PSI - Issue 33

Vitor E.L. Paiva et al. / Procedia Structural Integrity 33 (2021) 159–170 Author name / Structural Integrity Procedia 00 (2019) 000–000

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4. Discussion The test results for the buried tests presented in Table 1 show that the DIC and FBSG measured strain ranges agreed satisfactorily if uncertainties of both methods are taken into consideration: (+ 0.014% DIC and + 0.010% FBSG). This observation is also valid for non-buried specimens. Cases not reported in this Table refer to specimens where instrumented points with the fiber optic strain gages did not coincide with the hot-spot locations indicated by the DIC technique. Moreover, an important point to notice refers to the influence of the soil cover and its possible restraint effect on the strain ranges induced by the test pressure. Figures 11 and 12 and Table 1 show that measured strains by the FBSG gages before and after burying the pipe specimens present negligible differences helping to draw the conclusion that the soil cover did not restrain the deformation of the dent induced by the pressure variation. Using the strain ranges acquired using the DIC technique for the buried pressure-conditions inputs, fatigue damage calculations were performed using the Coffin-Manson equation (1) described in (e.g., Castro (2016)) to determine the fatigue life N c as a function of the applied (measured) circumferential strain amplitude ε a = Δε /2 (input in terms of µε or 10 -6 m/m). A similar approach was used in previous studies (Paiva (2018), Paiva (2019), Freire (2020) and (Paiva (2020)). To do so, quantitative strain data at the most critical (DIC measured maximum circumferential strain ranges) point were extracted from the second column and generated the fifth and sixth columns of Table 1. The formula used for calculating the fatigue damage is given in Equation (1), which uses the universal fatigue exponents -0.12 and -0.6, as proposed by Manson (Castro (2016)), and the measured mechanical properties of the employed material (Young Modulus E = 182GPa, engineering ultimate strength S ue = 420MPa and fatigue strain coefficient ε f = 0.36). Fatigue lives were also calculated using the commonly used Young Modulus E = 200 GPa for carbon steels, the measured true ultimate strength S u = 500MPa and the fatigue strain coefficient ε f = 0.36. One can see that the calculations did not take into consideration the mean cycle stress (σ m = 0). One reason for this is that, although the mean stress caused by the actuating pressure can be determined, the total mean stress is unknown due to the uncertain previous load history imposed on the pipe material (such as residual stresses caused by the pipe’s fabrication and the indentation processes). � � �3.5 � � �� � � � � � ��.�� � � �.� � � � ��.� � �� � � (1) Table 1 shows the fatigue damage calculations for all the buried tested specimens and the experimental results from the fatigue tests. It is important to compare the results presented in the last two columns. One can see that the fatigue lives (number of cycles), predicted by the Coffin-Manson equation (1), and the actual lives, determined via the tests, agree satisfactorily, considering all the uncertainties associated with fatigue calculations and experimental fatigue tests. Moreover, Table 1 also gives fatigue test results for other eight out of nine similar specimens that were tested at air (not buried specimens) and previously published (Freire (2020) and Paiva (2020)). The determined lives for the buried and not buried specimens agree well with the curve proposed by Eq. (1), this agreement being depicted by the plotted points in Figure 13. This Figure presents the above actual life results obtained for the buried tested specimens and results presented by Freire et al. (2020). The latter were obtained for tests carried out on dented specimens that were cyclic tested under similar in-lab test conditions. One can see that both sets of results fall within the two given Coffin-Manson fatigue curves without the mean stress presented in Eq. (1). This comparison justifies the use of the same curve to represent the fatigue behavior of buried and unburied specimens, under the assumption that actual actuating strains are used in the plot.