This thesis is a contribution to the construction of the Local Approach to fracture at the microscopic scale using polycrystalline aggregate modeling. It consists in taking into account the spatial variability of the microstructure of the material. To do this, the micromechanical modeling is carried out by finite element analysis of polycrystalline aggregates. The random stress fields (maximum principal et cleavage stress) in the material representing the spatial variability of the microstructure are then modeled 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.
