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

225

3

To carry out the DIC studies, a cylindrical surface was ground flat and polished to obtain a rectangular 7.45 mm × 7.40 mm plane field of interest (FOI). This sample was loaded according to the uniaxial compression scheme, where the speed of mot ion of the movable grip was 2 × 10 − 4 s − 1 . On one side of the sample, the surface images were captured using a Nikon D90 camera (Nikon Corp., Japan) every three seconds and recorded on a computer hard disk as separate files. Computer processing of a series of optical images gave series of displacement vector fields. Application of this approach to pseudo-images made it possible to obtain fields of deformation vectors. The DIC technique for such ceramics was described in details in Kibitkin et al. (2021). Schemes of loading conditions, coordinate system and areas of mean deformation estimation are shown at Fig. 2.

a

b

Fig. 2. Loading conditions, coordinate system (a) and areas of estimation of mean deformation (b).

3. Evolution of displacement vector fields and deformation Calculation of displacement fields with a minimum spatial period (T = 1) allows reconstructing a spatial distribution of deformation with high resolution, which can be turned them into pseudo-images. Let the deformation vary within the max min (x, y)      limits, where min  and max  are the minimum and maximum deformation values for a given displacement field, respectively. The brightness values of an eight-bit image may vary in a range 0 255 I(x, y)   . Dividing the deformation into 255 parts and relating each of them with the corresponding brightness values at the corresponding point allows obtaining a gray scale pseudo-image. If higher deformation value corresponds to a lower brightness value, then such an image is inverse. Further, these pseudo-images will be used in the same way as usual ones. Experiments show that from the very beginning of loading, the first macro-band begins to form in the central part of the sample. It is almost invisible in the field of displacements (Fig. 3, a), but this is clearly illustrated by the field of deformations (Fig. 3, e). With further loading, localization of inelastic deformation is revealed as a vertical macro-band (Fig. 3, b, f), and a crack is visible in the corresponding optical images. This crack is not a main one and has a near-surface character. With an increase in deformation, there is a gradual decrease in the level of localization of deformation around this crack (Fig. 3, c, g) until the complete disappearance of this localization (Fig. 3, d, h). Displacement field maps and strain field maps obtained from samples deformed at higher deformation levels demonstrate further formation of additional bands and simultaneous attenuation of the main ones, so that almost the entire region of the sample is involved in deformation (Fig. 3, c, g). And finally, with a further increase in deformation, the bands almost completely disappear (Fig. 3, d, h).