Modelling the random spatial variability of stress fields in polycrystalline aggregates – application to the local approach to fracture mechanics

Abstract

This thesis is a contribution to the construction of the Local Approach to fracture at the microscopic scale using polycrystalline aggregate modelling. It consists in taking into account the spatial variability of the microstructure of the material. To do this, the micro-mechanical modelling is carried out by finite element analysis of polycrystalline aggregates. The random stress fields (maximum principal et cleavage) in the material representing the spatial variability of the microstructure are then modelled by a stationary ergodic Gaussian random field. The properties of the spatial variability of these fields are identified by an identification method, e.g. periodogram method, variogram method, maximum likelihood method. The synthetic realizations of the stress fields are then simulated by a simulation method, e.g. discrete Karhunen-Loève method, Circulant embedding method, spectral method, without additional finite element calculations. Finally, a Local Approach to fracture by simulation of the cleavage stress field using the simulated realizations is constructed to estimate the rupture probability of the material. 

Keywords

Local approach to fracture - polycrystalline aggregates - finite element simulation - cleavage stress - spatial variability - stationary Gaussian random fields - ergodicity - simulation of realizations - Karhunen-Loève expansion - Circulant embedding method - identification - semi-variogram - periodogram

BibTeX cite

@PHDTHESIS{DangThesis,
  author = {Dang, H. X.},
  title = {Identification de la variabilité spatiale des champs de contraintes dans les agrégats polycristallins et application à l’approche locale de la rupture},
  school = {Universit\'e Blaise Pascal, Clermont-Ferrand, France},
  year = {2012}
}