Deformation measurements by digital image correlation: Implementation of a second-order displacement gradient

Abstract

ABSTRACT--This paper outlines the procedure for refining the digital image correlation (DIC) method by implementing a second-order approximation of the displacement gradients. The second-order approximation allows the DIC method to directly measure both the first-and second-order displacement gradients resulting from nonlinear deformation. Thirteen unknown parameters, consisting of the components of displacement, the first-and second-order displacement gradients and the gray-scale value offset, are determined through optimization of a correlation coefficient. The previous DIC method assumes that the local deformation in a subset of pixels is represented by a first-order Taylor series approximation for the displacement gradient terms, so actual deformations consisting of higher order displacement gradients tend to distort the infinitesimal strain measurements. By refining the method to measure both the first-and second-order displacement gradients, more accurate strain measurements can be achieved in large-deformation situations where second-order deformations are also present. In most cases, the new refinements allow the DIC method to maintain an accuracy of 4-0.0002 for the first-order displacement gradients and to reach 4-0.0002 per pixel for the second-order displacement gradients.

J-Integral Calculation by Finite Element Processing of Measured Full-Field Surface Displacements

“…The correlation coefficient for each subset is optimised using rigid body displacement of the subset and the first-order displacement gradients describing the local deformation values of the subset [23]. The second-order displacement gradient can also be included in the correlation analysis and has been shown to improve DIC accuracy [24]. Image acquisition setups using one camera are able to determine in-plane displacements, with a requirement of negligible out of plane displacements unless confocal optics are used; such an example is presented by Fazzalari [25].…”

A Review of Surface Deformation and Strain Measurement Using Two-Dimensional Digital Image Correlation

“…This can be achieved using a sub-pixel interpolation scheme which is employed to represent the grey level values between the sub-pixel locations before starting the image matching process. For example, bilinear interpolation [17,18], bi-cubic spline interpolation [19,20] and bi-cubic B-spline interpolation [21] have been reported in numerous papers. Higher-order interpolation schemes are always recommended in the analysis as they provide results with a higher degree of accuracy.…”

“…In order to improve the accuracy of the Digital Image Correlation (DIC) algorithm, Lu and Cary [20] applied the second-order approximation to determine the first and second-order displacement gradients. Besides, they also implemented the third-order polynomial interpolation known as Bi-cubic Spline to reconstruct the grey intensity values in each location of the images.…”

High Performance Digital Volume Correlation

“…In This mapping between the reference image and the deformed image is given by a shape function which defines the degrees-of-freedom (DOF) to be determined at each point. The linear shape function [12] Alternatively, the quadratic shape function results in greater accuracy in matching an underlying nonlinear deformation [48,70]. It adds second derivative terms, for a total of thirty DOF at each point.…”