Issue 33

M.A. Meggiolaro et alii, Frattura ed Integrità Strutturale, 33 (2015) 368-375; DOI: 10.3221/IGF-ESIS.33.40 371 algorithms or significant paths that can affect the calculation of an equivalent stress or strain, since all stress or strain components contribute altogether for the reversals that can be eliminated. Note that an amplitude filter is a most desirable feature in practical applications, to not only eliminate redundant measurement noise and oversampled data, but also small amplitudes that do not cause fatigue damage. In fact, it may be practically impossible to analyze unfiltered multiaxial fatigue data. A multiaxial version of the racetrack filter must perform such tasks even for NP histories. T HE M ULTIAXIAL R ACETRACK F ILTER n the multiaxial racetrack algorithm proposed here, the stress or strain history is represented in a 6D space, and a suitable filtering amplitude r must be chosen like in the 1D case. A small peg P  is then allowed to move in this 6D space, but instead of being restricted within a 1D slot, it is kept inside a 6D hyper-sphere of center O  and radius r . When the peg reaches the hyper-sphere surface and tries to move out of it, both the peg and the hyper-sphere translate altogether, similarly to the 1D slotted plate example. Fig. 3 shows a 2D tension-torsion example of a hyper-sphere translation caused by the peg movement from its current position i P  to the next 1 i P   , where i n  is the current normal vector that defines the surface translation direction (still to be determined), and b i , a i , and d i are distances (measured in stress or strain units) used in the filtering algorithm. Figure 3 : Hyper-sphere translation along i n  , caused by a peg movement from i P  to 1 i P   . For this 2D tension-torsion example, the hyper-sphere simply becomes a circle. The next peg location 1 i P   is given by the input load history. When combined with the current location i O  of the hyper- sphere center, and a known translation direction i n  , the values of b i , a i , and d i can be obtained from 2 1 1 ( ) ( ) T i i i i i b P O P O           , 1 ( ) T i i i i a P O n        , and 2 2 2 i i i d b a   (1) where b i must be greater than r to guarantee that 1 i P   is outside the current hyper-sphere, otherwise there is no translation. While a i  0 and d i  r , the next peg location 1 i P   can still be located on the border of the hyper-sphere translated in the i n  direction, where the center translation shown in Fig. 3 can be calculated by 2 2 1 ( ) i i i i i O O a r d n          (2) The process is then repeated for the next peg location. Fig. 4 shows two consecutive translations where the conditions a i  0 and d i  r are satisfied, allowing the hyper-sphere translation direction to remain constant, i.e. 1 i i n n     . In this example, point i P  can be filtered out, since it does not alter the translation direction during the (multiaxial) load history path 1 1 i i i P P P      . This filtering process that happens while the hyper-sphere is translated is called here dynamic filtering . I