Issue 41

M. A. Meggiolaro et alii, Frattura ed Integrità Strutturale, 41 (2017) 1-7; DOI: 10.3221/IGF-ESIS.41.01 3 Figure 1 : Application of the MRF on a tension-torsion  x   xy  3 history, adopting a filter amplitude r = 80MPa. It is important to note that the MRF does not filter out load reversals, which can be interpreted as sudden changes in path direction of more than 90 degrees. This is a major advantage over simplistic algorithms such as the “Peaks Procedure” [14], which filters out all points (events) whose components are not peaks or valleys. This non-conservative procedure potentially eliminates important load points that could have the highest Mises stresses or strains of the load history, even though each individual load component was not maximized. Moreover, the “Peaks Procedure” stores each and every event that constitutes a peak or valley from any single component, which for (unavoidably noisy) real measurements could result in no events at all being filtered out, even if the noise had very low amplitudes. Despite its efficiency and robustness, the MRF can still be optimized to better describe the original path using the same number of sampling points. For instance, in Fig. 1 it can be seen that the segment 4-5 faithfully describes the original sampled points, however the segments 6-7 and 7-8 do not reproduce well the originally curved path. One way to improve this issue is to use a smaller filter amplitude, lower than the adopted r = 80MPa, however at a cost of filtering out fewer points, requiring more than 8 to represent the load path in this case. A more efficient way is proposed next, where a pre- processing “partitioning” operation is performed on the original sampled points, resulting in a better description of the path with fewer data points. MRF O PTIMIZATION THROUGH P ARTITIONING efore applying the MRF algorithm, it is here proposed to perform an improved pre-processing “partitioning” operation on the multiaxial load history data, described as follows. The first step involves choosing the first sample point of the multiaxial load history, tagged with the number 1. For periodic histories, point 1 can be any point from the cyclic load path, see Fig. 2(a). Then, find the sampled point most distant to 1, labeling it as 2, creating two partitions of the original sample points, defined by the paths {1  2} and {2  1}. In the considered tension-torsion example in the  x   xy  3 space, point 2 results in the one with the highest relative Mises stress range with respect to point 1. If more than one point has the same maximum distance from 1, then choose any one of them to become point 2, ignoring the others. Note however that, for non-periodic load histories, points 1 and 2 should be simply defined as the first and last ones from the entire history, respectively. -500 0 500 -400 -300 -200 -100 0 100 200 300 400 normal stress (MPa) effective shear stress (MPa) 1 2 3 4 5 6 7 8 B