Issue 33

V. Anes et alii, Frattura ed Integrità Strutturale, 33 (2015) 309-318; DOI: 10.3221/IGF-ESIS.33.35 313 The Stress Scale factor (SSF) concept In the von Mises equivalent stress criterion, where the stress scale factor is a constant 3 and is defined under static loading conditions, it is not possible to capture the relation between axial, and shear damages for different stress amplitude ratios. It is assumed that the axial and shear damage relation given by the stress scale factor is constant for any stress amplitude ratios which has led to poor fatigue life estimates under multiaxial loading conditions. Fig. 6 depicts the reasoning that supports the damage scale concept used in the SSF method to reduce axial damage to the shear damage scale. Fig. 6 presents a new way to represents SN curves. Instead of using the usual practice where it is represented a damage parameter vs fatigue life ( f N ) it is depicted the axial and shear stress amplitudes (of a multiaxial loading) vs their fatigue life. Thus, Fig. 6 has three SN curves, one is the uniaxial shear SN curve ( _1 uniaxial  ), used here as reference damage across the fatigue life range, and the other two are the SN curves of the axial ( _ 2 load  ) and shear ( _ 2 load  ) loading components of a multiaxial loading. Now, suppose that a fatigue lifetime is selected, for example at 4E5 loading cycles, as shown in Fig. 6. The selected fatigue life can be achieved by using both loadings presented in Fig. 6 (the uniaxial shear loading (loading 1) and the multiaxial loading, loading 2). Thus, in the shear uniaxial loading it will be needed the 1  shear stress amplitude, and in the biaxial loading it will be needed the axial stress amplitude 2  and the shear stress amplitude 2  . Note that, the 2  value is not enough to cause failure, it is required 2  . Therefore, the damage difference between 1  and 2  , is given by the damage caused by 2  . Having this in mind, the damage from BC in the shear damage scale, is equal to the damage from AD in the axial damage scale. Figure 6: SFF damage scale concept. SSF equivalent stress Eq. (1) represents the SSF equivalent shear stress damage parameter [12], where the axial stress component of a multiaxial loading is reduced to the shear damage scale by a SSF damage function, the   , a ssf   .   . , a eq ssf         (1) The SSF damage function has as input the stress amplitude ratio and the axial stress amplitude where the stress amplitude ratios defines the axial and shear damage relation and the axial stress defines the stress level within a multiaxial loading; please see Eq. (2).   2 3 2 3 4 5 , a a a a ssf a b c d f g h i                         (2) Where, a  is the axial component of the biaxial loading and  is the stress amplitude ratio (SAR), see Fig. 7. The constants from “a” to “i" are determined through the experimental tests discussed above. Therefore, the objective of the SSF damage function is to update the damage scale accordingly to each loading direction (SAR) under cyclic loading conditions. The SSF damage function is determined based in proportional SN curves for the loading paths presented in