Fretting Fatigue. Etude & prédiction de la durée de vie. LTDS, CNRS, Ecole Centrale de Lyon, Ecully, France. contact :

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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 : siegfried.fouvry@ec-lyon.fr SFM Commission Fatigue 9 mars, PARIS Prise en compte des phénomènes aggravants dans la conception en fatigue Context and challenges pressure contact micro displacements [< ± µm] electrical connectors [Bosh] bridge cables blade / disk contacts in turbine engine [M. Park et al.]

2 Damage induced by plain fretting loading Small amplitude Partial Slip stick zone tangential force Q (N) Cyclic tangential displacement δ(t) Normal Force (P) Large amplitude Gross Slip tangential force Q (N) Hertzian contact displacement δ (µm) Cyclic tangential force Q(t) displacement δ (µm) Surface damages Cracking Wear Industrial application : Pressed fitted Wheels-Axles contact New Train Speed Record (April 7) FRETTING Cracking on the axle Ultra severe technological test Fretting-Fatigue Loading (Partial Slip) Pressure Fretting (R=-) AISI 34 Axle Fatigue (R=-) Fretting-Fatigue Loading Question : Are can be predicted the cracking risk?

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 3

4 Fretting Fatigue : Stress & Damage evolutions pressure cyclic tangential force σ (±MPa) Failure Heterogeneous stress field Fretting Loading + σ (±MPa) crack length (µm) Nucleation but crack arrest Fatigue Loading Homogeneous stress field No nucleation Number of fretting cycles (N) Fretting Fatigue : Fretting Fatigue Map Concept (Partial Slip) Q* µ.p GROSS SLIP CONTACT plain Fretting test P Q* Safe crack propagation Failure Crack arrest boundary Q P δ Fretting Fatigue Test Fretting loading (Q*/µP, R Q ) Crack nucleation boundary Safe crack nucleation Fatigue loading, R ) σ ( a σ P : Normal force Q* : Tangential force amplitude σ a : Fatigue stress amplitude σ a Plain fatigue test Fretting Loading σ a Q (N) σ σ a d Q* (N) δ (µm) 4

5 How can be formalized the Fretting Fatigue Mapping Concept? (i.e. How can be predicted the different damage s?) Materials Topics of the presentation Experimental strategy (combined plain fretting & fretting fatigue tests) Modelling (Contact stressing+ Crack Nucleation + Crack Propagation) Prediction of the Fretting-Fatigue crack nucleation boundary Prediction of the Fretting-Fatigue crack propagation boundary Conclusions 5

6 Material : Low carbon steel (AISI 34) Ferrite - Perlite structure Mechanical properties Matériau Young modulus, E (GPa) Poisson coefficient, ν (ratio) Yield stress, Re. (MPa) Maximum stress, Rm (MPa) Low carbon steel Crack propagation (long crack) & fatigue SIF range threshold, K maximum SIF, K c 7 ( MPa m ) C coefficient (Paris law) m exponant (Paris law) Fatigue limite (R=) MPa ( MPa m ) Gros V., Ph.D Thesis, Ecole Centrale de Paris, France,996. Fretting Experiments : Coupling Between Plain Fretting & Fretting Fatigue tests Plain Fretting Test (fretting wear test) P δ Q* Acquisition system displacement normal force tangential force temperature humidity Fretting Fatigue Test Q* P δ σ ext P P δ FRETING CYCLE (Partial Slip) 6

7 Fretting Experiments : Coupling Between Plain Fretting & Fretting Fatigue tests Similar contact condition AISI 34 5 Q* P Q* P= 3 N/mm Fn R= 4 mm p H = 45 MPa, a H = 3 µm δ iso-fretting loading (R=-) δ σ ext Plain Fretting Test - Friction behavior (Tribology) - Crack nucleation - Short crack propagation (systematic crack arrest conditions) fatigue loading (R=-) Fretting Fatigue Test - Crack propagation (short & long) - Crack arrest condition - Lifetime endurance This combined Plain Fretting and Fretting Fatigue test allow us to dissociate the impact of contact and bulk cyclic loading on the fretting fatigue damage Plain Fretting Wear Test Friction analysis Amplitude values Q[N] Partial Slip incremental method cycles Gross Slip Displacement Recorded cycle Fretting Cycles Tangential force δ[µm] tangential force ratio,q*/p coefficient of friction at the sliding transition µ t µ GT.8 Q* µ P Partial Gross Slip.6 Slip.4. Q* P E A = d 4. δg.q* Energy discontinuity displacement amplitude δ* (µm) energy ratio A, Coefficient of Friction (µ t ) =.85 7

8 Analytical description of Plain Fretting and Fretting Fatigue contacts Plain Fretting Contact surface pressure field p(x) - P p sliding zones sticking -c/a c/a zone Mindlin et al, 949 Y=y/a Q Loading shear stress field (+Q*) q(x) + q(x) X=x/a Unloading shear stress field (-Q*) Maximum loading located symetrically at the contact borders +σ a q(x ) Trailing edge Tension σ a Compression Fretting-Fatigue Contact p(x ) Tangential c / a force +Q* e a X=x/a - + sliding zones p(x ) q(x ) c / a Loading Tangential force -Q* - e + X=x/a a Unloading Nowell et al, 989 Maximum loading located at the trailling edges (at the Loading state) Contact modeling: Stress field analysis FEM ANALYSIS Analytical formulation: Green s functions Superposition of piecewise-line Overlapping triangular elements (K.L. Johnson, 985) [Elastic Half Space Hypothesis] p(x) X Can include plasticity Long and fastidious (inappropriate to develop A mapping investigation!!) Σ(M, t) = Σ Very fast!! 8

9 Crack Nucleation Analysis Plain Fretting Wear Test Friction Identification of the crack nucleation Fretting Test : Q*=± N/mm, 6 cycles Surface observation stick zone sliding zone A 8 6 cycles c A a crack length, b (µm) 6 4 * Q CN Crack nucleation threshold b 3 4 tangential force amplitude, Q* (N/mm) P=3N/mm, µ=.85 ( 6 cycles, p = 45 MPa) Cross section observation: measure of the crack length Q * CN = N / mm 9

10 Cracking risk Application of the Dang Van s (multiaxial criteria) Plain Fretting determination of the loading path stick P sliding Q (t) Z - a - c c a X Σ(M,t) M shakedown point M fixed σ$ ( t) = ρ * +Σ( t) computation of the cracking risk (Dang Van) tension p$ H ( t) shear τ$ ( n r, t ) Subsurface (Y=y/a) Surface (X=x/a) Cracking risk d DV Cracking at the contact borders r τˆ (n, t) ddv = max r t,n τd α.pˆ (t) if d DV > cracking ( ) ( ) α = τd σd / σd 3 τd σ d 3 α C = σ d 3 σ d : alternating bending fatigue limit τ d : alternating shear fatigue limit. Application of the Dang Van (Quantitative Prediction) d DV 8 crack length, b (µm) 6 4 * Q CN Crack nucleation threshold 3 4 tangential force amplitude, Q (N/mm) P=7N/mm, µ=.85 ( 6 cycles, p = 45 MPa) Q * CN =N / mm d DV = Subsurface (Y=y/a) Surface (X=x/a) Overestimation of the cracking risk!!

11 Non local approach to capture stress gradient effects Non local approach to capture stress gradient effects Non local fatigue approaches D plane strain condition (cylinder/plane) Σ(MPa) nucleation process volume approach «Hot point» nucleation process surface approach Critical distance method l 3D l D l D y a contact steep stress gradient Σ R3D ( x, y) Σ R D ( x) Σ RD ( x) Averaging over a constant square volume Averaging over a line Stress analysis At a critical distance from the Hot point

12 Identification of representative length scales (Dang Van) * Σ( Q CN ) R 3D ( x, y) l 3D Σ?? l 3D Reverse approach d DV (Q * CN ) d until DV (Q * CN ) = maximum Dang Van value : max(d C ) d DV (Q * CN ) ( l 3D l 3 = 6µm length scale parameter, l 3D (µm) D ) l 6 µm l 75 µm l = 8µm 3 D = D = D l 3D l D l D Consistent with notch description (Taylor and al) Questions? - What is the stability of the different averaging approaches regarding Fretting Fatigue stressing? - Is the length scale parameters defined from Plain Fretting configuration can be extrapolated to predict crack nucleation under Fretting Fatigue?

13 Fretting Fatigue Experiments : Identification of the crack nucleation Fretting Fatigue map Fatigue stress amplitude : σ a [MPa] (R=-) cycles Tangential force amplitude Q* [N/mm] (R=-) Cross section Examination CRACK NO CRACK CRACK CRACK CRACK NO CRACK NO CRACK CRACK NO CRACK normalized fretting loading: Q*/µP, (R=-) crack no crack PF threshold safe crack nucleation failure normalized fatigue loading: σ a /σ d, (R=-) Low influence of fatigue stress amplitude in the low fatigue stress range! (Conventional idea : crack nucleation is controlled by fretting) Correlation Experiments // Modelling (Dang Van) normalized fretting loading: Q*/µP, (R=-) crack no crack PF threshold safe crack nucleation failure normalized fatigue loading: σ a /σ d, (R=-) Theoretical prediction of the Fretting Fatigue crack nucleation boundary d DV = l 3 = 6 µm Similar tendencies!! D l = 75 µm l = 8µm D D Pessimistic (i.e. secure) prediction of the safe crack nucleation from Plain Fretting identification! 3

14 Comparison between Multiaxial Criteria (Crossland) Φ Σ(t) general stress path during fatigue loading Crossland Criterion ξ a + αc Phmax < τd Hydrostatic pressure Deviatoric tensor Φ' Deviatoric Plane P h max (t) J = max trace( Σ(t)) t T 3 component S(t) ξ a = max max (S(t) S(t )) : (S(t) S(t t T t T )) D ζ a = D d C ξa = τ α P d τ d σ d Fatigue material component α C = σ d 3 C h max 3 - If is greater than or equal to, there is a risk of cracking; - If remains less than, there is no risk of cracking. Comparison between Multiaxial Fatigue Criteria normalized fretting loading: Q*/µP, (R=-) crack no crack PF threshold safe crack nucleation failure normalized fatigue loading: σ a /σ d, (R=-) Σ R 3D ( x, y) Dang Van l 3 = 6 µm D Crossland l 3 = 45 µm D l 3D 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 4

15 How to prediction the Crack Arrest? SIF modeling at the fretting crack tip (decouple approach) SIF integration method by Weight Functions P Q τ(t) σ(t) t σ = cylinder h H W K = M(t) σ(t) dt π K = M(t) τ(t) dt π x yy t t M ( t ) = t + m * + m * σ = Stress field extraction (FEM) + Weigth Functions (WF) (Bueckner H.F.) yx K π r K π r h h K, Mpa.vm Fretting Wear condition Evolution of SIF (mode I) Kmax_P54_Q83 Weight Functions straight crack (º) Q*= 5 N/mm P= 3 N/mm Short crack (a<a ) crack length, µm a =7µm Other approaches : Distributed Dislocations Dubourg et al. Nowell et al; surface " the crack length increase but the contact stress field is decreasing very fast" 5

16 Comparison : Couple (FEM: contact+crack) // Decouple FEM(contact) + WF Couple approach (FEM: contact+crack) K Imax Couple approach (FEM: Contact+Crack) Uncouple approach (FEM+WF) Crack length "Crack box"- Automatic remeshing Selected SIF computation => FEM + Weigth Functions Evolution of the SIF below the contact: Non monotonic evolution! Increase of the crack length 8 Decrease of the contact Stress field Plain Fretting Plain Fretting condition Q*= 5 N/mm P= 3 N/mm K Imax, MPa m crack length, b(µm) the crack length increase but the contact stress field is decreasing very fast The crack stops! The crack stops! (situation of plain fretting condition) 6

17 Determination of the effective SIF (combining mode I and II) General formulation K eff = K Ieff + K IIeff Mode I Mode II Pure mode I (Usual hypothesis) K = K Because R=- (closure effect) eff _ I Im ax K Im in = Mixed Mode A (Crack edge with high friction) K eff _ mixed (µc ) = K Im ax + K I Im ax µ K I Imin = c >> Mixed Mode B (Crack edge friction free) Keff _ mixed(µc= ) = KImax + (KI Imax KI Imin ) µ c = K IImin < < K eff _ I K eff _ mixed (µc = ) K eff _ mixed (µc = ) Identification of the crack arrest approach : KT s formulation Specific behavior of the crack arrest condition for the small crack!!! Araujo J.A., Nowell D., Int. J. of. Fatigue, 999, σ max = MPa σ max =5 MPa Q*= 5 N/mm P= 3 N/mm K eff_mixed(µc=), MPa m Propagation area short crack non propagation area Stop! b K th = K b b long crack propagation K crack arrest boundary Crack arrest approach based on the Kitagawa-Takahashi diagram if short crack (b<b ) K b = f H π σ K th = K if long crack (b>b ) Kth = K b = 7µm b b crack length b, µm 7

18 Fretting Fatigue Experiments : Identification of the crack arrest Fretting Fatigue map 7 cycles Fretting Fatigue Test ( 7 cycles) FF FF FF FF3 FF4 FF5 FF6 FF7 FF8 Fatigue stress amplitude : σ a [MPa] (R=-) Tangential force amplitude Q* [N/mm] (R=-) Maximum crack length expertised : b (µm) broken broken broken broken broken broken normalized fretting loading: Q*/µP, (R=-) crack arrest failure failure non failure normalized fatigue loading: σ a /σ d, (R=-) Low influence of fretting stressing on the crack arrest boundary! (Conventional idea : crack propagation is controlled by fatigue) Comparison between experiments & Model (KT s hypothesis of Crack arrest process) normalized fretting loading: Q*/µP, (R=-) failure crack arrest Not predicted! normalized fatigue loading: σ a /σ d, (R=-) Pure mode I K eff _ I Mixed mode (Crack edge with friction) K eff _ mixed (µc ) Mixed mode (Crack edge without friction) K eff _ mixed (µc = ) Provide too much optimistic prediction of the crack arrest boundary (non conservative) 8

19 Alternative crack arrest approach : El Haddad et al. formulation Specific behavior of the crack arrest condition for the small crack!!! El Haddad approach K eff_mixed(µc=), MPa m K propagation area K th = K non propagation area b b + b propagation crack arrest boundary crack length b, µm Crack arrest approach based on the El Haddad et al approach Crack Boundary K th = K b b + b Continuous evolution of the crack arrest boundary (more conservative) CAFFM: Comparison between experiments & Modelling (EH et al. hypothesis of Crack arrest process) normalized fretting loading: Q*/µP, (R=-) crack arrest failure non failure failure Pure mode I K eff _ I Mixed mode (Crack edge with friction) K eff _ mixed (µc ) Mixed mode (Crack edge without friction) K eff _ mixed (µc = ) normalized fatigue loading: σ a /σ d, (R=-) Mixed mode (Crack edge without friction) K eff _ mixed (µc = ) + El Haddad s Short crack Arrest Most representative & conservative prediction of the Crack arrest boundary 9

20 Comparison of the crack arrest condition based on the crack length prediction K eff_mixed(µc=), MPa m Fretting Fatigue ( 7 cycles) Plain Fretting ( 6 cycles) crack arrest formulation KT crack arrest formulation EH KT Crack lenght, µm El Haddad et al. formulation provides a more conservative prediction of maximum crack length relate to crack arrest EH FFM: Synthetic Fretting Fatigue Map normalized fretting loading: Q*/µP, (R=-) crack arrest safe crack nucleation failure σ a _ CAth normalized fatigue loading: σ a /σ d, (R=-) cross section expertise ( 6 cycles) no crack failure crack crack nucleation threshold identified from plain fretting condition very long test ( 7 cycles) no failure crack nucleation boundary (Dang Van) d DV = l C 3D = 6µm crack arrest boundary (El Haddad approximation) K eff _ mixed(µ = ) C

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 Multiaxial fatigue approach (Dang Van, Crossland, etc.) but taking into account stress gradient effects (Length scale identification from plain fretting test is validated : safe prediction of the crack nucleation boundary) - The crack arrest boundary can be predicted combining mixed mode crack edge friction free estimation of the effective SIF range and a El Haddad description of the short crack arrest description. Part B : Prediction of the Finite Endurance Behaviour

22 Identification of the Fretting Fatigue Wohler curve for a constant fretting loading : "Iso fretting fretting-fatigue analysis" Modelling of the Endurance curve? fatigue stress amplitude (R=-), MPa Fatigue Limit σ d = 7 MPa Fretting loading P = 3 N/mm Q* = 5 N/mm R (cylinder) = 4 mm.e+6 4.E+6 6.E+6 8.E+6.E+7 number of cycles - Infinite endurance reduction? Fretting Fatigue Limit σ FF = MPa Modeling strategy P Fretting Load (heterogeneous) Q Cylinder - Nucleation N N : Fretting Cycle Related to the crack nucleation Finite endurance formulation short crack a = 7 µm long crack a N =µm a S a L - Short crack propagation N S - Fretting cycles in short crack propagation (a<a ) Dowling N.E. et al. ASTM-STP- 637 Vormwald M. IJF, 8 Fatigue Load (homegeneous) N = a FC da a C' J ( ) m' W Kmax > Kc rupture 3 - Long crack propagation N L - number of cycles in long crack propagation regime (a>a ) Loi de Paris Paris Law N = a FL da a C Keff ( ) m short crack transition K a f H = π σ Fretting Fatigue Endurance N Total =N N +N S +N L

23 Identification of the finite endurance behavior (reverse identification of plain fretting tests) Q* P δ Plain Fretting Experiments P= 3 N/mm R= 4 mm p H = 45 MPa, a H = 3 µm maximum crack length, l (N/mm) Fretting Cycles N=5 N=5 N=35 N=5 N=75 N= Q* 5kC tangential force amplitude, Q* (N/mm) m N N = K.(Q*) K=6. 3 m= tangential force amplitude, Q* (N/mm) crack nucleation fretting cycles N N (l= µm) Identification of the finite endurance behavior (N N computation) Plain Fretting Test condition P= 3 N/mm R= 4 mm p H = 45 MPa, a H = 3 µm N N = K.(Q*) m K=6. -3, m=-4. Crack nucleation master curve Identified from Plain fretting tests σ eq l σ _ Crossland l 3 D = eq _ Crossland 45 µm = ξ a ( 3 D + α C Fretting Fatigue ) P h max Plain Fretting 5 5 N = N H. H= n= -5.3 ( σ ) n eq_c σ ( D ) eq l _ Crossland crack nucleation fretting cycles N N (l= µm) N N (Fretting Fatigue) 3

24 Identification the short crack kinetics (a < a ) maximum crack length (µm) Plain Fretting Experiments fretting cycles (x 6 ) Q*= 5 N/mm P= 3 N/mm crack arrest log(da/dn) (m/cycles) E- E- E- E-8 da =.3e 7 ( J) dn E-6 E-4 E- E+ log( J) Short crack propagation under fretting reverse indentification of the Vormwald law integration!!! (da/dn=c J m ).97 Identification of the crack arrest approach Specific behavior of the crack arrest condition for the small crack!!! Araujo J.A., Nowell D., Int. J. of. Fatigue, 999, K eff_mixed(µc=), MPa m K propagation area K th = K non propagation area b b + b propagation crack arrest boundary crack length b, µm Crack arrest approach based on the El Haddad et al approach Crack Boundary K th = K b b + b Continuous evolution of the crack arrest boundary (more conservative) 4

25 Algorithm to identify the fretting fatigue endurance Propagation Stage a+ a Nucleation Initial imput N n N = H.( σeq _Crossland( l3d)) K I & K II extraction at the crack tip a+ a < a a+ a > a Vormwald law integration (da/dn=c J m ) Paris law integration (da/dn=c. Keff m ) short crack propagation N S N T = N T + N S long crack propagation N L N T = N T + NL KI Keff < K th th Yes Crack arrest! K Keff> Imax > Kc KIC Yes failure Yes Endurance N T N total = N Nucleation + N Propgation (Short Crack) +N Propagation (Long Crack) RESULTS : Prediction of the endurance and infinite life fatigue load amplitude, MPa Overrun tests number of cycles Fatigue Limit σ d =7 MPa Fretting Fatigue Limit σ FF = MPa 5 Experimental points Crack Arrest! modelised curve 5.E+6.E+7.E+7 Material limit reduction factor under fretting fatigue loading σdf(n) σdff(n) K FF (N)(%) = = 55% σ (N) df 5

26 Conclusions - Combined Fretting Wear and Fretting Fatigue analysis appears as pertinent 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 6

27 Impact of material properties : ratio K /σ d AISI 34 : K = 7 MPa m, σ d =7 MPa normalized fretting loading: Q*/µP, (R=-) crack arrest Crack nucleation boundary Crack arrest boundary failure. safe crack σ nucleation a _ CAth normalized fatigue loading: σ a /σ d(aisi 34) (R=-) normalized fretting loading: Q*/µP, (R=-) TA6V : K = 5 MPa m, σ d =45 MPa σ a _ CAth safe crack nucleation crack arrest failure normalized fatigue loading: σ a /σ d(aisi 34) (R=-) A designing based on a crack nucleation prediction is secured by the presence of an extended Crack arrest Very limited crack arrest : A designing based on a crack nucleation prediction is unstable. A damage tolerance approach appears more conservative than a crack Nucleation strategy!!! Increase of the Safe Crack Nucleation normalized fretting loading, Q*/µP, (R=-) crack arest safe crack nucleation σ a _ CAth failure normalized fatigue loading, σ a /σ d(aisi 34) (R=-) Coatings! -Hard coating inducing very high and Stable compressive stresses on top surface (ex. TiN, etc..) - Soft coating : capacity to accommodate The deformation by plasticity (Thick CuNiIn, Aluminum, Bronze, etc ) Plain Fretting experiments Plain steel Shot peening WC-Co No crack with WC-Co Pb. : Wear of Coating? Surf. & Coat. Technology,, 6 7

28 Increase of the Crack Arrest Domain normalized fretting loading, Q*/µP, (R=-) crack arest safe crack nucleation σ a _ CAth failure normalized fatigue loading, σ a /σ d(aisi 34) (R=-) Solution: Shot peening, laser Peening! Introduction of compressive residual Stresses which block the crack Propagation Plain Fretting experiments Don t modify the crack Nucleation! but reduce The crack extension! Plain steel Shot peening WC-Co Surf. & Coat. Technology,, 6 Pb. : Relaxation of residual stresses? Combined approach : crack nucleation & crack Arrest s extension normalized fretting loading, Q*/µP, (R=-) crack arest safe crack nucleation σ a _ CAth failure normalized fatigue loading, σ a /σ d(aisi 34) (R=-) Ex. : Shot peening + WC-Co (HVOF)! Fretting Fatigue Experiments Fretting Fatigue experiments Plain steel Shot peening Shot peening +WC-Co Suf. & Coat. Technology,, 6 8

29 CONCLUSIONS Different strategies are now effectives to predict the finite endurance induced by fretting fatigue loadings fatigue load amplitude, MPa E+6.E+7.E+7 number of cycles Fretting Fatigue But also to identified the Fretting Fatigue loading region where no crack can be nucleated Or at least are supposed to stop! - Non local fatigue approach - Short Crack Arrest pproach Q*/µP, (R=-) crack arrest safe crack nucleation failure σ a _ CAth σ a /σ d, (R=-) Adequate strategies can be developed to select Pertinent palliatives Q*/µP, (R=-) crack arest safe crack nucleation σ a _ CAth failure σ a /σ d(aisi 34) (R=-) 9

30 References (LTDS => Send a for copy : siegfried.fouvry@ec-lyon.fr) S. Fouvry, Ph. Kapsa, L. Vincent, K. Dang Van, "Theoretical analysis of fatigue cracking under dry friction for fretting loading conditions", WEAR, 95, (996), p.-34 S. Fouvry, Ph. Kapsa, F. Sidoroff, L. Vincent, "Identification of the characteristic length scale for fatigue cracking in fretting contacts, J. Phys. IV France 8 (998), Pr S. Fouvry, Ph. Kapsa, L. Vincent, A Multiaxial Fatigue Analysis of Fretting Contact Taking into Account the Size Effect, Fretting Fatigue 998,ASTM STP 367,, p 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 8, Issue 7, 6, Pages S. Muñoz, H. Proudhon, J. Domínguez and S. Fouvry "Prediction of the crack extension under fretting wear loading conditions" International Journal of Fatigue, Volume 8, Issue, December 6, Pages 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 (6) p 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 7, Pages 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 8, Pages 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 (9), 3, 5-6. S. Fouvry, K. Kubiak, Development of a fretting fatigue mapping concept: The effect of material properties and surface treatments, Wear (9), 67, JP : Fretting Fatigue & Fatigue de Contact Paris 3 4 mai 3