Mixed-Mode Stress Intensity Factors for Tubes under Pure Torsion Loading


Article Preview

Although it seems like a common load-geometry configuration, there is neither an analytical nor a numerical solution for Stress Intensity Factors (SIF) in cracked tubes under pure torsion. Standards such as API 579, BS 7910 or handbooks do not present such case. There is plenty of solutions based on FEM or weight functions calculations for an extensive load-geometry combinations, but not for tubes under pure torsion. This paper shows curves of KI, KII, and KIII for through-wall cracks obtained with ANSYS simulations for slim tubes, under pure torsion with a rounded horizontal slit, numerically calculated via J-integral. Additionally KI, KII, and KIII are calculated using relative displacement between two points along the crack lips using Linear Elastic Fracture Mechanics (LEFM) formulations for Crack Tip Opening Displacement (COD) and Crack Tip Sliding Displacement (CTSD). Results are compared with experimentally measured SIF using the Digital Image Correlation (DIC) technique for fatigued-growth cracks reported in literature.



Edited by:

Luis Rodríguez-Tembleque, Jaime Domínguez and Ferri M.H. Aliabadi




J. G. D. Rodríguez et al., "Mixed-Mode Stress Intensity Factors for Tubes under Pure Torsion Loading", Key Engineering Materials, Vol. 774, pp. 373-378, 2018

Online since:

August 2018




* - Corresponding Author

[1] H. Tada, P. Paris, and G. Irwing, The Stress Analysis of Cracks Handbook. ASME, (2000).

[2] Y. Murakami, Stress Intensity Factor Handbook. New York: Pergamon Press, (1986).

[3] A. Prior, D. Rooke, and D. Cartwright, Compendium of Stress Intensity Factors. London: UK, Ministry of Defence, (1985).

[4] S. Laham and R. Ainsworth, Stress Intensity Factor and Limit Load Handbook. Brithish Energy, (1998).

[5] Y. Yang, Linear elastic fracture mechanics-based simulation of fatigue crack growth under non- proportional mixed-mode loading,, Technischen Universität Darmstadt, (2014).

[6] J. Harter, K-Solutions for Through Cracks Under Biaxial Loading,, in AFGROW Workshop 2016, (2016).

[7] Y. Hos, Numerical and experimental investigation of crack growth in thin-walled metallic structures under nonproportional combined loading,, Technischen Universität Darmstadt, (2017).

[8] M. Vormwald, Y. Hos, J. J. . Freire, G. L. . Gonzáles, and Diaz, Crack tip displacement fields measured by digital image correlation for evaluating variable mode-mixity during fatigue crack growth,, Int. J. Fatigue, vol. 113, (2018).

DOI: https://doi.org/10.1016/j.ijfatigue.2018.04.030

[9] M. L. Williams, On the Stress State at the Base of a Stationary Crack,, J. Appl. Mech., vol. 24, no. march, p.109–114, (1957).

[10] J. R. Rice, A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks,, J. Appl. Mech., vol. 35, no. 2, p.379–386, (1968).

DOI: https://doi.org/10.1115/1.3601206

[11] M. R. Molteno and T. H. Becker, Mode I – III Decomposition of the J -integral from DIC Displacement Data,, Strain, vol. 51, no. 6, p.492–503, (2015).

DOI: https://doi.org/10.1111/str.12166

[12] J. F. Yau, S. S. Wang, and H. T. Corten, A Mixed-Mode Crack Analysis of Isotropic Solids Using Conservation Laws of Elasticity,, J. Appl. Mech., vol. 47, no. 2, p.335, (1980).

DOI: https://doi.org/10.1115/1.3153665

[13] M. Gosz and B. Moran, An interaction energy integral method for computation of mixed-mode stress intensity factors along non-planar crack fronts in three dimensions,, Eng. Fract. Mech., vol. 69, no. 3, p.299–319, (2002).

DOI: https://doi.org/10.1016/s0013-7944(01)00080-7

[14] P. A. Wawrzynek, B. J. Carter, and L. Banks-Sills, The M-integral for computing stress intensity factors in generally anisotropic materials,, (2005).

[15] S. Kibey, H. Sehitoglu, and D. A. Pecknold, Modeling of fatigue crack closure in inclined and deflected cracks,, Int. J. Fatigue, vol. 129, no. 3, p.279–308, (2004).

DOI: https://doi.org/10.1023/b:frac.0000047787.94663.c8