Issue 48

J. F. Barbosa et alii, Frattura ed Integrità Strutturale, 48 (2019) 400-410; DOI: 10.3221/IGF-ESIS.48.38 403 achieve a good fit to the experimental data. The Kohout-Věchet fatigue model (KV) can estimate the behavior of the material in low-cycle (LCF) and high-cycle (HCF) regions [6], being able to cover the estimate from the ultimate tensile strength to the permanent fatigue limit. This KV model can be expressed by the following Eqn. 4:   max b N B C a N C           (4) where a and b are the similar to Basquin parameters, B is the number of cycles corresponding to the intersection of the tangent line of the finite life region and the horizontal asymptote of the total tensile strength, and C is the number of cycles corresponding to the intersection of the tangent line of the region of the finite life and the horizontal asymptote of the fatigue limit. The details for obtaining the parameters can be obtained in ref. [6]. Normalized stress ranges The normalized stress ranges were suggested by Taras and Greiner [19] with aims to take into account the mean stress effects. The research work was developed for fatigue experimental results of riveted joints. This approach can be applied for fatigue results from metallic bridge materials to allow the comparison of experimental fatigue data from distinct mean stresses. The normalized stress ranges can be determined by   norm f R      (5) where, ∆σ norm is the normalized stress range, ∆σ is the tested stress range, and f ( R ) is a normalization function to account for stress ratio effects, defined as a function of the material. For wrought/puddle iron and mild steel manufactured before 1900, f ( R ) is defined as:     1 1 0 1 0.7 1 0 1 0.75 R f R R R R f R R R                (6) For mild steel after 1900, the normalization function to be used is the following:     1 1 0 1 0.4 1 0 1 0.6 R f R R R R f R R R                (7) However, the proposed normalization functions are only valid for high-cycle fatigue regimes, hence, they are not valid for low- and medium-cycle fatigue regimes. In this sense, fatigue design curves based on Goodman [20], Soderberg [21] and Gerber [22] diagrams become highly important for the fatigue life evaluation of old metallic bridges using local approaches. C OMPARISON OF THE M ODELING A BILITY OF THE S–N C URVE F ORMULATIONS comparison of the modelling performance of the S-N curves was made using the fatigue data of the materials from the ancient Portuguese riveted steel bridges (Eiffel, Luiz I, Fão and Trezói bridges). The performance of the mean fatigue curves was based on two methodologies of analysis. The first analysis the adjustment of the S-N curve is based on direct graphical observation, where the degree of adjustment in the LCF and HCF regions is empirically assessed. The second analysis, quantitative, estimates the quality of the curve adjustment to the experimental fatigue data by means of the mean square errors (MSE). This parameter was calculated for each fatigue model by defining the error as the difference between the logarithms of the experimental and estimated values for the cyclic stresses, based on the following equation: A