Issue 48

J. F. Barbosa et alii, Frattura ed Integrità Strutturale, 48 (2019) 400-410; DOI: 10.3221/IGF-ESIS.48.38 408 Figure 7 : Comparison of the S-N curves for the fatigue data at R=-1 (strain ratio) of the metallic materials from the all bridges. Fig. 7 presents a comparison between the S-N curves generated based on different fatigue formulations, such as ASTM standard, Power Law, Logistic and Kohout-Věchet models, for the fatigue data at R=-1 (under strain-controlled conditions) of the metallic materials from the several bridges under consideration in this research. A single S-N curve was estimated for each studied method considering a total of 66 experimental data available. These old metallic materials were extracted from members of the ancient metallic bridges of the 19th century, so this research sought to propose the method that is best suited to these materials. This analysis aims to consolidate what has already been observed in previous cases. The ASTM standard does not provide a good approximation in the low-cycle region even though experimental data are available in this region. The Power Law, Logistic and Kohout-Věchet S-N models obtained good adjustments to the low-cycle region when compated with the experimental data, as shown in Fig. 7. For the HCF region the Logistic, ASTM and Power Law methods presented a similar performance, however, only the Kohout-Věchet model didn’t obtain a good agreement to the fatigue data in the region above 10 6 cycles. In general the Logistic and Power Law method obtained the best fit according to the MSE estimation, however it is not conclusively due to the lack of data in regions above 10 6 cycles. C ONCLUSIONS he formulations of the S-N curves, using Logistic method, Kohout-Věchet model, Power Law and ASTM E739 standard, applied to the metallic materials of old bridges, obtained different performances mainly in the LCF and HCF regions. The ASTM standard does not perform well in estimating fatigue life in the low-cycle region. All analyzed graphs showed discrepant values of maximum stresses corresponding to the LCF region. Even following the recommendations of the ASTM E739 standard, of not extrapolating analysis beyond the experimental data, it is perceptible the difficulty of the method in approaching the LCF fatigue data. In the low-cycle region, the Logistic, Kohout-Věchet and Power Law methods presented satisfactory performance when compared with experimental data, however it is not possible to say which one has the best fit. A greater amount of experimental fatigue data would be needed in the LCF region to complete such analysis. In the high-cycle region, there is also a lack of experimental data, but assuming that the extrapolation of this region is expected to follow the permanent fatigue limit, it can be concluded that the Kohut-Vechet method presented better performance. The S-N curves of this model are distant from experimental fatigue data in regions above 10 5 cycles. The generalized simple Power Law model can yield good approximations in the low-cycle region and in some cases in the region above 10 5 cycles. The S-N logistic curve formulation, which was initially applied only to composite materials, obtained an interesting performance when applied to the metallic materials of old bridges. In terms of MSE, this model obtained similar performance to the results of the Kohout-Věchet model, using only 3 parameters in the equation. Both models presented a good agreement with little experimental data. The largest difference between these models is in HCF region. 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 0 200 400 600 Max. Stress [MPa] N(Number of Cycles) Logistic Kohout-Vechet Power Law ASTM E739 Exp. Data All Bridges T