Determination of Steady State Thermal Stress Intensity Factors for Semi-Elliptical Circumferential Cracks in Cylinders

Document Type : Research Article

Authors

Faculty of Aerospace Engineering, Malek-Ashtar University of Technology, Tehran, Iran

Abstract

In this paper, the closed-form stress intensity factors are calculated at the deepest
point of a circumferential semi-elliptical crack located at the inner surface of a cylinder. The cylinder
is subjected to pressure (internal and external) and the inner surface of the cylinder is subjected to
convection cooling. To solve the problem, initially, a weight function is derived for the deepest point of
the circumferential semi-elliptical crack using two reference loads. Then, the steady state solution of the
thermoelasticity problem is derived and, finally, the stress intensity factors are extracted using the weight
function method. For some special cases of loading, the results of the present theory are compared with
available solutions in the literature indicating an acceptable agreement. Moreover, the effects of crack
relative depth and aspect ratio and heat transfer type on the thermal stress intensity factors are studied.
The extracted results demonstrate that for some cases of loading and crack geometry, shallow cracks are
more critical than deep ones and the solution of conduction heat transfer is more conservative than the
forced convection one.

Keywords

Main Subjects

References

[1] S. Al Laham, S.I. Branch, R. Ainsworth, Stress intensity factor and limit load handbook, British Energy Generation Limited, 1998.
[2] Standard 579-1/ASME FFS-1 Fitness for Service,Houston, TX: American Petroleum Institute, 2007.
[3] M. Kuna, Finite elements in fracture mechanics, Springer,2013.
[4] X. Lin, R. Smith, Fatigue growth prediction of internal surface cracks in pressure vessels, Journal of Pressure Vessel Technology, 120(1) (1998) 17-23.
[5] C. Poette, S. Albaladejo, Stress intensity factors and influence functions for circumferential surface cracks in pipes, Engineering Fracture Mechanics, 39(4) (1991)641-650.
[6] M. Bergman, Stress intensity factors for circumferential surface cracks in pipes, Fatigue & Fracture of Engineering Materials & Structures, 18(10) (1995) 1155-1172.
[7] M. Bergman, B. Brickstad, Stress intensity factors for circumferential cracks in pipes analyzed by FEM using line spring elements, International Journal of Fracture,47(1) (1991) R17-R19.
[8] C. Wallbrink, D. Peng, R. Jones, Assessment of partly circumferential cracks in pipes, International Journal of Fracture, 133(2) (2005) 167-181.
[9] M. Perl, V. Bernshtein, 3-D stress intensity factors for arrays of inner radial lunular or crescentic cracks in a typical spherical pressure vessel, Engineering Fracture Mechanics, 77(3) (2010) 535-548.
[10] M. Perl, V. Bernshtein, 3-D stress intensity factors for arrays of inner radial lunular or crescentic cracks in thin and thick spherical pressure vessels, Engineering Fracture Mechanics, 78(7) (2011) 1466-1477.
[11] X.-M. Kong, S.-T. Zheng, Z.-Y. Cui, Studies on stress intensity factor KI of surface cracks in a cylinder under remote tension loads, Engineering Fracture Mechanics,33(1) (1989) 105-111.
[12] S.M.Nabavi, M. Kamyab, Determination of transient thermal stress intensity factors for circumferential cracks in cylinders. in: Proceedings of the 20th ISME Mechanical Engineering Conference, Shiraz University,Shiraz, Iran, (2012)
[13] F. Delale, F. Erdogan, Application of the line-spring model to a cylindrical shell containing a circumferential or axial part-through crack, Journal of Applied Mechanics, 49(1) (1982) 97-102.
[14] H. Grebner, U. Strathmeier, Stress intensity factors for circumferential semielliptical surface cracks in a pipe under thermal loading, Engineering Fracture mechanics,22(1) (1985) 1-7.
[15] V. Kumar, M. German, B. Schumacher, Analysis of elastic surface cracks in cylinders using the line-spring model and shell finite element method, Journal of Pressure Vessel Technology, 107(4) (1985) 403-411.
[16] I. Sattari-Far, Stress intensity factors for circumferential through-thickness cracks in cylinders subjected to local bending, International Journal of Fracture, 53(1) (1992)R9-R13.
[17] N.S. HUH, Elastic T stress estimates for circumferential surface‐cracked cylinders, Fatigue & Fracture of Engineering Materials & Structures, 29(1) (2006) 57-69.
[18] A. El Hakimi, P. Le Grognec, S. Hariri, Numerical and analytical study of severity of cracks in cylindrical and spherical shells, Engineering Fracture Mechanics, 75(5)(2008) 1027-1044.
[19] D.H. Cho, S.W. Woo, Y.-S. Chang, J.-B. Choi, Y.-J. Kim,M.J. Jhung, Y.H. Choi, Enhancement of J estimation for typical nuclear pipes with a circumferential surface crack under tensile load, Journal of Mechanical Science and Technology, 24(3) (2010) 681-686.
[20] H. Bueckner, Novel principle for the computation of stress intensity factors, Zeitschrift fuer Angewandte Mathematik & Mechanik, 50(9) (1970).
[21] J.R. Rice, Some remarks on elastic crack-tip stress fields, International Journal of Solids and Structures,8(6) (1972) 751-758.
[22] H. Petroski, J. Achenbach, Computation of the weight function from a stress intensity factor, Engineering Fracture Mechanics, 10(2) (1978) 257-266.
[23] G. Glinka, G. Shen, Universal features of weight functions for cracks in mode I, Engineering Fracture Mechanics, 40(6) (1991) 1135-1146.
[24] A. Zareei, Determination of weight function and stress intensity factors for circumferential semi-elliptical cracks in cylinders, Master’s thesis in Aerospace Engineering,Faculty of Aerospace Engineering, Malek-Ashtar University of technology, 2015.
[25] S.M. Nabavi, R. Azad, The effect of term numbers of a weight function on the accuracy of stress intensity factors in a cracked cylinder, in: Proceedings of the 20th ISME Mechanical Engineering Conference, Shiraz University,Shiraz, Iran, 2012.
[26] R.B. Hetnarski, M.R. Eslami, G. Gladwell, Thermal stresses: advanced theory and applications, Springer,2009.
[27] A. Moftakhar, G. Glinka, Calculation of stress intensity factors by efficient integration of weight functions,Engineering Fracture Mechanics, 43(5) (1992) 749-756.
[28] S.M. Nabavi, A. Shahani, Dynamic stress intensity factors for a longitudinal semi-elliptical crack in a thickwalled cylinder, International Journal of Engineering,Science and Technology, 6(5) (2014) 57-77.
Amirkabir Journal of Mechanical Engineering
Volume 49, Issue 4
March 2018
Pages 665-672

Files

Share

How to cite

Statistics