Issue 35

E. Giner et alii, Frattura ed Integrità Strutturale, 35 (2016) 285-294; DOI: 10.3221/IGF-ESIS.35.33 291 situation, the effect of the indenter causes the deflection of the crack to 79º. The results for the case 7 are presented in Fig. 7, middle. Here the nonproportionality is evident due to the high value of  P , which is equal to  Bulk , being the curves shifted ones with respect to the other. Due to the dominance of the constant normal load, the effect of the cyclic load is less evident and the range between  min and  max is not so important. This range is even less for case 8 (Fig. 7, right), due to the change in R from -1 to 0. In all cases, the predicted angle is around 79º. We remark that by application of a conventional orientation criterion, such as the MTS, at the instant of maximum bulk load, an incorrect prediction of the crack direction is obtained (pointing outwards, see [1]). Other examples of inaccurate growth orientations using the MTS criterion under non-proportional fretting loading can be found in Figs. 6 and 7 of one of our former works [8]. In that work, the MTS criterion was applied at the instant of maximum bulk load. All of our analyses predicted growth paths outwards the contact zone, which is in contradiction with experimental evidence. In [9], the application of the MTS criterion to a fretting fatigue analysis at the instant of maximum load is also reported, yielding growth directions outwards the contact zone as well. Variation of stiffness of the indenter and specimen materials Tab. 2 presents the results obtained when changing the material stiffness of the indenter, i.e. considering the indenter and specimen as made of dissimilar materials. It can be seen that the effect is much more evident that in the above cases. Despite the range of variation is not large (between 76º and 90º), this proves that the stiffness of the indenter (relative to the stiffness of the specimen) is the main cause of the crack deflection inwards the contact zone and allows to gain insight into the mechanisms that cause this effect. Case E indenter (MPa) σ P (MPa) σ B (MPa) R  (º) 14 1e-5 1e-6 200 -1 90 15 207000 1e-6 200 -1 78 16 20000 200 100 -1 84 17 30000 200 100 -1 82 18 50000 200 100 -1 79 19 72000 200 100 -1 77 20 207000 200 200 -1 77 21 600000 200 200 -1 79 22 1000000 200 50 -1 77 23 1000000 200 10 -1 76 24 207000 200 100 -1 76 Table 2 : Predicted orientation angles for different material stiffness of the indenter and some variations of  P and  Bulk . -100 -80 -60 -40 -20 0 20 40 60 80 100 -150 -100 -50 0 50 100 150 200 250  (º) [MPa] 12345678  12 max  12 min  12 -100 -80 -60 -40 -20 0 20 40 60 80 100 -200 -150 -100 -50 0 50 100 150 200 250 300  (º) [MPa] 1 2 3 4 5 6 7 8  12 max  12 min  12 Figure 8 : Application of the min(  ) criterion for cases 14 (left) and 15 (right), leading to predicted angles of 90ºand 78º, respectively. Cases 14 and 15 illustrate well this behaviour and the application of the min (  ) to them is shown in Fig. 8. In case 14 a negligible stiffness is given to the indenter. The behaviour is in practice proportional, as if there is no indenter. The