# Further Development of 3D Crack Growth Simulation Program to Include Contact Loading Situations
## 3 Simulation of 3D Structures with Contact Loading  
The problem of fatigue crack growth due to contact loading is common among mechanical components. Cracks due to fatigue are often detected in examples such as rail rolling contact [36], brake systems [37; 38], rotating machinery [39], or bearings [40]. Up until now,  
Figure 1: Structure of the crack growth simulation program Adapcrack3D. Adapcrack3D has only been able to simulate cracks in input models that consist of only one structure. Compared to such models, in FE models containing contact definitions, there will be definitions of multiple structures, contact interactions, coupling constraints, etc. Therefore, to incorporate contact loading in the program, Adapcrack3D has been updated to work with models containing such definitions. Because, in Adapcrack3D, the module Netadapt3D makes alterations to the FE mesh and generates FE models for the simulation, the further development of the program took place only in this module. As a result, this time the global model will be created with multiple structure definitions, etc., as in the input FE model. The process of crack insertion and submodel generation remains the same. A 3D model of sheets with a thickness of 1.5 mm each, joined with the clinching process, is considered as an example to simulate crack growth in Adapcrack3D with contact loading. The process cycle consists of four different steps, which are presented in Figure 2. In the first step, the two sheets to be clinched are positioned one above the other between the blankholder and the die assembly. The blankholder provides a preload force; thus, the joining parts cannot slip away during the joining process. The punch is subsequently moved downward and applies a force to the sheets. The metal sheets are enforced locally into the die assembly (Step 2). In the third step, the radial flow of material forms the clinch joint with its typical interlock as the punch moves further down and the die-sided sheet touches the bottom of the die assembly. In the last step, the punch is retracted [25]. The 3D model of the clinched joint, the contact definition between the punch-sided and the die-sided sheets, and the boundary conditions are shown in Figure 3. Because the clinched joints have rotational symmetry, only one half of the model is considered. The surfaces in the XY plane of the punch-sided sheet and the die-sided sheet have the symmetrical boundary condition in the z-direction, as shown in Figure 3a. One half of the curved surface of the die-sided sheet is restrained in the x- and y-directions, as displayed in Figure 3a,b. A distributed load of F = 350 N is applied on the punch-sided sheet as the loading condition (Figure 3c). A simulation of the model with the above specified boundary and loading conditions is performed. The location with the maximum value for principal normal stress is selected as the location for the initial crack, as shown in Figure 4. The place to insert the initial crack is in the punch-sided sheet; see Figure 4a. As shown in Figure 4b, an initial semi-circular crack of radius 0.15 mm is inserted in the punch-sided sheet at the place where the maximum principal stress is at its highest value. Figure 2: The process cycle of creating a clinched joint. The model with the initial crack is loaded in Adapcrack3D for crack growth simulation. Then, the program successfully inserts the crack in the model and generates the global model consisting of both sheets with crack, contact definitions, etc., and the submodel along the crack front. The material parameters used for the crack growth simulation are shown in Table 1 and characterize the base material of the sheets used. These are not for the stretched material in the vicinity of the clinched joints. The values used are taken from the experiments performed in [41], in which the Forman/Mettu Equation (1) is applied to obtain the fracture mechanical parameters of the material.