Gray level residual (GLR) field refers to the intensity differences between corresponding voxel points in the digital volume images acquired before and after deformation. Typically, internal damage in materials induces substantial variations in grayscale values between corresponding voxel points. Therefore, the GLR field helps to reveal the damage location. In the finite element-based global digital volume correlation (DVC) method, the GLR field, as the matching quality evaluation criteria, can be readily calculated and has been employed to characterize the evolution of internal cracks. However, the widely used subvolume-based local DVC, which can output displacement, strain, and correlation coefficient at discrete calculation points, cannot obtain the GLR directly. Compared with correlation coefficient and deformation information, the GLR field achieves voxelwise matching quality evaluation, thus demonstrating superior performance in visualizing internal damage. Therefore, accurate GLR calculation in local DVC is undoubtedly valuable in compensating for its shortcomings in fine-matching quality evaluation and expanding its applications in internal damage observation and localization.

The GLR field is obtained by subtracting the reference volume image from the deformed volume image after full-field correction. The key of its calculation is to utilize the continuous voxelwise data, including contrast and brightness correction coefficients and displacement, to correct the deformed volume image. In this work, a dense interpolation algorithm based on finite element mesh is adopted to estimate the voxelwise data within the volume of interest (VOI). 3D Delaunay triangulation algorithm is first utilized to generate tetrahedron element mesh from the discrete calculation points, and then the data of voxel points inside each tetrahedron element can be determined with the shape function of finite element. After acquiring the voxel-wise data of VOI within the reference volume image, the corrected deformed volume image can be reconstructed. Given that the corresponding voxel points in the deformed volume image normally fall into the subvoxel positions, a subvoxel intensity interpolation scheme is required during the calculation of correlation residual in local DVC. In this work, the advanced cubic B-spline interpolation method is adopted to estimate the grayscale of the corrected deformed volume image. In addition, a simulated mode I crack test and a tensile test of nodular cast iron are carried out to verify the feasibility of the GLR field based on local DVC and the reliability and robustness in damage observation and detection.

In simulated mode I crack test, the results show that the uncorrected GLR field still keeps a higher grayscale even in the region away from the crack compared with the corrected GLR field (Fig. 7), which degrades the damage observation and location. Therefore, contrast and brightness correction are necessary during the calculation of the GLR field. The crack plane can be detected clearly from the GLR field after threshold processing, and the position of the crack plane is very close to the preset value (Fig. 7). The proposed GLR based on local DVC effectively eliminates the influence of contrast and brightness changes and achieves precise crack location. Additionally, more information about the damage can be acquired from the GLR field. The crack morphology and orientation can be determined from the slice image at y=40 voxel in the real test. Besides, the debonding between the nodular graphite and matrix can also be detected roughly from the GLR field (Fig. 10). It should be noted that the GLR field after post-processing can only reflect the approximate morphology of damages and fails to reflect the opening of crack and debonding accurately since the interpolation used in displacement correlation may enlarge the region with damage. Despite all this, the location and morphology of damages extracted from the GLR field are helpful in understanding the fracture mechanics properties of nodular graphite cast iron.

A simple and practical method for GLR field calculation based on post-processing of local DVC measurements is proposed. The method addresses the limitations of existing local DVC in fine-matching quality evaluation. Compared with correlation coefficient and deformation information, the GLR field not only accurately reflects the location of internal damage but also facilitates visual observation of internal crack morphology and interface debonding behavior. It holds the potential for broader applications in visualizing and precisely locating internal damage within materials and structures.