Closed form solution of stress intensity factors for cracks emanating from surface semi-spherical cavity in finite body with energy release rate method

doi:10.1007/s10483-016-2148-8

Abstract

Abstract:

In this paper, a new semi-analytical and semi-engineering method of the closed form solution of stress intensity factors (SIFs) of cracks emanating from a surface semi-spherical cavity in a finite body is derived using the energy release rate theory. A mode of crack opening displacements of a normal slice is established, and the normal slice relevant functions are introduced. The proposed method is both effective and accurate for the problem of three-dimensional cracks emanating from a surface cavity. A series of useful results of SIFs are obtained.

Key words: three-dimensional crack, closed form solution, surface cavity, stress intensity factor (SIF), normal slice

2010 MSC Number:

74B99

Hualiang WAN, Qizhi WANG, Xing ZHANG. Closed form solution of stress intensity factors for cracks emanating from surface semi-spherical cavity in finite body with energy release rate method. Applied Mathematics and Mechanics (English Edition), 2016, 37(12): 1689-1706.

TrendMD

References

[1] Albuquerque, C., Silva, A. L. L., de Jesus, A. M. P., and Calçada, R. An efficient methodology for fatigue damage assessment of bridge details using modal superposition of stress intensity factors. International Journal of Fatigue, 81, 61-77(2015)
[2] Ayhan, A. O. and Yucel, U. Stress intensity factor equations for mixed-mode surface and corner cracks in finite thickness plates subjected to tension loads. International Journal of Pressure Vessels and Piping, 88, 181-188(2011)
[3] Sripichai, K. and Pan, J. Closed form structural stress and stress intensity factor solutions for spot welds in square overlap parts of cross tension specimens. Engineering Fracture Mechanics, 96, 307-327(2012)
[4] Perl, M. and Bernshtein, V. Three dimensional stress intensity factors for ring cracks and arrays of coplanar cracks emanating from the inner surface of a spherical pressure vessel. Engineering Fracture Mechanics, 94, 71-84(2012)
[5] Raju, I. S. and Newman, J. C., Jr. Stress-intensity factors for a wide range of semi-elliptical surface cracks in finite-thickness plates. Engineering Fracture Mechanics, 11, 817-829(1979)
[6] Chang, J. H. and Wu, D. J. Stress intensity factor computation along a non-planar curved crack in three dimensions. International Journal of Solids and Structures, 44, 371-386(2007)
[7] Perl, M. and Bernshtein, V. 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, 1466-1477(2011)
[8] Liu, G. R. On G space theory. International Journal of Computational Methods, 6, 257-289(2009)
[9] Sripichai, K. and Pan, J. Closed-form structural stress and stress intensity factor solutions for spot welds in square plates under opening loading conditions. Engineering Fracture Mechanics, 93, 168-188(2012)
[10] Sutradhar, A. and Paulino, G. H. Symmetric Galerkin boundary element computation of T-stress and stress intensity factors for mixed-mode cracks by the interaction integral method. Engineering Analysis with Boundary Elements, 28, 1335-1350(2004)
[11] Xiao, X. K. and Yan, X. Q. A numerical analysis for cracks emanating from a surface semi-spherical cavity in an infinite elastic body by FRANC3D. Engineering Failure Analysis, 15, 188-192(2008)
[12] Alatawi, I. A. and Trevelyan, J. A direct evaluation of stress intensity factors using the extended dual boundary element method. Engineering Analysis with Boundary Elements, 52, 56-63(2015)
[13] Lee, D. S. Torsion of a long circular cylinder having a spherical cavity with a peropheral edge crack. European Journal of Mechanics-A/Solids, 21, 961-969(2002)
[14] Lee, D. S. Tension of a long circular cylinder having a spherical cavity with a peripheral edge crack. International Journal of Solids and Structures, 40, 2659-2671(2003)
[15] Stefanescu, D., Edwards, L., and Fitzpatrick, M. E. Stress intensity factor correction for asymmetric through-thickness fatigue cracks at holes. International Journal of Fatigue, 62, 535-553(2003)
[16] Kastratovi?, G., Grbovi?, A., and Vidanovi?, N. Approximate method for stress intensity factors determination in case of multiple site damage. Applied Mathematical Modelling, 39, 6050-6059(2015)
[17] Yan, X. Q. An effective method of stress intensity factor calculation for cracks emanating from a triangular or square hole under biaxial loads. Fatigue and Fracture of Engineering Materials and Structures, 26, 1127-1133(2003)
[18] Yan, X. Q. A numerical analysis of cracks emanating from a square hole in a rectangular plate under biaxial loads. Engineering Fracture Mechanics, 71, 1615-1623(2004)
[19] Yan, X. Q. A numerical analysis of cracks emanating from an elliptical hole in a 2-D elasticity plate. European Journal of Mechanics-A/Solids, 25, 142-153(2006)
[20] Yan, X. Q. Cracks emanating from circular hole or square hole in rectangular plate in tension. Engineering Fracture Mechanics, 73, 1743-1754(2006)
[21] Xan, X. Q. and Liu, B. L. A numerical analysis of cracks emanating from a surface elliptical hole in infinite body in tension. Meccanica, 46, 263-278(2011)
[22] Zhao, W., Newman, J. C., Jr., Sutton, M. A., Wu, X. R., and Shivakumar, K. N. Stress intensity factors for corner cracks at a hole by a 3-D weight function method with stresses from the finite element method. Fatigue and Fracture of Engineering Materials and Structures, 20, 1255-1267(1997)
[23] Lin, X. B. and Smith, R. A. Stress intensity factors for corner cracks emanating from fastener holes under tension. Engineering Fracture Mechanics, 62, 535-553(1999)
[24] Perl, M., Steiner, M., and Perry, J. 3-D stress intensity factors due to autofrettage for an inner radial lunular or crescentic crack in a spherical pressure vessel. Engineering Fracture Mechanics, 131, 282-295(2014)
[25] Perl, M. and Steiner, M. 3-D stress intensity factors due to full autofrettage for inner radial or coplanar crack arrays and ring cracks in a spherical pressure vessel. Engineering Fracture Mechanics, 138, 233-249(2015)
[26] Wang, Q. Z. and Zhang, X. A closed form solution about stress intensity factors of shear modes for 3-D finite bodies with eccentric cracks by the energy release rate method. International Journal of Solids and Structures, 36, 971-998(1999)
[27] Liu, L. M., Wang, Q. Z., and Zhang, X. Explicit closed form solution of stress intensity factors for three-dimensional finite bodies with small corned cracks. Journal of Mechanical Strength, 26, 80-86(2004)
[28] Wu, J. G., Wang, Q. Z., Zhang, X., and Li, H. B. Explicit closed form solutions for three-dimensional stress intensity factors based on the energy release rate theory. Chinese Journal of Ship Research, 9, 81-90(2014)
[29] Isida, M. and Nakamura, Y. Edge cracks originating from an elliptical hole in a wide plate subjected to tension and in-plane shear. Transactions of the Japan Society of Mechanical Engineers, 46, 947-956(1980)
[30] Wu, S. F., Zhang, X., and He, Q. Z. Functional variable displacement method in analysis of singularity near the corner point in a three dimensional cracked solid. Engineering Fracture Mechanics, 31, 191-200(1988)