Höhere Werkstofftechnik: Tribologie Fretting and Fretting Fatigue 1 Fretting and Fretting Fatigue 1 www.uni-due.de/wt Universität Duisburg-Essen Lotharstr 1, 47057 Duisburg, Germany Werkstofftechnik Materials Science & Engineering Fretting Wear and Fretting Fatigue We would expect all four major wear mechanisms! SF-TCR-AB-AD Fretting and Fretting Fatigue 2 www.uni-due.de/wt Universität Duisburg-Essen Lotharstr 1, 47057 Duisburg, Germany Werkstofftechnik Materials Science & Engineering Fretting Wear from Sulzer Innotec, Switzerland Apperance of Fretting on IN718 at 500°C and 100 Hz. Predominantly severe tribochemical 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
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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
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
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
*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
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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
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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
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
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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:
- 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 and Fretting Fatigue44 www.uni-due.de/wt
Universität Duisburg-EssenLotharstr 1, 47057 Duisburg, Germany
WerkstofftechnikMaterials Science & Engineering
Fretting Fatigue
We would expect all four major wear mechanisms!SF-TCR-AB-AD
Höhere Werkstofftechnik: Tribologie Fretting and Fretting Fatigue
23
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
Höhere Werkstofftechnik: Tribologie Fretting and Fretting Fatigue
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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!
from Neuner, PhD Thesis, TU Erlangen-Nuremberg, Germany 2005
Fretting and Fretting Fatigue48 www.uni-due.de/wt
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
Höhere Werkstofftechnik: Tribologie Fretting and Fretting Fatigue
25
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)
Fretting and Fretting Fatigue50 www.uni-due.de/wt
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=
Höhere Werkstofftechnik: Tribologie Fretting and Fretting Fatigue
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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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