13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- Coupled fracture mode associated with anti-plane loading of cracks and notches Filippo Berto1, Paolo Lazzarin1, L.Pook2, A. Kotousov3 1Department of Management and Engineering, University of Padua, Stradella San Nicola 3 , 36100, Vicenza, Italy 3School of Mechanical Engineering, The University of Adelaide, South Australia, SA 5005, Australia; e-mail: Andrei.Kotousov@adelaide.edu.au 221 Woodside Road, Sevenoaks TN13 3HF, UK * Corresponding author: berto@gest.unipd.it Abstract The purpose of this paper is to investigate by means of the 3D Finite Element method a coupled fracture mode generated by anti-plane loading of a straight through-the-thickness crack in a linear elastic plate. This coupled fracture mode represents one of three-dimensional phenomena, which are currently largely ignored in numerical simulations and failure assessment of structural components weakened by cracks. It arises due to the boundary conditions on the plate free surfaces, which negate the transverse shear stress components corresponding to classical mode III. Instead, a new singular stress state in addition to the well-known 3D corner singularity is generated. This singular stress state (or coupled fracture mode) can affect or contribute significantly to the fracture initiation conditions. The coupled singular mode exists even if the applied anti-plane loading produces no singularities (K 0 III = ). In this case there is a strong thickness effect on the intensity of the coupled fracture mode. Keywords Crack, anti-plane loading, coupled fracture mode, 3D modelling 1. Introduction The first systematic study on the three-dimensional stress states of a through-the-thickness crack subjected to mode I loading was conducted in Refs [1-4]. Accurate studies on three-dimensional stress distributions in front of cracks have been carried out in those references, extending Williams’ two-dimensional eigenfunction expansions [5] to the three-dimensional case, and in [6] four distinct harmonic functions have been used to solve the problem according to Papkovich-Neuber's method. Utilising a variational principle, a system of simplified governing equations has been derived [1-4] for the extension and bending deformations of an elastic plate with a through-the-thickness crack and investigated the three-dimensional stress states surrounding the crack tip. One important result from this work is that the area of the three-dimensional stress state around the crack tip spreads in the plane direction to the distance of approximately half of the plate thickness. Beyond this distance the stress state follows the classical plane stress solution. Many experimental studies conducted in the past including those carried out in [7] who applied an optical technique confirmed this fundamental result. Another interesting three-dimensional effect, which was first presented in [8], is the disappearance of the in-plane singularity at a point when a corner front (crack front) intersects a free surface. At this point a new three-dimensional corner singularity develops instead. The problem of a vertex (corner) singularity is now well documented in a number of articles in the last thirty years (see, among the others, Refs [9-17]). This problem was recently re-examined in [18] with reference to fatigue crack growth. In this paper, the effect of a free surface on fatigue crack behaviour was investigated experimentally and numerically for relatively thick specimens, where the solutions provided in [8] for semi-infinite space can be applied. In [9] it was underlined that the 3D corner
RkJQdWJsaXNoZXIy MjM0NDE=