PSI - Issue 37

Mihaela Iordachescu et al. / Procedia Structural Integrity 37 (2022) 203–208 Iordachescu M. et al / Structural Integrity Procedia 00 (2019) 000 – 000

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and crack configuration of Fig. 5a, ∆K is given by :

∆ K = Y ∆σ π a (2) where ∆  is the tensile remote stress range, and Y(·) is a non-dimensional function of the ratios = a/b and = a/D.

Fig. 5. (a) Surface notched cylindrical specimen for fatigue testing; (b) stiffness specimen after each fatigue loading step; (c) fatigue crack growth with each fatigue loading step (colors from heat tinting). In order to compute Y in Eq. 2, the following expression was employed (Shih Y. S. and Chen J. J., 2002): Y A = 0 . 67 − 0 . 033 ξ + 5 . 73 ζ − 0 . 29 ξ 2 − 2 . 943 ξζ − 22 . 692 ζ 2 + 2 . 41 ξ 2 ζ + 10 . 684 ξζ 2 + 49 . 34 ζ 3 − 8 . 82 ξ 2 ζ 2 − 10 . 16 ξζ 3 − 21 . 43 ζ 4 (3) A couple of values (∆K, da/dN) for characterizing the Paris -Erdogan law of the bolt steel was provided by each fatigue step of the three tested specimens. The crack growth rate da/dN was computed as the quotient of the difference between the initial and final crack depths and the number of cycles of the step. The stress intensity range ∆K was identified with the mean value resulting from applying Eq. 2 and Eq. 3 to the initial and final crack fronts of the each step. Once the totality of the results are plotted together in a Paris diagram (Fig. 6b), the bolt steel follows a Paris law with constants C = 2.08 ・ 10 – 12 (MPa) – 3 m –  / cycle and m=3. Fig 6a shows the design fatigue strength as provided by the Eurocode 3 (2005) for relevant details in the steel structures. This is defined by a series of Wöhler curves and identified by a detail category through which they are assigned to each structural detail. For the analyzed threaded bolts, the detail category is 50 MPa. As explained by Valiente A. (2009), the curves in Fig. 6a can be derived from a unique Paris law curve, plotted in Fig. 6b together with the experimental results of this research. The two plots are parallel straight lines that coincide in the exponent m and differ in the constant C (by about a factor of 3). Therefore, the fatigue crack growth resistance of the failed steel bolts triplicates the design resistance given by the Eurocode 3. This high resistance of the steel is consistent with the prolonged fatigue life of the failed bolt, which survived 25 years before collapsing due to plastic overloading when the fatigue cracked area reached about 70% of the bolt cross-section. The tensile bearing capacity of the resistant ligament, if roughly estimated, coincides with the maximum design load acting on the bolt. According to Fig 6a, the design fatigue limit of the bolts is 37 MPa and is determined by the threshold value of the Paris law and the initial flaw condition of the bolt (Valiente A., 2009). When the environmental action worsens this condition, due to the fatigue initiators originated at the steel interface from local damage of the Zn-coating, the fatigue limit decreases and cycles of low amplitude contribute to the crack growth, and the fatigue life of the bolts is reduced.