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.
Similar content being viewed by others
References
M. A. Sutton, J. J. Orteu, and H. W. Schreier, Image Correlation for Shape, Motion and Deformation Measurements, Springer (2009).
V. Kibitkin, A. Solodushkin, V. Pleshanov, et al., Measurement, 95, 266 (2017).
R. F. Elhajjar and S. S. Shams, Compos. Sci. Technol., 122, 140 (2016).
V. V. Kibitkin, A. I. Solodushkin, and V. S. Pleshanov, Russ. J. Nondestruct. Test., 47, 65 (2011).
B. Pan, K. Qian, H. Xie, et al., Meas. Sci. Technol., 20, 17 (2009).
V. Kibitkin, M. Grigoriev, A. Burlachenko, et al., Materials, 14, 3720 (2021).
V. S. Pleshanov, V. E. Panin, and V. V. Kibitkin, Phys. Mesomech., 6, 77 (2003).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Kibitkin, V.V., Solodushkin, A.I., Zykova, A.P. et al. Mean Length Rate of a Vector Field as a Fracture Characteristic. Russ Phys J 66, 32–37 (2023). https://doi.org/10.1007/s11182-023-02901-8
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11182-023-02901-8