Effect of vertex singularities on stress intensities near plate free surfaces

Abstract

The stress intensity factor (SIF) distribution along the front of a through-the-thickness crack is significantly influenced by the presence of the 3D corner (vertex) singularities. All past 3D finite element studies indicated that for mode I, SIF rapidly decreases near the free surface and for mode II, it sharply increases. From the previous numerical simulations, it is unclear what the limiting values of SIF near the surface are and whether these values are infinite or bounded at the vertex point. In this paper, we conduct a careful finite element study and propose a theoretical equation, which describes the SIF behaviour near the vertex. We demonstrate that the asymptotic behaviour of SIF near the surface is governed by the difference in the strength of the corner and edge singularities. Furthermore, we validate our numerical approach and calculations by utilising the invariant properties of J-integral

A disk-shaped domain integral method for the computation of stress intensity factors using tetrahedral meshes

“…This does not mean that the stress is finite at the corner point, but it demonstrates that K I cannot be used to characterize the fields at the corner point. (iii) On the other hand, for the antisymmetric loading condition, the corner singularity is stronger than a crack singularity, and therefore the local K II approaches infinity at the free surfaces (Nakamura and Parks, 1989;Benthem, 1977;Bažant and Estenssoro, 1979;Benthem, 1980;He et al, 2015). (iv) The coupled mode III deformation behaves differently compared to K I and K II since K III must be zero at mid-plane and free surfaces due to the symmetry and traction free boundary conditions, respectively.…”

“…A few characteristics of the SIF variation along the crack front must be noted: (i) As explained earlier, although the cracked plate is primarily subjected to a mixed-mode I/II loading condition, a couple mode III crack deformation is also created due to the Poisson's effects. (ii) Under symmetric loading, the corner singularity is weaker than the crack singularity, and therefore the local K I must approach zero at the free surface (Nakamura and Parks, 1988;Benthem, 1977;Bažant and Estenssoro, 1979;Benthem, 1980;He et al, 2015). This does not mean that the stress is finite at the corner point, but it demonstrates that K I cannot be used to characterize the fields at the corner point.…”

Fatigue strength of steel rollers with failure occurring at the weld root based on the local strain energy values: modelling and fatigue assessment

“…As opposed to the direct evaluation of the NSIFs, which needs very refined meshes, the mean value of the elastic SED on the control volume can be determined with high accuracy by using coarse meshes [42][43][44] and directly takes into account the three-dimensional effects well described in [45][46][47][48]. Very refined meshes are necessary to directly determined the NSIFs from the local stress distributions.…”

The formation mechanism of characteristic region at crack initiation for very-high-cycle fatigue of high-strength steels

“…There is not an evident stress concentration on the specimen surface of such specimens and fatigue crack initiation shifts from the surface to the interior of specimen, which is a unique feature for VHCF of highstrength materials. For the cases of large curvature notched specimens [39,40], the stress concentration on the notch root is severe, which leads to crack initiation and growth inevitably from the notch root including in VHCF circumstances. The notch effect in VHCF regime is an interesting topic which is our in progress research.…”