Issue 33

V. Anes et alii, Frattura ed Integrità Strutturale, 33 (2015) 309-318; DOI: 10.3221/IGF-ESIS.33.35 310 synergistically presented in literature on a regular basis. Nevertheless, to analyse and estimate random multi-axial fatigue life it is necessary to account with all of them. Figure 1 : Fatigue levels of random fatigue characterization. At the base of the fatigue pyramid, shown in Fig. 1, one can find level 1, here it is studied the loading effects on the material cyclic response, such as cyclic hardening, cyclic softening, non-proportional hardening, ratcheting, among others. Essentially, level 1 is focused on elastic-plastic cyclic models that cyclically update stress-strain states accordingly to the material cyclic properties and loading type, the outcomes of level 1 are the input of level 2. Level 2 takes into account the damage parameter concepts. There are mainly four types of criteria to evaluate multiaxial fatigue; they are the critical plane criteria (which are stress-based, strain-based, and energy-based)[1–4], the equivalent stress criteria (mostly invariant-based)[5], the integral criteria, [6] and the spectral criteria [7]. The objective of these criteria is to capture multi-axial fatigue damage resulting from stress levels and several loading path types such as: sequential, proportional, non-proportional, stress gradient effects, mean stress effects, among others. These criteria are used to obtain multiaxial fatigue estimates based on reference damage curves such as uniaxial shear/axial S_N curves. Among these criteria, the most appreciated one is the equivalent stress, because they reduce complex stress states (stress tensors) to a scalar (equivalent stress), which is a very suitable feature widespread in finite element packages. Although, their success in static mechanical design, they have huge limitations regarding fatigue damage assessment. For instance, the equivalent stress concept under multi-axial loading conditions is independent from the loading path type, i.e. it can be reached the same equivalent stress in respect to different combinations of normal, and shear stresses, regarding the same stress level. However, experimental results show that the fatigue strength varies with different combinations of normal and shear stress amplitudes, even for the same equivalent stress amplitude. Thus, fatigue life estimates of equivalent stress criteria under multi-axial loading conditions give inconsistent results. At level 3, cycle counting techniques are used to account for variable amplitude and loading blocks damage using the damage parameters of level 2. There are very few cycle counting methods for multiaxial loading conditions [8,9]. Most of them are very complex to implement and consumes too much computational resources, which can be a shortcoming in damage assessment in random loading conditions. Also multiaxial cycle counting methods based on Rainflow method do not show, so far, good correlations with experimental lab data even for well-defined loading paths. Thus, level 3 is the fatigue level that has less contribution in literature despite having equal importance. Finally, in level 4, it is focused in damage accumulation rules. Damage accumulation rules translate an important procedure to estimate fatigue strength under complex loading paths [10]. Usually, they compute the unitary damage captured by the damage parameter in association with a cycle counting method. Thus, if a damage parameter and cycle counting method really capture the unitary damage of a loading block, thus the damage accumulation rule should be linear. It is found in literature some examples of non-linear damage accumulation rules, but in the present authors’ opinion, those approaches aim to capture the damage accumulation without having into account the physical damage mechanisms within the material. Therefore, damage accumulation rules based in the Palmgren-Miner must be able to capture damage accumulation under random loading conditions.