An Embedded Elliptical Crack, in an Infinite Solid, Subject to Arbitrary Crack-Face Tractions

Abstract

In this paper, following a critical assessment of earlier work of Green and Sneddon, Segedin, Kassir, and Sih (who obtained solutions for specific cases of normal loading on the crack face and the cases of constant and linear shear distribution on the crack face), Shah and Kobayashi (whose work is limited to the case of third-order polynomial distribution of normal loading on the crack face), and Smith and Sorensen (whose work is limited to the case of a third-order polynomial variation of shear loading on the crack face), a general solution is presented for the case of arbitrary normal as well as shear loading on the faces of an embedded elliptical crack in an infinite solid. The present solution is based on a generalization of the potential function representation used by Shah and Kobayashi. Expressions for stress-intensity factors near the flaw border, as well as for stresses in the far-field, for the foregoing general loadings, are given.

Automated Structural Optimization System (ASTROS) Damage Tolerance Module. Volume 1 - Final Report

“…The analytical solution for an embedded elliptical crack in an infinite body, subjected to arbitray crack face tractions [Vijayakumar and Atluri (1981)], is used to construct the 3D FEAM for surface flaws and corner cracks. A 20-node second order brick element is used in the 3D FEAM module.…”

“…When the ellipse becomes a circle, this numerical procedure is no longer valid. However, the analytical solution based on the ellipsoidal potential [Vijayakumar and Atluri (1981)] is still valid. An alternative numerical procedure was developed during Phase II of this project.…”

“…An alternative numerical procedure was developed during Phase II of this project. This alternative numerical procedure is documented in this section; while the reader is refered to Vijayakumar and Atluri (1981) and Nishioka and Atluri(1983) for other details on the analytical solution based on the ellipsoidal potentials.…”

Analysis of micro--macro material properties and mechanical effects of damaged material containing periodically distributed elliptical microcracks

“…The superposition method (Yagawa et al, 1975) that uses analytical solutions and finite element solutions is applied to the developed homogenization method. In this technique, the VNA solution (Vijayakumar and Atluri, 1981;Nishioka and Atluri, 1983a, b) is applied to the analytical solution, in order to evaluate the singularity of multiple elliptical cracks (Kato and Nishioka, 2002). Therefore, the superposition method makes it possible to solve the elliptical crack problem by using a relatively coarse regular mesh pattern that does not describe the shapes of the elliptical cracks.…”

Solution of flat crack problems in shear mode

“…Some solutions for the elliptic crack problems were obtained [3,4]. In the solutions, the displacements are expressed through a harmonic function, and the function in the problem is equivalent to a gravitational potential.…”