Issue 38

A. Bolchoun et alii, Frattura ed Integrità Strutturale, 38 (2016) 162-169; DOI: 10.3221/IGF-ESIS.18.22 163 interpolation for combined loadings. K EYWORDS . Magnesium welds; Multiaxial fatigue; Variable amplitude loading; Out-of-phase loading; Rainflow; Fatigue life assessment. I NTRODUCTION atigue life assessment of materials and components under multiaxial cyclic loading is a complex task, which requires to take a number of phenomena into account, e.g.:  Depending on the material state out-of-phase loadings can lead to a reduced or to an increased fatigue life compared to in-phase loadings [1];  Different slopes und knee points of the Wöhler-lines under pure axial and pure torsional loadings [2,3];  Influence of mean stresses [4]. Magnesium thin-walled welds exhibit a fatigue life reduction under non-proportional loadings as well as different slopes of the Wöhler-lines for pure axial and pure torsional loads. The influence of mean stresses is not considered in this paper. Fatigue life evaluation is often performed using stress-based methods because of their simplicity and convenience. Conventional stress-based methods, such as described in [5-7] were developed in order to calculate the so-called [8] fatigue limit. They usually lack the capability to assess the fatigue life reduction under out-of-phase loadings correctly. There is a number of more advanced methods, which take the out-of-phase behavior of the load into account explicitly, usually using an out-of-phase factor of some sort [9-13]. With these out-of-phase factors the stresses are scaled so, that the correct fatigue life is computed for an out-of-phase loading. Another approach is employed by the IDD-Method [14]: no equivalent stress value is computed, however the damage of a load-time history or its part is computed according to the formula: total in phase out of phase D D D 2 2 2      (1) where in phase D  and out of phase D   are the IDD-specific damages resulting from the amplitude values and from the out-of- phase behavior of the loading. In fact in [14] there are two types of the out-of-phase damage: the one which is associated with the rotating principal stress axes and the one associated with out-of-phase principal stress values and no rotation of the principal axes. A very similar approach is used in the current paper, however out-of-phase loadings with and without rotating principal stresses are characterized mathematically in a uniform way using a stress rate integral. The proposed method requires to consider a general (three-dimensional) stress state. Many methods are capable to take different slopes of the pure axial and pure torsional Wöhler-lines into account, usually they contain a parameter, which, if dependency of the number of cycles N is introduced, allows to “pull” the axial and torsion Wöhler-lines together. In this case iterative methods are required in order to compute the equivalent stress and hence the fatigue life. A method to avoid the iterative computation is to use a Wöhler-line interpolation, as presented e.g. in [3]. In order to perform Wöhler-line interpolation a numerical value, which characterizes, if the load is pure axial, pure torsional or a combined one, is required. Fatigue life evaluation under variable amplitude loadings requires a procedure, which identifies damaging events (“cycles”). In [3, 15] it is proposed to find the plane with the highest shear stress aplitude using the Maximum Variance Method (MVM) and perform the rainflow cycle counting. The 4-point rainflow cycle counting procedure [16, 17] was extended in order to keep track of the time intervals, in which each counting cycle occurred. The method discussed in this paper requires calculation of the local stress components, these are obtained using the FE- modeling according to the fictitious radius approach for thin-walled welds with ref r = 0.05 mm [2]. A SHORT OVERVIEW OF THE SPECIMENS AND EXPERIMENTAL RESULTS aserbeam-welded tube-tube specimens (specimen geometry is shown in Fig. 1) were tested in a servohydraulic testing rig with two actuators, so cyclic axial and torsional loadings can be induced independently from each other. The welds were made of two self-hardening magnesium alloys AZ31 and AZ61. The testing program included F L