Abstract:
The aim of the study is to calculate the coefficients of M. Williams' asymptotic expansion of stress and displacement fields using the data of finite element modeling of a plate with an inclined central crack in a uniaxial tension field. In this work, we also simulated the loading of a half-disk with a vertical and oblique notch under conditions of three-point bending. The simulation was carried out in the multifunctional software SIMULIA Abaqus. The paper proposes an algorithm for calculating the coefficients. The program, written in the MAPLE computer algebra system, allows calculating any predetermined number of M. Williams expansion coefficients (amplitude or scale factors) and uses the values of the stress tensor components at points in the vicinity of the crack and their coordinates as input. The analysis of the influence of the number of calculated coefficients on the accuracy of their determination is carried out. Recommendations on the choice of points for calculating the coefficients are given.
Keywords:
stress field, crack, mixed loading, expansion coefficients M. Williams, finite element modeling.
The study was carried out with the financial support of the Russian Foundation for Basic Research grant within the framework of the scientific project No. 19-01-00631.
Citation:
O. N. Belova, L. V. Stepanova, “Determination of the coefficients of asymptotic crack — tip stress expansion. Mixed mode loading of the plate”, Vestnik SamU. Estestvenno-Nauchnaya Ser., 26:3 (2020), 40–62
\Bibitem{BelSte20}
\by O.~N.~Belova, L.~V.~Stepanova
\paper Determination of the coefficients of asymptotic crack --- tip stress expansion. Mixed mode loading of the plate
\jour Vestnik SamU. Estestvenno-Nauchnaya Ser.
\yr 2020
\vol 26
\issue 3
\pages 40--62
\mathnet{http://mi.mathnet.ru/vsgu634}
\crossref{https://doi.org/10.18287/2541-7525-2020-26-3-40-62}
Linking options:
https://www.mathnet.ru/eng/vsgu634
https://www.mathnet.ru/eng/vsgu/v26/i3/p40
This publication is cited in the following 2 articles:
L. V. Stepanova, D. A. Semenov, G. S. Anisimov, “Primenenie metoda golograficheskoi interferometrii dlya rekonstruktsii ryada M. Uilyamsa polya napryazhenii u vershiny treschiny”, Vestn. SamU. Estestvennonauchn. ser., 29:1 (2023), 15–46
O. N. Belova, L. V. Stepanova, D. V. Chaplii, “Kompyuternoe modelirovanie rosta treschiny. Metod molekulyarnoi dinamiki”, Vestn. SamU. Estestvennonauchn. ser., 26:4 (2020), 44–55
Citation in format AMSBIB
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