# Study of Mixed-Mode Cracking of Dovetail Root of an Aero-Engine Blade Like Structure
## 5 Results and Discussion
### Untwist and Tip Clearances  
Understanding the crack progression on a blade root is not only important from the structural integrity point of view, but also in terms of displacements. The crack progression, in fact, may affect the displacements of the tip of the blade, both at the leading and trailing edge. Consequently, the untwist may be affected and even the entire performance of the subsystem it works within or its stability (surge may be caused by an excess of tip clearance). With the term \"untwist\" the reduction in the angle of torsion induced by the centrifugal force of a rotating component in a turbomachinery is meant. The initial angle of twist \(\varphi\) (undeformed geometry) is 30\({}^{\circ}\) for all the geometries analysed (Figure 29). Such an angle tends to become smaller when the centrifugal load is applied. The variation from this original angle is the \"untwist\".  
It is also useful to monitor the vertical displacements of point A (the leading edge tip) and point B (the trailing edge tip). Such a parameter is of particular interest when assessing tip clearances in a sub-system, such as axial compressors or turbines.  
Figure 28: Crack shape and direction, a direct comparison between K\({}_{\rm I}\) and K\({}_{\rm eq}\). The geometry is a 45\({}^{\circ}\) short flank.  
The results of such a deformation as a function of the crack progression are given in Tables 6 and 7 for the short flanks geometries with 30\({}^{\circ}\) and 60\({}^{\circ}\) flank angles.  
It can be noted that the deformation was not heavily affected. This happened because the blade root was heavily constrained within the disc slot as shown in Figures 6 and 7. As the crack progressed, a different distribution of stress was observed. The area of contact immediately close to the crack front tends to experience a stress relief whilst the undamaged area of the flank tends to experience a stress increase as shown in Figure 30.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Crack Length** & **Untwist** & **LE Vertical Deflection** & **TE Vertical Deflection** \\
**[mm]** & **[Degrees]** & **[mm]** & **[mm]** \\ \hline
0 & –7.2218 & 0.8828 & 0.7257 \\
1.3738 & –7.2202 & 0.8826 & 0.726 \\
2.0152 & –7.2157 & 0.8821 & 0.7268 \\
3.3353 & –7.2139 & 0.8819 & 0.7276 \\
6.5189 & –7.2054 & 0.8806 & 0.7297 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Deformation results for the 30\({}^{\circ}\) short flank geometry.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Crack Length** & **Untwist** & **LE Vertical Deflection** & **TE Vertical Deflection** \\
**[mm]** & **[Degrees]** & **[mm]** & **[mm]** \\ \hline
0 & –7.1913 & 0.9823 & 0.8126 \\
1.262 & –7.1874 & 0.9818 & 0.8137 \\
2.722 & –7.1787 & 0.9807 & 0.8163 \\
4.343 & –7.1639 & 0.9788 & 0.8207 \\
6.886 & –7.132 & 0.9752 & 0.8299 \\
9.894 & –7.0661 & 0.969 & 0.8468 \\
10.816 & –7.0595 & 0.9671 & 0.8524 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Deformation results for the 60\({}^{\circ}\) short flank geometry.  
Figure 29: Definition of angle of twist. Its reduction when a centrifugal load is applied is called “untwist”.  
It is important to remark that because of the above-mentioned re-distribution, cracks other than the one analysed may be initiated and propagate. This phenomenon has not been taken into account in this work.