Fracture-parameter inversion from DIC displacement fields using finite-element complex-network graph learning

Abstract

Fracture-parameter identification from digital image correlation (DIC) displacement fields commonly relies on local asymptotic-field fitting near the crack tip and is therefore sensitive to crack-tip localization, fitting-window selection, and measurement noise. Conventional data-driven models use regular pixel representations and cannot explicitly describe the mechanical coupling embedded in the spatial discretization. This study proposes a finite-element complex-network graph-learning (FE-CN) inversion method. Q4 elements serve as the local mechanical front end, and macro-graphs at three scales, 8 × 8, 16 × 16, and 32 × 32, are constructed from fatigue-crack DIC data. The two-channel displacement fields, crack-tip geometry, loading information, and finite-element-derived strain, stress, strain-energy, and internal-force concentration proxies are organized into a stiffness-coupled network for joint identification of the mode-I stress intensity factor $K_I$ and the non-singular $T$-stress. The results show that FE-CN outperforms deep-learning baselines trained under consistent conditions for both parameters. Prediction performance improves and generally stabilizes with graph-scale refinement, with a more pronounced improvement for the $T$-stress, and the finite-element nodal mechanical features are the primary source of the accuracy gain. $K_I$ is more sensitive to missing information at spatially scattered measurement points, whereas $T$ responds more strongly to missing information in the crack-tip region. Controlled elastoplastic sensitivity analysis and external testing on an independent DIC dataset further delineate the material-response and cross-domain applicability boundaries of the method. This study provides a structured basis for DIC field-of-view integrity inspection, speckle-quality control near the crack tip, and batch identification of fracture parameters.