The nuclear glasses currently used for the containment of fission products and minor actinides can include a mass loading rate of up to 18.5%. The glass-ceramic materials envisaged for this application would be an interesting alternative that would allow the volume of the package to be reduced by increasing this loading rate. However, during storage, the crystalline phase inclusions, rich in fission products, are subject to self-irradiation α causing swelling which may lead to cracking of the glass matrix. The objective of this thesis is to set up a powerful numerical simulation tool in order to evaluate the effect of the microstructure on the cracking of the material by relating to quantities of interest such as the time to first crack or the cracked surface.

FFT methods are particularly well suited to simulating the mechanical behaviour of heterogeneous materials. Indeed, compared to the use of “standard” Element-Finite codes, FFT codes are often much more efficient and very well adapted to a parallel implementation in distributed memory. Initially proposed for local, linear or non-linear behavioural models, the use of these methods is now being extended to the framework of non-local models, such as gradient damage [2]. In addition, for simulating cracking, phase field models [3], [4] are of increasing interest in the mechanics community. Thus, the implementation of the phase field model proposed by Bourdin et al [4] has recently been implemented in FFT codes [2] and in particular in the massively parallel code AMITEX_FFTP.

Particular attention will be paid here to the use of composite voxels [5] in order to improve the quality of the numerical simulations. The analyses were first performed on small cells and then on larger cells with a random distribution of inclusions using generic tools developed at the CEA to generate the microstructures, voxelise them and identify the composite voxels.

Finally, a part will be devoted to the first FFT simulations of the cracking of heterogeneous materials with swelling inclusions. A semi-analytical approach based on a homogeneous damage field per phase has recently been implemented in AMITEX_FFTP in order to estimate the critical swelling and will be compared with the numerical and analytical approaches. The analyses presented will be performed on geometries of increasing complexity ranging from a single inclusion to several randomly distributed inclusions.

If the objectives of the thesis are met, it will give access to the simulation of the failure of glass-ceramic matrix with swelling inclusions. The approaches developed will be used to estimate quantities of interest such as the critical swelling or the cracked surface as a function of microstructural parameters.

References :

[1] W. J. Weber et al., « Radiation effects in crystalline ceramics for the immobilization of high-level nuclear waste and plutonium », J. Mater. Res., vol. 13, no 6, p. 1434‑1484, 1998.
[2] Y. Chen, D. Vasiukov, L. Gélébart, et C. H. Park, « A FFT solver for variational phase-field modeling of brittle fracture », Comput. Methods Appl. Mech. Eng., vol. 349, p. 167‑190, juin 2019, doi: 10.1016/j.cma.2019.02.017.
[3] G. Francfort et J.-J. Marigo, « Revisiting brittle fracture as an energy minimization problem », J. Mech. Phys. Solids – J MECH PHYS SOLIDS, vol. 46, août 1998, doi: 10.1016/S0022-5096(98)00034-9.
[4] B. Bourdin, G. Francfort, et J.-J. Marigo, « Numerical experiments in revisited brittle fracture », J. Mech. Phys. Solids, vol. 48, p. 797‑826, avr. 2000, doi: 10.1016/S0022-5096(99)00028-9.
[5] L. Gélébart et F. Ouaki, « Filtering material properties to improve FFT-based methods for numerical homogenization », J. Comput. Phys., vol. 294, no C, p. 90‑95, août 2015, doi: 10.1016/j.jcp.2015.03.048.