Vallellano et al. 2004
from Alfredson et al. 2004
from Vallellano et al. 2004
Fretting and Fretting Fatigue46 www.uni-due.de/wt
Universität Duisburg-EssenLotharstr 1, 47057 Duisburg, Germany
WerkstofftechnikMaterials Science & Engineering
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 and Fretting Fatigue47 www.uni-due.de/wt
Universität Duisburg-EssenLotharstr 1, 47057 Duisburg, Germany
WerkstofftechnikMaterials Science & Engineering
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
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Universität Duisburg-EssenLotharstr 1, 47057 Duisburg, Germany
WerkstofftechnikMaterials Science & Engineering
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 and Fretting Fatigue49 www.uni-due.de/wt
Universität Duisburg-EssenLotharstr 1, 47057 Duisburg, Germany
WerkstofftechnikMaterials Science & Engineering
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)
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Universität Duisburg-EssenLotharstr 1, 47057 Duisburg, Germany
WerkstofftechnikMaterials Science & Engineering
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=
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Fretting and Fretting Fatigue51 www.uni-due.de/wt
Universität Duisburg-EssenLotharstr 1, 47057 Duisburg, Germany
WerkstofftechnikMaterials Science & Engineering
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
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Universität Duisburg-EssenLotharstr 1, 47057 Duisburg, Germany
WerkstofftechnikMaterials Science & Engineering
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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Universität Duisburg-EssenLotharstr 1, 47057 Duisburg, Germany
WerkstofftechnikMaterials Science & Engineering
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)