A COMPARISON OF DIC METHODS CONSIDERING THE FIRST- AND SECOND-ORDER DISPLACEMENT GRADIENTS IN SHEAR BAND MEASUREMENTS

In the existence of the second-order displacement gradient or strain gradient in a shear band, the differences between two kinds of digital image correlation (DIC) methods in measurements of the displacement, strain and strain gradient are investigated. Based on the theoretical solution of displacement in a shear band, which is based on gradient-dependent plasticity, fictitious shear bands with different averaged shear strains and strain gradients are generated using an affine transform in Matlab. The following results are obtained through calculation. When the averaged shear strain and corresponding gradient are higher in a shear band, compared with the DIC method only considering the first-order displacement gradient, the DIC method considering the second-order displacement gradient has obvious advantages and the calculated displacement, strain and strain gradient agree well with the theoretical solutions. However, the highest strain at the central region of the shear band is underestimated due to the fact that the measured strain is the averaged strain in DIC methods. When the averaged shear strain and corresponding gradient are lower, the highest strain in a shear band may be overestimated due to the influence of standard deviation. No advantage is found in the DIC method considering the second-order displacement gradient under this condition. Based on these results obtained, four kinds of results of three kinds of strain fields from the initial loading to pre-fracturing within a sand specimen are analyzed in uniaxial compression and stress-controlled loading. The maximum strain is found to be less than 0.25 and then the results obtained by the DIC method considering the second-order displacement gradient have no advantage.