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. Zhang-x, . J. Wang-q, Y. Wang, . Wang-z, H. Shen et al., Contact involving a functionally graded elastic thin film and considering surface effects, International Journal of Solids and Structures, vol.150, pp.184-196, 2018.

. S. Zhou-r, Surface Topography and Fatigue Life of Rolling Contact Bearings, Tribology Transactions, vol.36, pp.329-340, 1993.

. R. Zhou-z and . Vincent-m, Effect of external loading on wear maps of aluminium alloys, Wear, pp.619-623, 1993.

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, INSA Lyon, tous droits réservés 1.1 Emissions reduction roadmap, 2019.

, Growth in the use of composites in commercial aircraft

. .. Turbofan-engine, 7 1.4 LEAP fan blades in RTM woven composite materials, vol.8

, 8 1.6 LEAP-1A engine with Fan blades in RTM woven composite materials

, Evolution of solicitation frequencies and amplitude during a flight cycle

. .. Engines, 10 1.9 Fretting modes

, Fretting regimes

, Wear scar from fretting

. .. , Crack initiation in partial slip fretting regime [BRY 88], p.15

, Crack initiation and propagation in partial slip fretting regime

*. .. , 17 1.17 Surface initiated damage from RCF

, Subsurface damage mechanisms in RCF

, Cross sectional area of the RVE with a damaged area, p.21

, Stress strain curve with damage

, Parts made of composite materials

. .. Materials, 23 1.24 Mechanical behavior of a 2D woven composite, p.25

. .. 3d-woven-composite, 25 1.26 Initial state of 3D woven polymer matrix composite

. .. , Damage mechanisms at the microscopic level [COU 08], p.27

. .. Debonding-of-the-yarn, , p.27

, Matrix fracture in tension

. .. C/epoxy, 28 1.31 Geometrical approximation of the blade disk contact

. .. , 38 2.3 Discretizaton of the contact loading in N p rectangles of uniform pressure and shears

, Flow Chart of fully coupled semi-analytical elastic contact solver, p.44

. .. , 45 2.6 Decomposition of the half-space solution into three sub-problems, p.50

. .. , Flow chart of fully coupled semi-analytical solver, p.51

. .. , 60 3.2 Damage effect on macroscopic behavior

. .. , Stress-Strain plot with damage evolution for a cube, p.61

, Half-space with multiple cuboidal inclusions superimposition, p.62

, Algorithm of Heterogeneous Elastic-Damageable Contact Problem, p.63

, Validation of the enrichment technique with Hertzian analytical solution, p.66

. .. , Normal and tangential loads during one fretting cycle, p.67

.. .. Equivalent,

D. .. Damage-variable, 68 3.10 Evolution of damage and Young modulus with cycles for µ = 0.5, p.69

, Equivalent strain? along direction z

D. .. Damage-variable,

. .. , Evolution of damage function of friction coefficient, p.72

, Effect of computation discretization on damage evolution, p.73

. .. , 73 3.18 Comparison of contact pressure function of enrichment width, p.74

, Damage variable

. .. , Fretting regime and associated damage phenomena, p.78

, Coated half space with cuboidal inclusions

. .. , Equivalent strain? in soft coated materials, p.80

. .. , Equivalent strain? in hard coated materials, p.81

, Equivalent strain with a soft coating

, Equivalent strain along z with a hard coating

, Damage in coated materials

. .. , Damage variable D with model from literature, p.85

. .. Contact-pressure-with-damage, 86 3.35 Damage evolution between two damage models, p.86

. .. , Damage variable D in Stick Slip with a model from literature, vol.87, p.88

. .. , 89 3.39 Pressure distribution with wear and damage in gross slip and partial slip regimes

, 90 3.41 Comparison between wear scars and damage distribution in partial slip, p.91

, Stress history of a point located at 0.5a * in the subsurface of the material as the Hertzian load passes over

. .. , Butterfly wings observed around an inclusion, p.96

, Effect of over rolling direction on butterfly wings propagation, p.96

, Jump-in-cycles Algorithm

. .. , Enrichment technique around spherical inclusion, p.101

, Flowchart of the coupled contact solver and damage model, p.101

. .. , Rolling of a cylinder on a heterogeneous half-space, p.102

. .. , Effect of a spherical inclusion on the stress fields, p.103

. .. , 104 4.10 Critical stress in the REV around the inclusion

, Chronological order of butterfly propagation

, Sectioning of the damage variable D around an inclusion, p.108

. .. , Effect of inclusion depth on damage distribution, p.110

, Butterfly wings around a spherical inclusion at different depth, p.111

, Critical stress around a soft inclusion

. .. ,

, Effect of damage on contact pressure

. .. , Definition of Over Rolling Direction (ORD), p.116

, C-cracks observed around indented surface

, Contact pressure on indented surface

, Contact pressure on indented surface

, Damage after contact on indented surface

, Contact pressure on damaged indented surface

. Bruker and . .. Tribolab,

, 2 Description of Pin-on-Disk parameters

, Transverse isotropy of yarn

, View at 45 ? of the woven composite material without the matrix

, 6 Coefficient of friction between steel and woven composite, p.127

. .. Composite, 128 5.8 Wear volume between steel and woven composite, Wear depth between steel and woven, p.130

, Schematic view of the fretting experiment

. .. , Coefficient of friction during fretting on the matrix, p.133

. .. , Coefficient of friction during fretting on a yarn, p.134

, Fretting loops on woven composite

. .. , Microscopic observations during fretting on the matrix, p.136

. .. , Microscopic observations during fretting on a yarn, p.137

, Microscopic observations during fretting on the matrix in stick/slip, p.138

, Wear depth during fretting on the matrix

, Wear depth during fretting on a yarn

. .. , Wear volume during fretting on the matrix, p.140

. .. , 141 5.21 Schematic view of the compression experiment with MTS test rig, Wear volume during fretting on a yarn

. Dcd-fft, Algorithm applied on the heterogeneous subsurface problem, p.151

, Illustration of the duplicated padding in 2D

. .. , Stress field in the REV with duplicated padding, p.152

, Effective Young modulus for one spherical inclusion, p.154

. .. , Effective Young modulus for one cuboidal inclusion, p.154

, Indentation curve between homogenized and heterogeneous material V f = 0

, 156 6.8 Indentation curve between homogenized and periodic heterogeneous material V f = 0.1

, 157 6.10 2D woven composite geometry from WiseTex

. .. , Computed tomography of an interlock composite, p.160

. .. , Voxelized view of the woven composite material, p.162

, Stress on the top surface of a homogeneous material, p.164

. .. , , p.167

, Contact pressure on the voxelized composite material, p.167

. .. , Transversely Isotropic directions of the yarn, p.168

. .. , Stress field in a unique yarn embedded into the matrix, p.170

. .. , Contact pressure over a material with one yarn, p.171

, Equivalent strain in the two anisotropic direction of the yarn, p.171

, Microstructure of bearing steel AISI 52100

, The Voronoi tessellation process

, Example of a 3D Voronoi tessellation

, Voxelization of the domain accordingly to the Voronoi tessellation, p.177

, Von Mises stress in anisotropic domain

. .. , Contact pressure on the anisotropic domain, p.180

. .. , 183 6.31 Magnitude in the maximum Tresca stress

. .. , Magnitude in the maximum Von Mises stress, p.184

, Weibull plot for the maximum reversal shear stress criterion, p.185

. .. , Weibull plot for the maximum Tresca stress criterion, p.186

, Weibull plot for the maximum Von Mises stress criterion, p.186

, 195 C.1 Periodicity and overlapping created by the convolution product

C. and ]. .. , Deleting overlapping using zero padding

, Wrap-around and zero-padding for even coefficients

, Wrap-around and zero-padding for odd coefficients

, Microscopic surface observation in POD

. .. , Coefficient of friction in steel/steel contact, p.202

, Wear depth in steel/steel contact

D. , Wear volume in steel/steel contact

. .. Experiment, 204 D.8 Fretting Loop N=60000, W=125N and ? = 0.2mm, METL test rig for fretting, p.205