Regular Article

Micro-scale characterization of brittle fracture in UO₂ nuclear fuel: finite element methodology for 2D and 3D simulation

¹ CEA, DES, IRESNE, DEC, Cadarache, 13108, St Paul Lez Durance, France
² Univ. Lyon, INSA Lyon, Université Claude Bernard Lyon 1, CNRS, MATEIS, UMR5510, 69621 Villeurbanne, France

^* e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 30 July 2025
Received in final form: 10 April 2026
Accepted: 10 April 2026
Published online: 13 May 2026

Abstract

This work is conducted within the framework of nuclear fuel safety analyses involving multiscale modelling of UO₂ fuel pellet fragmentation process. In this paper, a Finite Element (FE) methodology is proposed in order to enable 2D and 3D simulation of brittle fracture in micro-scale specimens used for the characterization of irradiated nuclear fuel. More specifically, these developments address Finite Element simulations using Cohesive Zone Modelling with complex shape of defects, where a direct application of Griffith’s criterion with the fracture mechanics approach is not always possible. In the case of UO₂ ceramic material, the mesh refinement needed for the FE simulation of brittle fracture requires a specific attention due to the fact that the damage process zone has a characteristic size smaller than 10 nm. The main objectives are first to discuss the questions related to mesh convergence in the case of stress singularity, and secondly to enable the use of coarser meshes while maintaining accuracy compared to the converged mesh solution. The mesh convergence analysis and coarse mesh approach, established on a 2D configuration, are based on a Cohesive Zone Model (CZM) using two parameters: the critical cohesive stress σ_c, and the fracture energy G_c. The coarse mesh approach introduces a numerical critical cohesive stress, σ_c^*, replacing the physical one, σ_c. Thanks to this approach, the relative mesh size can be increased by a ratio of ten with a deviation of the fracture load assessment smaller than 1% compared to the Griffith’s solution. The FE methodology and the coarse mesh approach are then tested with 2D and 3D simulations of a micro-cantilever bending test on a notched specimen. The simulation results are consistent with the experiment where the parameter G_c controls the fracture load. The critical stress, σ_c, ahead of the notch tip, can vary in the range 5–20 GPa with no effect on the fracture load. The coarse mesh approach is validated with a deviation lower than 2% compared to the fine converged mesh.