Issue 35

E. Giner et alii, Frattura ed Integrità Strutturale, 35 (2016) 285-294; DOI: 10.3221/IGF-ESIS.35.33 290 R ESULTS he geometrical model with an initial crack of length a 0 =0.3 mm and initial orientation of  =90º has been analyzed under 24 different cases. The aim is to detect those parameters that have the largest influence in the crack orientation, since the growth is always directed slightly inwards beneath the contact zone, as shown in Fig. 1. Variation of normal load, bulk load and stress ratio Tab. 1 shows 13 load cases performed changing either the constant (with time) normal load P applied on the indenter and the corresponding  P , the variable bulk load on the specimen  Bulk and the stress ratio R . The material stiffness is 72 GPa in all cases, both for the indenter and specimen. The last column indicates the predicted angle using the minimum shear stress range criterion, min(  ). Contrary to was initially expected, the first thing that draws attention is that there is no practical variation on the predicted angle, since all cases lead to an orientation angle of 78º-79º. Even for the cases with negligible contacting normal load,  P =10 -6 , the prediction leads to angles pointing inwards. The influence of the wide ranges tested for  Bulk and R is also negligible. This is in full agreement with the experimental evidence collected by the authors [1,7], summarized in Fig. 1, with growing directions around 79º. Case σ P (MPa) σ B (MPa) R  (º) 1 1e-6 200 -1 79 2 1e-6 200 0 79 3 50 200 -1 79 4 50 200 0 79 5 100 200 -1 78 6 100 200 0 79 7 200 200 -1 78 8 200 200 0 79 9 1e-6 200 -0.5 79 10 50 200 -0.5 79 11 100 200 -0.5 79 12 200 200 -0.5 79 13 200 10 -1 79 Table 1 : Predicted orientation angles for different load cases, generated by variation of  P ,  Bulk and R . -100 -80 -60 -40 -20 0 20 40 60 80 100 -200 -150 -100 -50 0 50 100 150 200 250  (º) [MPa] 1234 5 6 7 8  12 max  12 min  12 -100 -80 -60 -40 -20 0 20 40 60 80 100 -250 -200 -150 -100 -50 0 50 100 150 200 250  (º) [MPa] 123456 7 8  12 max  12 min  12 -100 -80 -60 -40 -20 0 20 40 60 80 100 -250 -200 -150 -100 -50 0 50 100 150 200 250  (º) [MPa] 12345678  12 max  12 min  12 Figure 7 : Application of the min(  ) criterion for cases 1, 7 and 8, leading to predicted angles of 79º, 78º and 79º, respectively. Fig. 7 shows the variation of  versus the prospective crack orientation angle  for the last step of the loading cycle. This enables the application of the minimum shear stress range criterion. Fig. 7, left, shows the results for case 1. The high proportionality of the loads is demonstrated by the same location of the maxima and minima (no shifting of the curves). The load proportionality is caused by the extremely low value of  P considered in this case 1. However, even under this T