Torsional Fatigue Life Estimation for Steel Thin-Wall Specimens Considering Crack Initiation Phase

Document Type : Research Paper


Department of Mechanical Enginneering,, Payame Noor University (PNU), P.O.Box 19395-4697, Tehran, Iran.



An improved model for fatigue life evaluation of a steel thin-wall tubular specimen based on critical plane theory is presented. This new fatigue model incorporates the crack initiation phase in the life prediction model. The total fatigue life is a combination of both crack initiation and crack propagation lives. The initial crack length is not applied priory, but is calculated within the model. The crack initiation life is evaluated using a critical plane approach base on a modified Smith-Watson-Topper and the Fatemi-Socie criteria. The fatigue lives obtained from the proposed model are validated by experimental results for a thin-wall tubular specimen. Both critical plane criteria gave similar fatigue lives, with the Fatemi-Socie criteria giving a slightly more accurate initiation life. Without consideration of the crack initiation phase, the model absolute error is high. The proposed model indicates that a correct determination of the fatigue life requires consideration of the crack initiation phase.


  1. [1] J. A. Ferreira, C. M. Branco, J. C. Radon, Fatigue life

    assessment in welded rectangular hollow sections using

    fracture mechanics, Application of Fracture Mechanics

    to Materials and Structures. (1984) 749-761. https://doi.


    [2] Fash JW. An evaluation of damage development

    during multiaxial fatigue of smooth and notched speci-

    mens. In: Material engineering report no 123. University

    of Illinois at Urbana-Champaigne (1985).

    [3] K.A. Macdonald, P.J. Haagensen, Fatigue of welded

    aluminium hollow section profiles, Engineering Failure

    Analysis. 16 (2009) 254–261.


    [4] R. Pawliczek, D. Rozumek, Cyclic Tests of Smooth

    and Notched Specimens Subjected to Bending and Tor-

    sion Taking into Account the Effect of Mean Stress,

    Materials. 13(9) (2020) 2141.


    [5] T. Chen., X. Wang, M. Qi, Fatigue improvements

    of cracked rectangular hollow section steel beams

    strengthened with CFRP plates, Thin-Walled Struc-

    tures. 122 (2018) 371–377.


    [6] M. M. Kashani, S. Cai, S. A. Davis, P. J. Vardane-

    ga, Influence of Bar Diameter on Low-Cycle Fatigue

    Degradation of Reinforcing Bars, Journal of Materials

    in Civil Engineering 31(4) (2019) 06019002. https://doi.


    [7] E. Zhao, Q. Zhou, W. Qu, W. Wang, Fatigue Proper-

    ties Estimation and Life Prediction for Steels under Ax-

    ial, Torsional, and In-Phase Loading, Advances in Ma-

    terials Science and Engineering. (2020) 1-8.

    [8] A. Fatemi, R. Molaei, Novel specimen geometries for

    fatigue testing of additive manufactured metals under ax-

    ial, torsion, and combined axial-torsion loadings, Inter-

    national Journal of Fatigue. 130 (2020) 105287. https://

    [9] D. A. Renzo, E. Sgambitterra, C. Maletta, F. Furgi-

    uele, C. A. Biffi, J. Fiocchi, A. Tuissi, Multiaxial fatigue

    behavior of SLM Ti6Al4V alloy under different loading

    conditions, Fatigue & Fracture of Engineering Mate-

    rials & Structures. 2021;1–18.


    [10] Z. Ebrahimi, S. Negahban, Investigation of Stress

    Concentration Factors for Functionally Graded Hollow

    Tubes with Curved Edges under Torsion, Iranian Jour-

    nal of Materials Forming. 8(2) (2021) 22-34. https://doi:


    [11] A. Campagnolo, M. Vormwald, E. Shams, G. Me-

    neghetti, Multiaxial fatigue assessment of tube-tube steel

    joints with weld ends using the peak stress method. Inter-

    national Journal of Fatigue. 135 (2020) 105495. https://

    [12] M. Bӓckstӧrm, G. Marquis, A review of multiaxial

    fatigue of weldments: experimental results, design code

    and critical plane approaches, Fatigue & Fracture of En-

    gineering Materials & Structures. 24(5) (2001) 279–291.

    [13] C. Wang, D. G. Shang, X.W. Wang, A new multi-

    axial high-cycle fatigue criterion based on the critical

    plane for ductile and brittle materials, Journal of Materi-

    als Engineering and Performance. 24(2) (2015) 816-824.

    [14] F. Frendo, G. Marulo, A. Chiocca, L. Bertini, Fa-

    tigue life assessment of welded joints under sequences of

    bending and torsion loading blocks of different lengths,

    Fatigue & Fracture of Engineering Materials & Struc-

    tures. 43(6) (2020) 1290-1304.


    [15] C. Ronchei, S. Vantadori, Notch fatigue life es-

    timation of Ti-6Al-4V, Engineering Failure Analy-

    sis. 120 (2021) 105098.


    [16] L. Khalij, E. Pagnacco, R. Troian, Fatigue criterion

    improvement of Gough and Nishihara & Kawamoto to

    predict the fatigue damage of a wide range of metallic ma-

    terials, International Journal of Fatigue. 99 (2017) 137–


    [17] M. Mohammadi, M. Zehsaz, S. Hassanifard, A.

    Rahmatfam, An evaluation of total fatigue life prediction

    of a notched shaft subjected to cyclic bending load. Engi-

    neering Fracture Mechanics. 166 (2016) 128-138. https://

    [18] Y. L. Lee, M. E. Barkey, H. T. Kang, Metal fa-

    tigue analysis handbook: practical problem-solving

    techniques for computer-aided engineering, Elsevier Inc,