Stress Intensity Factor Expression for Welded Butt Joint with Undercut and Inclined Lack of Penetration Defects considering the Effect of Joint Shape

Document Type: Research Paper


Department of Mechanical Engineering, Amirkabir University of Technology, Tehran, Iran


In this paper, the stress intensity factor (SIF) expression for defected butt welds containing undercut and inclined lack of penetration (LOP) subject to far-field tensile stress is derived. Some of the standards such as ISO 5817 and BS EN 25817 have specified allowable limits for the length of the undercut and LOP defects and for the height of the weld. In addition, EN 29692 standard has determined an acceptable range for the groove angle. In this paper, the effect of these acceptable geometries on stress intensity factor (SIF) of butt welded joint is investigated through following steps: i) elastic analyses to predict crack tip stress intensity (KI, KII) and shape factors, ii) approximation of shape factors by Response Surface Method (RSM). These expressions provide design guidelines for welded butt joint containing unavoidable undercut and inclined lack of penetration (LOP) defects.


[1] Nguyen, T.N., and Wahab, M.A., The effect of weld geometry and residual stresses on the fatigue of welded joints under combined loading, Journal of Materials Processing Technology, 77(1), 1998, 201-208.

[2] Al-Mukhtar, A., Biermann, H., Henkel, S., and Hübner, P., Comparison of the stress intensity factor of load-carrying cruciform welded joints with different geometries, Journal of Materials Engineering and Performance, 19(6), 2010, 802-809.

[3] Burgess, N., Quality assurance of welded construction, CRC Press, 1989.

[4] Ali, A., and Sanuddin, A., Characterization of ASTM A516 Grade 70 Fusion Welded Joints, International Review of Mechanical Engineering, 3(5), 2009, 531-542.

[5] Handbook, A., Properties and selection: irons, steels, and high-performance alloys, Vol. 1, ASM International, 1990.

[6] Hu, L., Huang, J., Li, Z., and Wu, Y., Effects of preheating temperature on cold cracks, microstructures and properties of high power laser hybrid welded 10Ni3CrMoV steel, Materials & Design, 32(4), 2011, 1931-1939.

[7] Liu, Y., and Chan, S., Modern design method using NIDA for scaffolding systems, Tubular Structures XIII. Hong Kong: CRS Press, 2010, 443-447.

[8] Rahman, S., Probabilistic fracture mechanics: J-estimation and finite element methods, Engineering Fracture Mechanics, 68(1), 2001, 107-125.

[9] Wang, T., Yang, J., Liu, X., Dong, Z., and Fang, H., Stress intensity factor expression for butt joint with single-edge crack considering the effect of joint shape, Materials & Design, 36, 2012, 748-756.

[10] Melchers, R.E., and Beck, A.T., Structural reliability analysis and prediction, John Wiley & Sons, 2018.

[11] Lee, M., Strength, stress and fracture analyses of offshore tubular joints using finite elements, Journal of Constructional Steel Research, 51(3), 1999, 265-286.

[12] Hobbacher, A., Stress intensity factors of welded joints, Engineering fracture mechanics, 46(2), 1993, 173-182.

[13] Frank, K.H., and Fisher, J.W., Fatigue strength of fillet welded cruciform joints, Journal of the Structural Division, 105(9), 1979, 1727-1740.

[14] Hobbacher, A., Recommendations for fatigue design of welded joints and components, Springer, 2009.

[15] Wang, T., Yang, J., Liu, X., Dong, Z., and Fang, H., Stress intensity factor expression for center-cracked butt joint considering the effect of joint shape, Materials & Design, 35, 2012, 72-79.

[16] DIN, E., 5817: Welding–fusion-welded joints in steel, nickel, titanium and their alloys (beam welding excluded)–quality levels for imperfections, 2006.

[17] 25817, T.E.S.E., Arc-welded joints in steel - Guidance on quality levels for imperfections, 1992.

[18] Standard, B, Specification for “Metal-arc welding with covered electrode, gas-shielded metal-arc welding and gas welding-Joint preparations for steel, BS EN 29692, 1994.

[19] Wu, X.-F., Dzenis, Y.A., and Gokdag, E., Edge-cracked orthotropic bimaterial butt joint under antiplane singularity, International Journal of Nonlinear Sciences and Numerical Simulation, 5(4), 2004, 347-354.

[20] Reedy, E., and Guess, T., Butt joint tensile strength: interface corner stress intensity factor prediction, Journal of Adhesion Science and Technology, 9(2), 1995, 237-251.

[21] Kirkhope, K., Bell, R., Caron, L., Basu, R., and Ma, K.-T., Weld detail fatigue life improvement techniques. Part 1, Marine Structures, 12(6), 1999, 447-474.

[22] Kirkhope, K., Bell, R., Caron, L., Basu, R., and Ma, K.-T., Weld detail fatigue life improvement techniques. Part 2: application to ship structures, Marine Structures, 12(7-8), 1999, 477-496.

[23] Ninh, N.T., and Wahab, M.A., The effect of residual stresses and weld geometry on the improvement of fatigue life, Journal of Materials Processing Technology, 48(1-4), 1995, 581-588.

[24] Broek, D., Elementary engineering fracture mechanics, Springer Science & Business Media, 2012.

[25] Montgomery, D.C., and Runger, G.C., Applied statistics and probability for engineers, (With CD), John Wiley & Sons, 2007.

[26] Guinea, G.V., Planas, J., and Elices, M., KI evaluation by the displacement extrapolation technique, Engineering Fracture Mechanics, 66(3), 2000, 243-255.

[27] Courtin, S., Gardin, C., Bezine, G., and Hamouda, H.B.H., Advantages of the J-integral approach for calculating stress intensity factors when using the commercial finite element software ABAQUS, Engineering Fracture Mechanics, 72(14), 2005, 2174-2185.

[28] Zhu, W., and Smith, D., On the use of displacement extrapolation to obtain crack tip singular stresses and stress intensity factors, Engineering Fracture Mechanics, 51(3), 1995, 391-400.

[29] Banks-Sills, L., and Einav, O., On singular, nine-noded, distorted, isoparametric elements in linear elastic fracture mechanics, Computers & Structures, 25(3), 1987, 445-449.

[30] Thoft-Cristensen, P., and Baker, M.J., Structural reliability theory and its applications, Springer Science & Business Media, 2012.