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Category: Thesis defense and HDR

Vendredi 28 février 2020 : Soutenance de thèse de Komlavi Senyo ELOH : FFT-based modelling of X-Ray Diffraction peaks: application to dislocation loop

Komlavi Senyo ELOH  doctorant au sein de l'équipe "Physique, Mécanique et Plasticité" de l'Institut Jean Lamour, soutient sa thèse intitulée :

"FFT-based modelling of X-Ray Diffraction peaks: application to dislocation loop"

 

Date et lieu :
Vendredi 28 février 2020 à 14h00
Campus Artem
Amphithéâtre 200

 

Composition du jury :

Rapporteurs :

- Olivier THOMAS
Professeur, Université Aix-MarseilleProfesseur,

- Djimédo KONDOProfesseur,
Université Pierre et Marie Curie

Examinateurs :

- Marie-Ingrid RICHARD
Ingénieur de recherche  HDR, CEA et ERSF

- Istvàn GROMA
Professeur, Eötvös Loránd University, Budapest, Hongrie

- Lionel GELEBART
Ingénieur de recherche  HDR, CEA Saclay

Directeur de thèse :

- Alain JACQUES
Directeur de Recherche CNRS, Institut Jean Lamour, Université de Lorraine

Co-Directeur de thèse :

- Stéphane BERBENNI
Directeur de Recherche CNRS, Université de Lorraine

Invité :

- Laurent CAPOLUNGO
Directeur de Recherche, Los Alamos National Laboratory, USA

 

 

Abstract :
In  this  work,  we  propose  and  test  an  original  numerical  method  of  simulation  of  X-ray diffraction peaks by single crystals. This method is based on the use of Fast Fourier Transform (FFT) algorithms for the calculation of mechanical fields resulting from external loading and / or linear defects such as dislocation loops. These defects are modeled by stress-free strain fields (eigenstrains) in a periodic microstructuresubjected to thermomechanicalloadings. In the first part, we present an improved approach by FFT-type algorithms which allows to  accurately  obtain  the  local  mechanical  fields  without  numerical  oscillation  at  material's discontinuities.This improvement is due to the use of a discrete and periodic Green operator. This is obtained by solving the Lippmann-Schwinger equation in the Fourier space and using an  appropriate  spatial discretization.  The  fourth  order  modified  Green  operator  allowsto calculate the values of the strain and stress fields at all voxels. We also propose a third order periodic green operator to compute the displacement field.  The computed displacement field is then corrected by a sub-voxelizationmethod which removes the artifacts appearing in the case of dislocation loops inclined with respect to the reference grid. Numerical examples on reference cases show the effect of the Green operators for the calculation of local mechanical fields  without  oscillation  and  the  efficiency  of  the  sub-voxelizationmethod.  The  final displacement field obtained is the input data of the simulation of X-ray diffraction patterns.The method of simulation of X-ray diffraction peaks of FCC (Face-Centered Cubic) single crystals is then presented. The diffracting  material  is modelledby  a representative volume containing dislocation loops in (111) slip planes. We calculate the amplitude then the intensity of  the  diffracted  beam  near  a  node  of  the  reciprocal  lattice.  This   3Ddistribution  of  the diffracted intensity is processed to obtain 1Ddiagrams that will be analyzed.The  simulations  demonstrate  foremost  the  elimination  of  the  artifacts  on  the  diffraction diagrams  which  are  due  to  the  oscillations  of  the  uncorrected  mechanical  fields.  The diffraction peaks are analyzed by different statistical methods (Fourier transform of intensity, method of moments, etc.) which allow to evaluate the distribution parameters of dislocations (density, polarization factor, etc.) and to compare them with their theoretical values.

 

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