Acta Mechanica Solida Sinica

, Volume 26, Issue 3, pp 317–330 | Cite as

Weld Root Magnification Factors for Semi-Elliptical Cracks in T-Butt Joints

  • Zhanxun Song
  • Yeping Xiong
  • Jilong Xie
  • Jing Tang Xing
Article

Abstract

Many researchers have focused their efforts on fatigue failures occurring on weld toes. In recent years, more and more fatigue failures occur on weld roots. Therefore, it is important to explore the behaviour of weld root fatigues. This paper investigates numerically the Magnification factors (Mk) for types of semi-elliptical cracks on the weld root of a T-butt joint. The geometry of the joint is determined by four important parameters: crack depth ratio, crack shape ratio, weld leg ratio and weld angle. A singular element approach is used to generate the corresponding finite element meshes. For each set of given four parameters of the semi-elliptical root crack, the corresponding T-butt joint is numerically simulated and its Mk at the deepest point of the weld root crack is obtained for the respective tension and shear loads. The variation range of the four parameters covers 750 cases for each load, totaling 1500 simulations are completed. The numerical results obtained are then represented by the curve to explore the effects of four parameters on the Mk. To obtain an approximate equation representing Mk as a function of the four parameters for each load, a multiple regression method is adopted and the related regression analysis is performed. The error distributions of the two approximate equations are compared with the finite element data. It is confirmed that the obtained approximate functions fit very well to the database from which they are derived. Therefore, these two equations present a valuable reference for engineering applications in T-butt joint designs.

Key Words

welded root cracks singular element method stress intensity factors magnification factors multiple regressions 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Balasubramanian, V. and Guha, B., Analyzing the influences of weld size on fatigue life prediction of FCAW cruciform joints by strain energy concept. Int. J. Pressure Vessel Piping, 1999, 76: 759–768.CrossRefGoogle Scholar
  2. 2.
    Lu, Y.L., A practical procedure for evaluating SIFs along fronts of semi-elliptical surface cracks at weld toes in complex stress fields. Int. J. Fatigue, 1996, 18: 127–135.CrossRefGoogle Scholar
  3. 3.
    Lie, S.T., Zhao, Z. and Yan, S.H., Two-dimensional and three-dimensional magnification factors, Mk, for non-load-carrying fillet welds cruciform joints. Eng. Fract. Mech., 2000, 65: 435–453.CrossRefGoogle Scholar
  4. 4.
    Kirkhope, K.J., Bell, R., Caron, L., Basu, R.I. and Ma, K.T., Weld detail fatigue life improvement techniques. Mar. Struct., 1999, 12: 447–474.CrossRefGoogle Scholar
  5. 5.
    Fricke, W., Review fatigue analysis of welded joints: state of development. Mar. Struct., 2003, 16: 185–200.CrossRefGoogle Scholar
  6. 6.
    Poutiainen, I. and Marquis, G., A fatigue assessment method based on weld stress. Int. J. Fatigue, 2006, 28: 1037–1046.CrossRefGoogle Scholar
  7. 7.
    Khodadad Motarjenmi, A., Kokabi, A.H., Ziaie A.A., Manteghi, S. and Burdekin, F.M., Comparison of the stress intensity factor of T and cruciform welded joints with different main and attachment plate thickness. Eng. Fract. Mech., 2000, 65: 55–66.CrossRefGoogle Scholar
  8. 8.
    Choi, D.H., Choi, H.Y. and Lee, D., Fatigue life prediction of in-plane gusset welded joints using strain energy density factor approach. Theor Appl Fract Mech, 2006, 45: 108–116.CrossRefGoogle Scholar
  9. 9.
    Al, Mukhtar, A.M., Henkel, S., Biermann, H. and Hubner, P., A finite element calculation of stress intensity factor of cruciform and butt welded joints for some geometrical parameters. Jordan Journal of Mechanical and Industrial Engineering, 2009, 3: 236–245.Google Scholar
  10. 10.
    Dijkstra, O.D., Snijder, H.H. and van Straalen, I.J., Fatigue crack growth calculations using stress intensity factors for weld toe geometries. In: Proc. Eighth Int Conf Offshore Mech Arctic Engng, The Hague, 1989: 137–143.Google Scholar
  11. 11.
    Thurlbeck, S.D., A Fracture Mechanics Based Methodology for the Assessment of Weld Toe Cracks in Tubular Offshore Joints. PhD thesis, UMIST, 1991.Google Scholar
  12. 12.
    Hou, C.Y., Fatigue analysis of welded joints with the aid of real three-dimensional weld toe geometry. Int J Fatigue, 2007, 29: 772–785.CrossRefGoogle Scholar
  13. 13.
    Pommier, S., Sakae, C. and Murakami, Y. An empirical stress intensity factor set of Equations for a semi-elliptical crack in a semi-infinite body subjected to a polynomial stress distribution. Int J Fatigue, 1999, 21: 243–251.CrossRefGoogle Scholar
  14. 14.
    Balasubramanian, V. and Guha, B., Effect of weld size on fatigue crack growth behaviour of cruciform joints by strain energy density factor approach. Theor Appl Fract Mech, 1999, 31: 141–148.CrossRefGoogle Scholar
  15. 15.
    Brennan, F.P., Dover, W.D., Kare, R.F. and Hellier, A.K., Parametric equations for T-butt weld toe stress intensity factors. Int J Fatigue, 1999, 21: 1051–1062.CrossRefGoogle Scholar
  16. 16.
    Maddox, S.J., An analysis of fatigue cracks in fillet welded joints. Int J Fract, 1975, 11(2): 221–243.CrossRefGoogle Scholar
  17. 17.
    Newman, J.C. and Raju, I.S., An empirical stress intensity factor equation for the surface crack. Eng. Fract. Mech., 1981, 15: 185–192.CrossRefGoogle Scholar
  18. 18.
    Bowness, D. and Lee, M.M.K., Weld toe magnification factors semi-elliptical cracks in T-butt joints comparison with existing solutions. Int. J. Fatigue, 2000, 22: 389–396.CrossRefGoogle Scholar
  19. 19.
    Bowness, D. and Lee, M.M.K., Prediction of weld toe magnification factors for semi-elliptical cracks in T-butt joints. Int. J. Fatigue, 2000, 22: 369–387.CrossRefGoogle Scholar
  20. 20.
    Fu, B., Haswell, J.V. and Bettess, P., Weld magnification factors for semi-elliptical surface cracks in fillet welded T-butt joint models. Int. J. Fract., 1993, 63: 155–171.CrossRefGoogle Scholar
  21. 21.
    BS 7910: Guide to Methods for Assessing the Acceptability of Flaws in Metallic Structures, BSI 2005.Google Scholar
  22. 22.
    Gilles, P. and Franco, C., A new J-estimation scheme for cracks in mismatching welds—the ARAMIS method. In: Mismatching of Welds, Eds by Schwalbe, M. and Kocak, K.H., London: Mechanical Engineering Publications, 1994: 661–683.Google Scholar
  23. 23.
    Eripret, C. and Hornet, P., Prediction of overmatching effects on the fracture of stainless steel cracked welds. In: Mismatching of weld, Eds by Schwalbe, K.H. and Kocak, M., London: Mechanical Engineering Publications, 1994: 685–708.Google Scholar
  24. 24.
    Wang, Y.Y. and Kirk, M.T., Geometry effects on failure assessment diagrams. In: Proceedings of Second International Symposium on Mismatching of welds, Reinstorf-Luneburg, Germany, 1996.Google Scholar
  25. 25.
    Francis, M. and Rahman, S., Probabilistic analysis of weld cracks in center-cracked tension specimens. Computers and Structures, 2000, 76: 483–506.CrossRefGoogle Scholar
  26. 26.
    Ganta, B.R. and Ayres, D.J., Analysis of Cracked Pipe Weldments, EPRI Report No. NP–5057, Electric Power Research Institute, Palo Alto, February, 1987.Google Scholar
  27. 27.
    Rahman, S. and Brust, F., An estimation method for evaluating energy release rates of circumferential through-wall cracked pipe welds. Eng. Fract. Mech., 1992, 43: 417–430.CrossRefGoogle Scholar
  28. 28.
    O’Donoghue, P.E., Atluri, S.N. and Pipkins, D.S., Computational strategies for fatigue crack growth in three dimensions with application to aircraft components. Eng. Fract. Mech., 1995, 52: 51–64.CrossRefGoogle Scholar
  29. 29.
    Gurney, T.R., An analysis of some fatigue crack propagation data for steels, subjected to pulsating tension loading. Weld Res. Int., 1979, 9: 45–52.Google Scholar
  30. 30.
    Fricke, W. and Kahl, A., Numerical and experimental investigation of weld root fatigue in fillet-welded structures. International Shipbuilding Progress, 2008, 55: 29–45.Google Scholar
  31. 31.
    Zhou, C.Z., Yang, X.Q. and Luan, G.H., Effect of root flaws on the fatigue property of friction stir welds in 2024-T3 aluminum alloys. Mater. Sci. Eng. A, 2006, 418: 155–160.CrossRefGoogle Scholar
  32. 32.
    Kanvinde, A.M., Gomez, I.R., Roberts, M., Fell, B.V. and Grondin, G.Y., Strength and ductility of fillet welds with transverse root notch. Journal of Constructional Steel Research, 2009, 65: 948–958.CrossRefGoogle Scholar
  33. 33.
    Chung, H.Y., Liu, S.H., Lin, R.S. and Ju, S.H., Assessment of stress intensity factors for load-carrying fillet welded cruciform joints using a digital camera. Int. J. Fatigue, 2008, 30: 1861–1872.CrossRefGoogle Scholar
  34. 34.
    Kim, I.T., Weld root crack propagation under mixed mode and cyclic loading. Eng. Fract. Mech., 2005, 72: 523–534.CrossRefGoogle Scholar
  35. 35.
    Bowness, D. and Lee, M.M.K., Weld toe magnification factors for semi-elliptical cracks in T-butt joints. OTO Report 99014, Health and Safety Executive, 1999.Google Scholar
  36. 36.
    Henshell, R.D. and Shaw, K.G., Crack tip finite elements are unnecessary. Int. J. Numer. Meth. Engng., 1975, 9: 495–507.CrossRefGoogle Scholar
  37. 37.
    Barsoum, R.S., On the use of isoparametric finite elements in linear fracture mechanics. Int. J. Numer. Meth. Engng., 1976, 10: 25–37.CrossRefGoogle Scholar
  38. 38.
    ABAQUS User’s Manual, Version 6.3, Hibbitt, Karlsson and Sorensen, Inc. 2002.Google Scholar
  39. 39.
    Fung, Y.C., A First Course in Continuum Mechanics, 2nd ed., Prentice-Hall, 1977.Google Scholar
  40. 40.
    Cohen, J., Applied multiple regression/correlation analysis for the behavioral sciences, 3rd ed., Mahwah, NJ: L Erlbaum Associates, 2003.Google Scholar
  41. 41.
    Curve Fitting Toolbox, Functions, Data fitting for MATLAB, notes for R2009b. The Math Works Inc, 2009.Google Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2013

Authors and Affiliations

  • Zhanxun Song
    • 1
    • 2
  • Yeping Xiong
    • 2
  • Jilong Xie
    • 1
  • Jing Tang Xing
    • 2
  1. 1.School of Mechanical, Electronic & Control EngineeringBeijing Jiaotong UniversityBeijingChina
  2. 2.Faculty of Engineering & the Environments, Fluid-Structure Interaction Research GroupUniversity of Southampton, HighfieldSouthamptonUK

Personalised recommendations