Atomic Force Microscopy (AFM)

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Table of contents

1 State of the art 
1.1 Dislocation and crystal plasticity
1.1.1 Introduction to dislocations
1.1.2 Slip mechanism
1.1.3 Deformation Twinning
1.2 Grain boundary and free surface
1.2.1 Denition of a grain boundary
1.2.2 Denition and classication of grain boundaries
1.2.3 Free surface eects
1.3 Interaction between dislocation and grain boundary
1.3.1 Experimental observations
1.3.2 Dislocation pile-up
1.3.3 Image force and image dislocation
1.3.4 Slip transmission and geometrical criteria
1.3.5 Grain boundary strength
1.4 Experimental methods
1.4.1 SEM and EBSD
1.4.2 Ion Milling
1.4.3 Focused Ion Beam technique
1.4.4 Atomic Force Microscopy
1.4.5 Micro-beam size eects
1.5 Theoretical and numerical multi-scale modelling methods
1.5.1 Continuum dislocation mechanics
1.5.2 3D incompatibility stresses in bi-crystals
1.5.3 Two dimensional L-E-S (Leknitskii-Eshelby-Stroh) formalism for anisotropic elasticity
1.5.4 Crystal Plasticity Finite Element Method (CPFEM)
1.5.5 Discrete Dislocation Dynamics method (DDD)
1.5.6 Molecular Dynamics simulation (MD)
2 Experimental part: Nickel and -Brass bicrystalline micro-pillar compression test 
2.1 Introduction
2.2 Material choice
2.3 Sample preparation
2.3.1 Metallographic preparation
2.3.2 Heat treatment
2.3.3 Grain boundary choice
2.3.4 Micro-beam preparation
2.4 Preanalyses of slip information
2.5 Micro-pillar compression tests
2.6 Stress-strain analysis
2.7 Slip analysis by SEM and AFM
3 Elastic elds due to single dislocations and dislocation pile-ups in heterogeneous and anisotropic media 
3.1 Introduction
3.2 Elastic elds due to one single dislocation in dierent congurations
3.2.1 Homogeneous anisotropic medium
3.2.2 Heterogeneous anisotropic medium: bi-material
3.2.3 Anisotropic half-space with rigid or free surface
3.2.4 Heterogeneous anisotropic medium: tri-material
3.2.5 Heterogeneous anisotropic medium: multilayer material with free surfaces
3.3 Discrete dislocation pile-ups theory
3.4 Computational procedure
4 Results and discussions 
4.1 Introduction
4.2 Theoretical results
4.2.1 Computation congurations
4.2.2 Convergence of the series solutions within the tri-material conguration
4.2.3 Displacements and stresses distribution due to one single dislocation
4.2.4 Image force on dislocation in heterogeneous media
4.2.5 Results for discrete dislocation pile-ups
4.3 Prediction of stress-strain curves and study of incompatibility stresses using Crystal Plasticity Finite Element Method (CPFEM)
4.3.1 CPFEM conguration: geometry and mesh
4.3.2 Calibration of displacement and determination of material parameters
4.3.3 Incompatibility stresses
4.4 Computations of slip step height compared with experimental observations
4.4.1 Simulation conguration for experiment
4.4.2 Results of Ni micro-beam
4.4.3 Results of -Brass micro-beam
4.5 Conclusions of Chapter 4
Conclusions and Perspectives
Appendix
A Equivalence between the formulations of T.C.T. Ting and Z. Suo for the elastic elds of a dislocation in bi-materials with perfectly bonded interface
B Full coecient matrix of image decomposition method
C GB thickness and structure analyzed by Molecular Statics (MS) / Molecular Dynamics (MD) simulations
C.1 MD conguration
C.2 Results and discussions
Bibliographie