Issue 48

J. F. Barbosa et alii, Frattura ed Integrità Strutturale, 48 (2019) 400-410; DOI: 10.3221/IGF-ESIS.48.38 401 from the Eiffel, Luiz I, Fão and Trezói riveted steel bridges. Using a qualitative methodology of graphical adjustment analysis and another quantitative using the mean square error, it was possible to evaluate the performance of the mean S-N curve formulation. The results showed that the formulation of the S-N curve using the Logistic equation applied to the metallic materials from the old bridges resulted in a superior performance when compared with others models under consideration, both in the estimation of fatigue behaviour in the low-cycle fatigue (LCF) region and in the lowest mean square error. K EYWORDS . Fatigue; Kohout-Věchet model; Fatigue-life curve; Prediction; Logistic formulation. Copyright: © 2019 This is an open access article under the terms of the CC-BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. I NTRODUCTION he knowledge about the fatigue life expectancy of materials and structural components in engineering design is of great importance for the determination of load bearing during operation. Prediction of failure through mathematical and statistical modelling is a complex activity that attempts through an analytical model to consider the effects of cyclic stresses, stress intensity, predominance between traction and compression loading, frequency, number of experimental samples and the effects of manufacturing processes. Therefore, fatigue assessment is a difficult and still attractive challenge that remains an open problem in many situations. One way to synthesize the number of factors involved in the fatigue life prediction is to reduce the model to the variables that are able to explain cause/effect, i.e. to fit a fatigue test to a stress level ௜ (independent variable) to explain the number of cycles N i (dependent variable) required until failure. This fatigue model is known as S-N curves or Wöhler's curves, widely used in standards and standardization manuals such as ASTM E-739-10 [1], ISO 12107:2012 [2], EN 1993-1-9 [3], BS5400 [4], AASHTO [5], for engineering design of material and structural details. These standards are based on the Basquin equation [6,7] suggested in 1910, aiming at characterizing the fatigue behaviour in the high- (HCF) and low-cycle fatigue (LCF) regions. Typically, fatigue data for preliminary design are studied in regions of 10 3 to 10 7 cycles. However, depending on the application, there is a need to prioritize estimation in the LCF or HCF regions. For extrapolation of estimates in HCF region, one must observe the adjustment equation and insert more fatigue data for regions of unknown space. For LCF region, the combination between the static strength and low-cycle fatigue data can be used to better fit the model. Concepts of engineering design for low-cycle fatigue regimes have been important to the use of advanced materials in different applications in mechanical designs. Civil engineering structures, railway and roadway bridges, offshore and ground structures, logistic structures, among others, are designed for the HCF regimes. Recently, a series of failures of these structures cannot be explained only with the HCF regime, taking into account the extreme loading conditions to which the structural elements are subject (e.g., earthquakes). Recent studies [8,9] suggest the use of S-N or ε-N curves covering both the LCF and HCF regimes. The models used to estimate the S-N and ε-N curves, which have a good adjustment capacity in the low-cycle region, will provide greater reliability in estimating the fatigue damage parameters such as Smith-Watson-Topper, Strain, Walker-Like and energy-based criteria, among others. These approaches will allow the fracture mechanics to be able to predict crack onset by fatigue and residual life, more accurately. In addition, S-N curve with good adjustment in the low-cycle fatigue region allows the generalization of probabilistic fatigue models, and in this way, it is possible to estimate the load limit and reliability of the material or structural component at the beginning of the operation. The use of S-N curves in the fatigue life prediction can be related to fracture mechanics based approaches. Additionally, probabilistic approaches can be implemented to handle the uncertainties associated to the materials or models as observed in the research works [10–13] that have been applied and compared with existing fatigue data from the Portuguese riveted metallic bridges. With the principle of meeting the most accurate estimates for the low-cycle fatigue regions, ranging from ultimate tensile strength to the high-cycle fatigue region, the Kohout-Věchet S-N curve is currently being proposed. This model has been increasingly used in fatigue life assessment of existing bridge structures [6,14,15]. Another model similar to Kohout-Věchet relation is the model proposed by Mu et al [16], in which a multi-slope model capable of adjusting the S-N curve in the three target regions, low-cycle-, finite-life- and high-cycle-fatigue, using a logistic function of three parameters is proposed. T