A phase-field model of quasi-brittle fracture for pressurized cracks: Application to UO<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e486" altimg="si140.svg"><mml:msub><mml:mrow /><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math> high-burnup microstructure fragmentation

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