Issue 33

V. Anes et alii, Frattura ed Integrità Strutturale, 33 (2015) 309-318; DOI: 10.3221/IGF-ESIS.33.35 314 Fig. 7 considering the damage concept depicted in Fig. 6. These loadings have stress amplitude ratios that cover different relations between axial and shear damages, starting from pure axial (0º) and ended with the pure shear loading condition (90º). The SSF damage function is a material cyclic property, and like many others should be determined by experimental tests. There are some directions, between the ones depicted in Fig. 7, where it was not performed any experimental test. In these directions , the SSF damage function was established by using interpolation techniques between known experimental values of the SSF damage function. Eq. (3) shows the SSF criterion for fatigue life assessment.       max , a b f ssf A N        (3) The left side of Eq. (3), represents the maximum value of the SSF equivalent shear stress found within the loading period, where the shear component of a biaxial loading,  , is added to the axial component previously reduced to the shear damage scale,   , a ssf     . Then, the fatigue lifetime is estimated using the uniaxial shear SN curve, represented in the right side of Eq. (3). Figure 7 : Loading paths used in experiments to calculate the SSF damage function. C YCLE COUNTING (L EVEL 3) he equivalent SSF shear stress only captures the damage inherent to the SSF maximum value found in a loading cycle, thus it is not captured the damage associated to all local SSF equivalent stress reversals within a loading history. However, the damage estimated for loading blocks considering only the maximum equivalent stress found in that same loading block is smaller than it should be leading to un-conservative fatigue life results. Thus, the SSF equivalent stress criterion requires a cycle counting technique to evaluate fatigue damage for multiaxial variable amplitude loadings. Limitations of Maximum equivalent stress concept Usually variable amplitude time histories are transformed into an equivalent stress spectrum where each loading block is identified based on their stress amplitude level [15], please see Fig. 8. The equivalent spectrum approach is suitable to be used in damage accumulation rules based in the Palmgren-Miner concept, however, the transformation from variable amplitude time histories to constant amplitude load spectrum (as one can see in Fig. 8 b), lead to lose the real damage monitoring found in the stress time histories. This means that the stress or damage parameter spectrum will hardly capture the fatigue damage, especially under multiaxial loading conditions. Fig. 9 shows two different loadings with the same loading period and maximum stress level. Despite, the same maximum stress during the load period is obtained in both loading cases; the fatigue damage inherent to each loading is quite different. However, this is the approximation performed when it is used an equivalent stress spectrum where the varying amplitude is reduced to a constant one. The loading depicted in Fig. 9 a) cannot be considered a loading block because the unitary damage is related to one load cycle which is repeated until reach time t , thus in damage accumulation rules the T