Analysis of Stress Intensity Factors in Hollow Cylinders Reinforced by an Effective Coating Containing Multiple Cracks

Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering

مقاله 2، دوره 12، شماره 4 - شماره پیاپی 39، بهمن 2019، صفحه 19-40   

نوع مقاله: English

نویسندگان

Mostafa Karimi^{* 1}؛ Alireza Hassani²

¹Assistant Professor Fereydan Branch, Islamic Azad University, Isfahan, Iran

²Youth and Elite Research Club, Science and Research Branch, Islamic Azad University, Tehran, Iran

چکیده

In this paper, the solution of an isotropic hollow cylinder, with an isotropic coating, weakened by multiple radial cracks is studied. The hollow cylinder and its coating are under Saint-Venant torsional loading. The series solution is then derived for displacement and stress fields in the cross section of the cylinder containing a Volterra-type screw dislocation. The dislocation solution is employed to derive a set of Cauchy singular integral equations for the analysis of multiple curved cracks. The solution to these equations is used to determine the torsional rigidity of the domain and the stress intensity factors (SIFs) for the tips of the cracks. Finally, several examples are presented to show the effect of the coating on the reduction of the mechanical stress intensity factor in the hollow cylinder.According to the above review, the fracture problem of the shafts under torsion is an interesting problem. It is worth noting that all of the above mentioned works were limited to the shafts with particular orientation and geometry

کلیدواژه‌ها

several cracks؛ Stress intensity factor؛ Distribution dislocation technique؛ Torsional rigidity

مراجع

[1] ECSEDI, I. and BAKSA, A. Prandtl’s formulation for the Saint–Venant’s torsion of homogeneous piezoelectric beams, International Journal of Solids and Structures, 47, 3076-3083, (2010).

[2] ECSEDI, I. Elliptic cross section without warping under torsion, Mechanics Research Communications, 31, 147-150, (2004).

[3] RONGQIAO, X., JIANSHENG, H. and WEIQIU, C. Saint-Venant torsion of orthotropic bars with inhomogeneous rectangular cross section, Composite Structures, 92, 1449-1457, (2010).

[4] BASSALI, W.A. and OBAID, S.A. On the Torsion of Elastic Cylindrical Bars, ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 61, 639-650, (1981).

[5] LEBEDEV, N.I.N., SKALSKAYA, I.P., UFLAND, I.A.S. and SILVERMAN, R.A., Worked Problems in Applied Mathematics, Dover Publications 1979.

[6] XIAO-CHUN, W. and REN-JI, T. On the torsion of a cylinder with several cracks, Applied Mathematics and Mechanics, 9, 745-754, (1988).

[7] KARIMI, M., ATRIAN, A., GHASSEMI, A. and VAHABI, M. Torsion analysis of a hollow cylinder with an orthotropic coating weakened by multiple cracks, Theoretical and Applied Fracture Mechanics, 90, 110-121, (2017).

[8] WANG, Y.-B. and LU, Z.-Z. New boundary element method for torsion problems of cylinder with curvilinear cracks, Applied Mathematics and Mechanics, 26, 1531-1538, (2005).

[9] CHEN, Y.Z. Multiple crack problems for torsion thin-walled cylinder, International Journal of Pressure Vessels and Piping, 76, 49-53, (1999).

[10] TWEED, J. and ROOKE, D.P. The torsion of a circular cylinder containing a symmetric array of edge cracks, International Journal of Engineering Science, 10, 801-812, (1972).

[11] YUANHAN, W. Torsion of a thick-walled cylinder with an external crack: boundary collocation method, Theoretical and Applied Fracture Mechanics, 14, 267-273, (1990).

[12] CHEN, J.T., CHEN, K.H., YEIH, W. and SHIEH, N.C. Dual boundary element analysis for cracked bars under torsion, Engineering Computations, 15, 732-749, (1998).

[13] HASSANI, A.R. and FAAL, R.T. Saint-Venant torsion of orthotropic bars with a circular cross-section containing multiple cracks, Mathematics and Mechanics of Solids, 21, 1198-1214, (2014).

[14] YI-ZHOU, C. On the torsional rigidity for a hollow shaft with outer or inner keys, Computer Methods in Applied Mechanics and Engineering, 42, 107-118, (1984).

[15] FANG-MING, T. and REN-JI, T. Saint-Venant's torsion problem for a composite circular cylinder with aninternal edge crack, Applied Mathematics and Mechanics, 14, 507-516, (1993).

[16] SIH, G.C. Strength of Stress Singularities at Crack Tips for Flexural and Torsional Problems, Journal of Applied Mechanics, 30, 419-425, (1963).

[17] RENJI, T. and YULAN, L. Torsion problems for a cylinder with a rectangular hole and a rectangular cylinder with a crack, Acta Mechanica Sinica, 8, 165-172, (1992).

[18] LI, Y.L., HU, S.Y. and TANG, R.J. Interaction of crack-tip and notch-tip stress singularities for circular cylinder in torsion, Theoretical and Applied Fracture Mechanics, 18, 259-272, (1993).

[19] CHEN, Y.-Z. Solutions of torsion crack problems of a rectangular bar by harmonic function continuation technique, Engineering Fracture Mechanics, 13, 193-212, (1980).

[20] CHEN, Y.Z., LIN, X.Y. and CHEN, R.S. Solution of torsion crack problem of an orthotropic rectangular bar by using computing compliance method, Communications in Numerical Methods in Engineering, 13, 655-663, (1997).

[21] HASSANI, A.R. and FAAL, R.T. Saint-Venant torsion of orthotropic bars with rectangular cross section weakened by cracks, International Journal of Solids and Structures, 52, 165-179, (2015).

[22] BARBER, J.R., Elasticity, Springer 2009.

[23] HASSANI, A.R. and FAAL, R.T. Torsion analysis of cracked circular bars actuated by a piezoelectric coating, Smart Materials and Structures, 25, 125030, (2016).

[24] FAAL, R.T., FARIBORZ, S.J. and DAGHYANI, H.R. Antiplane deformation of orthotropic strips with multiple defects, Journal of Mechanics of Materials and Structures, 1, 1097-1114, (2006).

[25] TAO, F.M. and TANG, R.J. Saint-Venant's torsion problem for a composite circular cylinder with aninternal edge crack, Applied Mathematics and Mechanics, 14, 507-516, (1993).