Coupled Thermoelastic Analysis of Semi-elliptical Crack in Thick-walled Cylinder Considering Green-Lindsay and Green-Naghdi Type II Theories

Document Type : Original Research Paper


Aerospace Engineering Department, Shahid Sattari Aeronautical University of Science and Technology, Tehran, Iran.


In this paper, the stress intensity factors for semi-elliptical cracks in a homogeneous isotropic cylinder have been determined. Athick-walled cylinder is subjected to a one-dimensional axisymmetric thermal shock on the outer surface according to the classic thermo elasticity (CTE), Green-Lindsay (G-L), and Green-Naghdi (G-N) theories. The effect of temperature-strain coupling and the effect of inertia term in governing equations are considered. The semi-elliptical crack stress intensity factors (SIFs) at the deepest and surface pointsare determined using weight function method. The comparison between the temperature, stress, and SIF obtained from CTE, G-L, and G-N theories shows the different behavior of generalized theories and CTE. By considering relaxation times, prediction of higher temperature and stress values, in contrast to CTE theory, will be resulted. Furthermore, the SIF resulted from generalized theories is significantly higher than CTE theory. The temperature, stress, and maximum SIF obtained for G-N II is higher than G-L theory.


[1] A.E. Green, K.A. Lindsay, Thermoelasticity, J. Elast., 2(1) (1972) 1-7.
[2] A.E. Green, P.M. Naghdi, A re-examination of the basic postulate of thermomechanics, Proceedings of the Royal Society of London, 432(1885) (1991) 171-194.
[3] J.J. Vadasz, S. Govender, P. Vadasz, Heat transfer enhancement in nano-fluids suspensions: possible mechanisms and explanations, Int. J. Heat. Mass. Trans., 48(13) (2005) 2673-2683.
[4] A. Miranville, R. Quintanilla, A generalization of the Caginalp phase - field system based on the Cattaneo law, Nonlinear. Anal. Theor., 71(5) (2009) 2278-2290.
[5] G.E. Spinosa-Paredes, E.G. Espinosa-Martinez, Fuel rod model based on non-Fourier heat conduction equation, Ann. Nucl. Energy, 36(5) (2009) 680-693.
[6] J.A. Lopez Molina, M.J. Rivera, M. Trujillo, E.J. Berjano, Effect of the thermal wave in radiofrequency ablation modelling: an analytical study, Phys. Med. Biol., 53(5) (2008) 1447-1462.
[7] H.H. Sherief, M.N. Anwar, A problem in generalized thermoelasticity for an infinitely long annular cylinder, Int. J. Eng. Sci., 26(3) (1988) 301-306.
[8] H.H. Sherief, M.N. Anwar, A problem in generalized thermoelasticity for an infinitely long annular cylinder composed of two different materials, Actamechanica, 80(1-2) (1989) 137-149.
[9] J.W. Fu, Z.T. Chen, L.F. Qian, Coupled thermoelastic analysis of a multi-layered hollow cylinder based on the C-T theory and its application on functionally graded materials, Compos. Struct., 131(1) (2015) 139-150.
[10] T. Darabseh, N. Yilmaz, M. Bataineh, Transient thermoelasticity analysis of functionally gradedthick hollow cylinder based on GreenLindsay model, Int. J. Mech. Mater. Des., 8 (2012) 247-255.
[11] R. Simpson, J. Trevelyan, Evaluation of J1 and J2 integrals for curved cracks using an enriched boundary element method, Eng. Fract. Mech., 78(4) (2011) 623-637.
[12] P. Hosseini-Tehrani, M.R. Eslami, S. Azari, Analysis of thermoelastic crack problems using GreenLindsay theory, J. Thermal. Stress., 29(4) (2006) 317-330.
[13] S.H. Mallik, M. Kanoria, A unified generalized thermoelasticity formulation: application to pennyshaped crack analysis, J. Thermal. Stress., 32(9) (2009) 943-965.
[14] X.B. Lin, R.A. Smith, Numerical analysis of fatigue growth of external Surface cracks in pressurized cylinders, Int. J. Pres. Ves. Pip., 71(3) (1997) 293-300.
[15] H.J. Petroski, J.D. Achenbach, Computation of the weight function from a stress intensity factor, Eng. Fract. Mech., 27(6) (1987) 697-715.
[16] A.R. Shahani, S. M. Nabavi, Closed-form stress intensity factors for a semi-elliptical crack in a thick-walled cylinder under thermal stress, Int. J. Fatigue., 29(8) (2006) 926-933.
[17] S.M. Nabavi, A.R. Shahani, Thermal stress intensity factors for a cracked cylinder under transient thermal loading, Int. J. Pres. Ves. Pip., 86 (2009) 153-163.
[18] H.Y. Lee, Y.W. Kim, I. Yun, Stress intensity factor solution for radial and circumferential cracks in hollow cylinders using indirect boundary integral, Int. J. Pres. Ves. Pip., 69(1) (1996) 45-52.
[19] I.V. Varfolomeyev, L. Hodulak, Improved weight functions for infinitely long axial and circumferential cracks in a cylinder, Int. J. Pres. Ves. Pip., 70(2) (1197) 103-109.
[20] M.B. Nazari, O. Asemi, Stress intensity factor for a longitudinal semi-elliptical crack in a thickwalled cylinder under hyperbolic thermal loading, Modares Mechanical Engineering, 14(6) (2015) 143-151.
[21] R.B. Hetnarski, M.R. Eslami, Thermal Stresses: Advanced Theory and Applications, New York, Springer, (2009) 255-256.
[22] A. Bagri, M.R. Eslami,A unified generalized thermoelasticity; solution for cylinders and spheres, Int. J. Mech. Sci., 49(12) (2007) 13251335.
[23] H.F. Bueckner, principle for the computation of stress intensity factors, Zeitchrift fur Angewandte Math. Mech., 50(9) (1970) 129-146.
[24] J.R. Rice, Remarks on elastic crack-tip stress fields, Int. J. Solids. Struct., 8(6) (1972) 751-758.
[25] S.M. Nabavi, A.R. Shahani, Thermal stress intensity factors for a cracked cylinder under transient thermal loading, Int. J. Pres. Ves. Pip., 86(2) (2009) 153-163.
[26] K.Y. Lee, K.B. Sim, Thermal shock stress intensity factor by bueckners weight function method, Eng. Fract. Mech., 37(4) (1190) 779-804.
[27] G. Honig, U. Hirdes, A method for the numerical inversion of Laplace transform, J. Comput. Appl. Math., 10(1) (1984) 113-132.