# Further Development of 3D Crack Growth Simulation Program to Include Contact Loading Situations
## 4 Submodel for Models with Contact Definition between Crack Surfaces
Figure 5:2 Geometry of the new submodel: (**a**) Submodel with smaller elements close to the crack surfaces; (**b**) Cross-section of the submodel with ‘driven nodes’, in which the nodes from the crack surfaces are not selected; (**c**). The displacement in the new submodel in the x-direction. II loading at the crack front. The contact definition (sliding formulation: small sliding, discretization method: surface to surface, friction coefficient: 0.15) is created between the crack surfaces. Adapcrack3D generates a submodel with smaller elements close to the crack surfaces and contact definition between the crack surfaces as in the global model. This model with contact definitions between the crack surfaces was simulated successfully, and the displacement in the x-direction from the submodel simulation is shown in Figure 12b. The results show the Mode II loading at the crack front, which is evident in Figure 12b in the XY plane. In the case of alternating mixed mode loading situations, from a straight initial crack branching cracks can grow that do not affect each other during their growth. This happens only if the Mode II loading is large enough for the cracks to grow. In [43], experiments were performed with the CTS specimen to create an alternating mixed-mode loading situation at an R-ratio of \(-1.6\). The initial crack is spitted into two cracks: (i) the first crack grows at an angle of \(60^{\circ}\) upwards at maximum load and (ii) the second crack at \(70^{\circ}\) downwards when the load is minimum. Models for performing simulations are created with the initial cracks and the deflected cracks, as shown in Figure 5:3 Figure 13a is the crack that deflected at \(60^{\circ}\) upwards and Figure 13b is the crack that deflected downwards at \(70^{\circ}\). Because the cracks do not have an influence on one another during crack growth, they can be modelled and simulated separately. The loading situations for both cracks are also shown in Figure 13a,b, with the values as shown in Figure 5:4 For the crack that deflected downwards, the loads are \(-1.6\) times larger than the loads that are defined for the crack that deflected upwards. Because both crack branches grew simultaneously, the assumption here is that the loads were chosen in such a way that the stress intensity factors calculated are almost the same for both cracks. In both models, contact definitions along the crack surfaces are created. In order to calculate stress intensity factors, the newly proposed submodel in Adapcrack3D is created along the crack front for both cracks. The simulation results of the global models for both the models are shown in Figure 5:5 It is evident in Figure 14a that the crack opens up due to the load and a Mode I situation is almost evident at the crack front. Due to the compressive load, the crack that deflected downwards has almost a Mode I loading at the crack tip, whereas the initial crack undergoes a Mode II effect. This is visible in the global model displayed in Figure 14b. Figure 5:6 Models of CTS specimen and submodel: (**a**). The input model of CTS specimen along with the initial crack; (**b**) The submodel with the new geometry created for the initial crack. The stress intensity factors at the crack tip calculated from both models are shown in Figure 5:7 Figure 15a displays the stress intensity factors \(K_{\text{I}}\) along the crack front for both the cracks. For the crack that deflected upwards (Figure 14a), the values are shown in blue and for the crack that deflected downwards, the values are shown in orange. As assumed, the stress intensity factors calculated for both crack branches lie very close to each other. The difference between the stress intensity factors for both crack branches is shown in Figure 15b. The maximum difference between the values is 0.24, and the minimum difference is 0.13.