Mean Length Rate of a Vector Field as a Fracture Characteristic

• Published in: Russian physics journal 2023-05, Vol.66 (1), p.32-37
• Main Authors: Kibitkin, V. V., Solodushkin, A. I., Zykova, A. P., Rubtsov, V. E., Savchenko, N. L.
• Format: Article
• Language: English
• Subjects: Ceramic materials; Ceramics; Condensed Matter Physics; Deformation; Digital imaging; Error analysis; Fields (mathematics); Fluid flow; Fracture mechanics; Hadrons; Heavy Ions; Image compression; Lasers; Mathematical and Computational Physics; Nonlinear phenomena; Nuclear Physics; Optical Devices; Optics; Photonics; Physics; Physics and Astronomy; Standard deviation; Theoretical
• ISSN: 1064-8887; 1573-9228
• DOI: 10.1007/s11182-023-02901-8

The compensation of rotation makes it possible to diminish the deformation measurement error, and appropriate choice of the constant vector diminishes the sum of the vector components. This allows also to characterize a vector field by its mean length (algebraic or modulus) and related standard deviation. This approach was tested by the digital image correlation (DIC) technique by the example of porous ceramics in compression. The first fracture stage (0.006 ≤ ε ≤ 0.015) is related to local strain accumulation in the upper and lower parts of a specimen. The second stage (0.015 < ε ≤ 0.047) is the stage of stable ceramics flow. At the third stage (0.047 < ε ≤ 0.063), the unstable inelastic deformation is developed and accompanied by fragmentation or local vortices. The fourth stage (0.063 < ε ≤ 0.078) is characterized by nonlinear phenomena. Each stage has its typical deformation-induced structure, mean vector length rate, and standard deviation. Fracture mechanisms of the ceramics are investigated, and deformation structures are given. These amplitude characteristics vary by two or three orders of magnitude. As shown, the normalized standard deviation changes slightly, so it could be considered as a constant for the ceramics.