Closed form solution for an annular elliptic crack around an elliptic rigid inclusion in an infinite solid

Singh, Brij Mohan; Rokne, Jon G.; Dhaliwal, Ranjit S.

doi:10.1002/zamm.201100134

Cited by 8 publications

(4 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Kassir and Sih computed mode II and mode III edges stress intensity functions K II and K III for an elliptical crack in an infinite body under uniform shear (see [7]). These solutions have been used in many papers for computing the edge stress intensity functions by the superposition method [14,15], the weight function method (for example see [10,16]) and by Fourier approximation of the boundary condition or of the geometry (see [17,12,16,9]). Leblond and Torlai provided the mechanism for the point-wise derivation of the elastic solution up to second order for a general curved crack [8].…”

Section: @ 'mentioning

confidence: 99%

Singular asymptotic solution along an elliptical edge for the Laplace equation in 3-D

Shannon

Péron

Yosibash

2015

Engineering Fracture Mechanics

View full text Add to dashboard Cite

a b s t r a c tExplicit asymptotic solutions are still unavailable for an elliptical crack or sharp V-notch in a three-dimensional elastic domain. Towards their derivation we first consider the Laplace equation. Both homogeneous Dirichlet and Neumann boundary conditions on the surfaces intersecting at the elliptical edge are considered. We derive these asymptotic solutions and demonstrate, just as for the circular edge case, that these are composed of three series with eigenfunctions and shadows depending on two coordinates.

show abstract

Section: @ 'mentioning

confidence: 99%

Singular asymptotic solution along an elliptical edge for the Laplace equation in 3-D

Shannon

Péron

Yosibash

2015

Engineering Fracture Mechanics

View full text Add to dashboard Cite

show abstract

“…Finally, they showed how the same expression can be used to calculate the SIF of cracks emanating from elliptical holes when appropriate changes are made in the variables. Various types of research have been done on the cracks emanating from the elliptical hole [35][36][37][38]. Based on Kachanov's method and superposition principle, Zhu [39] investigated mode I and II SIF of parallel cracks in brittle solids.…”

Section: Introductionmentioning

confidence: 99%

Analytical calculation of stress intensity factors for orthotropic plates containing cracks emanating from a circular hole using Schwarz integration

Moussavian,

Jafari,

Hajimohammadi

2023

Z Angew Math Mech

View full text Add to dashboard Cite

In this paper, a new analytical method is presented to determine the stress intensity factors (SIFs) of a generally orthotropic plate with cracks emanating from a circular hole. Therefore, using the Schwartz integration method, for the first time, the analytical solution is provided based on the complex variable method. In order to use the Schwartz's theorem in solving complex integrals, a new presentation of the mapping function has been presented, which leads to providing a simpler solution. After calculating the potential functions, the SIFs are determined for the circular hole with one and two cracks. Then, the effect of parameters such as fiber angle, different and unequal crack lengths, and different loadings are studied. To validate the results of the present analytical solution, some results have been compared with the results from other references. Comparing the results showed that the current solution has good accuracy and is reliable and the fiber angle has a significant effect on the mode II SIF. In the case that the fibers are along the crack length and the loading is perpendicular to the crack direction, the mode II SIF is zero, but if the fibers are not along the crack length, the value of the mode II SIF will not be zero. It is also shown that increasing the length of one crack increases the SIF of another crack as well.

show abstract

“…Shodja et al [16] analyzed the interaction of the annular and penny-shaped crack in an infinite piezoelectric medium (see also [17]). The study of indentation of an elliptic crack by a rigid elliptic inclusion in the anti-plane shear mode was performed by Singh et al [18]. Eskandari-Ghadi et al [19] presented a mathematical formulation for the analysis of a transversely isotropic half-space containing a disc-shaped crack buried at an arbitrary depth.…”

Section: Introductionmentioning

confidence: 99%

Axial translation of a rigid disc inclusion embedded in a penny-shaped crack in a transversely isotropic solid

2017

View full text Add to dashboard Cite

In this paper, an analytical solution for the axisymmetric interaction of a rigid disc inclusion embedded in bonded contact with the surfaces of a penny-shaped crack and a transversely isotropic medium is investigated. By using a method of potential functions and treating dual and triple integral equations, the mixed boundary value problem is written in the form of two coupled integral equations, which are amenable to numerical treatments. The axial stiffness of the inclusion and the shearing stress intensity factor at the tip of the penny-shaped crack for different degrees of material anisotropy are illustrated graphically. Useful limiting cases such as a rigid disc inclusion in an uncracked medium and in a completely cracked solid are recovered.

show abstract

Closed form solution for an annular elliptic crack around an elliptic rigid inclusion in an infinite solid

Cited by 8 publications

References 19 publications

Singular asymptotic solution along an elliptical edge for the Laplace equation in 3-D

Singular asymptotic solution along an elliptical edge for the Laplace equation in 3-D

Analytical calculation of stress intensity factors for orthotropic plates containing cracks emanating from a circular hole using Schwarz integration

Axial translation of a rigid disc inclusion embedded in a penny-shaped crack in a transversely isotropic solid

Contact Info

Product

Resources

About