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Digital image correlation is a widely used technique in the field of experimental mechanics. In fracture mechanics, determining the precise location of the crack tip is crucial. In this paper, we introduce a novel crack tip detection algorithm based on displacement and strain fields obtained by digital image correlation. Iterative crack tip correction formulas are discovered by applying deep symbolic regression guided by physical unit constraints to a dataset of simulated cracks under mode I, II and mixed-mode conditions with variable T-stress. For the training dataset, we fit the Williams series expansion with super-singular terms to the simulated displacement fields at randomly chosen origins around the actual crack tip. We analyse the discovered formulas and apply the most promising one to digital image correlation data obtained from uniaxial and biaxial fatigue crack growth experiments of AA2024-T3 sheet material. Throughout the experiments, the crack tip positions are reliably detected leading to improved stability of the crack propagation curves. • Crack tip correction formulas learned from FE simulations with physical deep symbolic regression. • Distinct correction formulas based on Williams coefficients for mode I, mode II, and mixed mode load cases. • Application to uniaxial and biaxial fatigue crack growth experiments accompanied by full-field and high-resolution DIC. [ABSTRACT FROM AUTHOR]

• 3d finite element analysis of fatigue crack propagation including crack closure. • Plane stress and plane strain conditions dominate plasticity-induced crack closure. • Only the load ratio and the maximum stress intensity factor affect K op and K cl. • Crack surface contact has no influence on the general shape of the plastic zone. • The cyclic plastic wake denotes further plastic deformation on the fracture surface. The mutual interactions between intrinsic (damage) and extrinsic (shielding) mechanisms are essential for understanding fatigue crack growth in ductile materials. In the latter case, plasticity-induced crack closure is the dominating retardation mechanism in the Paris regime. The transition between plane strain and plane stress states leads to a locally different fracture surface contact, which is difficult to access during experiments. In this work, plasticity-induced crack closure under constant amplitude loading of an AlCu4Mg (AA2024) aluminium sheet material is studied from a three-dimensional perspective. An elastic–plastic 3D finite element model of an M(T)160 specimen with a bilinear isotropic hardening model is used to study the evolution of plasticity during fatigue crack growth. Cyclic crack propagation is simulated with the releasing-constraint method. In the results, plasticity-induced crack closure is present up to a load ratio R = 0.3. Detailed investigations of the contact pressure distributions indicate a strong dependence on the stress intensity factors and the sheet thicknesses. The contact pressure distributions on the fracture surface can be divided into three characteristic regions. Near the plastic zone, plastic energy is still induced during the unloading process after the crack is already closed. However, the crack surface contact does not affect the shape of the plastic zone. Additionally, further plastic energy accumulates in the plastic wake region during crack closure within subsequent load cycles, described here as cyclic plastic wake. In summary, the finite element model can reproduce the major features of fatigue crack closure like K op or K cl and the three-dimensional and load-dependent evolution of plasticity-induced crack closure. [ABSTRACT FROM AUTHOR]