# Further Development of 3D Crack Growth Simulation Program to Include Contact Loading Situations
## 4 Submodel for Models with Contact Definition between Crack Surfaces
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Load** & **Crack at Angle 60\({}^{\circ}\)** & **Crack at Angle 70\({}^{\circ}\)** \\ \hline F\({}_{1}\) & 109.533 & 175.253 \\ F\({}_{2}\) & 96.593 & 154.549 \\ F\({}_{3}\) & 83.652 & 133.843 \\ F\({}_{4}\) & 109.533 & 175.253 \\ F\({}_{5}\) & 96.593 & 154.549 \\ F\({}_{6}\) & 83.652 & 133.843 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The loads in newton for the CTS specimens presented in Figure 13.  
Figure 14: Maximum principal stresses in global models of CTS specimen with deflected cracks: (**a**). Crack with upward deflection of 60\({}^{\circ}\) and Mode I loading along the crack surfaces; (**b**) Crack with downward deflection of 70\({}^{\circ}\) and Mode I and Mode II loadings along the crack surfaces. Figure 13: Models of CTS specimen with cracks and loading situations: (**a**). Crack deflected upwards at 60\({}^{\circ}\); (**b**) Crack deflected downwards at 70\({}^{\circ}\). Another simulation carried out in Adapcrack3D considers rolling contact fatigue. In this simulation, the behavior of a crack in a rail is simulated when a wheel rolls over it. The rolling procedure and the finite element model are shown in Figure 16. The wheel starts on the left side of the crack and rolls over it to create a normal force and a traction force. The rolling direction and the traction force are shown in Figure 16a. The surface crack is oriented at an angle of 30\({}^{\circ}\), and the models are created with contact definitions between the wheel and rail as well as between the crack surfaces. A detail from the meshed model prepared for the simulation is displayed in Figure 16b. The stress intensity factors along the crack front are calculated in Adapcrack3D for plane strain state. The newly proposed submodel with the contact definition between the crack surfaces is also created for this simulation. In the simulation, the rolling of the wheel over the rail is performed for a distance of 3 mm, starting from the left side of the crack and then rolling over the crack to the right side. The course of the stress intensity factors is compared with the simulation results from [44]. The stress intensity factors, \(K_{\text{I}}\) and \(K_{\text{II}}\), from the literature and the same calculated in Adapcrack3D are displayed in Figure 17. The principal course of the stress intensity factors calculated in Adapcrack3D agrees well with the course of the stress intensity factors from the literature. The tendency of \(K_{\text{I}}\) having a maximum value when the wheel approaches the crack and thereafter reducing to values close to zero is apparent in the results (Figure 17a,c). Similarly, in the case of \(K_{\text{II}}\), the values rise as the wheel approaches the crack, and then the values drop below zero. When the wheel rolls away from the crack, the values advance back to zero (Figure 17b,d). Figure 16: Rolling procedure and FE model to simulate rolling contact fatigue (**a**). Rolling procedure with rolling direction, traction, and crack at an angle of 30\({}^{\circ}\); (**b**) Detail from the FE model along with the crack. Figure 15: Stress intensity factors calculated by Adapcrack3D for CTS specimens and the difference between the results: (**a**). Stress intensity factors, \(\text{K}_{\text{I}}\), along the crack fronts for cracks deflected upwards and downwards; (**b**) Difference between the values in Figure 15a along the crack front.