Analytical solutions of cracks emanating from an elliptic hole in an infinite plate under tension

Abstract

It is a common phenomenon that the cracks originating from a hole can cause structural damage in engineering. However, the fracture mechanics studies of hole edge crack problems are not sufficient. The problem of an elliptical hole with two collinear edge cracks of unequal length in an infinite plate under uniform tension at infinity is investigated. Based on the complex variable method, the analytical solutions of stress functions and stress intensity factors are provided. The stress distribution along the axes and the edge of the elliptical hole is given graphically. The numerical results show that there is obvious stress concentration near the hole and cracks, and the stresses tend to applied loads at distances far from the defect, which conform to Saint-Venant's principle. Hence, the stress functions are proved to be right. Under special conditions, the present configuration becomes the Griffith crack, two symmetrical cracks emanating from an elliptical hole, two cracks of unequal length emanating from a circular hole, a crack at the edge of a circular hole, or a crack emanating from an elliptical hole. Compared with available results, stress intensity factors for these special shapes of ellipses and cracks show good coincidence. The stress intensity factor for two cracks of unequal length at the edge of an elliptical hole increases with the crack length and the major-to-minor axis ratio of the elliptical hole. The stress distribution in an infinite plate containing an elliptic hole with unsymmetrical cracks is given for the first time.

Elastic Stress and Plastic Zone Distributions around a Deeply Buried Tunnel under the Nonhydrostatic Pressure

“…Closed-form solutions for simple shapes, such as an elliptical hole, a crack, and a square hole, have been discussed in detail. The exact solutions for cracks emanating from an elliptical hole were also studied [1][2][3]. This method has been successfully used to solve the tunnel problem.…”

Analytical Solutions for a Deep-Buried Tunnel with Noncircular Cross Sections in Orthotropic Rock Mass

“…Guo et al [7] obtained the explicit form of analytical solution caused by a shallow circular tunnel and analyzed the secondary stress eld with pile load combined with Mindlin's solution. e exact solutions for two unequal cracks emanating from an elliptical hole were also given [8][9][10].…”