A scaled boundary finite element method for modelling wing crack propagation problems

Abstract

In this paper, a new shape function based on the scaled boundary finite element method (SBFEM) with side-face loading is used to study the problem of wing crack propagation. Crack contact is modelled by introducing the contact interface constraint condition by the Lagrange multiplier method. In the crack propagation process, the contact state of the crack surface at each step is obtained by an iterative method of determination and validation, and an accurate simulation for the frictional contact expansion process of compressed wing cracks is carried out. Polygon SBFEM remeshing technology is used to simulate the propagation of single and multiple wing cracks. The correctness and effectiveness of the new SBFEM shape function method in modelling wing crack propagation are verified using related experimental and numerical simulation results. The results indicate that under pressure, the wing crack propagates along the direction of the maximum circumferential stress during initial expansion, and the crack propagation angle is −70°32′, which is a pure type II crack. The crack then opens and gradually expands towards the pressure. In the considered wing crack problems, contact phenomena only occur on the initial crack surface during crack propagation. The contact force gradually decreases from the centre to the tips of the initial crack. As the crack expands, the contact force decreases, and the contact area of the crack gradually decreases. The friction coefficient has a strong influence on the crack propagation direction. The larger the friction coefficient, the closer the propagation direction is to the linear extension in the direction of the applied load.