# Determination of the Crack Propagation Direction in Mixed-Mode Missions due to Cyclic Loading
## 5 Validation Using the Tension-Torsion Tests
Specimen 1\(1\)90_2 (Figure 13b) shows a more or less flat crack surface across the complete thickness of the specimen. Only very near the free surface, some wavy deflection can be noticed. Therefore, determining a deflection angle is difficult and was only done for \(R_{axial}=-1\). Figure 11: Three different experimental crack surfaces for loading conditions 0\(1\)90_1. Figure 12: Three different experimental crack surfaces for loading conditions 1\(1\)90_1. Figure 13: Experimental result: (**a**) 0\(1\)90_2 specimen; (**b**) 1\(1\)90_2 specimen. Finally, for specimens 0\(1\)90_3 and 1\(1\)90_3, for which \(\frac{\tau_{N}}{\sigma_{N}}\)=0.76, the crack surface was more or less flat, with some wavy behavior at the free surfaces. Here also, it was very difficult to measure any deflection angle. Summarizing, the results for a phase shift of 90\({}^{\circ}\) are ambiguous for a high torsion/tension ratio and tend to very low deflection angles the smaller this ratio is. The last column in Table 5 shows the deviation of the deflection angle for the dominant step criterion. The following observations can be made:  
* The deviation is generally quite low, which means that the underlying physical phenomena are well covered. * The deviation increases for increasing phase shift. It is only for nonzero phase shift that steps in the mission really start to compete. Therefore, more deviation is expected. * The deviation for \(R_{axial}=-1\) is less than for \(R_{axial}=0\). In the latter case, the tensile loading is less dominant (higher value of the crack opening function, i.e., smaller effective \(\Delta K\) range; furthermore, there is less friction between the crack faces, leading to a higher effect of the torsional loading), leading to a higher competition between the loading steps. * For the in-phase and 40\({}^{\circ}\) out-of-phase cases with axial traction (\(R_{axial}=0\)), it is evident that the higher the torsional moment, the more precise the numerical results are. When the axial force is applied with tension and compression (\(R_{axial}=-1\)), this is not so. In order to judge the potential of the dominant step versus the averaged angle criterion, the last two columns in Table 4 should be looked at. In the case of \(R_{axial}=0\) and a 0\({}^{\circ}\) phase shift, the current method generates a numerical prediction with a lower \(d_{ax}\) (%) than the new one. Indeed, as shown in Figure 14, the crack surface computed with the current criterion (in red) evolves nearer to the experimental surface (black triangulation) than the numerical prediction by the new approach (in blue). In this and subsequent figures, the right half of the broken specimen is shown. In the lower part of the figure, one notices the V-shaped starter notch. The blue rectangle represents the initial crack introduced by Mode I controlled fatigue. The (red and blue) numerically calculated crack propagation surfaces are only visible if they lie in front of the experimental surface. Since both the numerical, as well as the experimental surfaces are antisymmetric across the thickness due to the torsional loading, this is the case for half of the crack front (in the actual case, for the half that is closest to the observer). Analogously, the same findings can be observed for \(R_{axial}=0\) and a 40\({}^{\circ}\) phase shift. Figure 15 provides the reader with a graphical representation of specimen 0\(1\)40_2. Although the numerical crack behavior replicates the real surface trend evolution, the deviations are higher than for the in-phase cases. Figure 14: Specim 0\(1\)00_1 experimental crack surface with the numerical prediction by the current method (in red) and the new one (in blue). The difference between the dominant step and the averaged angle method becomes less significant for \(R_{axial}\) equal to \(-1\). For the specimen 1\(1\)00_1, \(d_{ax}\) (%) rounded to the second decimal digit is totally the same, as also graphically visible in Figure 16, where the two methods have almost identical predictions.