Issue 41

M. A. Meggiolaro et alii, Frattura ed Integrità Strutturale, 41 (2017) 1-7; DOI: 10.3221/IGF-ESIS.41.01 4 Figure 2 : Improved partitioning operation on tension-torsion data, showing: (a) joining the previously defined points 1 and 2 of the load history with a straight line; (b) finding the load points 3 and 4 most distant from this line, creating two partitions; (c) finding the points most distant to each segment to subdivide it into additional segments; and (d) continuing the process until reaching the chosen filter amplitude value. The next step of the pre-processing involves joining points 1 and 2 with a straight line, and then finding the load points 3 and 4 most distant from it. Note that point 3 lies in the 1  2 path whereas point 4 lies in the 2  1, as shown in Fig. 2(b). Since this maximum distance is higher than the chosen filter amplitude r, create further partitions {1  3}, {3  2}, {2  4} and {4  1} of the original path, see Fig. 2(b). Next, look for the load point in the {1  3} partition that is most distant from the straight line joining 1 and 3; if this maximum distance is higher than r, then create additional two partitions {1  5} and {5  3} from {1  3}, see Fig. 2(c). Analogously, look for the load point in the {3  2} partition that is most distant from the straight line joining 3 and 2; if this maximum distance is higher than r, then create two partitions {3  6} and {6  2} from {3  2}. The process continues for the remaining partitions, as long as the associated maximum distance is still higher than r. The pre-processing process continues for all created partitions, ending only when all such maximum distances are not higher than the chosen filter amplitude r. Consequently, each of the resulting partitions is such that all points it contains are within a distance r of the straight line joining its extremes. Note that the remaining sample points that were not labeled are not yet eliminated, because they could contain load reversions that are not detected in this pre-processing step, as discussed later. -500 -400 -300 -200 -100 0 100 200 300 400 500 -400 -300 -200 -100 0 100 200 300 400 normal stress (MPa) effective shear stress (MPa) -500 -400 -300 -200 -100 0 100 200 300 400 500 -400 -300 -200 -100 0 100 200 300 400 normal stress (MPa) effective shear stress (MPa) -500 -400 -300 -200 -100 0 100 200 300 400 500 -400 -300 -200 -100 0 100 200 300 400 normal stress (MPa) effective shear stress (MPa) -500 -400 -300 -200 -100 0 100 200 300 400 500 -400 -300 -200 -100 0 100 200 300 400 normal stress (MPa) effective shear stress (MPa) 2 1 2 1 3 4 2 1 3 4 6 5 8 7 2 1 3 4 6 5 8 7 13 9 11 15 12 10 16 14 (a) (b) (c) (d)