RUS  ENG
Full version
JOURNALS // Vestnik Samarskogo Universiteta. Estestvenno-Nauchnaya Seriya // Archive

Vestnik SamU. Estestvenno-Nauchnaya Ser., 2020 Volume 26, Issue 3, Pages 40–62 (Mi vsgu634)

This article is cited in 2 papers

Mechanics

Determination of the coefficients of asymptotic crack — tip stress expansion. Mixed mode loading of the plate

O. N. Belova, L. V. Stepanova

Samara National Research University, Samara, Russian Federation

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.

UDC: 629.7.05

Received: 13.03.2020
Revised: 27.03.2020
Accepted: 25.05.2020

DOI: 10.18287/2541-7525-2020-26-3-40-62



© Steklov Math. Inst. of RAS, 2025