Issue 41

M. A. Meggiolaro et alii, Frattura ed Integrità Strutturale, 41 (2017) 1-7; DOI: 10.3221/IGF-ESIS.41.01 5 In the studied tension-torsion example, this partitioning results in the 8 points from Fig. 2(c) for r  80MPa. Note how the resulting polygonal path better represents the original history than the one from Fig. 1, where no pre-processing had been performed, using the same number of points. Fig. 2(d) shows the partitioning results if the filter amplitude is refined adopting r  5MPa, resulting in 16 points per cycle, but with a better description of the load path. After (and only after) the pre-processing partitioning ends, the MRF is individually applied to each partition, with a filter surface translation direction [10-12] defined from the extremes of each partition. For instance, for r  80MPa, the partitioning output shown in Fig. 2(c) would require the application of the MRF on the points in the {1  5} path, starting from 1 and with a filter surface translation direction defined by the segment 1  5; then apply the MRF again in the {5  3} path, starting from 5 and in the 5  3 direction; and so on, until processing the segment {8  1}. In this particular example, all non-labelled sample points ended up filtered out by the MRF, but this might not be the case in more complex paths, as exemplified below. As a result, the output of the MRF will consist of all load points (from all partitions) that did not suffer static or dynamic filtering. This combination of partitioning followed by the MRF is very efficient, resulting in quasi-optimal filtered histories for a given r, without the need to arbitrarily define or optimize the hyper-sphere translation directions [10-12] in higher-dimensional cases. Fig. 3 shows a more complex NP tension-torsion stress path that needs both partitioning and MRF steps to properly filter its 488 sample points (per cycle) without losing significant load reversions. Point 1 is arbitrarily chosen as the initial one in the tension-torsion cycle, and a filter amplitude of r = 80MPa is considered (graphically represented as the radius of the dashed circle around point 1). The pre-processing step then finds point 2 as the most distant from 1. Points 3 and 4 are then the ones most distant from the 1  2 straight line, both with distances greater than r = 80MPa. Since all points in the {1  3} path are within r = 80MPa of the straight segment 1  3, no further points are selected in this portion. The same applies for the {3  2}, {2  4} and {4  1} portions of the load path, ending the pre-processing step with only 4 identified points, marked with squares in Fig. 3. The MRF is then individually applied to each of these portions, using the same filter amplitude r = 80MPa, to be able to identify the important load reversal points 5, 6, 7, 8, 9 and 10, marked with triangles in Fig. 3. Note that a few load reversal points are purposely not identified, such as the ones in the {4  1} path, because their associated oscillation amplitudes are smaller than the chosen r = 80MPa, a desirable feature that the simplistic “Peaks Procedure” [14] would not be able to reproduce. Figure 3 : Tension-torsion load path with 488 sample points per cycle, where the partitioning operation identifies points 1 through 4, followed by the application of the MRF in each partition to identify points 5 through 10, adopting a filter amplitude r = 80MPa. -400 -300 -200 -100 0 100 200 300 400 -300 -200 -100 0 100 200 300 normal stress (MPa) effective shear stress (MPa) 1 2 3 4 5 6 7 8 9 10