Measurement of crack tip opening displacement based on the sampling moiré method

Crack tip opening displacement (CTOD) is a key fracture parameter, but its measurement remains challenging when the crack-tip field is small, heterogeneous, and affected by local discontinuities. This study proposes a sampling moiré-based method for CTOD measurement that extracts the crack-opening displacement from the local displacement difference between the two crack flanks. Because the sampling moiré method is high precision, robust to image noise and well suited to periodic surface textures, it provides a promising route for crack-tip deformation measurement. The accuracy of the sampling moiré method relies on precise image phase computation, and the generation of cracks may lead to errors in phase unwrapping. To reduce phase-unwrapping errors near the crack, a two-stage phase-unwrapping strategy is introduced: preliminary unwrapping is used for crack-tip localization, and crack-around unwrapping is then used for displacement-field reconstruction. The complete workflow includes grating phase calculation, preliminary displacement-field estimation, crack-tip localization, crack-around phase unwrapping, displacement reconstruction, and CTOD extraction based on stable characteristic-distance selection. The proposed method was validated using numerical simulations and was further applied to natural very-high-cycle fatigue cracks generated under ultrasonic high-frequency vibration in TC4 titanium alloy. Simulations indicate that the proposed method outperforms the DIC method in terms of accuracy under the simulated operating conditions. In the practical application, the ∆CTOD measured by the proposed method increases monotonically with the net-section stress.