Issue 33

V. Anes et alii, Frattura ed Integrità Strutturale, 33 (2015) 309-318; DOI: 10.3221/IGF-ESIS.33.35 312 Mises equivalent stress uses the 3 constant to reduce shear damage to the axial one. This procedure can be found in a wide range of multiaxial fatigue criteria being a common practice to account combined fatigue damage [13]. Fig. 3 illustrates these damage patterns. Fig. 3 a) depicts a grid at rest without any load (it can be imagined as a material grain). Now, consider Fig. 3 b), in this case the grid is loaded with an axial loading with an elongation pattern. Fig. 3 c) presents the same grid but now with a uniaxial shear loading causing a distortion deformation. As can be seen, the deformation pattern is quite different in both loading conditions. Consider now a material grain structure loaded with the loading conditions shown in Fig. 3. Under these loading conditions, the grain structure will have different deformation patterns like the ones depicted in Fig. 3, under axial, shear, and multiaxial loadings. Due to the different deformation patterns, the material strength will be different for each loading conditions. Now, consider a biaxial loading having simultaneously two types of deformation patterns (axial and shear) above represented in Fig. 4 d). In this case, the deformation pattern is a mixture of axial deformation and shear distortion. To account the contribution of each damage pattern from axial and shear deformations (different deformation mechanisms), it is required reduce both damages to the same scale, because they cause different types of deformation within the material grain structure. From experiments it was found that the contribution percentage of each axial and shear loading components of a multiaxial loading to the overall damage does influence the material fatigue strength results [11]. The predominance of an axial damage over the shear one or vice versa causes different cyclic damage rates and therefore different fatigue lives are obtained. For each loading direction depicted in a stress space, given by the stress amplitude ratio a a     , there will be a damage scale that reduces axial damages to the shear damage scale. Zhang et al. published an interesting work that correlates proportional loadings, with different stress amplitude ratios, with their crack initiation planes on a 2A12–T4 aluminium alloy [11]. Fig. 4 shows the crack opening paths obtained by Zhang et al. in respect to the stress amplitude ratios within the range   0;  where it can be found different damage mechanisms associated to each stress amplitude ratio. These results corroborate the premise in which different stress amplitude ratios have different damage scales being required their assessment to account combined axial and shear damages. (a)  = 0 (b)  =  3/2 (c)  =  3 (d)  = 3 (e)  = ∞ Figure 4 : In-phase fracture appearance under different stress amplitude ratios [11]. (a)  = 0° (b)   = 24° (c)   = 46° (d)   = 68° (e)    = 90° Figure 5 : Out-of-phase (  ) fracture appearance for a constant stress amplitude ratio,  3 [11]. Fig. 5 shows the phase angle variation effect on the crack opening, here the stress amplitude ratio was maintained equal to 3 in each phase-shift  . Based on these results, it can be concluded that the phase-shift variation also induces different crack opening paths indicating different fatigue damage mechanisms. These mechanisms are related to the material sensitivity to non-proportional loadings, which is a level 1 issue. The present authors developed the Y non-proportional sensitivity factor to account with this phenomenon in the SSF multiaxial fatigue package, which can be found in [14].