Torsional analysis of an orthotropic long cylinder weakened by multiple axisymmetric cracks

Hassani, Alireza; Hassani, Amin; Monfared, Mojtaba Mahmoudi

doi:10.22061/jcarme.2018.2283.1214

Document Type : Research Paper

Authors

¹ Department of Mechanical Engineering, Hashtgerd Branch, Islamic Azad University, P.O. Box 33615-178, Alborz, Iran

² Young Researchers and Elite Club, Hashtgerd Branch, Islamic Azad University, Alborz, Iran. Email: aminhassani@msc.guilan.ac.ir

https://doi.org/10.22061/jcarme.2018.2283.1214

Abstract

Abstract: The solution to problem of an orthotropic long cylinder subjected to torsional loading is first obtained by means of separation valuables. The cylinder is twisted by two lateral shear tractions and the ends of the cylinder surface of the cylinder are stress-free. First, the domain under consideration is weakened by an axisymmetric rotational Somigliana ring dislocation. The dislocation solution is employed to derive a set of Cauchy singular integral equations for the analysis of multiple axisymmetric planner cracks. The numerical solution to these integral equations is used to determine the stress intensity factors (SIFs) for the tips of the concentric planar cracks A preliminary comparison between results of this study and those available in the literature is performed to confirm the validity of the proposed technique. Several examples of multiple concentric planner cracks are solved and displayed graphically. Furthermore, Configuration of the cracks and the interaction between cracks is studied.

Graphical Abstract

Keywords

20.1001.1.22287922.2018.8.1.5.6

Main Subjects

Fracture Mechanics

References

[1] M. Ozturk, F. Erdogan, An Axisymmetric Crack in Bonded Materials With a Nonhomogeneous Interfacial Zone Under Torsion, Journal of Applied Mechanics, Vol. 62, No. 1, pp. 116-125, (1995).

[2] W. Xuyue, Z. Zhenzhu, W. Duo, On the penny-shaped crack in a nonhomogeneous interlayer of adjoining two different elastic materials, International Journal of Solids and Structures, Vol. 34, pp. 3911-3921, (1997).

[3] W. Xuyue, Z. Zhenzhu, W. Duo, On the penny-shaped crack in a non-homogeneous interlayer under torsion, International Journal of Fracture, Vol. 82 No. 4, pp. 335-343, (1996).

[4] H. T. Danyluk, B. M. Singh, Problem of an infinite solid containing a flat annular crack under torsion, Engineering Fracture Mechanics, Vol. 24, No. 1, pp. 33-38, (1986).

[5] H. S. Saxena, R. S. Dhaliwal, W. He, J. G. Rokne, Penny-shaped interface crack between dissimilar nonhomogeneous elastic layers under axially symmetric torsion, Acta Mechanica, Vol. 99, No. 1, pp. 201-211, (1993).

[6] H. K. Hemed, R.S. Dhaliwal, Penny-shaped interface crack in a non-homogeneous multilayered medium under axially symmetric torsion, ZAMM - Journal of Applied Mathematics and Mechanics, Vol. 81, No. 3, pp. 205-211, (2001).

[7] H. Fildiş, O. S. Yahşi, The mode III axisymmetric crack problem in a non-homogeneous interfacial region between homogeneous half-spaces, International Journal of Fracture, Vol. 85, pp. 35-45, (1997).

[8] I. Demir, T. A. Khraishi, The Torsional Dislocation Loop and Mode III Cylindrical Crack, Journal of Mechanics, Vol. 21, No. 1, pp. 109-116, (2011).

[9] Y. Godin, The interaction between a penny-shaped crack and a spherical inclusion under torsion, Zeitschrift für angewandte Mathematik und Physik ZAMP, Vol. 46, No. 6, pp. 932-945, (1995).

[10] S. S. Chang, The general solution of a finite cylinder with a concentric penny-shaped crack under torsion, Engineering Fracture Mechanics, Vol. 22, No. 4, pp. 571-578, (1985).

[11] X. S. Zhang, The general solution of a finite orthotropic cylinder with a concentric penny-shaped crack under torsion, Engineering Fracture Mechanics, Vol. 31, No. 5, pp. 827-835, (1988).

[12] X. S. Zhang, Y. U. Zhang, A concentric penny-shaped crack off the middle plane of a finite orthotropic cylinder under torsional shear stress, Engineering Fracture Mechanics, Vol. 31, No. 3, pp. 385-393, (1988).

[13] X. S. Zhang, Off-plane concentric penny-shaped crack in a finite cylinder under arbitrary torsion, Theoretical and Applied Fracture Mechanics, Vol. 9, No. 3, pp. 263-270, (1988).

[14] B. Liang, X. S. Zhang, The problem of a concentric penny-shaped crack of mode III in a nonhomogeneous finite cylinder, Engineering Fracture Mechanics, Vol. 42, No. 1, pp. 79-85, (1992).

[15] H. Xue-Li, W. Duo, A circular or ring-shaped crack in a nonhomogeneous cylinder under torsional loading, International Journal of Fracture, Vol. 68, No. 3, pp. R79-R83, (1994).

[16] T. Akiyama, T. Hara, T. Shibuya, Torsion of an Infinite Cylinder with Multiple Parallel Circular Cracks, Theoretical and Applied Mechanics Letters, Vol. 50, pp. 137-143, (2001).

[17] P. Malits, Torsion of a cylinder with a shallow external crack, International Journal of Solids and Structures, Vol. 46, No. 16, pp. 3061-3067, (2009).

[18] A. N. Zlatin, Y. S. Uflyand, Torsion of an elastic cylinder slackened by an external circular notch II. The case of a finite cylinder, Journal of Elasticity, Vol. 13, No. 2, pp. 215-223, (1983).

[19] I. N. Zlatina, Application of dual integral equations to the problem of torsion of an elastic space, weakened by a conical crack of finite dimensions, Journal of Applied Mathematics and Mechanics, Vol. 36, No. 6, pp. 1062-1068, (1972).

[20] H. Z. Hassan, Torsion of a non-homogeneous infinite elastic cylinder slackened by a circular cut, Journal of Engineering Mathematics, Vol. 30, No. 5, pp. 547-555, (1996).

[21] S. Kazuyoshi, S. Toshikazu, K. Takashi, The torsion of an infinite hollow cylinder with an external crack, International Journal of Engineering Science, Vol. 16, No. 10, pp. 707-715, (1978).

[22] T. Shibuya, T. Koizumi, T. Okuya, The Axisymmetric Stress Field in an Infinite Solid Cylinder with an External Crack under Torsion, Bulletin of JSME, Vol. 22, No. 249, pp. 1049-1052, (1979).

[23] R. T. Faal, S. J. Fariborz, H. R. Daghyani, Antiplane deformation of orthotropic strips with multiple defects, Journal of Mechanics of Materials and Structures, Vol. 1, No. 7, pp. 1097-1114, (2006).

[24] F. Erdogan, G. D. Gupta, T. S. Cook, Numerical solution of integral equations. In: Sih, G. C. (Ed.), Methods of Analysis and Solution of Crack Problems, Noordhoof, Leyden, Holland, (1973).

[25] J. Q. Tarn, Y. M. Wang, Fundamental solutions for torsional problems of a cylindrical anisotropic elastic medium, Journal of the Chinese Institute of Engineers, Vol. 9, No. 1, pp. 1-8, (1986).

[26] W. Magnus, F. Oberhettinger, R. P. Soni, Formulas and theorems for the special functions of mathematical physics, Berlin, (1966).

[27] E. Asadi, S. J. Fariborz, M. Ayatollahi, Analysis of multiple axisymmetric annular cracks, Journal of Mechanics of Materials and Structures, Vol. 4, No. 1, pp. 1-11, (2009).

[28] D. A. Hills, P. A. Kelly, D. N. Dai, A. M. Korsunsky, Solution of Crack Problems: The Distributed Dislocation Technique, Springer, (1996).

[29] I. N. Sneddon, M. Lowengrub, Crack problems in the classical theory of elasticity, Wiley, (1969).

[30] I. Choi, R. T. Shield, A note on a flat toroidal crack in an elastic isotropic body, International Journal of Solids and Structures, Vol. 18, No. 6, pp. 479-486, (1982).

[31] J. P. Benthem, W. T. Koiter, Asymptotic approximations to crack problems, in: G. Sih (Ed.) Methods of analysis and solutions of crack problems, Springer Netherlands, pp. 131-178, (1973).

[32] W. Qizhi, SIF solutions of a cylinder with a concentric penny-shaped crack under various loading conditions, International Journal of Fracture, Vol. 74, pp. R65-R70, (1995).

[33] B. A. Kudriavtsev, V. Z. Parton, Torsion and extension of a cylinder with an external annular slit, Journal of Applied Mathematics and Mechanics, Vol. 37, No. 2, pp. 297-306, (1973).

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Journal of Computational & Applied Research in Mechanical Engineering (JCARME)

Torsional analysis of an orthotropic long cylinder weakened by multiple axisymmetric cracks

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References

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Volume 8, Issue 1 - Serial Number 15
September 2018
Pages 49-60

Torsional analysis of an orthotropic long cylinder weakened by multiple axisymmetric cracks

References

References

Send comment about this article

Volume 8, Issue 1 - Serial Number 15September 2018Pages 49-60

Volume 8, Issue 1 - Serial Number 15
September 2018
Pages 49-60