Issue 38

A. Bolchoun et alii, Frattura ed Integrità Strutturale, 38 (2016) 162-169; DOI: 10.3221/IGF-ESIS.18.22 167 The second step is to compute the damage resulting from the out-of-phase loading. For the out-of-phase loading represented by the input out-of-phase Wöhler-line the values I OP f ,  and OP F (Eq. 3) are computed, whereas the value   OP eq a F ,  depends on the equivalent stress amplitude. The value I OP f , allows to compute the interpolated Wöhler-line, which has the slope I OP k , . In the case of magnesium welds it lies above the experimental out-of-phase Wöhler-line due to fatigue life reduction under out-of-phase loading. Now for each amplitude the total damage   Total a eq D ,  can be computed using the experimental Wöhler-line and the in-phase damage   IF a eq D ,  using the interpolated Wöhler-line. The additional damage due to out-of-phase behaviour is then given by:         OF OP eq a Total eq a IF eq a D F D D 2 2 , , , .      (5) The value (5) depends on the equivalent stress amplitude eq a ,  and since there is a one-to-one correspondence between a eq ,  and OF F , OF D is a function of OF F and can be represented in the double logarithmic OF OF F D  diagram, which is somewhat similar to the Wöhler-diagram. The third step is the rainflow counting and identification of cycles and intervals in which these cycles occur. In the fourth step for each cycle C the equivalent stress amplitude a eq C , ,  , the value I C f , , the interpolated Wöhler-line with the slope I C k , and the out-of-phase stress rate integral OF C F , are computed. Now the damages   IF C a eq C D ,  , ,  and   OF C OF C D F ,  , can be calculated. The total damage of the cycle computes to k I C k I OP Total C IF C IF C D D D 2 , 2 , ,  , ,  .             The total damage of the loading sequence is then computed using Palmgren-Miner linear damage accumulation with modification according to Haibach with k k 2  2    [24]: Total Total C C D D ,   and finally correcting the theoretical damage sum th D 1.0  by the allowable one al D 1.0  based on the experimental observation [25] the fatigue life computes to S al Total L N D D  . F ATIGUE LIFE EVALUATION RESULTS AND CONCLUSIONS stress-based fatigue life evaluation method, which is capable to process arbitrary multiaxial cyclic loadings, is proposed. It is capable to take into account effects like fatigue life reduction as well as fatigue life increase under out-of-phase loading. The method was applied in order to evaluate fatigue life of magnesium welds under multiaxial variable amplitude fatigue loadings. The results are shown in Fig. 4. The method can be extended in order to handle the mean stresses. In each plane the mean normal stress as well as the mean shear stress can be defined. A suitable way to take these values into account is yet to be defined. For magnesium welds the integral of the normal stresses is chosen to be the equivalent stress in order to take into account the fact that combined in-phase Wöhler-line lies very close to the pure axial Wöhler-line. If necessary other effects can be taken into account, if other values of equivalent stress are chosen. For instance the maximum shear stress or the maximum normal stress amplitude will predict a fatigue life reduction under in-phase combined loading compared to the pure axial loading. A