# Determination of the Crack Propagation Direction in Mixed-Mode Missions due to Cyclic Loading
## 5 Validation Using the Tension-Torsion Tests
Then, the propagation range of interest was identified (from the notch tip up to the dashed vertical line in the figure). At half this distance, the angle \(2\varphi\) was measured and divided by two. This procedure worked well except for the specimens with a \(90^{\circ}\) phase shift, as will be explained next. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**No.** & **Label** & \(R_{axial}\) & \(R_{torsion}\) & **Phase (\({}^{\circ}\))** & \(\frac{\tau_{N}}{\sigma_{N}}\) & \(\frac{d_{ax}\) (mm)} & \(d_{ax}\) (mm) & \(a_{surf}\) & \(d_{ax}\) (\%) & \(d_{ax}\) (\%) \\  & & & & & **(Current)** & **(New)** & **(mm)** & **(Current)** & **(New)** \\ \hline  
76 & 0.1545 & 0.1106 & 3.7642 & 4.11 & 2.94 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Specimens load combinations and deviation results. Figure 10: Estimating the deflection angle from the triangulation of the fractured specimens. Before looking at the comparison between the experiment and numerical prediction, it is worthwhile to have a more detailed look at the experimental results themselves in the form of the deflection angle. For pure tension, the deflection angle was zero; for pure torsion, one ends up with a deflection angle of \(\pm 62^{\circ}\), taking the K-values published in [38] and the deflection angle formula by [PERSON] [3]. For the tension-torsion loading, the values should be somewhere in between. Looking at the column for \(\varphi\) in Table 5, one can conclude for phase shift \(0^{\circ}\) and \(40^{\circ}\) the following:  
* For fixed \(R_{axial}\) and a fixed phase shift, the deflection angle increases with increasing torque. This is to be expected since the torsion leads to the nonzero deflection. * Changing \(R_{axial}\) from zero to \(-1\) leads to a decrease of the deflection angle. This also seems logical since the crack opening function by [PERSON] [52] decreases for R decreasing from zero to \(-1\). This means that for decreasing R in that range, the effective stress intensity range due to the tensile force increases, leading to less deflection. The increasing friction between the crack surfaces for \(R=-1\) may also play a role. * In nearly all cases, a switch from a \(0^{\circ}\) to a \(40^{\circ}\) phase shift leads to an increase of the deflection angle. This indicates that the time at maximum tensile force, which corresponds to a higher tension/torsion stress ratio compared to zero phase shift, is not dictating the crack propagation direction. To the contrary, the time at which the tensile to torsion stress has decreased must be dominant for a phase shift of \(40^{\circ}\). For a phase shift of \(90^{\circ}\), the picture is much more difficult. For the specimens 0\(1\)90_1 and 1\(1\)90_1 (\(\frac{7\
u_{3}}{\
u_{3}}\)=1.31), the experimental results are not consistent. This is illustrated in Figures 11 and 12. The figures show three different results for three different specimens with the same loading conditions. Therefore, a deflection angle could not be determined. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multirow{2}{*}{**Label**} & **Specimen** & \multirow{2}{*}{**\(R_{axial}\)**} & \multirow{2}{*}{**\(R_{torsion}\)**} & **Phase (\({}^{\circ}\))** & \(\frac{\pi_{N}}{\sigma_{N}}\) & \multirow{2}{*}{\(\varphi(^{\circ})\)} & \multirow{2}{*}{\(\Delta\varphi(^{\circ})\)} \\  & & **Number** & & & & & & \\ \hline  
76 & 0.0 & 2.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Experimental deflection angle and numerical deviation (current). Specimens 0\(1\)90_2 and 1\(1\)90_2, for which \(\frac{\gamma_{N}}{\sigma_{N}}=1\), are shown in Figure 13. Specimen 0\(1\)90_2 in Figure 13a (the view angle for this specimen was chosen differently from the other specimens, in order to have a better view on the crack surface) shows propagation in the same direction at both free surfaces; only at crack front positions immediately underneath the right free surface, a local area with propagation in the opposite direction can be noticed.