# Further Development of 3D Crack Growth Simulation Program to Include Contact Loading Situations
## 1 Introduction  
Fatigue cracks are often detected in structures, and their propagation due to cyclic loading have led to cases of damage (in nuclear reactor components, pipelines, and transport systems, among others) [1, 2]. Due to the high maintenance costs and the need for robust structures or for damage tolerant design, it is of high importance that the fatigue strength of materials is also taken into account in the development and manufacturing process [3, 4, 5]. In addition to this, simulation of fatigue crack growth in structures provides an estimation of the propagation of cracks within the structure and of the residual lifetime of structures, thereby enabling structural replacement before the ultimate failure. For these estimations, crack growth simulation programs such as Adapcrack3D are utilized [6, 7]. The models that are used for these crack growth simulations have to incorporate all kinds of loadings acting on the component in order to predict the crack growth as accurately as possible. Currently, Adapcrack3D simulates models that are defined with mechanical loads such as pressure and concentrated loads [8, 9]. The program can also simulate cracks in FE models with static thermal loads [10]. Another important loading condition that is very common in the engineering field is contact loading, which generally occurs in rails, wheels, gears, bearings, etc. There are numerous works in the literature that simulate crack growth under contact loads in which contact definitions are defined between structures or between crack surfaces. One of the most common examples found in the literature is crack growth due to rolling contact fatigue [11, 12, 13]. This can be extensively found on rails [14, 15, 16, 17]. There are also crack growth simulations carried out under contact loading in other mechanicalcomponents such as gears, bearingss, etc. [18; 19]. Numerical methods such as the boundary element method, the finite element method and the extended finite element method are all adopted for simulations with contact loads [20; 21; 22; 23]. Contact loading can also be found in components that are joined together with processes such as clinching. This joining process enables the joining of different and coated materials without additional joining parts or heat input. In addition, the process is carried out in a single step, resulting in a cost-effective and simple joining process [24]. In the joining process, two sheets are arranged one above the other and pressed against the die with the aid of a punch, forming an undercut and, thus, a form-fit and force-fit connection. The joining process creates a large contact area between the die and the punch-sided metal sheet, which influences crack growth [25]. In order to extend the scope of application to other components, Adapcrack3D has to be extended to also consider contact loading. Crack growth simulation programs such as Beasy [26], Franc3D [22], and Zencrack [27] can simulate models with contact loading. Furthermore, the programs Beasy and Zencrack can also simulate crack face interactions [28; 29]. This paper focuses on the newly implemented features of contact interactions in the three-dimensional crack growth simulation program Adapcrack3D. The paper addresses contact interactions between components as well as contact interactions between crack faces. The next section therefore gives a short overview of the functionality of the program. It provides details of how Adapcrack3D is designed to simulate crack growth in an FE model. With the help of a practical example of a clinched joint, the Section 3 provides the details of crack growth simulation in structures with contact definitions. There, the clinching process is also briefly described. In addition to the contact interactions between structures, there are also cases in which contact interactions appear between the crack surfaces. The architecture of the submodel generated by Adapcrack3D is also updated to accommodate models that have contact interactions between the crack surfaces.