# Further Development of 3D Crack Growth Simulation Program to Include Contact Loading Situations
## 4 Submodel for Models with Contact Definition between Crack Surfaces  
As described previously, Adapcrack3D adopts the submodel technique for fracture mechanical evaluation [7]. The global model, which is actually the FE model of the structure to be analyzed, is meshed with tetrahedral elements and the submodel, which is only around the crack front, is meshed with hexahedral elements. This creates the possibility of creating meshes for any complex 3D models and a regularly shaped mesh along the crack front for analyzing the region around the crack. Moreover, a coarse mesh can be applied to the regions that are not in the proximity of the crack and a fine mesh in the vicinity of the crack. By using the submodel technique, the region around the crack can be meshed finer than the region around the crack in the global model [42]. The submodel and various aspects of it are shown in Figure 6. In Figure 6a, the global model with the crack and the position of the submodel with respect to the global model is displayed. The hexahedral meshed geometry of the submodel for a through crack is presented in Figure 6b, in which the user-defined value, \(l_{s}\), is the size of the submodel from the crack front in all four directions. The submodel with no stresses applied on it is depicted in Figure 6b. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Young’s Modulus** & **Poisson’s Ratio** & \(\Delta K_{\text{th}}\) & \(K_{\text{C}}\) & \(\gamma\) & \(C\) & \(n\) & \(p\) & \(q\) \\ \hline
210,000 & 0.3 & 169.001 & 2213.594 & 0.26242 & \(2.6\times 10^{-12}\) & 2.5 & 0.3 & 0.87 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Material parameters and fracture mechanical material parameters. Figure 5: Global model and crack growth simulation from Adapcrack3D: (**a**) Global model generated by Adapcrack3D for the first step, inserted initial crack in inset; (**b**) Crack growth simulation in the punch-sided sheet as calculated by Adapcrack3D, initial crack, and the crack fronts in inset. In the submodel technique, the displacements on the 'driven nodes' are calculated by the FE solver from the results of the simulation performed on the global model. The 'driven nodes' are nodes that are on the outer surfaces of the submodel, which intersects the global model. For the example in Figure 6b, the 'driven nodes' are nodes that are on the yellow surfaces. Because the displacement of 'driven nodes' that are part of the crack surfaces need to be mapped from the correct side of the crack from the global model, Adapcrack3D creates a gap between the crack surfaces. However, in real world situations, e.g., rolling contact fatigue in the railway industry, there is friction defined between the crack surfaces [28]. Due to the gap between the crack surfaces of the submodel created by Adapcrack3D, as in Figure 6b, this submodel cannot be utilized for contact definitions between the crack surfaces. For such situations, the submodel has to be created without the gap between the crack surfaces. Nevertheless, during the submodel simulation, the displacements have to be mapped from the appropriate side of the crack. To explain the procedure of such simulations, a simple model of a CT specimen is utilized in this paper. The model of the CT specimen and the submodel for the initial crack are shown in Figure 7. The CT specimen with the loading situation and the initial crack are displayed in Figure 7a. In this case, the crack lies in the XZ plane, which is one of the three principal planes. The submodel along the crack front generated by Adapcrack3D for this structure is illustrated in Figure 7b. The cross-section of the submodel without the gap between the crack faces is shown in Figure 7c. When the crack surfaces lie on top of each other, the nodes on crack surfaces, which appear above each other, also have the same coordinates. In Figure 7b, the nodes on the crack surfaces, and especially the 'driven nodes' on the red and blue line, not only lie on top of each other but also have the same coordinates.