Issue 33

M.A. Meggiolaro et alii, Frattura ed Integrità Strutturale, 33 (2015) 368-375; DOI: 10.3221/IGF-ESIS.33.40 373 Note that the kinking and reversal criteria could happen at the same time, as exemplified in Fig. 5(b), where the path kinks at i P  because 1 i P   has d i > r and thus the translation direction needs to change, while i P  can also be interpreted as a load reversal point because 1 0 i i n n      and thus a i < 0 . Since the distance between i O  and 1 i P   is equal to b i , see Fig. 3, the hyper-surface center translation during kinking and/or reversal, shown in Fig. 5(b), can be calculated by 1 ( ) i i i i O O b r n         (3) The filtered history is then composed of the initial point and all kinking and reversal points. The reversal criterion a i < 0 keeps track of abrupt changes in loading direction that might characterize a “peak” condition, while the kinking criterion given by d i > r guarantees that a significant curvature of the load history path between two points is accounted for without assuming it is a straight line. Such path curvature is important in the calculation of path-equivalent stress and strain ranges, because the use of a straight path could lead to a non-conservative range calculation when compared to the actual NP curved stress or strain path. Fig. 6 summarizes the procedures involved in the multiaxial racetrack algorithm. Note that it exactly reproduces the classical uniaxial racetrack algorithm if P  and O  are represented by scalars. Figure 6 : Multiaxial racetrack algorithm, with static and dynamically-filtered history resulting from the P  output values, where n  is the hyper-sphere translation direction. T ENSION -T ORSION E XAMPLE ig. 7(a) shows an example of a normal  effective shear stress path obtained under tension-torsion, used to exemplify the multiaxial racetrack algorithm. Fig. 7(b) shows the filtered history for a given relatively large filter amplitude r , where only four out of the sixteen original data points were not filtered, significantly decreasing the computational cost of multiaxial fatigue life calculations for this load history. In this figure, the points that suffered static filtering are marked with an × , while the dynamically-filtered ones are represented with triangular markers. Note once again the immense practical importance of these amplitude filter procedures. Since the calculation of multiaxial fatigue damage accumulation is an intrinsically intensive computational procedure, it is most important to eliminate from the calculation effort all points that are not essential for its result, i.e. all points that do not cause significant fatigue damage. F