Sonsuz silindirde iki çatlak ile bir rijit enklozyonun etkileşimi

Bu çalışmada, içinde iki dairesel çatlak ile bir rijit enklozyon bulunan sonsuz silindir problemi incelenmektedir. Malzemenin lineer elastik ve izotrop olduğu kabul edilmektedir. Silindirin sonsuzdaki uçlarına eksenel çekme yükleri uygulanmaktadır. Bu problemin çözümü, (I) sonsuzda eksenel çekme yüküne maruz sonsuz bir silindir problemi ile (II) z = 0 düzleminde bir dairesel rijit enklozyon ve z = ± L düzlemlerinde iki dairesel çatlağa sahip sonsuz silindir probleminin süperpozisyonu ile elde edilebilir. Problem (II) için genel ifadeler, Navier denklemlerinin Fourier ve Hankel integral dönüşüm teknikleri kullanılarak çözülmesiyle elde edilmektedir. Formülasyon önce üç tekil integral denklem sistemine indirgenir. Bu denklemler, Gauss-Lobatto integrasyon formülü kullanılarak, lineer cebrik denklem takımına dönüştürülür ve sayısal olarak çözülür.

Interaction of two penny-shaped cracks and a rigid inclusion in an infinite cylinder

This work considers the analysis of a cracked infinite cylinder with a rigid inclusion. Material of the cylinder is assumed to be linearly elastic and isotropic. Two ends of the cylinder are subjected to axial tension. Solution of this problem can be obtained by superposition of solutions for an infinite cylinder subjected to uniformly distributed tensile load at infinity (I) and an infinite cylinder having a penny-shaped rigid inclusion at z = 0 and two penny-shaped cracks at z = ± L (II). General expressions for the perturbation problem (II) are obtained by solving Navier equations using Fourier and Hankel transforms. Formulation of the problem is reduced to a system of three singular integral equations. By using Gauss-Lobatto integration formula, these three singular integral equations are converted to a system of linear algebraic equations which is solved numerically.

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1. Sneddon, I. N., Welch, J. T., (1963). A note on the distribution of stress in a cylinder containing a penny-shaped crack. International Journal of Engineering Science, 1, 411-419.
2. Agarwal, Y. K., (1978). Axisymmetric solution of the end problem for a semi-infinite elastic circular cylinder and its application to joined dissimilar cylinders under uniform tension. International Journal of Engineering Science, 16, 985-998.
3. Erdöl, R., Erdoğan, F., (1978). Thick-walled cylinder with an axisymmetric internal or edge crack. Journal of Applied Mechanics-Transactions of ASME, 45, 281-286.
4. Isida, M., Hirota, K., Noguchi, H., Yoshida, T., (1985). Two parallel elliptical cracks in an infinite solid subjected to tension. International Journal of Fracture, 27, 31-48.
5. Xiao, Z. M., Lim, M. K., Liew, K. M., (1996). Determination of stress field in an elastic solid weakened by parallel penny-shaped cracks. Acta Mechanica, 114, 83-94.
6. Leung, A. Y. T., Su, R. K. L., (1998). Two level finite element study of axisymmetric cracks. International Journal of Fracture, 89, 193-203.
7. Selvadurai, A. P. S., (2002). Mechanics of a rigid circular disk bonded to a cracked elastic half-space. International Journal of Solids and Structures, 39, 6035-6053.
8. Tsang, D. K. L., Oyadiji, S. O., Leung, A. Y. T., (2003). Multiple penny-shaped cracks interaction in a finite body and their effect on stress intensity factor. Engineering Fracture Mechanics, 70, 2199-2214.
9. Chaudhuri, A., (2003). Three dimensional asymptotic stress field in the vicinity of the circumference of a penny shaped discontinuity. International Journal of Solids and Structures, 40, 3787-3805.
10. Geçit, M. R., (1988). Axisymmetric pull-off test for a cracked adhesive layer. Journal of Adhesion Science and Technology, 2, 349-362.
11. Artem, H. S. A., Geçit, M. R., (2002). An elastic hollow cylinder under axial tension containing a crack and two rigid inclusions of ring shape. Computers and Structures, 80, 2277-2287.
12. Toygar, E. M., Geçit, M. R., (2006). Cracked infinite cylinder with two rigid inclusions under axisymmetric tension. International Journal of Solids and Structures, 43, 4777-4794.
13. Kaman, M. O., (2006). Cracked Semi-Infinite Cylinder and Finite Cylinder Problems. Doktora Tezi, Orta Doğu Teknik Üniversitesi Fen Bilimleri Enstitüsü, 208s.
14. Muskhelishvili, N. I., (1953). Singular Integral Equations, P. Noordhoff, Gröningen, Hollanda.
15. Cook, T. S., Erdoğan, F., (1972). Stresses in bonded materials with a crack perpendicular to the interface. International Journal of Engineering Science, 10, 677-697.
16. Krenk, S., (1978). Quadrature formulae of closed type for solution of singular integral equations. Journal of Institute of Mathematical Applications, 22, 99-107.
17. Erdoğan, F., Sih, G. C., (1963). On the crack extension in plates under plane loading and transverse shear. Journal of Basic Engineering-Transactions of ASME, 85, 519-527.