Physics-Informed Neural Network Framework for Phase-Field Modeling of Intergranular Fracture

Intergranular fracture, characterised by the preferential growth of crack along the grain boundaries is a critical failure mode in polycrystalline materials. While phase-field models have been widely used to simulate such fracture within finite-element frameworks, their combination with physics-informed neural networks (PINNs) for microstructure-dependent crack growth remains largely unexplored. This work develops a PINN-based phase-field formulation to model intergranular fracture. Introducing a reduced resistance to an interface, by representing the grain boundary through a spatially varying fracture toughness field, the fracture problem is solved, in the present work, using a staggered two-network architecture. While one network handles the displacement field, the other solves the phase-field damage variable, collectively mirroring the classical operator-split approach, which in this formulation replaces finite-element discretization with neural-network approximation. Comparing the evolution of the crack in two distinct cases of homogeneous and spatially-varying fracture-toughness, under identical loading condition, demostrates that the crack in the latter intergranular medium ($G_c^{gb} = 0.20$) elongates preferentially along the weakened interface, producing greater vertical extension, whereas the damage-field higher restricted in the intragranular setting ($G_c = 1.0$). Correspondingly, this work offers novel evidence for the ability of the PINN-based phase-field approach to model intergranular cracking.