PSI - Issue 42

T. Koščo et al. / Procedia Structural Integrity 42 (2022) 1600 – 1606

1601

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Koščo, T., Chmelko, V. / Structural Integrity Procedia 00 (2019) 000 – 000

enables to measure on non-planar surfaces as well. This stereo camera configuration enables to partially overcome the image registration problem on the edge by appropriate camera positioning with partial view on the cylindrical surface of open-hole specimen. By this deployment, the notch root is not located on the edge of the evaluated area and therefore there is no loss of information in the roof of the notch. Even more challenging is the measurement of specimens with small radii, non-defined geometries e.g., welded joints in practical conditions outside the laboratory. In this case it’s a general notch with general geometry and arbitrary size. In practice usually occur sharp notches. As long as sharp notches are mentioned, rapid strain change in general have to be mentioned as well. Technically, measurement of notched specimen could be generalized to the problem of measurement of sharp strain peak e.g., defects or functionally graded materials etc. Only difference between the general strain peak and the notch strain peak is the shape curvature in the close neighborhood of the peak. Therefore, the notched case can be considered as a worse case in terms of measurement by optical method such as DIC. If we assume the use of conventional subset based stereo DIC, many factors of the measurement system, speckle pattern, specimen, and result postprocessing effects the result and its accuracy.

Nomenclature F

matrix of grey level values for reference frame matrix of grey level values for loaded frame pseudo-affine transformation parameters

G

a 0 -a 7 i 0 -i 1 x, y

illumination parameters

coordinates on reference image x * , y * coordinates on loaded image

2. Basic principle of digital image correlation Generally, DIC is based on acquisition of a set of monochromatic images of random speckle pattern on specimen surface under different loading conditions and subsequent matching of specific points between the images (reference and loaded image). Grid or mesh is created on the region of interest (ROI). In case of subset based DIC, the information of the position of a specific grid point is defined by square set of neighboring pixels, so called subset or facet. In general, size of the grid tends to be related to the subset size. Finer grids provide better spatial resolution, while smaller subsets store less information about the position. 2.1. Random speckle pattern In most cases speckle pattern consists of randomly distributed black speckles on white background or rarely white speckles on black background. The speckled are projected on the image in form of grey level values (intensity) of each pixel. The size of the speckles plays a significant role especially their size on the image. The number of pixels occupied by single speckle influences the result. Fine speckle pattern with speckles smaller than one pixel may create a grey image without significant intensity gradient. On the other hand, too rough patterns can lead to similar case where significant part of the subset consists of highest or lowest intensity values. In both cases the amount of information stored in subset of specific size is insufficient neither optimal. Therefore, multiple criteria to evaluate the speckle pattern quality has been proposed. Sum of Square of Subset Intensity Gradients (SSSIG) proposed by Pan (2008), Mean intensity gradient (MIG) proposed by Pan (2010), mean subset fluctuation proposed by Hua (2011), or subset entropy proposed by Sun (2007) etc. Authors consider a SSSIG and MIG criteria as the most suitable. SSSIG because of the information from a specific subset of specific size and direct relation of the criterion with the Sum of Square Differences (SSD) correlation criterion utilized in DIC algorithm used by authors. MIG criterion on the other hand gives an information about the pattern without relation to the subset size. 2.2. Image registration algorithm Image matching or image registration is provided by tracking of the speckle pattern between the reference and loaded image. The relation between the gray value patterns of reference and loaded image is described by so called pseudo-affine transformation eq.1., eq.2. Transformation parameters a 0 ... a 7 describe the displacement, tension, shear of the subset. Parameters are unknown in the iterative minimisation process shown in eq.3. Deeply described by Sutton (2009) ∗ ( 0 , 1 , 2 , 3 , , ) = 0 + 1 + 2 + 3 (1) ∗ ( 4 , 5 , 6 , 7 , , ) = 4 + 5 + 6 + 7 (2) min ∑( ( , ) − 0 + 1 ( ∗ , ∗ )) 2 (3) By minimizing the previous equation, the transformation parameters are evaluated. Strain field can be evaluated directly from the affine transformation or by deformation gradient. Authors consider the deformation gradient approach as generally more accurate. The main problem arises with noise occurring in the acquired image data. Noise causes a convergence of the minimization