A recently developed integral equation method has been used to derive the crack opening displacement of an elliptic crack in an infinite elastic medium subjected to a concentrated pair of point force loading at an arbitrary location on the crack faces. These results have been used to obtain the stress intensity factor along the elliptic crack front which corresponds to the weight function for an elliptic crack under normal loading. Analytical expression of the weight function can be used to derive the stress intensity factor for both polynomial loading as well as non-polynomial loading.

A ROY

T K SAHA

University of Calcutta (informally known as Calcutta University or CU) is a collegiate public state university located in Kolkata, West Bengal, India.&nbsp;Within India it is recognized as a &quot;Five-Star University&quot; and accredited &quot;A&quot; Grade by National Assessment and Accreditation Council.

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The University of Calcutta has secured the Fifth position among the Universities of India in the prestigious &quot;Indian University Ranking 2019&quot; list, released by the NIRF of the Ministry of Human Resource Development, Government of India.

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It was established on 24 January 1857, and was one of the first institutions in Asia to be established as a multidisciplinary and Western-style university. Its alumni and faculty include several heads of state, heads of government, social reformers, prominent artists, only academy award winner and Dirac medal winner in India, many Fellows of the Royal Society and five Nobel laureates as of 2019 which is highest in South Asia.

University Of Calcutta

Weight function for an elliptic crack in an infinite medium. I. Normal loading

International Journal of Fracture

The scattering of normally incident elastic waves by an embedded elliptic crack in an infinite isotropic elastic medium has been solved using an analytical numerical method. The representation integral expressing the scattered displacement field has been reduced to an integral equation for the unknown crack-opening displacement. This integral equation has been further reduced to an infinite system of Fredholm integral equation of the second kind and the Fourier displacement potentials are expanded in terms of Jacobi's orthogonal polynomials. Finally, proper use of orthogonality property of Jacobi's polynomials produces an infinite system of algebraic equations connecting the expansion coefficients to the prescribed dynamic loading. The matrix elements contains singular integrals which are reduced to regular integrals through contour integration. The first term of the first equation of the system yields the low-frequency asymptotic expression for scattering cross section analytically which agrees completely with previous results. In the intermediate and high-frequency scattering regime the system has been truncated properly and solved numerically. Results of quantities of physical interest, such as the dynamic stress intensity factor, crack-opening displacement scattering cross section, and backscattered displacement amplitude have been given and compared with earlier results.

Journal of Applied Mechanics, Transactions ASME

Scattering from an elliptic crack by an integral equation method: Normal loading

A recently developed integral equation method is used to solve the problem of interaction between coplanar, elliptic cracks under normal loading. The pair of dual integral equations, in a Cartesian system is first transformed to four sets of infinite systems of Fredholm integral equations of the second kind in a cylindrical polar coordinate system. For cracks which are well separated, a perturbed solution of these integral equations can be obtained in terms of the separation parameter β. Analytical expressions for the stress intensity factor and the strain energy of deformation per crack, when subjected to a constant normal loading, have been given up to the order β6. Results have been illustrated graphically. © 1993.

International Journal of Solids and Structures

Interaction between coplanar elliptic cracks-I. Normal loading

In this paper we consider the effect of the free surface on the stress distribution of an elliptic crack aligned parallel to the free boundary and at a depth h below it. The title problem is posed as a dual integral equation in Cartesian coordinate system. By suitable transformation the dual integral equation is first reduced to an infinite system of dual integral equation in cylindrical coordinates. Then they are further reduced by a recently developed technique to an infinite system of Fredholm integral equation of the second kind. When the boundary is at a large distance away from the crack, the system of integral equation is solved by perturbation technique as powers of δ = a/h, a being the length of semi major axes and h the depth of the crack below the boundary. The analytical expressions for the three stress-intensity factors at the crack edges for normal loading are given upto order δ5. Effect of the boundary on the stress-intensity factor is illustrated graphically. © 1992.

Journal	International Journal of Fracture
Publisher	Kluwer Academic Publishers, Dordrecht, Netherlands
ISSN	0376-9429