A comparison of domain integral and multi-parameter methods for the strain intensity factor estimation of rigid line inclusion using digital image correlation

Abstract

A comparative study is carried out between two methods to estimate the strain intensity factor of a rigid line inclusion using the displacement and strain fields from digital image correlation (DIC). The two methods are (i) a proposed hybrid domain integral method and (ii) the linear over-deterministic least-squares technique involving multi-parameter displacement field equations (multi-parameter method). The multi-parameter method uses the displacement data obtained from the DIC experiments to find the unknowns in the multi-parameter equation. The proposed hybrid methodology uses a domain integral method to calculate the strain intensity factor using the full-field displacement and strain data obtained from DIC. The strain intensity factor estimated using the proposed domain integral method, and the multi-parameter method agrees with the analytical estimate. The influence of the size of the annular region and the mesh sensitivity is also reported. The sensitivity to the variance and bias errors in measurement for both the methods is investigated. To investigate the effect of variance error, a Gaussian noise is introduced over the reference and deformed images before post-processing, and its influence on the strain intensity factor estimate is discussed. The effect of random perturbations of displacements and strains on the strain intensity factor estimates is also investigated. The domain integral method is less sensitive to the variance error when compared to the multi-parameter solution approach. Further, the bias errors due to uncorrected lens distortions, over-smoothing of data, and DIC algorithm adopted are introduced into the measurements, and its effect on both the methods is investigated. The multi-parameter method is less sensitive to bias errors when compared to the domain integral method. Therefore, it is recommended that the domain integral method may be used for the experimental determination of strain intensity factor in measurements with variance errors and the multi-parameter method for measurements with bias errors.