Advanced grid method for discontinuous displacement field measurement

Accurate measurement of displacement fields during material deformation is critial for understanding and predicting mechanical failure. However, conventional grid-based optical methods often fail to reliably quantify displacement fields near discontinuities, such as cracks, due to error propagation during phase unwrapping. In this study, we present an advanced grid method that overcomes this limitation. This method combines the sampling moiré method (SMM) with a novel adaptive weighted least-squares (AW-LS) phase unwrapping algorithm. The key innovation is a continuous, data-driven weight matrix derived from the local variance of wrapped phase gradients. This matrix adaptively guides the unwrapping process, effectively isolating phase error propagation sources associated with discontinuities while preserving complete deformation information. Rigorous numerical simulations validate the sub-pixel accuracy of our method in measuring displacement fields for grid images severed by theoretical cracks. Furthermore, this method was applied to measure the displacement field around cracks in-situ tensile experiments on nickel-based single crystal (NBSC) superalloy specimen. The experimental results provide the first quantitative characterization of full-field displacement evolution during micro-crack initiation and propagation in NBSC specimen under uniaxial tension. Quantitative experimental error analysis demonstrates that even under conditions of severe grid damage, measurement errors remain below 10% of the grid pitch. This study establishes a robust optical metrology framework for discontinuous deformation, offering significant potential for material design, structural integrity assessment, and experimental mechanics.