. .. Microstructure, 2.2 FE modeling, results and analysis

.. .. Bibliography,

, Outlooks and conclusion 169

. .. Outlooks, 170 6.1.1.4 Adaptation for industrial use, vol.170

. .. At-the-micro-scale, 171 6.1.2.2 Influence of the spherulite morphology, vol.173

. .. Towards-the-nano-scale, 174 6.1.3.1 Molecular dynamics, a quick review

.. .. Bibliography,

. .. Art, 181 7.2.1 Polyamide 6,6 renforcé

C. De-durée-de-vie and .. .. ,

. .. Mécanismes-d'endommagement, , p.185

. .. Approfondissement,

. .. Structure-de-la-sphérolite-orientée, , p.188

. .. Retour-au-matériau-composite, , p.189

. .. 4échelle-macroscopique,

. .. 5échelle-microscopique, 196 7.5.1.3 Principaux mécanismes d'endommagement

. .. Calculséléments-finis,

.. .. Conclusion,

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, Structure of spherulites in a semi-crystalline thermoplastic as usually described

, 11 1.4 PA610 spherulites as observed using cross-polarized microscopy. From Magill [29]

, Shish-kebab structure in semi-crystalline thermoplastics, p.13

, Heterogeneous fiber orientation in an injection molded plate. From Rolland [43]

. .. , Fiber-matrix interface in fiber reinforced polymers, p.16

. .. , Specimen orientation in an injection molded plate, p.17

, Results from tensile testing for different specimen orientations

, Results from fatigue testing for different specimen orientations -RH50, R=0.1, 4Hz. From Bernasconi [50]

, Fatigue cracks in 0°, 45°and 90°notched specimens of under R=0.1. From Tanaka [51]

. .. , Schematics of fatigue crack propagation mechanisms, p.20

, Haigh diagram: Relationship between stress amplitude ? a and mean stress ? m , with modified Gerber equation

, Influence of temperature on the S-N curves of RH0 PA66GF33. From Handa [60]

, Model of displacement of sorbed water in PA6. From Puffr, vol.62

, Wet polyamide at saturated vapor pressure: 1, firmly bound water; 2, loosely bound water; 3, sites for capillary condensed water

. S-n-curves-for-pa66gf30, T. F. R=-1,-f=10hz, and . Barbouchi,

, 27 1.20 Influence of notches on the fatigue strength of PA66GF35. From Sonsino [75]

, Schematic of a typical evolution of the cyclic strain and cyclic strain rate during fatigue loading, with controlled load. (For cyclic loading with controlled displacement, cyclic stress relaxation would be observed), p.29

. .. , 32 1.24 Comparison between experimental and assessed fatigue lives using a Principal Stress criterion on PBT-PET GF30 specimens at R=0.1. From Klimkeit [83]

, 33 1.26 Study of PA66GF30 specimens -RH50 -f = 3Hz -forced convection, Equivalent stress amplitude vs. fatigue life for PBT and PA6 specimens at various temperatures -R=-1 -0°, 18°, 45°, 90°.F r o mFat e m i, vol.56

, Section of polyethylene after fatigue showing "many inter-spherulitic cracks

]. .. , Damage at fiber tip and fiber failure as observed during in situ microtomography tensile testing, p.42

. .. , 43 1.31 Fatigue damage mechanisms as observed by synchrotron tomography, p.43

, Microcracks observed by micro-tomography and proposed damage mechanism as a function of spherulite organization -RH50 -0°specimen -N f =2468cycles

. .. , 46 1.34 Computed void volume fraction for PA6 axisymmetric specimens, Creep rate vs

, 50 1.36 Deformations at the fiber end. Overall imposed strain are indicated

, Comparison between X-Ray CT micrograph (a-c) and reconstructed model in the FEM code (b-d). Arrows indicate the direction of maximum principal stress during tensile loading

, Comparison of the crazing criterion with the damage observed by tomography. Tensile test on a 45°RH50 specimen

, Snapshot during an crystallization of a polymer (upper row) and numerical simulation of the crystallization process using the multi-phase field method (lower row)

. .. , 55 2.1 Fiber length and orientation distribution in the composite material

, Segmented fibers at the center of a 0°specimen as observed using synchrotron tomography. The core layer is visible, but only part of the shells can be seen in the field of view

, Spherulites in PA66 observed using polarized light microscopy on thin slices obtained by microtomy

, Spherulites observed using polarized light microscopy on thin slices of reinforced PA66 obtained by microtomy

, Note that they are the same for smooth and notched specimens

. .. Geometry, 72 2.7 Dimensions of notched specimens, stress concentration factor K T and stress triaxiality ratio ? (see definitions given in section 2.2.1.4), p.73

. Experimental and . .. Testing, 75 2.10 Position of the virtual extensometer on a notched U2 specimen for NOD measurement

, Example of the cyclic strain measurement for cyclic-creep evaluation during fatigue loading

, Experimental setups for in-situ testing, on the PSICHE beamline

, Secondary electron imagery in SEM

. .. Micro-tomography,

. .. Atomic-force-microscopy,

, Damage at fiber ends and crazing -RH50 -0°specimen -N f =2 4 6 8 cycles. Cavitation is evidenced by arrows, p.86

, Fiber failure induced by the proximity of a crossing fiber in the shell -U2 0°specimen -RH50 -f=0.5Hz -R=0.1 -Normalized ? max =0

, Note how difficult it can be to determine if, where and when adjacent fibers are actually in contact, vol.87

, Evidences of contact inducing damage and failure of fibers during fatigue loading -U2 0°specimen -RH50 -f=0.5Hz -R=0.1 -Normalized ? max = 0, vol.87

, Cavity distribution by diameter as obtained by various methods, p.88

, Detail view of cavitation ahead of crack tip in neat PA66 -U0.5 specimen -RH50 -f=0.5Hz -R=0.1 -Normalized ? max =0.30 -N f =2123, p.89

, Early stage of debonding at the interface, seen here at N/N f =2 0, p.89

, Damage at the interface along a transversely broken fiber after fatigue loading -0°specimen

, 90 3.10 Crack tip in a 0°PA66GF30 specimen as observed by microtomography -f=3Hz -RH50 -Normalized ? max =0.69 -N =2462, p.91

S. Geometries, , p.92

, Tomographic observation and segmentation of the crack tip in a PA66 notched specimen, test interrupted at 4221 cycles and 90% of estimated fatigue life

, Crack tip in a PA66 notched specimen as observed by microtomography, test interrupted at 2531 cycles and 95% of estimated fatigue life, p.95

, Short cracks in a 45°PA66GF30 smooth specimen as observed by microtomography, test interrupted at 1500 cycles and 98% of estimated fatigue life

. .. , Advance of the crack tip, segmented in a RH50 0°specimen and viewed in the plane orthogonal to the loading direction, p.96

, Fracture surface of a notched PA66 specimen after fatigue testing -Normalized ? max =0, vol.29

. .. , SEM fractography of a notched PA66 specimen (N f =917), p.98

, Spherulitic damage ahead of the fatigue crack in a notched U0.5 PA66 specimen after cryofractography, test interrupted at 4221 cycles and 90% of estimated fatigue life

, Schematic of the influence of the spherulitic structure of the polymer on fatigue crack advance

, Orientation of the 40 nuclei observed on 3 different PA66 specimens after fatigue testing

, SEM observations of the nuclei for three different specimens orientation

, 102 3.23 SEM fractography a notched "tomo" PA66 specimen -N/N f =7 3 %-f=0.5Hz -Normalized ? max =0

S. Complementary and . Fractography, PA66 specimen showing damage initiating from the nucleus -N/N f =7 3 %-f=0.5Hz -Normalized ? max =0

. .. , 103 3.26 SEM fractography a notched U0.5 90°PA66GF30 specimen -f=0.5Hz -Normalized ? max =0.34 -N f =24565

, Evolution of the mean strain for several load ratios and fatigue lives on smooth 0°PA66GF30 specimens -RH50 -f = 3Hz -forced convection, p.108

, 1) vs. experimental number of cycle to failure on smooth PA66GF30 45°specimens -f = 0.5Hz -free convection. Scatter band of factor 2 is marked in dashed lines

, Analysis to establish a relationship between the number of cycle to failure N f , the anelastic energy W an and the cyclic strain rate? cycl -RH50 specimens -f = 3Hz -forced convection -all fiber orientations, p.110

, 4) vs. experimental number of cycle to failure -RH50 specimens -f = 3Hz -forced convection -all fiber orientations. Scatter bands of factor 2 and 10 are marked in dashed and dotted lines respectively

, Weight function f for various values of the parameter ?, p.112

, for all fiber orientations. Scatter bands of factor 2 and 10 are marked in dashed and dotted lines respectively

, Relative error on N f using the mixed criterion eq. (4.7) identified on various datasets

, Relative error on N f using several criteria

, Note that U2 and U0.5 refers to the notch geometry as defined in fig

, Tomographic slice of a notched "tomo" PA66 specimens during in-situ quasi-static tensile testing

, Tensile test on notched PA66GF30 specimens at? =10 ?3 s ?1, p.119

, Cyclic strain evolution and local strain rate as measured by timed DIC in a PA66 specimen -U0.5 notch -Normalized ? max =0.26, p.120

, Fatigue damage in a "tomo" notched PA66 specimen as observed by micro-tomography

, Segmented fatigue cracks in 3 interrupted notched "tomo" PA66 specimens as observed by micro-tomography -Number corresponds on the number of applied loading cycles before the test was interrupted for tomographic imaging -Normalized ? max =0

, SEM fractography of a notched U0.5 PA66 specimen -N f =917, p.122

. .. S-n-;, curves for notched reinforced PA66 specimens, p.123

, Maximum principal cyclic strain rate as measured on the surface of the specimens by timed DIC

, 124 4.21 Tomographic evaluation of fatigue damage in a notched "tomo" 0°spec-imen -Normalized ? max =0.60

, Identification of several fatigue criteria for notched PA66GF30 specimens -R=0.1 -0.5 Hz. Scatter band of factor 2 is marked in dotted lines, p.128

. .. , 130 4.24 Normalized stress vs. NOD for a U2 notched PA66 specimen during tensile testing

. .. , Shell-Core geometry and stress-strain curves for U2 notched PA66GF30 specimens during tensile testing at? =10 ?3 s ?1, p.132

, Cyclic loading of a notched U2 PA66 specimen with parameters from the quasi-static loading identification and the readjusted parameters for improved cyclic strain rate calculation -f=0.5Hz -R=0.1 -Normalized ? max =0

, Global axial cyclic strain rate for notched PA66 specimens (R=0.1 -f=0.5Hz), determined experimentally from the crosshead displacement and the top surface displacement in the numerical model, p.134

, Global axial cyclic strain rate for notched PA66GF30 specimens, p.135

. .. , Profile of the axial cyclic strain rate between notches during at N = N f /2.136 4.30 Notch opening rate for notched PA66 specimens, p.136

, Process to plot local cyclic strain rate maps, here on a U2 specimen, p.137

, Axial cyclic strain rate fields measured at N = N f /2 and calculated at the corresponding number of computed cycles

, Principal cyclic strain rate in composite specimens -U2 notch -Normalized ? max =0

, Principal cyclic strain rate in a 0°specimen during the secondary stage of cyclic creep -U2 notch -Normalized ? max =0

, Computed void volume fraction f in a notched PA66 "tomo" specimen -Normalized ? max =0

, Computed void volume fraction f and corresponding tomographic slice. Notched PA66 "tomo" specimen -Normalized ? max =0.36, p.140

, Cyclic strain rate and computed void volume fraction after 500 loading cycles in notched "tomo" specimens -Normalized ? max =0.36, p.141

, Comparison between computed N f and experimental values, p.142

, Slicing is made perpendicularly to the fiber direction

. .. , Example of segmented microstructure for FFT micro-modeling, p.149

, Strain rate distribution in the matrix and sensitivity of the matrix model to the imposed macroscopic strain rate -FFT modeling, p.150

, Experimental stress-strain curves vs. microstructure calculation -FFT modeling

, Local mechanical fields distribution in the matrix for different RH and fiber orientation at iso-macroscopic axial strain ? =3 .6% after loading at? =10 ?4 s ?1 -FFT modeling

. .. , Study of a short glass fiber failure -FFT modeling, p.154

, Modeling voiding at fiber end by an extra phase with degraded properties -FFT modeling. Small oscillations in the computed fields come from an aliasing effect as the conditions of the Nyquist-Shannon are not formally respected (high contrast between the phases)

, Results for monotonic tensile loading of a RH 50 -0°specimen at? = 10 ?4 s ?1 until a global strain of ? =3.6%-FFT modeling, p.156

, Hydrostatic stress in two microstructures after quasi-static loading a? ? =1 0 ?4 s ?1 until a global strain of ? =3 .6%. At this imposed strain, different stresses are reached depending on the fiber orientation, p.158

. .. , 159 5.13 Cartography of ?? 11 ?N max , with the locations of the cavities observed on the corresponding tomographic slice, in a RH 50 -45°specimen -FFT modeling

. .. , 162 5.16 Cyclic strain evolution for FE microstructure modeling -0°-RH50 -R=0.1 -f=0.5Hz -Normalized ? max =0

, Calculated void volume fraction after 10 loading cycles at a normalized ? max =0.21 overlaid on the corresponding tomographic slice, in a RH50 -0°specimen after 1500 loading cycles at a normalized ? max =0 .69 -FEM modeling

S. , curves for normal and nucleated matrix in composite material specimens

. .. , AFM imaging of a fatigue fracture surface in PA66, p.172

, Influence of the exposition to synchrotron radiation on the failure mode of PA66 under cyclic loading

, Molecular dynamics tensile test on amorphous PE at different imposed strain rates. 10 polymer chains, 1000 atoms per chain, p.175

, (a) to B.1(d)) and non-bonded (figs. B.1(e) to B.1(g)) interactions between atoms

X. B. , 3 Mapping between atomistic and CG models of PA66. The circles denote which atoms are joined into CG beads

X. ,