Weight function for an elliptical planar crack embedded in a homogeneous elastic medium

Abstract

The method of simultaneous dual integral equations is used for obtaining the exact analytical solution for the weight function for an elliptical crack embedded in an infinite elastic solid. We show that the solution is unique and can be reduced to the known solutions for a number of particular cases.

New weight functions and second order approximation of the Oore–Burns integral for elliptical cracks subject to arbitrary normal stress field

“…However, when the b/a ratio reaches 0.5 the second order expansions of the OB integral, in the example proposed herein, gives maximum errors around 5% while the more significant parameter I K max error does not exceed 3%. Atroshchenko et al (2010) In order to shown the accuracy of the second order approximation of equation ( 108 66) and ( 106), respectively.…”

Stress intensity factor for a semi-elliptical crack subjected to an arbitrary mode I loading

“…In the present paper, the SIF for a surface semi-elliptical crack has been derived using the weight function for an embedded elliptical crack in conjunction with the alternating method. It has been demonstrated that the application of the exact weight function for an elliptical crack, obtained in Atroshchenko et al [5], yields accurate SIF solutions for a semi-elliptical crack subjected to an arbitrary applied stress field. Numerical results have been compared with the known solutions for particular cases of applied uniform and quadratic stress fields, and have been found to be in good agreement…”

“…In order to calculate the SIF for an elliptical crack, we use the weight function derived in Atroshchenko et al [5]. The weight function W ( Q ′, Q 0 ), corresponding to the point Q 0 ( x 0 , y 0 ) where the point force of magnitude P = 1 is applied (Figure 3), is obtained in the following form.…”

“…Recently, an exact analytical SIF solution has been derived for an elliptical crack subjected to an arbitrary applied stress field and embedded in an infinite elastic solid [4]. The method introduced in Atroshchenko et al [4] was subsequently used in Atroshchenko et al [5] to derive the SIF solution for an elliptical crack for a particular case of the applied concentrated force, i.e. the weight function .…”

A Model for Determining Strength for Embedded Elliptical Crack in Ultra-high-temperature Ceramics

“…Chen et al [ 8 ] evaluated the stress intensity factor of elliptical crack by using differential-integral equations. Atroshchenko et al [ 9 ] proposed the stress intensity factor for any elliptical crack embedded in a homogeneous elastic medium using the weight function concept.…”