# Determination of the Crack Propagation Direction in Mixed-Mode Missions due to Cyclic Loading
## 2 Crack Propagation in Tension-Torsion Tests: Experimental Setup  
The experiments under superimposed cyclic tension-compression and torsional loading were carried out with specimens made of the high-strength steel 34 CrNiMo6 in quenched and tempered conditions. To avoid additional influences due to the rolling direction, the corresponding flat specimens were made from a forged ingot with the chemical composition shown in Table 2 and the mechanical properties given in Table 3. \begin{table}
\begin{tabular}{c c} \hline \hline
**Symbol** & **Meaning** \\ \hline \(A_{i}\) & area of triangle \(i\) \\ \(a_{surf}\) & crack length measured on the specimen free surface \\ \(d_{ax}\) & distance in the axial direction \\ \(da/dN\) & crack propagation rate \\ \((da/dN)_{ref}\) & Paris law constant \\ \(f_{C}\) & critical correction \\ \(f_{th}\) & threshold correction \\ \(f_{R}\) & R-value correction \\ \(F\) & axial force \\ \(K_{C}\) & critical value \\ \(K_{eq}\) & equivalent stress intensity factor \\ \(K_{I}\) & Mode I stress intensity factor \\ \(K_{II}\) & Mode II stress intensity factor \\ \(K_{III}\) & Mode III stress intensity factor \\ \(m\) & Paris law exponent \\ \(M_{t}\) & torsional moment \\ \(N_{step}\) & number of steps in the mission \\ \(r\) & radial polar coordinate at the crack tip \\ \(R\) & \(K_{min}/K_{max}\) \\ \(R_{axial}\) & \(F_{min,axial}/F_{max,axial}\) \\ \(R_{p0.2}\) & yield strength \\ \(R_{torsion}\) & \(M_{t,min}/M_{t,max}\) \\ \(T\) & temperature \\ \(V_{i}\) & volume of the triangular prism built on \(A_{i}\) \\ \(x\) & Cartesian coordinate at the crack tip in the propagation direction \\ \(y\) & normal Cartesian coordinate at the crack tip \\ \(z\) & tangential Cartesian coordinate at the crack tip \\ \(\Delta a\) & crack increment \\ \(\Delta K_{eq}\) & equivalent stress intensity factor range \\ \(\Delta K_{ref}\) & Paris law constant \\ \(\Delta K_{th}\) & threshold value \\ \(\Delta\varphi\) & error in the deflection angle \\ \(\varphi_{N}\) & max nominal axial stress \\ \(\sigma^{\star}\) & self-similar stress tensor \\ \(\tau_{N}\) & max nominal torsional stress \\ \(\varphi\) & angular polar coordinate at the crack tip \\ deflection angle \\ \(\varphi_{o}\) & polar angle made by the highest self-similar principal stress plane \\ \(\psi\) & twist angle \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Nomenclature. Single-edge notched-tension-compression specimens (SEN-TC) with a length of 230 mm, a width of 50 mm, and a thickness of 10 mm were used (Figure 1a). Under the superimposed loading condition, these specimens' shape guarantees the presence of all three crack modes along the crack front. Furthermore, the SEN specimen also allows for a good observation of the crack propagation on the surfaces. To create comparable and reproducible conditions, the specimens were provided with a sharp V-shaped starter notch by wire erosion (see the detail in Figure 1a). In addition, initiation of a Mode I controlled fatigue crack was performed at a tension-compression load of \(\pm 25\) kN with \(R_{axial}=-1\) until a crack increment of \(\Delta a=0.3\) mm was reached. For this purpose, the potential drop technique with the appropriate measuring device (MATELECT [41]) was used, whereby the crack increment to be achieved corresponded to a 2% change in the electrical potential. Both the initiation of the cracks and the experimental tests were performed on a servo-hydraulic tension/torsion testing machine (Figure 1b), with which axial loads up to \(\pm 250\) kN and torsional moments up to \(\pm 2\) kNm can be realized. Regarding the determination of the superimposed tension-compression and torsional loading, at first, a fixed load level for the axial loading was defined. In detail, this level is described by the quotient of the maximum nominal axial stress \(\sigma_{N}\) to the yield strength \(R_{p0,2}\) for 0.2% plastic strain of the material (Table 3) and amounts to \(\sigma_{N}/R_{p0,2}=0.07\). This results in a maximum load amplitude of the axial force of \(F=27.5\) kN.