Theoretical estimation of systematic errors in local deformation measurements using digital image correlation

The measurement accuracy using the digital image correlation (DIC) method in local deformations such as the Portevin-Le Chatelier bands, the deformations near the gap, and the crack tips has raised a major concern. The measured displacement and strain results are heavily affected by the calculation parameters (such as the subset size, the grid step, and the strain window size) due to under-matched shape functions (for displacement measurement) and surface fitting functions (for strain calculation). To evaluate the systematic errors in local deformations, theoretical estimations and approximations of displacement and strain systematic errors have been deduced when the first-order shape functions and quadric surface fitting functions are employed. The following results come out: (1) the approximate displacement systematic errors are proportional to the second-order displacement gradients and the ratio is only determined by the subset size; (2) the approximate strain systematic errors are functions of the third-order displacement gradients and the coefficients are dependent on the subset size, the grid step and the strain window size. Simulated experiments have been carried out to verify the reliability. Besides, a convenient way by comparing displacement results measured by the DIC method with different subset sizes is proposed to approximately evaluate the displacement systematic errors.