A phase-field model of quasi-brittle fracture for pressurized cracks: Application to UO2 high-burnup microstructure fragmentation

• Published in: Theoretical and applied fracture mechanics Vol. 119; p. 1
• Main Authors: Jiang, Wen, Hu, Tianchen, Aagesen, Larry K., Biswas, Sudipta, Gamble, Kyle A.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Ltd 01-06-2022; Elsevier BV; Elsevier
• Subjects: Brittle fracture; Crack initiation; Crack propagation; Critical pressure; Exact solutions; External pressure; Fracture mechanics; Fragmentation; High-burnup structure; Linear elastic fracture mechanics; MATERIALS SCIENCE; Mathematical models; Nucleation; Numerical analysis; Phase-field fracture; Plane strain; Pressure dependence; Recrystallization; Regularization; Simulation; Softening; Stress propagation; Two dimensional analysis; UO2; Uranium dioxide; UO2; High-burnup structure; Phase-field fracture; Fragmentation
• ISSN: 0167-8442; 1872-7638
• DOI: 10.1016/j.tafmec.2022.103348

In this paper, we present a phase-field model of quasi-brittle fracture with pressurized cracks, with dedicated applications for polycrystalline materials. The model is formulated as a minimization problem within the variational framework. The external work done by pressure on the crack surfaces is included in the objective function. Several careful modeling choices lead to a regularization-length-independent critical strength. The model is constructed to give a softening response with an underlying linear traction-separation law. The pressure-dependent softening response and the regularization of the prescribed pressure are demonstrated with a (quasi) one-dimensional numerical analysis. In a two-dimensional numerical analysis under plane strain assumptions, the critical stress corresponding to crack propagation (as predicted by our quasi-brittle fracture model) is compared with linear elastic fracture mechanics (LEFM) analytical solutions. Our model is further utilized to simulate fission-gas-induced fragmentation of the UO2 high-burnup structure (HBS). Simulation results show that pressurized bubbles can cause crack nucleation and propagation, and that the bubble size and the surrounding external pressure affect the critical pressure corresponding to crack nucleation. Simulations of a partial HBS at different recrystallization stages show that different grain structures (due to recrystallization) also influence crack paths and fragmentation morphology.
•We presented a variational consistent phase-field model of quasi-brittle fracture for pressurized cracks under small deformations.•We showed the critical strength is independent of phase-field regularization length and applied pressure value.•We showed softening response is affected by the pressure applied on the crack surfaces, and the approximated external work done by pressure matches the prescribed value.•We utilized the model to simulate fission-gas-induced fragmentation of the UO2 high-burnup structure.