PSI - Issue 40

V. Kibitkin et al. / Procedia Structural Integrity 40 (2022) 223–230 V. Kibitkin et al/ Structural Integrity Procedia 00 (2022) 000 – 000

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5. Fields of deformation vectors The field of displacement vectors shows where the point of the material surface has been displaced to as a result of deformation. The digital image correlation method shows where some elementary surface area has moved to. When choosing the input design parameters (R, m, T), they strive to ensure that the conditions. Based on a pair of images, the field of displacement vectors can be calculated. This, in turn, enables us to obtain the spatial distribution of ( ) x, y  local deformation, which can be transformed into a pseudo-image. A natural question arises: is it possible to construct a field of displacement vectors based on a pair of pseudo-images? The check showed that this is indeed possible if the pseudo-images are obtained with a minimum spatial period ( 1 T  ) and a program with a subpixel error is used. Such a vector field reflects where and to what extent the individual regions with some local deformation are displaced. Therefore, these displacement fields will be called deformation vector fields (DVF). As a result of additional calculations, a set of pseudo images of deformation structures was obtained from the very beginning of loading and up to fracture. It was found that each fracture stage corresponds to its own typical DVF. Thus, when the formation of a macrocrack occurs at the first stage, the displacement fields have the form of a localized deformation bands. In this case, DVFs have a complex, close to chaotic character, where separate regions with local vortices or / and deformation domains are formed (Fig. 7, a). At the stage of macro crack opening, the displacement fields and DVF are similar (Fig. 7, b). At the stage of unstable flow, the DVF reflects a complex system of meso- vortices resembling a “checkerboard” structure (Fig. 7, c). Each of the datasets of deformation fields can also be approximated by a plane, which allows applying the approach discussed above for displacement fields. The deformation intensity obviously loses its meaning in this case, but it is still possible to speak about the dispersion of displacements from the mean (Fig. 8). The dispersion of deformation vectors behaves very unstable, which is associated either with the formation of a macrocrack, or with the development of a system of vortices. Its average values are approximately an order of magnitude less than the variance of the displacement vectors, which speaks not so much of a larger spread as of smaller values of the displacement amplitudes themselves for strain vectors.

a c Fig. 7. Evolution of fields of deformation vectors ( =30 s t  ). 1 30 s, =30 s; t t   2 33 s, =30 s t t   (a); 1 81 s, =30 s; t t   2 t =90 s, Δt=30 s (b); 1 2 228 s, =30 s; 231 s, =30 s t t t t     (c). b