Issue 38

A. Bolchoun et alii, Frattura ed Integrità Strutturale, 38 (2016) 162-169; DOI: 10.3221/IGF-ESIS.18.22 165     OP dF dA d t t d dt 1   . 2           n n n n n n τ τ n Figure 2 : Trajectory of the shear stress vector in a given plane and the area dA n . For a finite time interval   t t 1 2 ,  the overall out-of-phase measure computes to:     t OP t F t t d dt 2 1 1  . 2     n n n τ τ n (3) Formula (3) allows to express the out-of-phase behaviour of the loading in an arbitrary time interval, however it is dependent on the shear stress amplitudes and can attain any value between 0 and  . Therefore, it is different from many out-of-phase measures, which can be found in the literature and attain values in the interval   0,1 , e.g. [9-12]. M AXIMUM NORMAL AND SHEAR STRESS AMPLITUDES AND W ÖHLER - LINE INTERPOLATION s described in [3, 15] the Maximum Variance Method (MVM) can be used in order to determine the plane, the direction and the value of the maximum shear stress amplitude a max ,  , it can also be applied in the same manner in order to determine the value of the maximum normal stress amplitude a max ,  as well as the plane, where it occurs. These two values can be computed for an arbitrary time interval and an arbitrary time-dependent stress history defined over this interval. For a pure torsional loading it follows a max a max , ,    and for a pure axial loading a max a max , , 1 2    . Condition a max , 0   corresponds to a hydrostatic cyclic loading. Whether there exists a cyclic loading with a max a max , ,    , is not known to the authors. If such loading exists, it should be a non-proportional one. The ratio a max I a max f , ,    can be used to interpolate a Wöhler-line for a cyclic loading in the region between the pure axial loading and pure torsion, that is I f 1  1 2   , as follows:   ax I tors I X X f X f 1 2   1 . 2                 (4) Where X is a Wöhler-line parameter k k N ,  or k L , furthermore ax tors k k k , ,  represent the slopes of the respective Wöhler-lines, k k ax k tors N N N , ,  ,  ,  represent the number of cycles and k k ax k tors L L L ,  ,  ,  ,  the load amplitudes at the knee point. The values k k ax k tors L L L ,  ,  ,  ,  must refer to the same damage parameter, for instance v. Mises equivalent stress A